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Title: Military schools and courses of instruction in the science and art of war - (Revised Edition)
Author: Barnard, Henry
Language: English
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  Military Schools



  in the



  France, Prussia, Austria, Russia, Sweden, Switzerland, Sardinia,
  England, and the United States.

  Drawn from Recent Official Reports and Documents.



  New York:
  Published By E. Steiger,
  22 & 24 Frankfort Street.


The first edition of Military Schools in France and Prussia was issued
in 1862, as a number of the American Journal of Education; and
subsequently in the same year this portion was printed as Part I. of a
comprehensive survey of the whole field of Instruction in the Science
and Art of War in different countries. The circumstances under which the
publication was begun, are set forth in the Preface to the imperfect
edition of 1862. Now that the survey in the serial chapters of the
Journal is as complete as the material at the command of the Editor, and
the space which he can give to this special subject enable him to make
it, the several chapters have been revised and brought together in a
single volume, to present the actual condition of this important
department of national education in the principal states of Europe, as
well as in our own country.

It is due to the late Col. Samuel Colt, the inventor of the Colt
Revolver, and the founder of the Colt Patent Fire-Arms Factory--two
enterprises which have changed the character and the mode of
constructing fire-arms in every country--to state that the information
contained in the first edition of this Treatise, was collected and
prepared at his request, to assist him in maturing the plan of a School
of Mechanical Engineering, which he proposed to establish on his estate
at Hartford, and on which, after the breaking out of the War of
Secession, he decided to engraft both military drill, and military
history, and to give that scientific instruction which every graduate of
our national Military and Naval Academies ought to possess. Soon after
Col. Colt’s death (Jan. 10, 1862), Mrs. Elizabeth Jarvis Colt, learning
what had been done in the direction of her husband’s wishes, authorized
the use which has been made, of the material already collected, in the
preparation of this treatise, and of the volume already published on
Technical Schools in different countries, and of any more which might be
collected and prepared at her expense, to illustrate any department of
his plan of a scientific school at Hartford.

  HARTFORD, CONN., March, 1872.


  INTRODUCTION,                                                      3


  OUTLINE OF MILITARY SYSTEM,                                        9
    System of Military Instruction,                                 10
      I. Polytechnic School at Paris,                               11
         1. Subject and Methods of Instruction prescribed
                for Admission,                                      13
         2. Scientific Course in _Lycées_ and other Schools
                in reference to,                                    49
         3. History, Management, Studies, Examinations,             55
         4. Public Services, Legal and Military,
                provided for by,                                    88
         5. Programmes of Lectures and Courses of Instruction,      91
     II. The Artillery and Engineer School of Application
             at Metz,                                              133
    III. The Regimental Schools of Practice for Artillery
             and Engineers,                                        221
     IV. The Infantry and Cavalry School at St. Cyr,               225
      V. The Cavalry School of Practice at Saumur,                 241
     VI. The Staff School at Paris,                                245
    VII. The Military Orphan School at La Fleche,                  257
   VIII. The School of Musketry at Vincennes,                      259
     IX. The Military and Naval Schools of Medicine
             and Pharmacy,                                         261
      X. The Naval School at Brest,                                263
     XI. The Military Gymnastic School at Vincennes,               265
    Remarks on French Military Education,                          273


      I. Outline of Military System,                               281
     II. Historical View of Military Education,                    284
    III. Present System of Military Education and Promotion,       293
     IV. Examinations; General and Professional for
             a Commission,                                         297
         1. Preliminary or Ensign’s Examination,                   297
         2. Officers’ Examination,                                 302
      V. Military Schools preparatory to the Officers’
              Examination,                                         310
         1. The Cadet Schools, or Cadet Houses,                    310
         2. The Division Schools,                                  321
         3. The United Artillery and Engineers’ School,            325
     VI. The School for Staff Officers at Berlin,                  330
    VII. Elementary Military Schools for Non-commissioned
             Officers,                                             329
         1. Military Orphan Houses,                                339
            Orphan-House at Potsdam,                               340
            Orphan-House at Annaburg,                              345
         2. The School Division or Non-commissioned Officers’
                School,                                            348
         3. Regimental Schools,                                    350
         4. The Noble-School at Liegnitz,                          350
   VIII. Remarks on the System of Military Education
             in Prussia,                                           351
  APPENDIX,                                                        351
    The Artillery and Engineer School at Berlin,                   353
    The Staff School at Berlin,                                    395


  MILITARY SYSTEM AND INSTRUCTION                              409-464
      I. Schools of non-commissioned officers                      411
     II. School for officers                                       429
    III. Special Military Schools                                  436
     IV. Staff School at Vienna                                    447
      V. Reorganization of Military Schools in 1868                453
     VI. Cavalry Brigade School for officers                       463


  MILITARY SYSTEM AND SCHOOLS OF BAVARIA                       465-480
      I. Cadet Corps--War School--Artillery, Engineers, and
             Staff Schools                                         467
     II. MILITARY ACADEMY AT DRESDEN                               471
    III. MILITARY ACADEMY AT BREDA                                 477


  MILITARY SYSTEM AND SCHOOLS                                  481-500
      I. Military Academy at Turin                                 483
     II. Artillery and Engineer School                             489
    III. Staff School and Staff Corps                              492
     IV. Regimental School for officers                            494
      V. School for Artillery officers                             498
     VI. Nautical School at Genoa                                  499


  MILITARY SYSTEM AND SCHOOLS                                  501-514
      I. Imperial Staff School at St. Petersburg                   505

  VII. SWEDEN, &c.

  MILITARY SYSTEM AND SCHOOLS                                  515-516


  MILITARY SYSTEM AND SCHOOLS                                  511-686
      I. Council of Military Education                             535
     II. Royal Military College at Sandhurst                       557
    III. Royal Military Academy at Woolwich                        585
     IV. Royal School of Military Engineering at Chatham           595
      V. Professional Instruction for officers.
         1. Survey Class at Aldershot.
         2. Advanced Class of Artillery at Woolwich.
         3. School of Gunnery at Shoeburyness                      605
      VI. Staff College and Staff appointments                     619
      VII. School of Musketry, and Army Schools                    625
      VIII. Naval and Navigation Schools                           627
      IX. English and other Naval Systems and Schools compared     655
         1. French Naval and Navigation Schools                    659
         2. German Naval and Navigation Schools                    681


      I. Federal Militia--Cantonal Cadet System--
             Target Shooting                                       689
     II. Federal Instruction of officers--experience of 1870       710


  MILITARY SYSTEM AND SCHOOLS                                  713-940
    A. Military Education for Land Service                         715
      I. National Military Academy at West Point                   721
     II. Special Artillery School at Fortress Monroe               819
    III. Military element in State Schools                         825
     IV. Individual and Corporate Institutions                     838
      V. Military Drill in Public Schools                          865
    B. Naval and Navigation Schools                                887
      I. United States Naval Academy at Annapolis                  897
     II. School of Naval Construction and Marine Engineering       937
    III. Instruction for the Mercantile Marine                     939


An account of the Military and Naval Schools of different countries,
with special reference to the extension and improvement, among
ourselves, of similar institutions and agencies, both national and
state, for the special training of officers and men for the exigencies
of war, was promised by the Editor in his original announcement of “_The
American Journal and Library of Education_.” Believing that the best
preparation for professional and official service of any kind, either of
peace or war, is to be made in the thorough culture of all manly
qualities, and that all special schools should rest on the basis, and
rise naturally out of a general system of education for the whole
community, we devoted our first efforts to the fullest exposition of the
best principles and methods of elementary instruction, and to
improvements in the organization, teaching, and discipline of schools,
of different grades, but all designed to give a proportionate culture of
all the faculties. We have from time to time introduced the subject of
Scientific Schools--or of institutions in which the principles of
mathematics, mechanics, physics, and chemistry are thoroughly mastered,
and their applications to the more common as well as higher arts of
construction, machinery, manufactures, and agriculture, are
experimentally taught. In this kind of instruction must we look for the
special training of our engineers, both civil and military; and schools
of this kind established in every state, should turn out every year a
certain number of candidates of suitable age to compete freely in open
examinations for admission to a great National School, like the
Polytechnic at Paris, or the purely scientific course of the Military
Academy at West Point, and then after two years of severe study, and
having been found qualified by repeated examinations, semi-annual and
final, by a board composed, not of honorary visitors, but of experts in
each science, should pass to schools of application or training for the
special service for which they have a natural aptitude and particular

The terrible realities of our present situation as a people--the fact
that within a period of twelve months a million of able bodied men have
been summoned to arms from the peaceful occupations of the office, the
shop, and the field, and are now in hostile array, or in actual
conflict, within the limits of the United States, and the no less
alarming aspect of the future, arising not only from the delicate
position of our own relations with foreign governments, but from the
armed interference of the great Military Powers of Europe in the
internal affairs of a neighboring republic, have brought up the subject
action with an urgency which admits of no delay. Something must and will
be done at once. And in reply to numerous letters for information and
suggestions, and to enable those who are urging the National, State or
Municipal authorities to provide additional facilities for military
instruction, or who may propose to establish schools, or engraft on
existing schools exercises for this purpose,--to profit by the
experience of our own and other countries, in the work of training
officers and men for the ART OF WAR, we shall bring together into a
single volume, “_Papers on Military Education_,” which it was our
intention to publish in successive numbers of the NEW SERIES of the
“_American Journal of Education_.”

This volume, as will be seen by the Contents, presents a most
comprehensive survey of the Institutions and Courses of Instruction,
which the chief nations of Europe have matured from their own
experience, and the study of each other’s improvements, to perfect their
officers for every department of military and naval service which the
exigences of modern warfare require, and at the same time, furnishes
valuable hints for the final organization of our entire military
establishments, both national and state.

We shall publish in the Part devoted to the United States, an account of
the Military Academy at West Point, the Naval Academy at Newport, and
other Institutions and Agencies,--State, Associated, and Individual, for
Military instruction, now in existence in this country, together with
several communications and suggestions which we have received in
advocacy of Military Drill and Gymnastic exercises in Schools. We do not
object to a moderate amount of this Drill and these exercises, properly
regulated as to time and amount, and given by competent teachers. There
is much of great practical value in the military element, in respect
both to physical training, and moral and mental discipline. But we do
not believe in the physical degeneracy, or the lack of military aptitude
and spirit of the American people--at least to the extent asserted to
exist by many writers on the subject. And we do not believe that any
amount of juvenile military drill, any organization of cadet-corps, any
amount of rifle or musket practice, or target shooting, valuable as
these are, will be an adequate substitute for the severe scientific
study, or the special training which a well organized system of military
institutions provides for the training of officers both for the army and

Our old and abiding reliance for industrial progress, social well being,
internal peace, and security from foreign aggression rests on:--

I. The better Elementary education of the whole people--through better
homes and better schools--through homes, such as Christianity
establishes and recognizes, and schools, common because cheap enough for
the poorest, and good enough for the best,--made better by a more
intelligent public conviction of their necessity, and a more general
knowledge among adults of the most direct modes of effecting their
improvement, and by the joint action of more intelligent parents, better
qualified teachers, and more faithful school officers. This first great
point must be secured by the more vigorous prosecution of all the
agencies and measures now employed for the advancement of public
schools, and a more general appreciation of the enormous amount of
stolid ignorance and half education, or mis-education which now
prevails, even in states where the most attention has been paid to
popular education.

II. The establishment of a System of Public High Schools in every
state--far more complete than exists at this time, based on the system
of Elementary Schools, into which candidates shall gain admission only
after having been found qualified in certain studies by an open
examination. The studies of this class of schools should be preparatory
both in literature and science for what is now the College Course, and
for what is now also the requirements in mathematics in the Second
Year’s Course at the Military Academy at West Point.

III. A system of Special Schools, either in connection with existing
Colleges, or on an independent basis, in which the principles of science
shall be taught with special reference to their applications to the Arts
of Peace and War. Foremost in this class should stand a National School
of Science, organized and conducted on the plan of the Polytechnic
School of France, and preparatory to Special Military and Naval Schools.

IV. The Appointment to vacancies, in all higher Public Schools, either
among teachers or pupils, and in all departments of the Public Service
by Open Competitive Examination.

  HARTFORD, CONN., 1862.

  [Errata for (first) Table of Contents:
  ... V. 2. Advanced Class of Artillery at Woolwich.

       *       *       *       *       *



       *       *       *       *       *


The following account of the SYSTEM OF MILITARY EDUCATION IN FRANCE,
except in the case of three or four schools, where credit is given to
other authorities, is taken from an English Document entitled “_Report
of the Commissioners appointed_ (by the Secretary of War) _to consider
the best mode of reorganizing the system of Training Officers for the
Scientific Corps: together with an Account of Foreign and other Military
Education._” Reference has been had, especially in the Programmes and
Courses of Instruction to the original authorities referred to by the

    Vauchelle’s Course d’ Administration Militaire, 3 vols.

      1. Fourcy’s Histoire de l’Ecole Polytechnique.
      2. Décret portant l’Organisation, &c.
      3. Règlement pour le Service Interieur.
      4. Programme de l’Enseignement Interieur.
      5. Programme des Connaissances Exigées pour Admission, &c.
      6. Rapport de la Commission Mixte, 1850.
      7. Répertoire de l’Ecole Polytechnique; by M. Marielle.
      8. Calenders from 1833.
      9. Pamphlets--by M. le Marquis de Chambray, 1836; by V. D.
             Bugnot, 1837; by M. Arago, 1853.

    Décret Impérial, &c., 1854.

    Manuel Réglementaire a l’Usage, &c.




The French armies are composed of soldiers levied by yearly conscription
for a service of seven years. Substitutes are allowed, but in accordance
with a recent alteration, they are selected by the state. Private
arrangements are no longer permitted; a fixed sum is paid over to the
authorities, and the choice of the substitutes made by them.

The troops are officered partly from the military schools and partly by
promotion from the ranks. The proportions are established by law.
One-third of the commissions are reserved for the military schools, and
one-third left for the promotion from the ranks. The disposal of the
remaining third part is left to the Emperor.

The promotion is partly by seniority and partly by selection.

The following regulations exist as to the length of service in each rank
before promotion can be given, during a period of peace:--

  A second Lieutenant can not be promoted to Lieutenant
      under 2 years’ service.
  A Lieutenant          “  “  Captain     “  2  “
  A Captain             “  “  Major       “  4  “
  A Major               “  “  Lieut-Col.  “  3  “
  A Lieutenant-Colonel  “  “  Colonel     “  2  “

But in time of war these regulations are not in force.

Up to the rank of captain, two-thirds of the promotion takes place
according to seniority, and the other one-third by selection.

From the rank of captain to that of major (_chef de bataillon ou
d’escadron_) half of the promotion is by seniority and the other half by
selection, and from major upwards, it is entirely by selection.

The steps which lead to the selection are as follows:--The general
officers appointed by the minister at war to make the annual inspections
of the several divisions of the army of France, who are called
inspectors-general, as soon as they have completed their tours of
inspection, return to Paris and assemble together for the purpose of
comparing their notes respecting the officers they have each seen, and
thus prepare a list arranged in the order in which they recommend that
the selection for promotion should be made.

We were informed that the present minister of war almost invariably
promoted the officers from the head of this list, or, in other words,
followed the recommendation of the inspector-general.


The principal Military Schools at present existing in France are the

  1. The Polytechnic School at Paris (_Ecole Impériale Polytechnique_,)
preparatory to--

  2. The Artillery and Engineers School of Application at Metz (_Ecole
Impériale d’Application de l’Artillerie et du Génie_.)

  3. The Military School at St. Cyr (_Ecole Impériale Spéciale
Militaire_,) for the Infantry and Cavalry, into which the Officers’
Department of the Cavalry School at Saumur has lately been absorbed.

  4. The Staff School at Paris (_Ecole Impériale d’Application d’Etat

  5. The Military Orphan School (_Prytanée Impériale Militaire_) at La

  6. The Medical School (_Ecole Impériale de Médicine et de Pharmacie
Militaires_.) recently established in connection with the Hospital of

  7. The School of Musketry (_Ecole Normale de Tir_) at Vincennes,
founded in 1842.

  8. The Gymnastic School (_Ecole Normale de Gymnastique_) near

  9. The Music School (_Gymnase Musical_.)

  10. The Regimental Schools (_Ecoles Régimentaires_.)

The military schools are under the charge of the minister of war, with
whom the authorities of the schools are in direct communication.

The expenses to the state of the military schools, including the pay of
the military men who are employed in connection with them, for the year
1851, are as follows:--

  For Polytechnic School at Paris,               _fr._ 554,911. 91
   “  Artillery and Engineers School at Metz,          187,352. 06
   “  Infantry and Cavalry School at St. Cyr,          682,187. 35
   “  Cavalry School at Saumur,                        196,170. 27
   “  Staff School at Paris,                           145,349. 96
   “  Gymnastic School of Musketry at Vincennes,        33,211. 33
   “  Regimental Schools,                              108,911½,30

From this sum, 2,224,542_fr._, should be deducted 421,372_fr._ secured
from paying pupils, leaving the total cost to the state to be
1,803,308_fr._, or about $360,000, for about 2,100 pupils. The cost to
the state for training an officer of Artillery and Engineers is about
$1,500, and that of an officer of the Staff is about $1,400.



“L’ÉCOLE POLYTECHNIQUE” is too well known, by name at least, to need
eulogy in this journal. Its course of instruction has long been famed
for its completeness, precision, and adaptation to its intended objects.
But this course had gradually lost somewhat of its symmetrical
proportions by the introduction of some new subjects and the excessive
development of others. The same defects had crept into the programme of
the subjects of examination for admission to the school. Influenced by
these considerations, the Legislative Assembly of France, by the law of
June 5th, 1850, appointed a “_Commission_” to revise the programmes of
admission and of internal instruction. The President of the Commission
was THENARD, its “Reporter” was LE VERRIER, and the other nine members
were worthy to be their colleagues. They were charged to avoid the error
of giving to young students, subjects and methods of instruction “too
elevated, too abstract, and above their comprehension;” to see that the
course prescribed should be “adapted, not merely to a few select
spirits, but to average intelligences;” and to correct “the excessive
development of the preparatory studies, which had gone far beyond the
end desired.”

The Commission, by M. Le Verrier, prepared an elaborate report of 440
quarto pages, only two hundred copies of which were printed, and these
merely for the use of the authorities. A copy belonging to a deceased
member of the Commission (the lamented Professor _Theodore Olivier_),
having come into the hands of the present writer, he has thought that
some valuable hints for our use in this country might be drawn from it,
presenting as it does a precise and thorough course of mathematical
instruction, adapted to any latitude, and arranged in the most perfect
order by such competent authorities. He has accordingly here presented,
in a condensed form, the opinions of the Commission on _the proper
subjects for examination in mathematics, preparatory to admission to the
Polytechnic School, and the best methods of teaching them_.

The subjects which will be discussed are ARITHMETIC; GEOMETRY; ALGEBRA;


A knowledge of Arithmetic is indispensable to every one. The merchant,
the workman, the engineer, all need to know how to calculate with
rapidity and precision. The useful character of arithmetic indicates
that its methods should admit of great simplicity, and that its teaching
should be most carefully freed from all needless complication. When we
enter into the spirit of the methods of arithmetic, we perceive that
they all flow clearly and simply from the very principles of numeration,
from some precise definitions, and from certain ideas of relations
between numbers, which all minds easily perceive, and which they even
possessed in advance, before their teacher made them recognize them and
taught them to class them in a methodical and fruitful order. We
therefore believe that there is no one who is not capable of receiving,
of understanding, and of enjoying well-arranged and well-digested
arithmetical instruction.

But the great majority of those who have received a liberal education do
not possess this useful knowledge. Their minds, they say, are not suited
to the study of mathematics. They have found it impossible to bend
themselves to the study of those abstract sciences whose barrenness and
dryness form so striking a contrast to the attractions of history, and
the beauties of style and of thought in the great poets; and so on.

Now, without admitting entirely the justice of this language, we do not
hesitate to acknowledge, that the teaching of elementary mathematics has
lost its former simplicity, and assumed a complicated and pretentious
form, which possesses no advantages and is full of inconveniences. The
reproach which is cast upon the sciences in themselves, we out-and-out
repulse, and apply it only to the vicious manner in which they are now

Arithmetic especially is only an instrument, a tool, the theory of which
we certainly ought to know, but the practice of which it is above all
important most thoroughly to possess. The methods of analysis and of
mechanics, invariably lead to solutions whose applications require
reduction into numbers by arithmetical calculations. We may add that the
numerical determination of the final result is almost always
indispensable to the clear and complete comprehension of a method ever
so little complicated. Such an application, either by the more complete
condensation of the ideas which it requires, or by its fixing the mind
on the subject more precisely and clearly, develops a crowd of remarks
which otherwise would not have been made, and it thus contributes to
facilitate the comprehension of theories in such an efficacious manner
that the time given to the numerical work is more than regained by its
being no longer necessary to return incessantly to new explanations of
the same method.

The teaching of arithmetic will therefore have for its essential object,
to make the pupils acquire the habit of calculation, so that they may be
able to make an easy and continual use of it in the course of their
studies. The theory of the operations must be given to them with
clearness and precision; not only that they may understand the mechanism
of those operations, but because, in almost all questions, the
application of the methods calls for great attention and continual
discussion, if we would arrive at a result in which we can confide. But
at the same time every useless theory must be carefully removed, so as
not to distract the attention of the pupil, but to devote it entirely to
the essential objects of this instruction.

It may be objected that these theories are excellent exercises to form
the mind of the pupils. We answer that such an opinion may be doubted
for more than one reason, and that, in any case, exercises on useful
subjects not being wanting in the immense field embraced by mathematics,
it is quite superfluous to create, for the mere pleasure of it,
difficulties which will never have any useful application.

Another remark we think important. It is of no use to arrive at a
numerical result, if we cannot answer for its correctness. The teaching
of calculation should include, as an essential condition, that the
pupils should be shown how every result, deduced from a series of
arithmetical operations, may always be controlled in such a way that we
may have all desirable certainty of its correctness; so that, though a
pupil may and must often make mistakes, he may be able to discover them
himself, to correct them himself, and never to present, at last, any
other than an exact result.

   *   *   *

The _Programme_ given below is made very minute to avoid the evils which
resulted from the brevity of the old one. In it, the limits of the
matter required not being clearly defined, each teacher preferred to
extend them excessively, rather than to expose his pupils to the risk of
being unable to answer certain questions. The examiners were then
naturally led to put the questions thus offered to them, so to say; and
thus the preparatory studies grew into excessive and extravagant
development. These abuses could be remedied only by the publication of
programmes so detailed, that the limits within which the branches
required for admission must be restricted should be so apparent to the
eyes of all, as to render it impossible for the examiners to go out of
them, and thus to permit teachers to confine their instruction within

The new programme for arithmetic commences with the words Decimal
numeration. This is to indicate that the Duodecimal numeration will not
be required.

The only practical verification of Addition and Multiplication, is to
recommence these operations in a different order.

The Division of whole numbers is the first question considered at all
difficult. This difficulty arises from the complication of the methods
by which division is taught. In some books its explanation contains
twice as many reasons as is necessary. The mind becomes confused by such
instruction, and no longer understands what is a demonstration, when it
sees it continued at the moment when it appeared to be finished. In most
cases the demonstration is excessively complicated and does not follow
the same order as the practical rule, to which it is then necessary to
return. There lies the evil, and it is real and profound.

The phrase of the programme, Division of whole numbers, intends that the
pupil shall be required to explain the practical rule, and be able to
use it in a familiar and rapid manner. We do not present any particular
mode of demonstration, but, to explain our views, we will indicate how
we would treat the subject if we were making the detailed programme of a
_course_ of arithmetic, and not merely that of an _examination_. It
would be somewhat thus:

“The quotient may be found by addition, subtraction, multiplication;

“Division of a number by a number of one figure, when the quotient is
less than 10;

“Division of any number by a number less than 10;

“Division of any two numbers when the quotient has only one figure;

“Division in the most general case.

  “_Note._--The practical rule may be entirely explained by this
consideration, that by multiplying the divisor by different numbers, we
see if the quotient is greater or less than the multiplier.”

The properties of the Divisors of numbers, and the decomposition of a
number into prime factors should be known by the student. But here also
we recommend simplicity. The theory of the greatest common divisor, for
example, has no need to be given with all the details with which it is
usually surrounded, for it is of no use in practice.

The calculation of Decimal numbers is especially that in which it is
indispensable to exercise students. Such are the numbers on which they
will generally have to operate. It is rare that the data of a question
are whole numbers; usually they are decimal numbers which are not even
known with rigor, but only with a given decimal approximation; and the
result which is sought is to deduce from these, other decimal numbers,
themselves exact to a certain degree of approximation, fixed by the
conditions of the problem. It is thus that this subject should be
taught. The pupil should not merely learn how, in one or two cases, he
can obtain a result to within 1/_n_, _n_ being any number, but how to
arrive by a practicable route to results which are exact to within a
required decimal, and on the correctness of which they can depend.

Let us take decimal multiplication for an example. Generally the pupils
do not know any other rule than “to multiply one factor by the other,
without noticing the decimal point, except to cut off on the right of
the product as many decimal figures as there are in the two factors.”
The rule thus enunciated is methodical, simple, and apparently easy.
But, in reality, it is practically of a repulsive length, and is most
generally inapplicable.

Let us suppose that we have to multiply together two numbers having each
six decimals, and that we wish to know the product also to the sixth
decimal. The above rule will give twelve decimals, the last six of
which, being useless, will have caused by their calculation the loss of
precious time. Still farther; when a factor of a product is given with
six decimals, it is because we have stopped in its determination at that
degree of approximation, neglecting the following decimals; whence it
results that several of the decimals situated on the right of the
calculated product are not those which would belong to the rigorous
product. What then is the use of taking the trouble of determining them?

We will remark lastly that if the factors of the product are
incommensurable, and if it is necessary to convert them into decimals
before effecting the multiplication, we should not know how far we
should carry the approximation of the factors before applying the above
rule. It will therefore be necessary to teach the pupils the abridged
methods by which we succeed, at the same time, in using fewer figures
and in knowing the real approximation of the result at which we arrive.

Periodical decimal fractions are of no use. The two elementary questions
of the programme are all that need be known about them.

The Extraction of the square root must be given very carefully,
especially that of decimal numbers. It is quite impossible here to
observe the rule of having in the square twice as many decimals as are
required in the root. That rule is in fact impracticable when a series
of operations is to be effected. “When a number N increases by a
comparatively small quantity _d_, the square of that number increases
very nearly as 2N_d_.” It is thus that we determine the approximation
with which a number must be calculated so that its square root may
afterwards be obtained with the necessary exactitude. This supposes that
before determining the square with all necessary precision, we have a
suitable lower limit of the value of the root, which can always be done
without difficulty.

The Cube root is included in the programme. The pupils should know this;
but while it will be necessary to exercise them on the extraction of the
square root by numerous examples, we should be very sparing of this in
the cube root, and not go far beyond the mere theory. The calculations
become too complicated and waste too much time. Logarithms are useful
even for the square root; and quite indispensable for the cube root, and
still more so for higher roots.

When a question contains only quantities which vary in the same ratio,
or in an inverse ratio, it is immediately resolved by a very simple
method, known under the name of _reduction to unity_. The result once
obtained, it is indispensable to make the pupils remark that it is
composed of the quantity which, among the data, is of the nature of that
which is sought, multiplied successively by a series of abstract ratios
between other quantities which also, taken two and two, are of the same
nature. Hence flows the rule for writing directly the required result,
without being obliged to take up again for each question the series of
reasonings. This has the advantage, not only of saving time, but of
better showing the spirit of the method, of making clearer the meaning
of the solution, and of preparing for the subsequent use of formulas.
The consideration of “homogeneity” conduces to these results.

We recommend teachers to abandon as much as possible the use of examples
in abstract numbers, and of insignificant problems, in which the data,
taken at random, have no connection with reality. Let the examples and
the exercises presented to students always relate to objects which are
found in the arts, in industry, in nature, in physics, in the system of
the world. This will have many advantages. The precise meaning of the
solutions will be better grasped. The pupils will thus acquire, without
any trouble, a stock of precise and precious knowledge of the world
which surrounds them. They will also more willingly engage in numerical
calculations, when their attention is thus incessantly aroused and
sustained, and when the result, instead of being merely a dry number,
embodies information which is real, useful, and interesting.

The former arithmetical programme included the theory of _progressions_
and _logarithms_; the latter being deduced from the former. But the
theory of logarithms is again deduced in algebra from exponents, much
the best method. This constitutes an objectionable “_double emploi_.”
There is finally no good reason for retaining these theories in

The programme retains the questions which can be solved by making two
arbitrary and successive hypotheses on the desired result. It is true
that these questions can be directly resolved by means of a simple
equation of the first degree; but we have considered that, since the
resolution of problems by means of hypotheses, constitutes the most
fruitful method really used in practice, it is well to accustom students
to it the soonest possible. This is the more necessary, because teachers
have generally pursued the opposite course, aiming especially to give
their pupils direct solutions, without reflecting that the theory of
these is usually much more complicated, and that the mind of the learner
thus receives a direction exactly contrary to that which it will have to
take in the end.

“Proportions” remain to be noticed.

In most arithmetics problems are resolved first by the method of
“reduction to unity,” and then by the theory of proportions. But beside
the objection of the “_double emploi_,” it is very certain that the
method of reduction to unity presents, in their true light and in a
complete and simple manner, all the questions of ratio which are the
bases of arithmetical solutions; so that the subsequent introduction of
proportions teaches nothing new to the pupils, and only presents the
same thing in a more complicated manner. We therefore exclude from our
programme of examination the solution of questions of arithmetic,
presented under the special form which constitutes the theory of

This special form we would be very careful not to invent, if it had not
already been employed. Why not say simply “The ratio of M to N is equal
to that of P to Q,” instead of hunting for this other form of
enunciating the same idea, “M _is to_ N _as_ P _is to_ Q”? It is in vain
to allege the necessities of geometry; if we consider all the questions
in which proportions are used, we shall see that the simple
consideration of the equality of ratios is equally well adapted to the
simplicity of the enunciation and the clearness of the demonstrations.
However, since all the old books of geometry make use of proportions, we
retain the properties of proportions at the end of our programme; but
with this express reserve, that the examiners shall limit themselves to
the simple properties which we indicate, and that they shall not demand
any application of proportions to the solution of arithmetical problems.


  Decimal numeration.

  Addition and subtraction of whole numbers.

  Multiplication of whole numbers.--Table of Pythagoras.--The product of
several whole numbers does not change its value, in whatever order the
multiplications are effected.--To multiply a number by the product of
several factors, it is sufficient to multiply successively by the
factors of the product.

  Division of whole numbers.--To divide a number by the product of
several factors, it is sufficient to divide successively by the factors
of the product.

  Remainders from dividing a whole number by 2, 3, 5, 9, and
11.--Applications to the characters of divisibility by one of those
numbers; to the verification of the product of several factors; and to
the verification of the quotient of two numbers.

  Prime numbers. Numbers prime to one another.

  To find the greatest common divisor of two numbers.--If a number
divides a product of two factors, and if it is prime to one of the
factors, it divides the other.--To decompose a number into its prime
factors.--To determine the smallest number divisible by given numbers.

  _Vulgar fractions._

  A fraction does not alter in value when its two terms are multiplied
or divided by the same number. Reduction of a fraction to its simplest
expression. Reduction of several fractions to the same denominator.
Reduction to the smallest common denominator.--To compare the relative
values of several fractions.

  Addition and subtraction of fractions.--Multiplication. Fractions of

  Calculation of numbers composed of an entire part and a fraction.

  _Decimal numbers._

  Addition and subtraction.

  Multiplication and division.--How to obtain the product of the
quotient to within a unit of any given decimal order.

  To reduce a vulgar fraction to a decimal fraction.--When the
denominator of an irreducible fraction contains other factors than 2 and
5, the fraction cannot be exactly reduced to decimals; and the quotient,
which continues indefinitely, is periodical.

  To find the vulgar fraction which generates a periodical decimal
fraction: 1º when the decimal fraction is simply periodical; 2º when it
contains a part not periodical.

  _System of the new measures._

  Linear Measures.--Measures of surface.--Measures of volume and
capacity.--Measures of weight.--Moneys.--Ratios of the principal foreign
measures (England, Germany, United States of America) to the measures of

  _Of ratios. Resolution of problems._

  General notions on quantities which vary in the same ratio or in an
inverse ratio.--Solution, by the method called _Reduction to unity_, of
the simplest questions in which such quantities are considered.--To show
the homogeneity of the results which are arrived at; thence to deduce
the general rule for writing directly the expression of the required

  Simple interest.--General formula, the consideration of which
furnishes the solution of questions relating to simple interest.--Of
discount, as practised in commerce.

  To divide a sum into parts proportional to given numbers.

  Of questions which can be solved by two arbitrary and successive
hypotheses made on the desired result.

  _Of the square and of the square root. Of the cube and of the cube

  Formation of the square and the cube of the sum of two numbers.--Rules
for extracting the square root and the cube root of a whole number.--If
this root is not entire, it cannot be exactly expressed by any number,
and is called incommensurable.

  Square and cube of a fraction.--Extraction of the square root and cube
root of vulgar fractions.

  Any number being given, either directly, or by a series of operations
which permit only an approximation to its value by means of decimals,
how to extract the square root or cube root of that number, to within
any decimal unit.

  _Of the proportions called geometrical._

  In every proportion the product of the extremes is equal to the
product of the means.--Reciprocal proportion.--Knowing three terms of a
proportion to find the fourth.--Geometrical mean of two numbers.--How
the order of the terms of a proportion can be inverted without
disturbing the proportion.

  When two proportions have a common ratio, the two other ratios form a

  In any proportion, each antecedent may be increased or diminished by
its consequent without destroying the proportion.

  When the corresponding terms of several proportions are multiplied
together, the four products form a new proportion.--The same powers or
the same roots of four numbers in proportion form a new proportion.

  In a series of equal ratios, the sum of any number of antecedents and
the sum of their consequents are still in the same ratio.


Some knowledge of Geometry is, next to arithmetic, most indispensable to
every one, and yet very few possess even its first principles. This is
the fault of the common system of instruction. We do not pay sufficient
regard to the natural notions about straight lines, angles, parallels,
circles, etc., which the young have acquired by looking around them, and
which their minds have unconsciously considered before making them a
regular study. We thus waste time in giving a dogmatic form to truths
which the mind seizes directly.

The illustrious _Clairaut_ complains of this, and of the instruction
commencing always with a great number of definitions, postulates,
axioms, and preliminary principles, dry and repulsive, and followed by
propositions equally uninteresting. He also condemns the profusion of
self-evident propositions, saying, “It is not surprising that Euclid
should give himself the trouble to demonstrate that two circles which
intersect have not the same centre; that a triangle situated within
another has the sum of its sides smaller than that of the sides of the
triangle which contains it; and so on. That geometer had to convince
obstinate sophists, who gloried in denying the most evident truths. It
was therefore necessary that geometry, like logic, should then have the
aid of formal reasonings, to close the mouths of cavillers; but in our
day things have changed face; all reasoning about what mere good sense
decides in advance is now a pure waste of time, and is fitted, only to
obscure the truth and to disgust the reader.”

_Bezout_ also condemns the multiplication of the number of theorems,
propositions, and corollaries; an array which makes the student dizzy,
and amid which he is lost. All that follows from a principle should be
given in natural language as far as possible, avoiding the dogmatic
form. It is true that some consider the works of Bezout deficient in
rigor, but he knew better than any one what really was a demonstration.
Nor do we find in the works of the great old masters less generality of
views, less precision, less clearness of conception than in modern
treatises. Quite the contrary indeed.

We see this in Bezout’s _definition of a right line_--that it tends
continually towards one and the same point; and in that of _a curved
line_--that it is the trace of a moving point, which turns aside
infinitely little at each step of its progress; definitions most
fruitful in consequences. When we define a right line as the shortest
path from one point to another, we enunciate a property of that line
which is of no use for demonstrations. When we define a curved line as
one which is neither straight nor composed of straight lines, we
enunciate two negations which can lead to no result, and which have no
connection with the peculiar nature of the curved line. Bezout’s
definition, on the contrary, enters into the nature of the object to be
defined, seizes its mode of being, its character, and puts the reader
immediately in possession of the general idea from which are afterwards
deduced the properties of curved lines and the construction of their

So too when Bezout says that, in order to form an exact idea of an
angle, it is necessary to consider the movement of a line turning around
one of its points, he gives an idea at once more just and more fruitful
in consequences, both mathematical and mechanical, than that which is
limited to saying, that the indefinite space comprised between two
straight lines which meet in a point, and which may be regarded as
prolonged indefinitely, is called an _angle_; a definition not very
easily comprehended and absolutely useless for ulterior explanations,
while that of Bezout is of continual service.

We therefore urge teachers to return, in their demonstrations, to the
simplest ideas, which are also the most general; to consider a
demonstration as finished and complete when it has evidently caused the
truth to enter into the mind of the pupil, and to add nothing merely for
the sake of silencing sophists.

   *   *   *

Referring to our Programme of Geometry, given below, our first comments
relate to the “Theory of parallels.” This is a subject on which all
students fear to be examined; and this being a general feeling, it is
plain that it is not their fault, but that of the manner in which this
subject is taught. The omission of the natural idea of the constant
direction of the right line (as defined by Bezout) causes the
complication of the first elements; makes it necessary for Legendre to
demonstrate that all right angles are equal (a proposition whose meaning
is rarely understood); and is the real source of all the pretended
difficulties of the theory of parallels. These difficulties are now
usually avoided by the admission of a _postulate_, after the example of
Euclid, and to regulate the practice in that matter, we have thought
proper to prescribe that this proposition--_Through a given point only a
single parallel to a right line can be drawn_--should be admitted purely
and simply, without demonstration, and as a direct consequence of our
idea of the nature of the right line.

We should remark that the order of ideas in our programme supposes the
properties of lines established without any use of the properties of
surfaces. We think that, in this respect, it is better to follow Lacroix
than Legendre.

When we prove thus that three parallels always divide two right lines
into proportional parts, this proposition can be extended to the case in
which the ratio of the parts is incommensurable, either by the method
called _Reductio ad absurdum_, or by the method of _Limits_. We
especially recommend the use of the latter method. The former has in
fact nothing which satisfies the mind, and we should never have recourse
to it, for it is always possible to do without it. When we have proved
to the pupil that a desired quantity, X, cannot be either larger or
smaller than A, the pupil is indeed forced to admit that X and A are
equal; but that does not make him understand or feel why that equality
exists. Now those demonstrations which are of such a nature that, once
given, they disappear, as it were, so as to leave to the proposition
demonstrated the character of a truth evident _à priori_, are those
which should be carefully sought for, not only because they make that
truth better felt, but because they better prepare the mind for
conceptions of a more elevated order. The method of limits, is, for a
certain number of questions, the only one which possesses this
characteristic--that the demonstration is closely connected with the
essential nature of the proposition to be established.

In reference to the relations which exist between the sides of a
triangle and the segments formed by perpendiculars let fall from the
summits, we will, once for all, recommend to the teacher, to exercise
his students in making numerical applications of relations of that kind,
as often as they shall present themselves in the course of geometry.
This is the way to cause their meaning to be well understood, to fix
them in the mind of students, and to give these the exercise in
numerical calculation to which we positively require them to be

The theory of similar figures has a direct application in the art of
surveying for plans (_Lever des plans_). We wish that this application
should be given to the pupils in detail; that they should be taught to
range out and measure a straight line on the ground; that a graphometer
should be placed in their hands; and that they should use it and the
chain to obtain on the ground, for themselves, all the data necessary
for the construction of a map, which they will present to the examiners
with the calculations in the margins.

It is true that a more complete study of this subject will have to be
subsequently made by means of trigonometry, in which calculation will
give more precision than these graphical operations. But some pupils may
fail to extend their studies to trigonometry (the course given for the
Polytechnic school having become the model for general instruction in
France), and those who do will thus learn that trigonometry merely gives
means of more precise calculation. This application will also be an
encouragement to the study of a science whose utility the pupil will
thus begin to comprehend.

It is common to say that an angle is measured by the arc of a circle,
described from its summit or centre, and intercepted between its sides.
It is true that teachers add, that since a quantity cannot be measured
except by one of the same nature, and since the arc of a circle is of a
different nature from an angle, the preceding enunciation is only an
abridgment of the proposition by which we find the ratio of an angle to
a right angle. Despite this precaution, the unqualified enunciation
which precedes, causes uncertainty in the mind of the pupil, and
produces in it a lamentable confusion. We will say as much of the
following enunciations: “A dihedral angle is measured by the plane angle
included between its sides;” “The surface of a spherical triangle is
measured by the excess of the sum of its three angles above two right
angles,” etc.; enunciations which have no meaning in themselves, and
from which every trace of homogeneity has disappeared. Now that
everybody is requiring that the students of the Polytechnic school
should better understand the meaning of the formulas which they are
taught, which requires that their homogeneity should always be apparent,
this should be attended to from the beginning of their studies, in
geometry as well as in arithmetic. The examiners must therefore insist
that the pupils shall never give them any enunciations in which
homogeneity is not preserved.

The proportionality of the circumferences of circles to their radii must
be inferred _directly_ from the proportionality of the perimeters of
regular polygons, of the same number of sides, to their apothems. In
like manner, from the area of a regular polygon being measured by half
of the product of its perimeter by the radius of the inscribed circle,
it must be _directly_ inferred that the area of a circle is measured by
half of the product of its circumference by its radius. For a long time,
these properties of the circle were differently demonstrated by proving,
for example, with Legendre, that the measure of the circle could not be
either smaller or greater than that which we have just given, whence it
had to be inferred that it must be equal to it. The “Council of
improvement” finally decided that this method should be abandoned, and
that the method of limits should alone be admitted, in the examinations,
for demonstrations of this kind. This was a true advance, but it was not
sufficient. It did not, as it should, go on to consider the circle,
purely and simply, as the limit of a series of regular polygons, the
number of whose sides goes on increasing to infinity, and to regard the
circle as possessing every property demonstrated for polygons. Instead
of this, they inscribed and circumscribed to the circle two polygons of
the same number of sides, and proved that, by the multiplication of the
number of the sides of these polygons, the difference of their areas
might become smaller than any given quantity, and thence, finally,
deduced the measure of the area of the circle; that is to say, they took
away from the method of limits all its advantage as to simplicity, by
not applying it _frankly_.

We now ask that this shall cease; and that we shall no longer reproach
for want of rigor, the Lagranges, the Laplaces, the Poissons, and
Leibnitz, who has given us this principle: that “A curvilinear figure
may be regarded as equivalent to a polygon of an infinite number of
sides; whence it follows that whatsoever can be demonstrated of such a
polygon, no regard being paid to the number of its sides, the same may
be asserted of the curve.” This is the principle for _the most simple_
application of which to the measure of the circle and of the round
bodies we appeal.

Whatever may be the formulas which may be given to the pupils for the
determination of the ratio of the circumference to the diameter (the
“Method of isoperimeters” is to be recommended for its simplicity), they
must be required to perform the calculation, so as to obtain at least
two or three exact decimals. These calculations, made with logarithms,
must be methodically arranged and presented at the examination. It may
be known whether the candidate is really the author of the papers, by
calling for explanations on some of the steps, or making him calculate
some points afresh.

The enunciations relating to the measurement of areas too often leave
indistinctness in the minds of students, doubtless because of their
form. We desire to make them better comprehended, by insisting on their
application by means of a great number of examples.

As one application, we require the knowledge of the methods of surveying
for content (_arpentage_), differing somewhat from the method of
triangulation, used in the surveying for plans (_lever des plans_). To
make this application more fruitful, the ground should be bounded on one
side by an irregular curve. The pupils will not only thus learn how to
overcome this practical difficulty, but they will find, in the
calculation of the surface by means of trapezoids, the first application
of the method of quadratures, with which it is important that they
should very early become familiar. This application will constitute a
new sheet of drawing and calculations to be presented at the

Most of our remarks on plane geometry apply to geometry of three
dimensions. Care should be taken always to leave homogeneity apparent
and to make numerous applications to the measurement of volumes.

The theory of similar polyhedrons often gives rise in the examination of
the students to serious difficulties on their part. These difficulties
belong rather to the form than to the substance, and to the manner in
which each individual mind seizes relations of position; relations
always easier to feel than to express. The examiners should be content
with arriving at the results enunciated in our programme, by the
shortest and easiest road.

The simplicity desired cannot however be attained unless all have a
common starting-point, in the definition of similar polyhedrons. The
best course is assuredly to consider that theory in the point of view in
which it is employed in the arts, especially in sculpture; i.e. to
conceive the given system of points, M, N, P, . . . . to have lines
passing from them through a point S, the _pole of similitude_, and
prolonged beyond it to M’, N’, P’, . . . . so that SM’, SN’, SP’,
. . . . are proportional to SM, SN, SP, . . . . . Then the points M’,
N’, P’, . . . . form a system _similar_ to M, N, P, . . . . .

The areas and volumes of the cylinder, of the cone, and of the sphere
must be deduced from the areas and from the volumes of the prism, of the
pyramid, and of the polygonal sector, with the same simplicity which we
have required for the measure of the surface of the circle, and for the
same reasons. It is, besides, the only means of easily extending to
cones and cylinders with any bases whatever, right or oblique, those
properties of cones and cylinders,--right and with circular
bases,--which are applicable to them.

Numerical examples of the calculations, by logarithms, of these areas
and volumes, including the area of a spherical triangle, will make
another sheet to be presented to the examiners.



  Measure of the distance of two points.--Two finite right lines being
given, to find their common measure, or at least their approximate

  _Of angles._--Right, acute, obtuse angles.--Angles vertically opposite
are equal.

  _Of triangles._--Angles and sides.--The simplest cases of
equality.--Elementary problems on the construction of angles and of

  _Of perpendiculars and of oblique lines._

  Among all the lines that can be drawn from a given point to a given
right line, the perpendicular is the shortest, and the oblique lines are
longer in proportion to their divergence from the foot of the

  _Properties of the isosceles triangle._--Problems on tracing
perpendiculars.--Division of a given straight line into equal parts.

  Cases of equality of right-angled triangles.

  _Of parallel lines._

  Properties of the angles formed by two parallels and a
secant.--Reciprocally, when these properties exist for two right lines
and a common secant, the two lines are parallel.[1]--Through a given
point, to draw a right line parallel to a given right line, or cutting
it at a given angle.--Equality of angles having their sides parallel and
their openings placed in the same direction.

    [Footnote 1: It will be admitted, as a postulate, that only one
    parallel to a given right line can pass through a given point.]

  Sum of the angles of a triangle.

  The parts of parallels intercepted between parallels are equal, and
reciprocally. Three parallels always divide any two right lines into
proportional parts. The ratio of these parts may be incommensurable.--
Application to the case in which a right line is drawn, in a triangle,
parallel to one of its sides.

  To find a fourth proportional to three given lines.

  The right line, which bisects one of the angles of a triangle, divides
the opposite side into two segments proportional to the adjacent sides.

  _Of similar triangles._

  Conditions of similitude.--To construct on a given right line, a
triangle similar to a given triangle.

  Any number of right lines, passing through the same point and met by
two parallels, are divided by these parallels into proportional parts,
and divide them also into proportional parts.--To divide a given right
line in the same manner as another is divided.--Division of a right line
into equal parts.

  If from the right angle of a right-angled triangle a perpendicular is
let fall upon the hypothenuse, 1º this perpendicular will divide the
triangle into two others which will be similar to it, and therefore to
each other; 2º it will divide the hypothenuse into two segments, such
that each side of the right angle will be a mean proportional between
the adjacent segment and the entire hypothenuse; 3º the perpendicular
will be a mean proportional between the two segments of the hypothenuse.

  In a right-angled triangle, the square of the number which expresses
the length of the hypothenuse is equal to the sum of the squares of the
numbers which express the lengths of the other two sides.

  The three sides of any triangle being expressed in numbers, if from
the extremity of one of the sides a perpendicular is let fall on one of
the other sides, the square of the first side will be equal to the sum
of the squares of the other two, _minus_ twice the product of the side
on which the perpendicular is let fall by the distance of that
perpendicular from the angle opposite to the first side, if the angle is
_acute_, and _plus_ twice the same product, if this angle is _obtuse_.

  _Of polygons._

  Parallelograms.--Properties of their angles and of their diagonals.

  Division of polygons into triangles.--Sum of their interior
angles.--Equality and construction of polygons.

  Similar polygons.--Their decomposition into similar triangles.--The
right lines similarly situated in the two polygons are proportional to
the homologous sides of the polygons.--To construct, on a given line, a
polygon similar to a given polygon.--The perimeters of two similar
polygons are to each other as the homologous sides of these polygons.

  _Of the right line and the circumference of the circle._

  Simultaneous equality of arcs and chords in the same circle.--The
greatest arc has the greatest chord, and reciprocally.--Two arcs being
given in the same circle or in equal-circles, to find the ratio of their

  Every right line drawn perpendicular to a chord at its middle, passes
through the centre of the circle and through the middle of the arc
subtended by the chord.--Division of an arc into two equal parts.--To
pass the circumference of a circle through three points not in the same
right line.

  The tangent at any point of a circumference is perpendicular to the
radius passing through that point.

  The arcs intercepted in the same circle between two parallel chords,
or between a tangent and a parallel chord, are equal.

  _Measure of angles._

  If from the summits of two angles two arcs of circles be described
with the same radius, the ratio of the arcs included between the sides
of each angle will be the same as that of these angles.--Division of the
circumference into degrees, minutes, and seconds.--Use of the

  An angle having its summit placed, 1º at the centre of a circle; 2º on
the circumference of that circle; 3º within the circle between the
centre and the circumference; 4º without the circle, but so that its
sides cut the circumference; to determine the ratio of that angle to the
right angle, by the consideration of the arc included between its sides.

  From a given point without a circle, to draw a tangent to that circle.

  To describe, on a given line, a segment of a circle capable of
containing a given angle.

  _To make surveys for plans._ (_Lever des plans._)

  Tracing a straight line on the ground.--Measuring that line with the

  Measuring angles with the graphometer.--Description of it.

  Drawing the plan on paper.--Scale of reduction.--Use of the rule, the
triangle, and the protractor.

  To determine the distance of an inaccessible object, with or without
the graphometer.

  Three points, A, B, C, being situated on a smooth surface and
represented on a map, to find thereon the point P from which the
distances AB and AC have been seen under given angles. “The problem of
the three points.” “The _Trilinear_ problem.”

  _Of the contact and of the intersection of circles._

  Two circles which pass through the same point of the right line which
joins their centres have in common only that point in which they touch;
and reciprocally, if two circles touch, their centres and the point of
contact lie in the same right line.

  Conditions which must exist in order that two circles may intersect.

  _Properties of the secants of the circle._

  Two secants which start from the same point without the circle, being
prolonged to the most distant part of the circumference, are
reciprocally proportional to their exterior segments.--The tangent is a
mean proportional between the secant and its exterior segment.

  Two chords intersecting within a circle divide each other into parts
reciprocally proportional.--The line perpendicular to a diameter and
terminated by the circumference, is a mean proportional between the two
segments of the diameter.

  A chord, passing through the extremity of the diameter, is a mean
proportional between the diameter and the segment formed by the
perpendicular let fall from the other extremity of that chord.--To find
a mean proportional between two given lines.

  To divide a line in extreme and mean ratio.--The length of the line
being given numerically, to calculate the numerical value of each of the

  _Of polygons inscribed and circumscribed to the circle._

  To inscribe or circumscribe a circle to a given triangle.

  Every regular polygon can be inscribed and circumscribed to the

  A regular polygon being inscribed in a circle, 1º to inscribe in the
same circle a polygon of twice as many sides, and to find the length of
one of the sides of the second polygon; 2º to circumscribe about the
circle a regular polygon of the same number of sides, and to express the
side of the circumscribed polygon by means of the side of the
corresponding inscribed polygon.

    To inscribe in a circle polygons of 4, 8, 16, 32,   sides.
    To inscribe in a circle polygons of 3, 6, 12, 24,   sides.
    To inscribe in a circle polygons of 5, 10, 20, 40,  sides.
    To inscribe in a circle polygons of 15, 30, 60,     sides.

  Regular polygons of the same number of sides are similar, and their
perimeters are to each other as the radii of the circles to which they
are inscribed or circumscribed.--The circumferences of circles are to
each other as their radii.

  To find the approximate ratio of the circumference to the diameter.

  _Of the area of polygons and of that of the circle._

  Two parallelograms of the same base and of the same height are
equivalent.--Two triangles of the same base and height are equivalent.

  The area of a rectangle and that of a parallelogram are equal to the
product of the base by the height.--What must be understood by that
enunciation.--The area of a triangle is measured by half of the product
of the base by the height.

  To transform any polygon into an equivalent square.--Measure of the
area of a polygon.--Measure of the area of a trapezoid.

  The square constructed on the hypothenuse of a right-angled triangle
is equivalent to the sum of the squares constructed on the other two
sides.--The squares constructed on the two sides of the right angle of a
right-angled triangle and on the hypothenuse are to each other as the
adjacent segments and entire hypothenuse.

  The areas of similar polygons are to each other as the squares of the
homologous sides of the polygons.

  Notions on surveying for content (_arpentage_).--Method of
decomposition into triangles.--Simpler method of decomposition into
trapezoids.--Surveyor’s cross.--Practical solution, when the ground is
bounded, in one or more parts, by a curved line.

  The area of a regular polygon is measured by half of the product of
its perimeter by the radius of the inscribed circle.--The area of a
circle is measured by half of the product of the circumference by the
radius.--The areas of circles are to each other as the squares of the

  The area of a sector of a circle is measured by half of the product of
the arc by the radius.--Measure of the area of a segment of a circle.


  Conditions required to render a right line and a plane respectively

  Of all the lines which can be drawn from a given point to a given
plane, the perpendicular is the shortest, and the oblique lines are
longer in proportion to their divergence from the foot of the

  Parallel right lines and planes.--Angles which have their sides
parallel, and their openings turned in the same direction, are equal,
although situated in different planes.

  Dihedral angle.--How to measure the ratio of any dihedral angle to the
right dihedral angle.

  Planes perpendicular to each other.--The intersection of two planes
perpendicular to a third plane, is perpendicular to this third plane.

  Parallel planes.--when two parallel planes are cut by a third plane
the intersections are parallel.--Two parallel planes have their
perpendiculars common to both.

  The shortest distance between two right lines, not intersecting and
not parallel.

  Two right lines comprised between two parallel planes are always
divided into proportional parts by a third plane parallel to the first

  Trihedral angle.--The sum of any two of the plane angles which compose
a trihedral angle is always greater than the third.

  The sum of the plane angles which form a convex polyhedral angle is
always less than four right angles.

  If two trihedral angles are formed by the same plane angles, the
dihedral angles comprised between the equal plane angles are
equal.--There may be absolute equality or simple symmetry between the
two trihedral angles.

  _Of polyhedrons._

  If two tetrahedrons have each a trihedral angle composed of equal and
similarly arranged triangles, these tetrahedrons are equal. They are
also equal if two faces of the one are equal to two faces of the other,
are arranged in the same manner, and form with each other the same
dihedral angle.

  When the triangles which form two homologous trihedral angles of two
tetrahedrons are similar, each to each, and similarly disposed, these
tetrahedrons are similar. They are also similar if two faces of the one,
making with each other the same angle as two faces of the other, are
also similar to these latter, and are united by homologous sides and

  Similar pyramids.--A plane parallel to the base of a pyramid cuts off
from it a pyramid similar to it.--To find the height of a pyramid when
we know the dimension of its trunk with parallel bases.

  Sections made in any two pyramids at the same distance from these
summits are in a constant ratio.

  Parallelopipedon.--Its diagonals.

  Any polyhedron can always be divided into triangular pyramids.--Two
bodies composed of the same number of equal and similarly disposed
triangular pyramids, are equal.

  _Similar polyhedrons._

  The homologous edges of similar polyhedrons are proportional; as are
also the diagonals of the homologous faces and the interior diagonals of
the polyhedrons.--The areas of similar polyhedrons are as the squares of
the homologous edges.

  _Measure of volumes._

  Two parallelopipedons of the same base and of the same height are
equivalent in volume.

  If a parallelogram be constructed on the base of a triangular prism,
and on that parallelogram, taken as a base, there be constructed a
parallelopipedon of the same height as the triangular prism, the volume
of this prism will be half of the volume of the parallelopipedon.--Two
triangular prisms of the same base and the same height are equivalent.

  Two tetrahedrons of the same base and the same height are equivalent.

  A tetrahedron is equivalent to the third of the triangular prism of
the same base and the same height.

  The volume of any parallelopipedon is equal to the product of its base
by its height.--What must be understood by that enunciation.--The volume
of any prism is equal to the product of its base by its height.

  The volume of a tetrahedron and that of any pyramid are measured by
the third of the product of the base by the height.

  Volume of the truncated oblique triangular prism.

  The volumes of two similar polyhedrons are to each other as the cubes
of the homologous edges.


  _Of the right cone with circular base._

  Sections parallel to the base.--Having the dimensions of the trunk of
a cone with parallel bases, to find the height of the entire cone.

  The area of a right cone is measured by half of the product of the
circumference of its circular base by its side.--Area of a trunk of a
right cone with parallel bases.

  Volume of a pyramid inscribed in the cone.--The volume of a cone is
measured by the third of the product of the area of its base by its

    [Footnote 2: The volume of the cone is derived from that of the
    pyramid; and it is to be noted that the demonstration applies to
    the cone with closed base, whatever the figure of that base.]

  Which of the preceding properties belong to the cone of any base

  _Of the right cylinder with circular base._

  Sections parallel to the base.

  The area of the convex surface of the right cylinder is measured by
the product of the circumference of its base by its height.--This is
also true of the right cylinder of any base.

  Measure of the volume of a prism inscribed in the cylinder.--The
volume of a right cylinder is measured by the product of the area of its
base by its height.--This is also true of any cylinder, right or
oblique, of any base whatever.

  _Of the sphere._

  Every section of the sphere, made by a plane, is a circle.--Great
circles and small circles.

  In every spherical triangle any one side is less than the sum of the
other two. The shortest path from one point to another, on the surface
of the sphere, is the arc of a great circle which joins the two given

  The sum of the sides of a spherical triangle, or of any spherical
polygon, is less than the circumference of a great circle.

  Poles of an arc of a great or small circle.--They serve to trace arcs
of circles on the sphere.

  Every plane perpendicular to the extremity of a radius is tangent to
the sphere.

  Measure of the angle of two arcs of great circles.

  Properties of the polar or supplementary triangle.

  Two spherical triangles situated on the same sphere, or on equal
spheres, are equal in all their parts, 1º when they have an equal angle
included between sides respectively equal; 2º when they have an equal
side adjacent to two angles respectively equal; 3º when they are
mutually equilateral; 4º when they are mutually equiangular. In these
different cases the triangles may be equal, or merely symmetrical.

  The sum of the angles of any spherical triangle is less than six, and
greater than two, right angles.

  The lune is to the surface of the sphere as the angle of that lune is
to four right angles.

  Two symmetrical spherical triangles are equivalent in surface.

  The area of a spherical triangle is to that of the whole sphere as the
excess of the sum of its angles above two right angles is to eight right

  When a portion of a regular polygon, inscribed in the generating
circle of the sphere, turns around the diameter of that circle, the
convex area engendered is measured by the product of its height by the
circumference of the circle inscribed in the generating polygon.--The
volume of the corresponding polygonal sector is measured by the area
thus described, multiplied by the third of the radius of the inscribed

  The surface of a spherical zone is equal to the height of that zone
multiplied by the circumference of a great circle.--The surface of the
sphere is quadruple that of a great circle.

  Every spherical sector is measured by the zone which forms its base,
multiplied by the third of the radius. The whole sphere is measured by
its surface multiplied by the third of its radius.[3]

    [Footnote 3: Numerical examples on the areas and volumes of the
    round bodies, including the area of a spherical triangle, will be
    required by the examiners. The calculations will be made by


Algebra[4] is not, as are Arithmetic and Geometry, indispensable to
every one. It should be very sparingly introduced into the general
education of youth, and we would there willingly dispense with it
entirely, excepting logarithms, if this would benefit the study of
arithmetic and geometry. The programme of it which we are now to give,
considers it purely in view of its utility to engineers, and we will
carefully eliminate every thing not necessary for them.

    [Footnote 4: The true distinction between ALGEBRA and ARITHMETIC
    is so commonly overlooked that it maybe well to present it here,
    in the words of Comte. “The complete solution of every question of
    calculation is necessarily composed of two successive parts, which
    have essentially distinct natures. In the first, the object is to
    _transform_ the proposed equations, so as to make apparent the
    manner in which the unknown quantities are formed by the known
    ones; it is this which constitutes the _Algebraic_ question. In
    the second, our object is _to find the value_ of the formulas thus
    obtained; that is, to determine directly the values of the numbers
    sought, which are already represented by certain explicit
    functions of given numbers; this is the _Arithmetical_ question.
    Thus the stopping-point of the algebraic part of the solution
    becomes the starting-point of the arithmetical part.

    “ALGEBRA may therefore be defined as having for its object the
    _resolution of equations_; taking this expression in its full
    logical meaning, which signifies the transformation of _implicit_
    functions into equivalent _explicit_ ones. In the same way
    ARITHMETIC may be defined as intended for _the determination of
    the values of functions_. Henceforth, therefore, we may call
    ALGEBRA _the Calculus of Functions_, and ARITHMETIC _the Calculus
    of Values_.”]

Algebraical calculation presents no serious difficulty, when its
students become well impressed with this idea, that every letter
represents a number; and particularly when the consideration of negative
quantities is not brought in at the outset and in an absolute manner.
These quantities and their properties should not be introduced except as
the solution of questions by means of equations causes their necessity
to be felt, either for generalizing the rules of calculation, or for
extending the meaning of the formulas to which it leads. CLAIRAUT
pursues this course. He says, “I treat of the multiplication of negative
quantities, that dangerous shoal for both scholars and teachers, only
after having shown its necessity to the learner, by giving him a problem
in which he has to consider negative quantities independently of any
positive quantities from which they are subtracted. When I have arrived
at that point in the problem where I have to multiply or divide negative
quantities by one another, I take the course which was undoubtedly taken
by the first analysts who have had those operations to perform and who
have wished to follow a perfectly sure route: I seek for a solution of
the problem which does not involve these operations; I thus arrive at
the result by reasonings which admit of no doubt, and I thus see what
those products or quotients of negative quantities, which had given me
the first solution, must be.” BEZOUT proceeds in the same way.

We recommend to teachers to follow these examples; not to speak to their
pupils about negative quantities till the necessity of it is felt, and
when they have become familiar with algebraic calculation; and above all
not to lose precious time in obscure discussions and demonstrations,
which the best theory will never teach students so well as numerous

It has been customary to take up again, in algebra, the calculus of
fractions, so as to generalize the explanations given in arithmetic,
since the terms of literal fractions may be any quantities whatsoever.
Rigorously, this may be well, but to save time we omit this, thinking it
better to employ this time in advancing and exercising the mind on new
truths, rather than in returning continually to rules already given, in
order to imprint a new degree of rigor on their demonstration, or to
give them an extension of which no one doubts.

The study of numerical equations of the first degree, with one or
several unknown quantities, must be made with great care. We have
required the solution of these equations to be made by the method of
_substitution_. We have done this, not only because this method really
comprehends the others, particularly that of _comparison_, but for this
farther reason. In treatises on algebra, those equations alone are
considered whose numerical coefficients and solutions are very simple
numbers. It then makes very little difference what method is used, or in
what order the unknown quantities are eliminated. But it is a very
different thing in practice, where the coefficients are complicated
numbers, given with decimal parts, and where the numerical values of
these coefficients may be very different in the same equation, some
being very great and some very small. In such cases the method of
_substitution_ can alone be employed to advantage, and that with the
precaution of taking the value of the unknown quantity to be eliminated
from that equation in which it has relatively the greatest, coefficient.
Now the method of _comparison_ is only the method of substitution put in
a form in which these precautions cannot be observed, so that in
practice it will give bad results with much labor.

The candidates must present to the examiners the complete calculations
of the resolution of four equations with four unknown quantities, made
with all the precision permitted by the logarithmic tables of Callet,
and the proof that that precision has been obtained. The coefficients
must contain decimals and be very different from one another, and the
elimination must be effected with the above precautions.

The teaching of the present day disregards too much the applicability of
the methods given, provided only that they be elegant in their form; so
that they have to be abandoned and changed when the pupils enter on
practice. This disdain of practical utility was not felt by our great
mathematicians, who incessantly turned their attention towards
applications. Thus the illustrious Lagrange made suggestions like those
just given; and Laplace recommended the drawing of curves for solving
directly all kinds of numerical equations.

As to literal equations of the first degree, we call for formulas
sufficient for the resolution of equations of two or three unknown
quantities. Bezout’s method of elimination must be given as a first
application of that fruitful method of indeterminates. The general
discussion of formulas will be confined to the case of two unknown
quantities. The discussion of three equations with three unknown
quantities, _x_, _y_, and _z_, in which the terms independent of the
unknown quantities are null, will be made directly, by this simple
consideration that the system then really includes only two unknown
quantities, to wit, the ratios of _x_ and _y_, for example, to _z_.

The resolution of inequalities of the first degree with one or more
unknown quantities, was added to equations of the first degree some
years ago. We do not retain that addition.

The equations of the second degree, like the first, must be very
carefully given. In dwelling on the case where the coefficient of
_x_^{2} converges towards zero, it will be remarked that, when the
coefficient is very small, the ordinary formula would give one of the
roots by the difference of two numbers almost equal; so that sufficient
exactness could not be obtained without much labor. It must be shown how
that inconvenience may be avoided.

It is common to meet with expressions of which the maximum or the
minimum can be determined by the consideration of an equation of the
second degree. We retain the study of them, especially for the benefit
of those who will not have the opportunity of advancing to the general
theory of maxima and minima.

The theory of the algebraic calculation of imaginary quantities, given
_à priori_, may, on the contrary, be set aside without inconvenience.
It is enough that the pupils know that the different powers of √-1
continually reproduce in turn one of these four values, ±1, ±√-1. We
will say as much of the calculation of the algebraic values of radicals,
which is of no use. The calculation of their _arithmetical_ values will
alone be demanded. In this connection will be taught the notation of
fractional exponents and that of negative exponents.

The theory of numbers has taken by degrees a disproportionate
development in the examinations for admission; it is of no use in
practice, and, besides, constitutes in the pure mathematics a science

The theory of continued fractions at first seems more useful. It is
employed in the resolution of algebraic equations, and in that of the
exponential equation _a_^{_x_}=_b_. But these methods are entirely
unsuited to practice, and we therefore omit this theory.

The theory of series, on the contrary, claims some farther developments.
Series are continually met with in practice; they give the best
solutions of many questions, and it is indispensable to know in what
circumstances they can be safely employed.

We have so often insisted on the necessity of teaching students to
calculate, as to justify the extent of the part of the programme
relating to logarithms. We have suppressed the inapplicable method of
determining logarithms by continued fractions, and have substituted the
employment of the series which gives the logarithm of _n_+1, knowing
that of _n_. To exercise the students in the calculation of the series,
they should be made to determine the logarithms of the numbers from 1 to
10, from 101 to 110, and from 10,000 to 10,010, the object of these last
being to show them with what rapidity the calculation proceeds when the
numbers are large; the first term of the series is then sufficient, the
variations of the logarithms being sensibly proportional to the
variations of the numbers, within the limits of the necessary exactness.
In the logarithmic calculations, the pupils will be exercised in judging
of the exactness which they may have been able to obtain: the
consideration of the numerical values of the proportional parts given in
the tables is quite sufficient for this purpose, and is beside the only
one which can be employed in practice.

The use of the sliding rule, which is merely an application of
logarithms, gives a rapid and portable means of executing approximately
a great number of calculations which do not require great exactness. We
desire that the use of this little instrument should be made familiar to
the candidates. This is asked for by all the professors of the “School
of application,” particularly those of Topography, of Artillery, of
Construction, and of Applied Mechanics, who have been convinced by
experience of the utility of this instrument, which has the greatest
possible analogy with tables of logarithms.

Before entering on the subjects of higher algebra, it should be
remembered that the reductions of the course which we have found to be
so urgent, will be made chiefly on it. The general theory of equations
has taken in the examinations an abnormal and improper development, not
worth the time which it costs the students. We may add, that it is very
rare to meet a numerical equation of a high degree requiring to be
resolved, and that those who have to do this, take care not to seek its
roots by the methods which they have been taught. These methods moreover
are not applicable to transcendental equations, which are much more
frequently found in practice.

The theory of the greatest common algebraic divisor, in its entire
generality, is of no use, even in pure science, unless in the
elimination between equations of any degree whatever. But this last
subject being omitted, the greatest common divisor is likewise dispensed

It is usual in the general theory of algebraic equations to consider the
derived polynomials of entire functions of _x_. These polynomials are in
fact useful in several circumstances, and particularly in the theory of
equal roots; and in analytical geometry, they serve for the discussion
of curves and the determination of their tangents. But since
transcendental curves are very often encountered in practice, we give in
our programme the calculation of the derivatives of algebraic and
fractional functions, and transcendental functions, logarithmic,
exponential, and circular. This has been long called for, not only
because it must be of great assistance in the teaching of analytical
geometry, but also because it will facilitate the elementary study of
the infinitesimal calculus.

We have not retrenched any of the general ideas on the composition of an
entire polynomial by means of factors corresponding to its roots. We
retain several theorems rather because they contain the germs of useful
ideas than because of their practical utility, and therefore wish the
examiners to restrict themselves scrupulously to the programme.

The essential point in practice is to be able to determine conveniently
an incommensurable root of an algebraic or transcendental equation, when
encountered. Let us consider first an algebraic equation.

All the methods which have for their object to separate the roots, or to
approximate to them, begin with the substitution of the series of
consecutive whole numbers, in the first member of the equation. The
direct substitution becomes exceedingly complicated, when the numbers
substituted become large. It may be much shortened, however, by deducing
the results from one another by means of their differences, and guarding
against any possibility of error, by verifying some of those results,
those corresponding to the numbers easiest to substitute, such as ±10,
±20. The teacher should not fail to explain this to his pupils.

Still farther: let us suppose that we have to resolve an equation of the
third degree, and that we have recognized by the preceding calculations
the necessity of substituting, between the numbers 2 and 3, numbers
differing by a tenth, either for the purpose of continuing to effect the
separation of the roots, or to approximate nearer to a root comprised
between 2 and 3. If we knew, for the result corresponding to the
substitution of 2, the first, second, and third differences of the
results of the new substitutions, we could thence deduce those results
themselves with as much simplicity, as in the case of the whole numbers.
The new third difference, for example, will be simply the thousandth
part of the old third difference. We may also remark that there is no
possibility of error, since, the numbers being deduced from one another,
when we in this way arrive at the result of the substitution of 3, which
has already been calculated, the whole work will thus be verified.

Let us suppose again that we have thus recognized that the equation has
a root comprised between 2.3 and 2.4; we will approximate still nearer
by substituting intermediate numbers, differing by 0.01, and employing
the course just prescribed. As soon as the third differences can be
neglected, the calculation will be finished at once, by the
consideration of an equation of the second degree; or, if it is
preferred to continue the approximations till the second differences in
their turn may be neglected, the calculation will then be finished by a
simple proportion.

When, in a transcendental equation _f_(X) = 0, we have substituted in
_f_(X) equidistant numbers, sufficiently near to each other to allow the
differences of the results to be neglected, commencing with a certain
order, the 4th, for example, we may, within certain limits of _x_,
replace the transcendental function by an algebraic and entire function
of _x_, and thus reduce the search for the roots of _f_(X) = 0 to the
preceding theory.

Whether the proposed equation be algebraic or transcendental, we can
thus, when we have obtained one root of it with a suitable degree of
exactness, continue the approximation by the method of Newton.


  _Algebraic calculation._

  Addition and subtraction of polynomials.--Reduction of similar terms.

  Multiplication of monomials.--Use of exponents.--Multiplication of
polynomials. Rule of the signs.--To arrange a polynomial.--Homogeneous

  Division of monomials. Exponent _zero_.--Division of polynomials. How
to know if the operation will not terminate.--Division of polynomials
when the dividend contains a letter which is not found in the divisor.

  _Equations of the first degree._

  Resolution of numerical equations of the first degree with one or
several unknown quantities by the method of substitution.--Verification
of the values of the unknown quantities and of the degree of their

  Of cases of impossibility or of indetermination.

  Interpretation of negative values.--Use and calculation of negative

  Investigation of general formulas for obtaining the values of the
unknown quantities in a system of equations of the first degree with two
or three unknown quantities.--Method of Bezout.--Complete discussion of
these formulas for the case of two unknown quantities.--Symbols m/o and

  Discussion of three equations with three unknown quantities, in which
the terms independent of the unknown quantities are null.

  _Equations of the second degree with one unknown quantity._

  Calculus of radicals of the second degree.

  Resolution of an equation of the second degree with one unknown
quantity.--Double solution.--Imaginary values.

  When, in the equation _ax^{2} + bx + c = 0_, _a_ converges towards 0,
one of the roots increases indefinitely.--Numerical calculation of the
two roots, when _a_ is very small.

  Decomposition of the trinomial _x^{2} + px + q_ into factors of the
first degree.--Relations between the coefficients and the roots of the
equation _x^{2} + px + q = 0_.

  Trinomial equations reducible to the second degree.

  Of the maxima and minima which can be determined by equations of the
second degree.

  Calculation of the _arithmetical_ values of radicals.

  Fractional exponents.--Negative exponents.

  _Of series._

  Geometrical progressions.--Summation of the terms.

  What we call a series.--Convergence and divergence.

  A geometrical progression is convergent, when the ratio is smaller
than unity; diverging, when it is greater.

  The terms of a series may decrease indefinitely and the series not be

  A series, all the terms of which are positive, is converging, when the
ratio of one term to the preceding one tends towards a _limit_ smaller
than unity, in proportion as the index of the rank of that term
increases indefinitely.--The series is diverging when this _limit_ is
greater than unity. There is uncertainty when it is equal to unity.

  In general, when the terms of a series decrease indefinitely, and are
alternately positive and negative, the series is converging.

   *   *   *

  Combinations, arrangements, and permutations of _m_ letters, when each
combination must not contain the same letter twice.

  Development of the entire and positive powers of a binomial.--General

  Development of _(a + b √-1)^{m}_.

  Limit towards which _(1 + 1/m)^{m}_ tends, when _m_ increases

  Summation of piles of balls.

  _Of logarithms and of their uses._

  All numbers can be produced by forming all the powers of any positive
number, greater or less than _one_.

  General properties of logarithms.

  When numbers are in geometrical progression, their logarithms are in
arithmetical progression.

  How to pass from one system of logarithms to another system.

  Calculation of logarithms by means of the series which gives the
logarithm of _n + 1_, knowing that of _n_.--Calculation of Napierian
logarithms.--To deduce from them those of Briggs. Modulus.

  Use of logarithms whose base is 10.--Characteristics.--Negative
characteristics. Logarithms entirely negative are not used in

  A number being given, how to find its logarithm in the tables of
Callet. A logarithm being given, how to find the number to which it
belongs.--Use of the proportional parts.--Their application to
appreciate the exactness for which we can answer.

  Employment of the sliding rule.

  Resolution of exponential equations by means of logarithms.

  Compound interest. Annuities.

  _Derived functions._

  Development of an entire function F(_x + h_) of the binomial
(_x + h_).--Derivative of an entire function.--To return from the
derivative to the function.

  The derivative of a function of _x_ is the limit towards which tends
the ratio of the increment of the function to the increment _h_ of the
variable, in proportion as _h_ tends towards zero.

  Derivatives of trigonometric functions.

  Derivatives of exponentials and of logarithms.

  Rules to find the derivative of a sum, of a product, of a power, of a
quotient of functions of _x_, the derivatives of which are known.

  _Of the numerical resolution of equations._

  Changes experienced by an entire function _f(x)_ when _x_ varies in a
continuous manner.--When two numbers _a_ and _b_ substituted in an
entire function _f(x)_ give results with contrary signs, the equation
_f(x) = 0_ has at least one real root not comprised between _a_ and _b_.
This property subsists for every species of function which remains
continuous for all the values of _x_ comprised between _a_ and _b_.

  An algebraic equation of uneven degree has at least one real root.--An
algebraic equation of even degree, whose last term is negative, has at
least two real roots.

  Every equation _f(x) = 0_, with coefficients either real or imaginary
of the form _a + b √-1_, admits of a real or imaginary root of the same
form. [Only the enunciation, and not the demonstration of this theorem,
is required.]

  If _a_ is a root of an algebraic equation, the first member is
divisible by _x - a_. An algebraic equation of the _m_^{th} degree has
always _m_ roots real or imaginary, and it cannot admit
more.--Decomposition of the first members into factors of the first
degree. Relations between the coefficients of an algebraic equation and
its roots.

  When an algebraic equation whose coefficients are real, admits an
imaginary root of the form _a + b √-1_, it has also for a root the
conjugate expression _a - b √-1_.

  In an algebraic expression, complete or incomplete, the number of the
positive roots cannot surpass the number of the variations; consequence,
for negative roots.

  Investigation of the product of the factors of the first degree common
to two entire functions of _x_.--Determination of the roots common to
two equations, the first members of which are entire functions of the
unknown quantity.

  By what character to recognize that an algebraic equation has equal
roots.--How we then bring its resolution to that of several others of
lower degree and of unequal roots.

   *   *   *

  Investigation of the commensurable roots of an algebraic equation with
entire coefficients.

  When a series of equidistant numbers is substituted in an entire
function of the _m_^{th} degree, and differences of different orders
between the results are formed, the differences of the _m_^{th} order
are constant.

  Application to the separation of the roots of an equation of the third
degree.--Having the results of the substitution of -1, 0, and +1, to
deduce therefrom, by means of differences, those of all other whole
numbers, positive or negative.--The progress of the calculation leads of
itself to the limits of the roots.--Graphical representation of this

  Substitution of numbers equidistant _by a tenth_, between two
consecutive whole numbers, when the inspection of the first results has
shown its necessity.--This substitution is effected directly, or by
means of new differences deduced from the preceding.

  How to determine, in continuing the approximation towards a root, at
what moment the consideration of the first difference is sufficient to
give that root with all desirable exactness, by a simple proportion.

  The preceding method becomes applicable to the investigation of the
roots of a transcendental equation X = 0, when there have been
substituted in the first member, numbers equidistant and sufficiently
near to allow the differences of the results to be considered as
constant, starting from a certain order.--Formulas of interpolation.

  Having obtained a root of an algebraic or transcendental equation,
with a certain degree of approximation, to approximate still farther by
the method of Newton.

   *   *   *

  Resolution of two numerical equations of the second degree with two
unknown quantities.

  Decomposition of rational fractions into simple fractions.


In explaining the use of trigonometrical tables, the pupil must be able
to tell with what degree of exactness an angle can be determined by the
logarithms of any of its trigonometrical lines. The consideration of the
proportional parts will be sufficient for this. It will thus be seen
that if the _sine_ determines perfectly a small angle, the degree of
exactness, which may be expected from the use of that line, diminishes
as the angle increases, and becomes quite insufficient in the
neighborhood of 90 degrees. It is the reverse for the _cosine_, which
may serve very well to represent an angle near 90 degrees, while it
would be very inexact for small angles. We see, then, that in our
applications, we should distrust those formulas which give an angle by
its sine or cosine. The _tangent_ being alone exempt from these
difficulties, we should seek, as far as possible, to resolve all
questions by means of it. Thus, let us suppose that we know the
hypothenuse and one of the sides of a right-angled triangle, the direct
determination of the included angle will be given by a cosine, which
will be wanting in exactness if the hypothenuse of the triangle does not
differ much from the given side. In that case we should begin by
calculating the third side, and then use it with the first side to
determine the desired angle by means of its tangent. When two sides of a
triangle and the included angle are given, the tangent of the half
difference of the desired angles may be calculated with advantage; but
we may also separately determine the tangent of each of them. When the
three sides of a triangle are given, the best formula for calculating an
angle, and the only one never at fault, is that which gives the tangent
of half of it.

The surveying for plans, taught in the course of Geometry, employing
only graphical methods of calculation, did not need any more accurate
instruments than the chain and the graphometer; but now that
trigonometry furnishes more accurate methods of calculation, the
measurements on the ground require more precision. Hence the requirement
for the pupil to measure carefully a base, to use telescopes, verniers,
etc., and to make the necessary calculations, the ground being still
considered as plane. But as these slow and laborious methods can be
employed for only the principal points of the survey, the more
expeditious means of the plane-table and compass will be used for the

In spherical trigonometry, all that will be needed in geodesy should be
learned before admission to the school, so that the subject will not
need to be again taken up. We have specially inscribed in the programme
the relations between the angles and sides of a right-angled triangle,
which must be known by the students; they are those which occur in
practice. In tracing the course to be pursued in the resolution of the
three cases of any triangles, we have indicated that which is in fact
employed in the applications, and which is the most convenient. As to
the rest, ambiguous cases never occur in practice, and therefore we
should take care not to speak of them to learners.

In surveying, spherical trigonometry will now allow us to consider cases
in which the signals are not all in the same plane, and to operate on
uneven ground, obtain its projection on the plane of the horizon, and at
the same time determine differences of level.

It may be remarked that Descriptive Geometry might supply the place of
spherical trigonometry by a graphical construction, but the degree of
exactitude of the differences of level thus obtained would be



  Trigonometrical lines.--Their ratios to the radius are alone
considered.--Relations of the trigonometric lines of the same
angle.--Expressions of the sine and of the cosine in functions of the

  Knowing the sines and the cosines of two arcs _a_ and _b_, to find the
sine and the cosine of their sum and of their difference.--To find the
tangent of the sum or of the difference of two arcs, knowing the
tangents of those arcs.

  Expressions for sin.2_a_ and sin.3_a_; cos.2_a_ and cos. 3_a_;
tang.2_a_ and tang.3_a_.

  Knowing sin._a_ or cos._a_, to calculate sin.½_a_ and cos.½_a_.

  Knowing tang._a_, to calculate tang.½_a_.

  Knowing sin._a_, to calculate sin.⅓_a_--Knowing cos._a_, to
calculate cos.⅓_a_.

  Use of the formula cos._p_+cos._q_ = 2cos.½(_p + q_)cos.½(_p - q_), to
render logarithms applicable to the sum of two trigonometrical lines,
sines or cosines.--To render logarithms applicable to the sum of two

  Construction of the trigonometric tables.

  Use in detail of the tables of Callet.--Appreciation, by the
proportional parts, of the degree of exactness in the calculation of the
angles.--Superiority of the tangent formulas.

  _Resolution of triangles._

  Relations between the angles and the sides of a right-angled triangle,
or of any triangle whatever.--When the three angles of a triangle are
given, these relations determine only the ratios of the sides.

  Resolution of right-angled triangles.--Of the case in which the
hypothenuse and a side nearly equal to it are given.

  Knowing a side and two angles of any triangle, to find the other
parts, and also the surface of the triangle.

  Knowing two sides _a_ and _b_ of a triangle and the included angle C,
to find the other parts and also the surface of the triangle.--The
tang.½(A - B) may be determined; or tang.A and tang.B directly.

  Knowing the three sides _a_, _b_, _c_, to find the angles and the
surface of the triangle.--Employment of the formula which gives

  _Application to surveying for plans._

  Measurement of bases with rods.

  Measurement of angles.--Description and use of the circle.--Use of the
telescope to render the line of sight more precise.--Division of the

  Measurement and calculation of a system of triangles.--Reduction of
angles to the centres of stations.

  How to connect the secondary points to the principal system.--Use of
the plane table and of the compass.


  Fundamental relations (cos._a_ = cos._b_ cos._c_ + sin._b_ sin._c_
cos.A) between the sides and the angles of a spherical triangle.

  To deduce thence the relations sin.A : sin.B = sin._a_ : sin._b_;
cot._a_ sin._b_ - cot.A sin.C = cos._b_ cos.C, and by the consideration
of the supplementary triangle cos.A = -cos.B cos.C + sin.B sin.C

  Right-angled triangles.--Formulas cos._a_ = cos._b_ cos._c_; sin._b_ =
sin._a_ sin.B; tang._c_ = tang._a_ cos.B, and tang._b_ = sin._c_ tang.B.

  In a right-angled triangle the three sides are less than 90°, or else
two of the sides are greater than 90°, and the third is less. An angle
and the side opposite to it are both less than 90°, or both greater.

  Resolution of any triangles whatever:

  1º Having given their three sides _a_, _b_, _c_, or their three angles
A, B, C.--Formulas tang.½_a_ and tang.1/2A, calculable by logarithms:

  2º Having given two sides and the included angle, or two angles and
the included side.--Formulas of Delambre:

  3º Having given two sides and an angle opposite to one of them, or two
angles and a side opposite to one of them. Employment of an auxiliary
angle to render the formulas calculable by logarithms.

  Applications.--Survey of a mountainous country.--Reduction of the base
and of the angles to the horizon.--Determination of differences of

  Knowing the latitude and the longitude of two points on the surface of
the earth, to find the distance of those points.


The important property of homogeneity must be given with clearness and

The transformation of co-ordinates must receive some numerical
applications, which are indispensable to make the student clearly see
the meaning of the formulas.

The determination of tangents will be effected in the most general
manner by means of the derivatives of the various functions, which we
inserted in the programme of algebra. After having shown that this
determination depends on the calculation of the derivative of the
ordinate with respect to the abscissa, this will be used to simplify the
investigation of the tangent to curves of the second degree and to
curves whose equations contain transcendental functions. The discussion
of these, formerly pursued by laborious indirect methods, will now
become easy; and as curves with transcendental equations are frequently
encountered, it will be well to exercise students in their discussion.

The properties of foci and of the directrices of curves of the second
degree will be established directly, for each of the three curves, by
means of the simplest equations of these curves, and without any
consideration of the analytical properties of foci, with respect to the
general equation of the second degree. With even greater reason will we
dispense with examining whether curves of higher degree have foci, a
question whose meaning even is not well defined.

We retained in algebra the elimination between two equations of the
second degree with two unknown quantities, a problem which corresponds
to the purely analytical investigation of the co-ordinates of the points
of intersection of two curves of the second degree. The final equation
is in general of the fourth degree, but we may sometimes dispense with
calculating that equation. A graphical construction of the curves,
carefully made, will in fact be sufficient to make known, approximately,
the co-ordinates of each of the points of intersection; and when we
shall have thus obtained an approximate solution, we will often be able
to give it all the numerical rigor desirable, by successive
approximations, deduced from the equations. These considerations will be
extended to the investigation of the real roots of equations of any form
whatever with one unknown quantity.

Analytical geometry of three dimensions was formerly entirely taught
within the Polytechnic school, none of it being reserved for the course
of admission. For some years past, however, candidates were required to
know the equations of the right line in space, the equation of the
plane, the solution of the problems which relate to it and the
transformation of co-ordinates. But the consideration of surfaces of the
second order was reserved for the interior teaching. We think it well to
place this also among the studies to be mastered before admission, in
accordance with the general principle now sought to be realized, of
classing with them that double instruction which does not exact a
previous knowledge of the differential calculus.

We have not, however, inserted here all the properties of surfaces of
the second order, but have retained only those which it is indispensable
to know and to retain. The transformation of rectilinear co-ordinates,
for example, must be executed with simplicity, and the teacher must
restrict himself to giving his pupils a succinct explanation of the
course to be pursued; this will suffice to them for the very rare cases
in which they may happen to have need of them. No questions will be
asked relating to the general considerations, which require very
complicated theoretical discussions, and especially that of the general
reduction of the equation of the second degree with three variables. We
have omitted from the problems relating to the right line and to the
plane, the determination of the shortest distance of two right lines.

The properties of surfaces of the second order will be deduced from the
equations of those surfaces, taken directly in the simplest forms. Among
these properties, we place in the first rank, for their valuable
applications, those of the surfaces which can be generated by the
movement of a right line.



  Rectilinear co-ordinates.--Position of a point on a plane.

  Representation of geometric loci by equations.

  Homogeneity of equations and of formulas.--Construction of algebraic

  Transformation of rectilinear co-ordinates.

  Construction of equations of the first degree.--Problems on the right

  Construction of equations of the second degree.--Division of the
curves which they represent into three classes.--Reduction of the
equation to its simplest form by the change of co-ordinates.[5]

    [Footnote 5: The students will apply these reductions to a
    numerical equation of the second degree, and will determine the
    situation of the new axes with respect to the original axes, by
    means of trigonometrical tables. They will show to the examiner
    the complete calculations of this reduction and the trace of the
    two systems of axes and of the curves.]

  Problem of tangents.--The coefficient of inclination of the tangent to
the curve, to the axis of the abscissas, is equal to the derivative of
the ordinate with respect to the abscissa.

  _Of the ellipse._

  Centre and axes.--The squares of the ordinates perpendicular to one of
the axes are to each other as the products of the corresponding segments
formed on that axis.

  The ordinates perpendicular to the major axis are to the corresponding
ordinates of the circle described on that axis as a diameter, in the
constant ratio of the minor axis to the major.--Construction of the
curve by points, by means of this property.

  Foci; eccentricity of the ellipse.--The sum of the radii vectors drawn
to any point of the ellipse is constant and equal to the major
axis.--Description of the ellipse by means of this property.

  Directrices.--The distance from each point of the ellipse to one of
the foci, and to the directrix adjacent to that focus, are to each other
as the eccentricity is to the major axis.

  Equations of the tangent and of the normal at any point of the
ellipse.[6]--The point in which the tangent meets one of the axes
prolonged is independent of the length of the other axis.--Construction
of the tangent at any point of the ellipse by means of this property.

    [Footnote 6: They will be deduced from the property, previously
    demonstrated, of the derivative of the ordinate with respect to
    the abscissa.]

  The radii vectores, drawn from the foci to any point of the ellipse,
make equal angles with the tangent at that point or the same side of
it.--The normal bisects the angle made by the radii vectores with each
other.--This property may serve to draw a tangent to the ellipse through
a point on the curve, or through a point exterior to it.

  The diameters of the ellipse are right lines passing through the
centre of the curve.--The chords which a diameter bisects are parallel
to the tangent drawn through the extremity of that diameter.--
Supplementary chords. By means of them a tangent to the ellipse can be
drawn through a given point on that curve or parallel to a given right

  Conjugate diameters.--Two conjugate diameters are always parallel to
supplementary chords, and reciprocally.--Limit of the angle of two
conjugate diameters.--An ellipse always contains two equal conjugate
diameters.--The sum of the squares of two conjugate diameters is
constant.--The area of the parallelogram constructed on two conjugate
diameters is constant.--To construct an ellipse, knowing two conjugate
diameters and the angle which they make with each other.

  Expression of the area of an ellipse in function of its axes.

  _Of the hyperbola._

  Centre and axes.--Ratio of the squares of the ordinates perpendicular
to the transverse axes.

  Of foci and of directrices; of the tangent and of the normal; of
diameters and of supplementary chords.--Properties of these points and
of these lines, analogous to those which they possess in the ellipse.

  Asymptotes of the hyperbola.--The asymptotes coincide with the
diagonals of the parallelogram formed on any two conjugate
diameters.--The portions of a secant comprised between the hyperbola and
its asymptotes are equal.--Application to the tangent and to its

  The rectangle of the parts of a secant, comprised between a point of
the curve and the asymptotes, is equal to the square of half of the
diameter to which the secant is parallel.

  Form of the equation of the hyperbola referred to its asymptotes.

  _Of the parabola._

  Axis of the parabola.--Ratio of the squares of the ordinates
perpendicular to the axis.

  Focus and directrix of the parabola.--Every point of the curve is
equally distant from the focus and from the directrix.--Construction of
the parabola.

  The parabola may be considered as an ellipse, in which the major axis
is indefinitely increased while the distance from one focus to the
adjacent summit remains constant.

  Equations of the tangent and of the normal.--Sub-tangent and
sub-normal. They furnish means of drawing a tangent at any point of the

  The tangent makes equal angles with the axis and with the radius
vector drawn to the point of contact.--To draw, by means of this
property, a tangent to the parabola, 1º through a point on the curve; 2º
through an exterior point.

  All the diameters of the parabola are right lines parallel to the
axis, and reciprocally.--The chords which a diameter bisects are
parallel to the tangent drawn at the extremity of that diameter.

  Expression of the area of a parabolic segment.

   *   *   *

  Polar co-ordinates.--To pass from a system of rectilinear and
rectangular co-ordinates to a system of polar co-ordinates, and

  Polar equations of the three curves of the second order, the pole
being situated at a focus, and the angles being reckoned from the axis
which passes through that focus.

  Summary discussion of some transcendental curves.--Determination of
the tangent at one of their points.

  Construction of the real roots of equations of any form with one
unknown quantity.--Investigation of the intersections of two curves of
the second degree.--Numerical applications of these formulas.


  The sum of the projections of several consecutive right lines upon an
axis is equal to the projection of the resulting line.--The sum of the
projections of a right line on three rectangular axes is equal to the
square of the right line.--The sum of the squares of the cosines of the
angles which a right line makes with three rectangular right lines is
equal to unity.

  The projection of a plane area on a plane is equal to the product of
that area by the cosine of the angle of the two planes.

  Representation of a point by its co-ordinates.--Equations of lines and
of surfaces.

  Transformation of rectilinear co-ordinates.

  _Of the right line and of the plane._

  Equations of the right line.--Equation of the plane.

  To find the equations of a right line, 1º which passes through two
given points, 2º which passes through a given point and which is
parallel to a given line.

  To determine the point of intersection of two right lines whose
equations are known.

  To pass a plane, 1º through three given points; 2º through a given
point and parallel to a given plane; 3º through a point and through a
given right line.

  Knowing the equations of two planes, to find the projections of their

  To find the intersection of a right line and of a plane, their
equations being known.

  Knowing the co-ordinates of two points, to find their distance.

  From a given point to let fall a perpendicular on a plane; to find the
foot and the length of that perpendicular (rectangular co-ordinates).

  Through a given point to pass a plane perpendicular to a given right
line (rectangular co-ordinates).

  Through a given point, to pass a perpendicular to a given right line;
to determine the foot and the length of that perpendicular (rectangular

  Knowing the equations of a right line, to determine the angles which
that line makes with the axes of the co-ordinates (rectangular

  To find the angle of two right lines whose equations are known
(rectangular co-ordinates).

  Knowing the equation of a plane, to find the angles which it makes
with the co-ordinate planes (rectangular co-ordinates).

  To determine the angle of two planes (rectangular co-ordinates).

  To find the angle of a right line and of a plane (rectangular

  _Surfaces of the second degree._

  They are divided into two classes; one class having a centre, the
other not having any. Co-ordinates of the centre.

  Of diametric planes.

  Simplification of the general equation of the second degree by the
transformation of co-ordinates.

  The simplest equations of the ellipsoid, of the hyperboloid of one
sheet and of two sheets, of the elliptical and the hyperbolic
paraboloid, of cones and of cylinders of the second order.

  Nature of the plane sections of surfaces of the second order.--Plane
sections of the cone, and of the right cylinder with circular
base.--Anti-parallel section of the oblique cone with circular base.

  Cone asymptote to an hyperboloid.

  Right-lined sections of the hyperboloid of one sheet.--Through each
point of a hyperboloid of one sheet two right lines can be drawn, whence
result two systems of right-lined generatrices of the hyperboloid.--Two
right lines taken in the same system do not meet, and two right lines of
different systems always meet.--All the right lines situated on the
hyperboloid being transported to the centre, remaining parallel to
themselves, coincide with the surface of the asymptote cone.--Three
right lines of the same system are never parallel to the same
plane.--The hyperboloid of one sheet may be generated by a right line
which moves along three fixed right lines, not parallel to the same
plane; and, reciprocally, when a right line slides on three fixed lines,
not parallel to the same plane, it generates a hyperboloid of one sheet.

  Right-lined sections of the hyperbolic paraboloid.--Through each point
of the surface of the hyperbolic paraboloid two right lines may be
traced, whence results the generation of the paraboloid by two systems
of right lines.--Two right lines of the same system do not meet, but two
right lines of different systems always meet.--All the right lines of
the same system are parallel to the same plane.--The hyperbolic
paraboloid may be generated by the movement of a right line which slides
on three fixed right lines which are parallel to the same plane; or by a
right line which slides on two fixed right lines, itself remaining
always parallel to a given plane. Reciprocally, every surface resulting
from one of these two modes of generation is a hyperbolic paraboloid.

  General equations of conical surfaces and of cylindrical surfaces.


The general methods of Descriptive Geometry,--their uses in
Stone-cutting and Carpentry, in Linear Perspective, and in the
determination of the Shadows of bodies,--constitute one of the most
fruitful branches of the applications of mathematics. The course has
always been given at the Polytechnic School with particular care,
according to the plans traced by the illustrious _Monge_, but no part of
the subject has heretofore been required for admission. The time given
to it in the school, being however complained of on all sides as
insufficient for its great extent and important applications, the
general methods of Descriptive Geometry will henceforth be retrenched
from the internal course, and be required of all candidates for

As to the programme itself, it is needless to say any thing, for it was
established by _Monge_, and the extent which he gave to it, as well as
the methods which he had created, have thus far been maintained. We
merely suppress the construction of the shortest distance between two
right-lines, which presents a disagreeable and useless complication.

Candidates will have to present to the examiner a collection of their
graphical constructions (_épures_) of all the questions of the
programme, signed by their teacher. They are farther required to make
free-hand sketches of five of their _épures_.


    _Problems relating to the point, to the straight line, and to the

    [Footnote 7: The method of the change of the planes of projection
    will be used for the resolution of these problems.]

    Through a point given in space, to pass a right line parallel to a
given right line, and to find the length of a part of that right line.

    Through a given point, to pass a plane parallel to a given plane.

    To construct the plane which passes through three points given in

    Two planes being given, to find the projections of their

    A right line and a plane being given, to find the projections of the
point in which the right line meets the plane.

    Through a given point, to pass a perpendicular to a given plane, and
to construct the projections of the point of meeting of the right line
and of the plane.

    Through a given point, to pass a right line perpendicular to a given
right line, and to construct the projections of the point of meeting of
the two right lines.

    A plane being given, to find the angles which it forms with the
planes of projection.

    Two planes being given, to construct the angle which they form
between them.

    Two right lines which cut each other being given, to construct the
angle which they form between them.

    To construct the angle formed by a right line and by a plane given
in position in space.

    _Problems relating to tangent planes._

    To draw a plane tangent to a cylindrical surface or to a conical
surface, 1º through a point taken on the surface; 2º through a point
taken out of the surface; 3º parallel to a given right line.

    Through a point taken on a surface of revolution, whose meridian is
known, to pass a plane tangent to that surface.

  _Problems relating to the intersection of surfaces._

  To construct the section made, on the surface of a right and vertical
cylinder, by a plane perpendicular to one of the planes of
projection.--To draw the tangent to the curve of intersection.--To make
the development of the cylindrical surface, and to refer to it the curve
of intersection, and also the tangent.

  To construct the intersection of a right cone by a plane perpendicular
to one of the planes of projection. Development and tangent.

  To construct the right section of an oblique cylinder.--To draw the
tangent to the curve of intersection. To make the development of the
cylindrical surface, and to refer to it the curve which served as its
base, and also its tangents.

  To construct the intersection of a surface of revolution by a plane,
and the tangents to the curve of intersection.--To resolve this
question, when the generating line is a right line which does not meet
the axis.

  To construct the intersection of two cylindrical surfaces, and the
tangents to that curve.

  To construct the intersection of two oblique cones, and the tangents
to that curve.

  To construct the intersection of two surfaces of revolution whose axes


The preceding six heads complete the outline of the elementary course of
mathematical instruction which it was the object of this article to
present; but a few more lines may well be given to a mere enumeration of
the other requirements for admission to the school.

MECHANICS comes next. The programme is arranged under these heads:
Simple motion and compound motion; Inertia; Forces applied to a free
material point; Work of forces applied to a movable point; Forces
applied to a solid body; Machines.

PHYSICS comprises these topics: General properties of bodies;
Hydrostatics and hydraulics; Densities of solids and liquids; Properties
of gases; Heat; Steam; Electricity; Magnetism; Acoustics; Light.

CHEMISTRY treats of Oxygen; Hydrogen; Combinations of hydrogen with
oxygen; Azote or nitrogen; Combinations of azote with oxygen;
Combination of azote with hydrogen, or ammonia; Sulphur; Chlorine;
Phosphorus; Carbon.

COSMOGRAPHY describes the Stars; the Earth; the Sun; the Moon; the
Planets; Comets; the Tides.

HISTORY and GEOGRAPHY treat of Europe from the Roman Empire to the
accession of Louis XVI.

GERMAN must be known sufficiently for it to be translated, spoken a
little, and written in its own characters.

DRAWING, besides the _épures_ of descriptive geometry, must have been
acquired sufficiently for copying an academic study, and shading in
pencil and in India ink.

Will not our readers agree with M. Coriolis, that “_There are very few
learned mathematicians who could answer perfectly well at an examination
for admission to the Polytechnic School_”?


There are strictly speaking no Junior Military Schools preparatory to
the Polytechnic School, or to the Special Military School at St. Cyr.
These schools are recruited in general from the _Lycées_ and other
schools for secondary instruction, upon which they exert a most powerful
influence. Until 1852 there was no special provision made in the courses
of instruction in the _Lycées_ for the mathematical preparation required
for admission into the Polytechnic, and the Bachelor’s degree in science
could not be obtained without being able to meet the requirements in
Latin, rhetoric, and logic for graduation in the arts, which was
necessary to the profession of law, medicine, and theology. In
consequence, young men who prepared to be candidates for the preliminary
examinations at the Polytechnic and the St. Cyr, left the _Lycées_
before graduation in order to acquire more geometry and less literature
in the private schools, or under private tuition.

A new arrangement, popularly called the _Bifurcation_, was introduced by
the Decrees of the 10th of April, 1852; and has now come into operation.
The conditions demanded for the degree in science were adapted to the
requirements of the Military Schools; and in return for this concession
it is henceforth to be exacted from candidates for the Military Schools.
The diploma of arts is no longer required before the diploma of science
can be given. The instruction, which in the upper classes of the
_Lycées_ had hitherto been mainly preparatory for the former, takes
henceforth at a certain point (called that of _Bifurcation_) two
different routes, conducting separately, the one to the baccalaureate of
arts, the other to that of science. The whole system of teaching has
accordingly been altered. Boys wanting to study algebra are no longer
carried through a long course of Latin; mathematics are raised to an
equality with literature; and thus military pupils--pupils desirous of
admission at the Polytechnic and St. Cyr, may henceforth, it is hoped,
obtain in the _Lycées_ all the preparation which they had latterly
sought elsewhere.

Under this new system the usual course for a boy seems to be the

He enters the _Lycée_, in the Elementary Classes; or, a little later, in
the Grammar Classes, where he learns Latin and begins Greek. At the age
of about fourteen, he is called upon to pass an examination for
admission into the Upper Division, and here, in accordance with the new
regulations, he makes his choice for mathematics or for literature, the
studies henceforth being divided, one course leading to the bachelorship
of science, the other to that of arts.

In either case he has before him three yearly courses, three
classes--the Third, the Second, and what is called the Rhetoric. At the
close of this, or after passing, if he pleases, another year in what is
called the Logic, he may go up for his bachelor’s degree. The boy who
wants to go to St. Cyr or the Polytechnic chooses, of course, the
mathematical division leading to the diploma he will want, that of a
bachelor of _science_. He accordingly begins algebra, goes on to
trigonometry, to conic sections, and to mechanics, and through
corresponding stages in natural philosophy, and the like. If he chooses
to spend a fourth year in the Logic, he will be chiefly employed in
going over his subjects again. He may take his bachelor’s degree at any
time after finishing his third year; and he may, if he pleases, having
taken that, remain during a fifth or even a sixth year, in the class of
Special Mathematics.

If he be intended for St. Cyr, he may very well leave at the end of his
year in Rhetoric, taking of course his degree. One year in the course of
Special Mathematics will be required before he can have a chance for the
Polytechnic. Usually the number of students admitted at the latter, who
have not passed more than one year in the _mathematiques spéciales_ is
very small. Very probably the young aspirant would try at the end of his
first year in this class, and would learn by practice to do better at
the end of the second.

The following are the studies of the mathematical section of the upper
division as laid down by the ordinance of 30th August, 1854.

  THE THIRD CLASS (_Troisième_,) at fourteen years old.

  Arithmetic and first notions of Algebra. Plane Geometry and its
applications. First notions of Chemistry and Physics. General notions of
Natural History; Principles of classification. Linear and imitative

  THE SECOND CLASS (_Seconde_,) at fifteen years old.

  Algebra; Geometry, figures in space, recapitulation; Applications of
Geometry, notions of the geometrical representations of bodies by
projections; Rectilineal Trigonometry; Chemistry; Physics; and Drawing.

  THE RHETORIC, at sixteen years old.

  Exercises in Arithmetic and Algebra; Geometry; notions on some common
curves; and general recapitulation; Applications of Geometry; notions of
leveling and its processes; recapitulation of Trigonometry; Cosmography;
Mechanics; Chemistry concluded and reviewed; Zoölogy and Animal
Physiology; Botany and Vegetable Physiology; Geology; Drawing. (The
pupil may now be ready for the Degree and for St. Cyr.)

  THE LOGIC, at seventeen years old.

  Six lessons a week are employed in preparation for the bachelorship of
science, and in a methodical recapitulation of the courses of the three
preceding years according to the state of the pupil’s knowledge.

  Two lessons a week are allowed for reviewing the literary instruction;
evening lessons in Latin, French, English, and German, and in History
and Geography, having been given through the whole previous time.

  THE SPECIAL MATHEMATICS, at eighteen and nineteen years old.

  Five lessons a week are devoted to these studies; in the other lessons
the pupils join those of the Logic class for reviewing all their
previous subjects, whether for the bachelorship in science or for
competition for admission at the _Ecole Normale_ or the Polytechnic.

It will only be necessary to add a few sentences in explanation of the
methods pursued in the upper classes of the _Lycées_. The classes are
large--from 80 to above 100; the lessons strictly professorial lectures,
with occasional questions, as at the Polytechnic itself. In large
establishments the class is divided, and two professors are employed,
giving two parallel courses on the same subject. To correct and fortify
this general teaching, we find, corresponding to the interrogations of
the Polytechnic, what are here called conferences. The members of the
large class are examined first of all in small detachments of five or
six by their own professors once a week; and, secondly, a matter of yet
greater importance, by the professor who is conducting the parallel
course, and by professors who are engaged for this purpose from other
_Lycées_ and preparatory schools, and from among the _répétiteurs_ of
the Polytechnic and the Ecole Normale themselves. It appeared by the
table of the examinations of this latter kind which had been passed by
the pupils of the class of Special Mathematics at the _Lycée_ St. Louis,
that the first pupil on the list had in the interval between the opening
of the school and the date of our visit (February 16th) gone through as
many as twenty-four.

The assistants, who bear the name of _répétiteurs_ at the _Lycées_, do
not correspond in any sense to those whom we shall hereafter notice at
the Ecole Polytechnique. They are in the _Lycées_ mere superintendents
in the _salles d’étude_, who attend to order and discipline, who give
some slight occasional help to the pupils, and may be employed in
certain cases, where the parents wish for it, in giving private tuition
to the less proficient. The system of _salles d’étude_ appears to
prevail universally; the number of the pupils placed in each probably
varying greatly. At the Polytechnic we found eight or ten pupils in
each; at St. Cyr as many as 200. The number considered most desirable at
the _Lycée_ of St. Louis was stated to be thirty.

It thus appears that in France not only do private establishments
succeed in giving preparation for the military schools, but that even in
the first-class public schools, which educate for the learned
professions, it has been considered possible to conduct a series of
military or science classes by the side of the usual literary or arts
classes. The common upper schools are not, as they used to be, and as
with us they are, _Grammar_ schools, they are also _Science_ schools. In
every _Lycée_ there is, so to say, a sort of elementary polytechnic
department, giving a kind of instruction which will be useful to the
future soldier, and at the same time to others, to those who may have to
do with mines, manufactures, or any description of civil engineering.
There is thus no occasion for Junior Military Schools in France, for all
the schools of this class are more or less of a military character in
their studies.

The conditions of admission to the examination for the degree of
Bachelor of Science are simply, sixteen years of age, and the payment of
fees amounting to about 200 fr. (10_l._) Examinations are held three
times a year by the Faculties at Paris, Besançon, Bordeaux, Caen,
Clermont, Dijon, Grenoble, Lille, Lyons, Marseilles, Montpellier, Nancy,
Poitiers, Rennes, Strasburg, and Toulouse, and once a year at Ajaccio,
Algiers, and nineteen other towns. There is a written examination of six
hours, and a viva voce examination of an hour and a quarter. It is, of
course, only a _pass_ examination, and is said to be much less difficult
than the competitive examination for admission to St. Cyr.--_Report of
English Commissioners_, 1856.




  POLYTECHNIC SCHOOL AT PARIS,                                        11
      PREPARATORY COURSE IN THE LYCEES,                               49
        EXAMINATIONAL SYSTEM, AND RESULTS,                            55
   I. FOUNDATION AND HISTORY,                                         55
        Out growth of the Necessities of the Public Service
            in 1794,                                                  56
        High Scientific Ability of its first Teachers,                58
        Peculiar Method of Scientific Teaching,                       59
        Characteristic features of the _Répétitorial_ System,         59
        The _Casernement_, or Barrack Residence of the Pupils,        60
        Permanent Organization in 1809,                               60
        Commission of 1850,                                           62
        Public Services provided for in its General Scientific
            Course,                                                   63
        Admission by Competition in an Open Examination,              63
        Annual Charge for Board and Instruction,                      64
        Exhibitions, (or _bourses, demi-bourses_,) and Outfits
            (_trousseaux_,)                                           64
        Length of Course of Study,                                    64
        Number of Professors and Teachers, besides its Military
            Staff,                                                    64
          Military Establishment,                                     65
          Civil Establishment,                                        65
        General Control and Supervision,                              65
          1. Board of Administration,                                 65
          2. Board of Discipline,                                     65
          3. Board of Instruction,                                    65
          4. Board of Improvement,                                    66
        Who may be Candidates for Admission,                          66
        Subjects of Entrance Examination,                             66
        Preliminary Examination,                                      67
        Written Examination,                                          67
        Oral Examination,                                             68
        Scale of Merit, and Latitude in Amount of Credit given,       68
        Reports of Examiners to Minister of War,                      69
        Co-efficients of Influence, varying with the Study and
            Mode of Examination,                                      69
        Decision of Jury on all the Documents of each Candidate,      70
        Final Action of the Minister of War,                          70
        Situation, Number, and Purposes of Buildings,                 70
        Daily Routine of Exercises,                                   72
        Method of Teaching and Study,                                 73
          Professorial and Répétitorial,                              74
          Interrogations, _Général_,                                  74
                “         _Particulieres_ by the _Répétiteurs_,       74
          One Répétiteur to every eight Pupils,                       74
        System of Credits for every Lecture, every Interrogation,
            and Exercise,                                             75
        Final Admission to Public Service, depends on daily and
            hourly fidelity,                                          76
        Division of First Year’s Work into three portions,            76
          First portion--Analysis and Descriptive Geometry,           76
          Second “  Mechanics, Geodesy, Physics, &c.,                 76
          Third  “  General Private Study,                            76
        Number and Subjects of Lectures in Second Course,             78

   V. EXAMINATIONAL SYSTEM,                                           78
        Ordinary Examinations,                                        78
          1. By Professors on their own Lectures, both Written
                 and Oral,                                            78
          2. By Examiners on the Manipulations of the Pupils,         78
          3. By Répétiteurs every ten or fourteen days,               78
          4. By Professors and Répétiteurs at the close of
                 each Course,                                         79
        First Annual Examination,                                     79
          Table--Co-efficient of Influence in Second Division of
              First Year’s Course,                                    79
          Specimen of Credits gained by one Student in First
              Year’s Course,                                          80
          Persons excluded from the Second Year’s Course,             81
        Second Annual or Great Final Examination,                     81
          Conducted by the same Examiners as the First,               81
          Oral, and extends over the whole Two Years’ Course,         81
          Results based on each Day’s Study’s, Year’s, and
              Examination’s results,                                  82
        Tables--Co-efficients of Influence in Final
              Classification, &c.,                                    82
        Order in which the Public Services are Selected,              83

          POLYTECHNIC SCHOOL,                                         84
      APPENDIX,                                                       88
          1. Gunpowder and Saltpetre,                                 88
          2. Navy,                                                    88
          3. Marine Artillery and Foundries,                          88
          4. Naval Architects. School of Application at L’Orient,     88
          5. Hydrographers,                                           88
          6. Roads and Bridges. School of Application at Paris,       89
          7. Mining Engineers. School of Mines at Paris and
                 St. Etienne,                                         89
          8. Tobacco Department                                       90
          9. Telegraphs,                                              90
            OF STUDY,                                                 91
          1. Analysis,                                                91
               First Year--Calculus, Differential,                    91
                           Calculus, Integral,                        93
               Second Year--Calculus, Integral, (continuation,)       94
          2. Descriptive Geometry and Stereotomy,                     97
               First Year--Descriptive Geometry, Geometrical
                           Drawing,                                   97
               Second Year--Stereotomy: Wood-work,                   103
                            Masonry,                                 103
          3. Mechanics and Machines,                                 104
               First Year--Kinematics,                               105
                           Equilibrium of Forces,                    105
               Second Year--Dynamics,                                112
                            Hydrostatics,                            115
                            Hydraulics,                              115
                            Machines in Motion,                      116
          4. Physics,                                                116
               First Year--General Properties of Bodies,
                   Hydrostatics, Hydrodynamics,                      117
                           Heat,                                     119
                           Statical Electricity,                     123
               Second Year--Dynamical Electricity,                   124
                            Acoustics,                               125
                            Optics,                                  126
          5. Manipulations in Physics,                               129
               First and Second Year,                                130
               Distribution of Time,                                 131


    [Footnote 8: Compiled from “_Report and Appendix of English
    Commissioners on Military Education_.” 1857.]


The origin of the _Ecole Polytechnique_ dates from a period of disorder
and distress in the history of France which might seem alien to all
intellectual pursuits, if we did not remember that the general stimulus
of a revolutionary period often acts powerfully upon thought and
education. It is, perhaps, even more than the Institute, the chief
scientific creation of the first French Revolution. It was during the
government of the committee of public safety, when Carnot, as war
minister, was gradually driving back the invading armies, and
reorganizing victory out of defeat and confusion, that the first steps
were taken for its establishment. A law, dating the 1st Ventose, year
II., the 12th of March 1794, created a “Commission des Travaux Publics,”
charged with the duty of establishing a regular system for carrying on
public works; and this commission ultimately founded a central school
for public works, and drew up a plan for the competitive examination of
candidates for admission to the service. It was intended at first to
give a complete education for some of the public services, but it was
soon changed into a preparatory school, to be succeeded by special
schools of application. This was the Ecole Polytechnique.

The school and its plan were both owing to an immediate and pressing
want. It was to be partly military and partly civil. Military, as well
as civil education had been destroyed by the revolutionists. The
committee of public safety had, indeed, formed a provisional school for
engineers at Metz, to supply the immediate wants of the army on the
frontier, and at this school young men were hastily taught the elements
of fortification, and were sent direct to the troops, to learn as they
best could, the practice of their art. “But such a method,” says the
report accompanying the law which founded the school, “does not form
engineers _in any true sense of the term_, and can only be justified by
the emergency of the time. The young men should be recalled to the new
school to complete their studies.” Indeed no one knew better than
Carnot, to use the language of the report, “that patriotism and courage
can not always supply the want of knowledge;” and in the critical
campaigns of 1793-4, he must often have felt the need of the institution
which he was then contributing to set on foot. Such was the immediate
motive for the creation of this school. At first, it only included the
engineers amongst its pupils. But the artillery were added within a

We must not, however, omit to notice its civil character, the
combination of which with its military object forms its peculiar
feature, and has greatly contributed to its reputation. Amongst its
founders were men, who though ardent revolutionists, were thirsting for
the restoration of schools and learning, which for a time had been
totally extinguished. The chief of these, besides Carnot, were Monge and
Fourcroy, Berthollet and Lagrange. Of Carnot and Lagrange, one amongst
the first of war ministers, the other one of the greatest of
mathematicians, we need not say more. Berthollet, a man of science and
practical skill, first suggested the school; Monge, the founder of
Descriptive Geometry, a favorite _savant_ of Napoleon though a zealous
republican, united to real genius that passion for teaching and for his
pupils, which makes the _beau idéal_ of the founder of a school; and
Fourcroy was a man of equal practical tact and science, who at the time
had great influence with the convention, and was afterwards intrusted by
Napoleon with much of the reorganization of education in France.

When the school first started there was scarcely another of any
description in the country. For nearly three years the revolution had
destroyed every kind of teaching. The attack upon the old schools, in
France, as elsewhere, chiefly in the hands of the clergy, had been begun
by a famous report of Talleyrand’s, presented to the legislative
assembly in 1791, which recommended to suppress all the existing
academies within Paris and the provinces, and to replace them by an
entirely new system of national education through the country. In this
plan a considerable number of military schools were proposed, where boys
were to be educated from a very early age. When the violent
revolutionists were in power, they adopted the destructive part of
Talleyrand’s suggestions without the other. All schools, from the
university downwards, were destroyed; the large exhibitions or
_Bourses_, numbering nearly 40,000, were confiscated or plundered by
individuals, and even the military schools and those for the public
works (which were absolutely necessary for the very roads and the
defense of the country) were suppressed or disorganized. The school of
engineers at Mézières (an excellent one, where Monge had been a
professor,) and that of the artillery at La Fère, were both broken up,
whilst the murder of Lavoisier, and the well known saying in respect to
it, that “the Republic had no need of chemists,” gave currency to a
belief, which Fourcroy expressed in proposing the Polytechnic, “that the
late conspirators had formed a deliberate plan to destroy the arts and
sciences, and to establish their tyranny on the ruins of human reason.”

Thus it was on the ruin of all the old teaching, that the new
institution was erected; a truly _revolutionary_ school, as its founders
delighted to call it, using the term as it was then commonly used, as a
synonym for all that was excellent. And then for the first time avowing
the principle of public competition, its founders, Monge and Fourcroy,
began their work with an energy and enthusiasm which they seem to have
left as a traditional inheritance to their school. It is curious to see
the difficulties which the bankruptcy of the country threw in their way,
and the vigor with which, assisted by the summary powers of the
republican government, they overcame them. They begged the old Palais
Bourbon for their building; were supplied with pictures from the Louvre;
the fortunate capture of an English ship gave them some uncut diamonds
for their first experiments; presents of military instruments were sent
from the arsenals of Havre; and even the hospitals contributed some
chemical substances. In fine, having set their school in motion, the
government and its professors worked at it with such zeal and effect,
that within five months after their project was announced, they had held
their first entrance examination, open to the competition of all France,
and started with three hundred and seventy-nine pupils.

The account of one of these first pupils, who is among the most
distinguished still surviving ornaments of the Polytechnic, will convey
a far better idea of the spirit of the young institution than could be
given by a more lengthy description. M. Biot described to us vividly the
zeal of the earliest teachers, and the thirst for knowledge which,
repressed for awhile by the horrors of the period, burst forth with
fresh ardor amongst the French youth of the time. Many of them, he said,
like himself, had been carried away by the enthusiasm of the revolution,
and had entered the army. “My father had sent me,” he added, “to a
mercantile house, and indeed I never felt any great vocation to be a
soldier, but _Que voulez vous? les Prussiens etaient en Champagne._” He
joined the army, served two years under Dumouriez, and returned to Paris
in the reign of terror, “to see from his lodgings in the Rue St. Honore
the very generals who had led us to victory, Custine and Biron, carried
by in the carts to the guillotine. “Imagine what it was when we heard
that Robespierre was dead, and that we might return safely to study
after all this misery, and then to have for our teachers La Place,
Lagrange, and Monge. We felt like men brought to life again after
suffocation. Lagrange said, modestly, “Let me teach them arithmetic.”
Monge was more like our father than our teacher; he would come to us in
the evening, and assist us in our work till midnight, and when he
explained a difficulty to one of our _chefs de brigade_, it ran like an
electric spark through the party.” The pupils were not then, he told us,
as they have since been, shut up in barracks, they were left free, but
there was no idleness or dissipation amongst them. They were united in
zealous work and in good _camaraderie_, and any one known as a bad
character was avoided. This account may be a little tinged by
enthusiastic recollections, but it agreed almost entirely with that of
M. de Barante, who bore similar testimony to the early devotion of the
pupils, and the unique excellence of the teaching of Monge.

We are not, however, writing a history of this school, and must confine
ourselves to such points as directly illustrate its system of teaching
and its organization. These may be roughly enumerated in the following

1. Its early history is completed by the law of its organization, given
it by La Place in his short ministry of the interior. This occurred in
the last month of 1799, a memorable era in French history, for it was
immediately after the revolution of the 18th of Brumaire, when Napoleon
overthrew the Directory and made himself First Consul. One of his
earliest acts was to sign the charter of his great civil and military
school. This charter or decree deserves some attention, because it is
always referred to as the law of the foundation of the school. It
determined the composition of the two councils of instruction and
improvement, the bodies to which the direction of the school was to be,
and still is, intrusted; some of its marked peculiarities in the mode
and subject of teaching. It is important to notice each of the two

The direction of the school was at first almost entirely in the hands of
its professors, who formed what is still called its Council of
Instruction. Each of them presided over the school alternately for one
month, a plan copied from the revolutionary government of the
Convention. In the course of a few years, however, another body was
added, which has now the real management of the school. This is called
the “Council of Improvement” (_Conseil de perfectionnement_,) and a part
of its business is to see that the studies form a good preparation for
those of the more special schools (_écoles d’application_) for the civil
and military service. It consists of eminent men belonging to the
various public departments supplied by the school, and some of the
professors. It has had, as far as we could judge, an useful influence;
_first_, as a body not liable to be prejudiced in its proposals by the
feelings of the school, and yet interested in its welfare and
understanding it; _secondly_, as having shown much skill in the
difficult task of making the theoretical teaching of the Polytechnic a
good introduction to the practical studies of the public service;
_thirdly_, as being sufficiently influential, from the character of its
members, to shield the school from occasional ill-judged interference.
It should be added that hardly any year has passed without the Council
making a full report on the studies of the school, with particular
reference to their bearing on the Special Schools of Application.

The method of scientific teaching has been peculiar from the beginning.
It is the most energetic form of what may be called the _repetitorial_
system, a method of teaching almost peculiar to France, and which may be
described as a very able combination of professional and tutorial
teaching. The object of the _répétiteur_, or private tutor, is to second
every lecture of the professor, to explain and fix it by ocular
demonstration, explanations, or examination. This was a peculiarity in
the scheme of Monge and Foureroy. The latter said, in the first
programme, “Our pupils must not only learn, they must at once carry out
their theory. We must distribute them into small rooms, where they shall
practice the plans of descriptive geometry, which the professors have
just shown them in their public lectures. And in the same manner they
must go over in practice (_répéteront_) in separate laboratories the
principal operations of chemistry.” To carry out this system the twenty
best pupils, of whom M. Biot was one, were selected as _répétiteurs_
soon after the school had started. Since then the vacancies have always
been filled by young but competent men, aspiring themselves to become in
turn professors. They form a class of teachers more like the highest
style of private tutors in our universities, or what are called in
Germany _Privat-docenten_, than any other body--with this difference,
that they do not give their own lectures, but breaking up the
professor’s large class into small classes of five and six pupils,
examine these in _his_ lecture. The success of this attempt we shall
describe hereafter.

2. A change may be noticed which was effected very early by the Council
of Improvement--the union of pupils for artillery and engineers in a
single school of application. The first report in December 1800, speaks
of the identity in extent and character of the studies required for
these two services; and in conformity with its recommendation, the law
of the 3rd of October 1802, (12th Vendémiaire, XI.) dissolved the
separate artillery school at Châlons, and established the united school
for both arms in the form which it still retains at Metz.

3. In 1805 a curious change was made, and one very characteristic of the
school. The pupils have always been somewhat turbulent, and generally on
the side of opposition. In the earliest times they were constantly
charged with _incivisme_, and the aristocracy was said to have “taken
refuge within its walls.” In fact, one of its earliest and of its few
great _literary_ pupils, M. de Barante, confirmed this statement,
adding, as a reason, that the school gave for a while the only good
instruction in France. It was in consequence of some of these changes
that the pupils who had hitherto lived in their own private houses or
lodgings in Paris, were collected in the school building. This
“_casernement_” said to be immediately owing to a burst of anger of
Napoleon, naturally tended to give the school a more military character;
but it was regarded as an unfortunate change by its chief scientific
friends. “_Ah! ma pauvre école!_” M. Biot told us he had exclaimed, when
he saw their knapsacks on their beds. He felt, he said, that the
enthusiasm of free study was gone, and that now they would chiefly work
by routine and compulsion.

4. The year 1809 may be called the epoch at which the school attained
its final character. By this time the functions, both of boards and
teachers, were accurately fixed, some alterations in the studies had
taken place, and the plan of a final examination had been drawn up,
according to which the pupils were to obtain their choice of the branch
of the public service they preferred. In fact, the school may be said to
have preserved ever since the form it then assumed, under a variety of
governments and through various revolutions, in most of which, indeed,
its pupils have borne some share; and one of which, the restoration of
1816, was attended with its temporary dissolution.

Thus, during the first years after its foundation the Polytechnic grew
and flourished in the general dearth of public teaching, being indeed
not merely the only great school, but, until the Institute was founded,
the only scientific body in France. Working on its first idea of high
professorial lectures, practically applied and explained by
_répétiteurs_, its success in its own purely scientific line was, and
has continued to be, astonishing. Out of its sixteen earliest
professors, ten still retain an European name. Lagrange, Monge,
Fourcroy, La Place, Guyton de Morveau were connected with it. Malus,
Hauy, Biot, Poisson, and De Barante, were among its earliest pupils.
Arago, Cauchy, Cavaignac, Lamoricière, with many more modern names, came
later. All the great engineers and artillerymen of the empire belonged
to it, and the long pages in its calendar of distinguished men are the
measure of its influence on the civil and military services of France.
In fact its pupils, at a time of enormous demands, supplied all the
scientific offices of the army, and directed all the chief public works,
fortresses, arsenals, the improvement of cities, the great lines of
roads, shipbuilding, mining--carried out, in a word, most of the great
improvements of Napoleon. He knew the value of his school, “the hen” as
he called it, “that laid him golden eggs”--and perhaps its young pupils
were not improved by the excessive official patronage bestowed by him
upon “the envy of Europe,” “the first school in the world.” It can not,
however, be matter of surprise, that its vigor and success should have
caused Frenchmen, even those who criticise its influence severely, to
regard it with pride as an institution unrivaled for scientific

It is not necessary to give any detailed account of the later history of
the school, but we must remark that disputes have frequently arisen with
regard to the best mode of harmonizing its teaching with that of the
special schools of application to which it conducts. These disputes have
been no doubt increased by the union of a civil and military object in
the same school. The scientific teaching desirable for some of the
higher civil professions has appeared of doubtful advantage to those
destined for the more practical work of war. There has been always a
desire on the one side to qualify pure mathematics by application, a
strong feeling on the other that mathematical study sharpens the mind
most keenly for some of the practical pursuits of after life. We should
add, perhaps, that there has been some protest in France (though little
heard among the scientific men who have been the chief directors of the
school) against the _esprit faux_, the exclusive pursuit of mathematics
to the utter neglect of literature, and the indifference to moral and
historical studies. Some one or other of these complaints any one who
studies the _literature_, the pamphlets, and history of the school will
find often reproduced in the letters of war ministers, of artillery and
engineer officers commanding the school of application at Metz, or of
committees from the similar schools for the mines and the roads and
bridges. The last of these occasions illustrates the present position of
the school.

On the 5th of June 1850, the legislative assembly appointed a mixed
commission of military men and civilians, who were charged to revise all
the programs of instruction, and to recommend all needful changes in the
studies of the pupils, both those preparatory to entrance[9] and those
actually pursued in the school. The commission was composed as

  M. Thenard, Member of the Academy of Sciences, and of the Board of
Improvement of the Polytechnic School, President.

  Le Verrier, Member of the Academy of Sciences and of the Legislative
Assembly, Reporter.

  Noizet, General of Brigade of Engineers.

  Poncelet, General of Brigade of Engineers, Commandant of the
Polytechnic School, Member of the Academy of Sciences.

  Piobert, General of Brigade of Artillery, Member of the Academy of

  Mathieu, Rear Admiral.

  Duhamel, Member of the Academy of Sciences, Director of Studies at the
Polytechnic School.

  Mary, Divisional Inspector of Roads and Bridges.

  Morin, Colonel of Artillery, Member of the Academy of Sciences.

  Regnault, Engineer of Mines, Member of the Academy of Sciences.

  Olivier, Professor at the _Conservatoire des Arts et Metiers_.

  Debacq, Secretary for Military Schools at the Ministry of War,

    [Footnote 9: In an Analysis of the Report of this Commission, see
    page 97.]

A chronic dispute which has gone on from the very first year of the
school’s existence, between the exclusive study of abstract mathematics
on the one hand, and their early practical application on the other, was
brought to a head (though it has scarcely been set at rest) by this
commission. All the alterations effected have been in the direction of
eliminating a portion of the pure mathematics, and of reducing abstract
study to the limits within which it was believed to be most directly
applicable to practice. The results, however, are still a subject of
vehement dispute, in which most of the old scientific pupils of the
Polytechnic, and many of what may be styled its most practical members,
the officers of the artillery and engineers, are ranged on the side of
“early and deep scientific study _versus_ early practical applications.”
It is, indeed, a question which touches the military pupils nearly,
since it is in their case particularly that the proposed abstract
studies of the Polytechnic might be thought of the most doubtful
advantage. We do not try to solve the problem here, though the facts
elsewhere stated will afford some materials for judgment. We incline to
the opinion of those who think that the ancient _genius loci_, the
traditional teaching of the school, will be too strong for legislative
interference, and that, in spite of recent enactments, abstract science
and analysis will reign in the lecture-rooms and halls of study of the
Polytechnic, now as in the days of Monge.


The Polytechnic, as we have said, is a preparatory and general
scientific school; its studies are not exclusively adapted for any one
of the departments to which at the close of its course the scholars will
find themselves assigned; and on quitting it they have, before entering
on the actual discharge of their duties of whatever kind, to pass
through a further term of teaching in some one of the schools of
application specially devoted to particular professions.

The public services for which it thus gives a general preparation are
the following:

  _Military: Under the Minister at War._
    Artillery (_Artillerie de terre_.)
    Engineers (_Génie_.)
    The Staff Corps (_Corps d’Etat Major_.)
    The Department of Powder and Saltpetre (_Poudres et Salpétres_.)

  _Under the Minister of Marine._
    Navy, (_Marine_.)
    Marine Artillery (_Artillerie de mer_.)
    Naval Architects (_Génie maritime_.)
    The Hydrographical Department (_Corps des Ingénieurs Hydrographes_.)

  _Civil: Under the Minister of Public Works._
    The Department of Roads and Bridges (_Ponts-et-chaussées_.)
    The Department of Mines (_Mines_.)

  _Under the Minister of the Interior._
    The Telegraph Department (_Lignes Télégraphiques_.)

  _Under the minister of Finance._
    The Tobacco Department (_Administration des Tabacs_.)

To these may be added at any time, by a decree on the part of the
government, any other departments, the duties of which appear to require
an extensive knowledge of mathematics, physics, or chemistry.

Admission to the school is, and has been since its first commencement in
1794, obtained by competition in a general examination, held yearly, and
open to all. Every French youth, between the age of sixteen and twenty,
(or if in the army up to the age of twenty-five,) may offer himself as a

A board of examiners passes through France once every year, and examines
all who present themselves, that have complied with the conditions,
which are fully detailed in the decree given in the appendix. It
commences at Paris.

A list of such of the candidates as are found eligible for admittance to
the Polytechnic is drawn up from the proceedings of the board, and
submitted to the minister at war; the number of places likely to be
vacant has already been determined, and the minister fixes the number of
admissions accordingly. The candidates admitted are invariably taken in
the order of merit.

The annual charge for board and instruction is 40_l._ (1,000 fr.,)
payable in advance in four installments. In addition there is the cost
of outfit, varying from 20_l._ to 24_l._ Exhibitions, however, for the
discharge of the whole or of one-half of the expense (_bourses_ and
_demi-bourses_,) are awarded by the state in favor of _all_ the
successful candidates, whose parents can prove themselves to be too poor
to maintain their children in the school. Outfits and half outfits
(_trousseaux_) and _demi-trousseaux_) are also granted in these cases,
on the entrance of the student into the school; and the number of these
_boursiers_ and _demi-boursiers_ amounts at the present time to
one-third of the whole.

The course of study is completed in two years. On its successful
termination which is preceded by a final examination, the students are
distributed into the different services, the choice being offered them
in the order of their merit, and laid down in the classified list drawn
up after the examination. If it so happen that the number of places or
the services which can be offered is not sufficient for the number of
qualified students, those at the bottom of the list are offered service
in the infantry or cavalry, and those who do not enter the public
service, are supplied with certificates of having passed successfully
through the school. Students who have been admitted into the school from
the army, are obliged to re-enter the army.

All others, as has been said, have the right of choosing, according to
their position on the list, the service which they prefer, so far, that
is, as the number of vacancies in that service will allow; or they may
if they please decline to enter the public service at all.

Such is a general outline of the plan and object of the school. We may
add that, besides its military staff, it employs no less than
thirty-nine professors and teachers; that it has four boards of
management, and that ten scientific men unconnected with the school, and
amongst the most distinguished in France, conduct its examinations. The
magnitude of this establishment for teaching may be estimated by the
fact, that the number of pupils rarely exceeds three hundred and fifty,
and is often much less.

A fuller enumeration of these bodies will complete our present sketch.

I. The military establishment consists of:--

  The Commandant, a General Officer, usually of the Artillery or the
Engineers, at present a General of Artillery.

  A Second in Command, a Colonel or Lieutenant-Colonel, chosen from
former pupils of the school; at present a Colonel of Engineers.

  Three Captains of Artillery and Three Captains of Engineers, as
Inspectors of Studies, chosen also from former pupils of the school.

  Six Adjutants (_adjoints_,) non-commissioned officers, usually such as
have been recommended for promotion.

II. The civil establishment consists of:--

  1. A Director of Studies, who has generally been a civilian, but is at
present a Lieutenant-Colonel of Engineers.

  2. Fifteen Professors, viz.:--Two of Mathematical Analysis. Two of
Mechanics and Machinery. One of Descriptive Geometry. Two of Physics.
Two of Chemistry. One of Military Art and Fortification. One of Geodesy.
One of Architecture. One of French Composition. One of German. One of
Drawing. Of these one is an officer of the Staff, another of the
Artillery, and a third of the Navy; two are Engineers in Chief of the
Roads and Bridges; nine are civilians, of whom two are Members of the
Academy of Sciences.

  3. Three Drawing Masters for Landscape and Figure Drawing; one for
Machine Drawing, and one for Topographical Drawing.

  4. Nineteen Assistant and Extra Assistant Teachers, (_répétiteurs_ and
_répétiteurs adjoints_) whose name and functions are both peculiar.

  5. Five Examiners for Admission, consisting at present of one Colonel
of Artillery, as President, and four civilians.

  6. Five Examiners of Students (civilians,) four of them belonging to
the Academy of Sciences.

  7. There is also a separate Department for the ordinary Management of
Administration of the affairs of the school, the charge of the fabric
and of the library and museums; and a Medical Staff.

III. The general control or supervision of the school is vested, under
the war department, in four great boards of councils, viz.:--

1. A board of administration, composed of the commandant, the second in
command, the director of studies, two professors, two captains, and two
members of the administrative staff. This board has the superintendence
of all the financial business and all the minutiae of the internal
administration of the school.

2. A board of discipline, consisting of the second in command, the
director, two professors, three captains (of the school,) and two
captains of the army, chosen from former pupils. The duty of this board
is to decide upon cases of misconduct.

3. A board of instruction, whose members are, the commandant, the second
in command, the director, the examiners of students, and the professors;
and whose chief duty is to make recommendations relating to
ameliorations in the studies, the programmes of admission and of
instruction in the school, to--

4. A board of improvement, charged with the general control of the
studies, formed of--

  The Commandant, as President.

  The Second in Command.

  The Director of Studies.

  Two Delegates from the Department of Public Works.

  One Delegate from the Naval Department.

  One Delegate from the Home Department.

  Three Delegates from the War Department.

  Two Delegates from the Academy of Sciences.

  Two Examiners of Students.

  Three Professors of the School.


The entrance examination is held yearly in August; the most important
conditions for admission to it are always inserted in the _Moniteur_
early in the year, and are--

1st. All candidates must be bachelors of science.

2nd. All candidates (unless they have served in the army) must have been
as much as sixteen and not more than twenty years old on the 1st of
January preceding.

3rd. Privates and non-commissioned officers of the army must be above
twenty and under twenty-five years of age; must have served two years,
and have certificates of good conduct.

4th. Candidates who propose to claim pecuniary assistance (a _bourse_ or
_demi-bourse_) must present formal proofs of their need of it.

The subjects of the entrance examination are the following:--

  _Arithmetic_, including Vulgar and Decimal Fractions, Weights and
Measures, Involution and Evolution; Simple Interest.

  _Geometry_ of Planes and Solids; application of Geometry to Surveying;
Properties of Spherical Triangles.

  _Algebra_, including Quadratic Equations with one unknown quantity,
Series and Progressions in general; Binomial Theorem and its
applications; Logarithms and their use; on Derived Functions; on the
Theory of Equations; on Differences; application of the Theory of
Differences to the Numerical Solution of Equations.

  _Plane and Spherical Trigonometry_; Solution of Triangles; application
of Trigonometry to Surveying.

  _Analytical Geometry_, including Geometry of two dimensions;
Co-ordinates; Equations of the first and second degree, with two
variables; Tangents and Asymptotes; on the Ellipse, Hyperbola, and
Parabola; Polar Co-ordinates; Curved Lines in general.

  _Geometry of three dimensions_, including the Theory of Projections;
Co-ordinates; the Right Line and Plane; Surfaces of the second degree;
Conical and Cylindrical Surfaces.

  _Descriptive Geometry_; Problems relative to a Point, Right Line and
Plane; Tangent Planes; Intersection of Surfaces.

  _Mechanics_; on the Movement of a Point considered geometrically; on
the Effect of Forces applied to points and bodies at rest and moving; on
the Mechanical Powers.

  _Natural Philosophy_, including the Equilibrium of Liquids and Gasses;
Heat; Electricity; Magnetism; Galvanism; Electro-magnetism and Light;

  _Chemistry_, the Elements; _French_; _German_; _Drawing_, and
(optionally) _Latin_.

This examination is partly written and partly oral. It is not public,
but conducted in the following manner:--

Five examiners are appointed by the minister of war to examine the
candidates at Paris, and at the several towns named for the purpose
throughout France.

Two of these examiners conduct what may be called a preliminary
examination (_du premier degré_,) and the other three a second
examination (_du second degré_.) The preliminary examiners precede by a
few days in their journey through France those who conduct the second
examination. The written compositions come before either.

The preliminary examination (_du premier degré_) is made solely for the
purpose of ascertaining whether the candidates possess sufficient
knowledge to warrant their being admitted to the second examination; and
the second examination serves, in conjunction with the written
compositions, for their classification in the order of merit.

Prior to the examination, each candidate is called upon to give in
certain written sheets containing calculations, sketches, plans and
drawings, executed by him at school during the year, certified and dated
by the professor under whom he has studied. Care is taken to ascertain
whether these are the pupils’ own work, and any deception in this
matter, if discovered, excludes at once from the competition of the

This done, the candidates are required to reply in writing to written or
printed questions, and to write out French and German exercises; great
care being taken to prevent copying. This written examination occupies
about twenty-four hours during three and a half separate days, as shown
in the following table. It usually takes place in the presence of
certain official authorities, the examiners not being present.

      _First Sitting._
  Arithmetic,                             1
  Geometry,                               1
  Latin,                                  1

      _Second Sitting._

  Algebra,                                1
  History, geography, and French,         3

      _Third Sitting._

  Descriptive geometry, and }
    diagram, or sketch,     }             4

       _Fourth Sitting._

  Mechanics,                              1
  Physics, chemistry, and cosmography,    2

      _Fifth Sitting._
  Applied analysis,                     1½
  German exercise,                      1½

      _Sixth Sitting._

  Solution of a triangle by logarithms    3

      _Seventh Sitting._

  Drawing                                 4
  Total                                  24 hours

Next, each candidate is examined orally for three-quarters of an hour,
on two successive days, by each of the two examiners separately, and
each examiner makes a note of the admissibility or non-admissibility of
the candidate.

At the close of this oral examination, the notes relating to the various
candidates are compared, and if the examiners differ as to the
admissibility of any candidate, he is recalled, further orally examined,
and his written exercises carefully referred to, both examiners being
present. A final decision is then made.

The preliminary examiners then supply the others with a list of the
candidates who are entitled to be admitted to the second oral
examination. On this occasion each candidate is separately examined for
one hour and a half by each examiner, but care is taken that in all the
principal subjects of study the candidate is examined by at least two
out of the three examiners.

Each examiner records his opinion of the merits of every candidate in
replying, orally and in writing, by awarding him a credit varying
between O and 20, the highest number indicating a very superior result.

This scale of merit is employed to express the value of the oral
replies, written answers, or drawings. It has the following
signification, and appears to be generally in use in the French military

  20    denotes perfect.

  18}    “   very good.

  16}    “   good.

  13}    “   passable.

  10}    “   middling.

   7}    “   bad.

   4}    “   very bad.

   1}    “   almost nothing.

   0}    “   nothing.

Considerable latitude is granted to the examiner engaged in deciding
upon the amount of credit to be allowed to the student, for the manner
in which he replies to the various questions. He is expected to bear in
mind the temperament of the candidate, his confidence or timidity, as
well as the difficulty of the questions, when judging of the quality of
the reply, more value being given for an imperfect answer to a difficult
question than for a more perfect reply to an easy one.

The reports of the examiners, together with the various documents
belonging to each candidate, are sent from each town to the minister at
war, who transmits them to the commandant of the Polytechnic School to
make out a classified list.

Very different value of course is attached to the importance of some of
the subjects, when compared with others; and the measure of the
importance is represented in French examinations by what are termed
_co-efficients of influence_, varying for the several subjects of study
and kind of examination. The particular co-efficients of influence for
each subject in these written and oral examinations, are as follows:--

                                      Co-efficients of Influence.

  Oral examination--analytical mathematics,                   20}
   “        “       geometrical ditto,                        14}  52
   “        “       physics and mechanics,                    16}
   “        “       German language,                           2}

  Written compositions on mathematical subjects,               5}
     “         “      descriptive geometry, drawing, and
                        description,                           5}
     “         “    logarithmic calculations of a triangle,    2}
     “         “    mechanics,                                 2}
     “         “    physics or chemistry,                      4}  34
  German exercise,                                             1}
  French composition,                                          5}
  Latin translation,                                           5}
  Copy of a drawing,                                           5}
  Total,                                                       86

In order to make out the above mentioned classified list, the respective
credits awarded by the examiners to each candidate are multiplied by the
co-efficients representing the weight or importance attached to each
subject; and the sum of their products furnishes a numerical result,
representing the degree of merit of each candidate.

A comparison of these numerical results is then made, and a general list
of all the candidates is arranged in order of merit.

This list, and the whole of the documents from which it has been drawn
up, are then submitted to a jury composed of the

  Commandant of the School.

  The Second in Command.

  The Director of Studies.

  Two Members of the Board of Improvement.

  The Five Examiners.

It is the special business of this jury carefully to scrutinize the
whole of the candidates’ documents, drawings, &c., and they further take
care that a failure in any one branch of study is duly noted, as such
failure is a sufficient reason for the exclusion of the candidate from
the general list.

As soon as this general list has been thoroughly verified, it is
submitted to the minister of war, who is empowered to add one-tenth to
the number actually required for the public services; and thus it may
happen that one-tenth of the pupils may annually be disappointed.


A brief description of the buildings may be a suitable introduction to
an account of the studies that are pursued, and the life that is led in

The Polytechnic School stands near the Pantheon, and consists of two
main buildings, one for the official rooms and the residence of the
commandant and director of studies, the other, and larger one, for the
pupils. Detached buildings contain the chemical lecture room and
laboratory, the laboratory of natural philosophy, the library, fencing
and billiard rooms.

The basement floor of the larger building contains the kitchen and
refectories. On the first floor, are the two amphitheaters or great
lecture rooms, assigned respectively to the pupils of the two years or
divisions, in which the ordinary lectures are given. The rooms are large
and well arranged; the seats fixed, the students’ names attached to
them. The students are admitted by doors behind the upper tier of seats;
at the foot of all is a platform for the professor, with a blackboard
facing his audience, and with sufficient room for a pupil to stand and
work questions beside him. Room also is provided for one of the
captains, inspectors of studies, whose duty it is to be present, for the
director of studies, whose occasional presence is expected, and for the
assistant teachers or _répétiteurs_, who in the first year of their
appointment are called upon to attend the course upon which they will
have to give their subsequent questions and explanations. On this floor
are also the museums, or repositories of models, instruments, machines,
&c., needed for use in the amphitheaters, or elsewhere. The museum
provided for the lecturer on Physics (or Natural Philosophy) appeared in
particular to be well supplied.

The whole of the second floor is taken up with what are called the
_salles d’interrogation_, a long series of small cabinets or studies,
plainly furnished with six or eight stools and a table, devoted to the
_interrogations particulières_, which will presently be described.

The third floor contains the halls of study, _salles d’étude_, or
studying rooms, in which the greater part of the student’s time during
the day is passed--where he studies, draws, keeps his papers and
instruments, writes his exercises, and prepares his lectures. These are
small chambers, containing eight or, exceptionally, eleven occupants. A
double desk runs down the middle from the window to the door, with a
little shelf and drawers for each student. There is a blackboard for the
common use, and various objects are furnished through the senior
student, the sergeant, a selected pupil, more advanced than the rest,
who is placed in charge of the room, and is responsible for whatever is
handed in for the use of the students. He collects the exercises, and
generally gives a great deal of assistance to the less proficient. “When
I was sergeant,” said an old pupil, “I was always at the board.” The
spirit of _camaraderie_, said to exist so strongly among the Polytechnic
students, displays itself in this particular form very beneficially.
Young men of all classes work heartily and zealously together in the
_salles d’étude_, and no feeling of rivalry prevents them from assisting
one another. The sergeant does not, however, appear to exercise any
authority in the way of keeping discipline.

These chambers for study are arranged on each side of a long corridor
which runs through the whole length of the building, those of the
juniors being separated from those of the seniors by a central chamber
or compartment, the _cabinet de service_, where the officers charged
with the discipline are posted, and from hence pass up and down the
corridor, looking in through the glass doors and seeing that no
interruption to order takes place.

The fourth story is that of the dormitories, airy rooms, with twelve
beds in each. These rooms are arranged as below, along the two sides of
a corridor, and divided in the same manner into the senior and junior
side. A non-commissioned officer is lodged at each end of the corridor
to see that order is kept.

Such is the building into which at the beginning of November the
successful candidates from the _Lycées_ and the _Ecoles préparatoires_
are introduced, in age resembling the pupils whom the highest classes of
English public schools send annually to the universities, and in number
equal perhaps to the new under-graduates at one of the largest colleges
at Cambridge. There is not, however, in other points much that is
common, least of all in the methods and habits of study we are about to
describe. This will be best understood by a summary of a day’s work.

The students are summoned to rise at half-past five, have to answer the
roll-call at six, from six to eight are to occupy themselves in study,
and at eight they go to breakfast. On any morning except Wednesday, at
half-past eight, we should find the whole of the new admission assembled
in an amphitheater, permanent seats in which are assigned to them by
lot, and thus placed they receive a lecture from a professor, rough
notes of which they are expected to take while it goes on. The first
half hour of the hour and a half assigned to each lecture is occupied
with questions put by the professor relating to the previous lecture.
A name is drawn by lot, the student on whom the lot falls is called up
to the blackboard at which the professor stands, and is required to work
a problem and answer questions. The lecture concluded, the pupils are
conducted to the _salles d’étude_, which have just been described, where
they are to study. Here for one hour they devote themselves to
completing and writing out in full the notes of the lecture they have
just heard. The professor and his assistants, the _répétiteurs_, are
expected to follow and make a circuit through the corridors, to give an
opportunity to ask for information on any difficult points in the
lecture. A lithographed summary of the substance of the lecture,
extending perhaps to two octavo pages, is also furnished to each
studying room for the use of its pupils.

The lecture, as we have said, commences at half-past eight o’clock; it
lasts an hour and a half; the hour of writing up the notes brings us to
eleven. The young men are now relieved by a change of occupation, and
employ themselves (still in their places in the rooms of study) at
drawing. A certain number, detached from the rest, are sent to the
physical and chemical laboratories. The rotation is such as to admit
each student once a month to two or three hours’ work at a furnace for
chemistry, and once in two months to make experiments in electricity, or
other similar subjects. In this way, either at their drawing or in the
laboratories, they spend three hours, and at two o’clock go to their
dinner in the refectories below, and after dinner are free to amuse
themselves in the court-yard, the library, the fencing and the billiard
rooms, till five. At five they return to the studying rooms, and for two
hours, on Mondays and Fridays, they may employ themselves on any work
they please (_étude libre_;) on Tuesday there is a lecture in French
literature, and on Thursday in German; at seven o’clock they commence a
lesson, which lasts till nine, in landscape and figure drawing, or they
do exercises in French writing or in German; at nine they go down to
supper; at half-past nine they have to answer to a roll-call in their
bedrooms, and at ten all the lights are put out.

Wednesday is a half-holiday, and the pupils are allowed to leave the
school after two o’clock, and be absent till ten at night. The morning
is occupied either in study, at the pleasure of the students, or in set
exercises till eleven, when there is a lecture of one hour and a half,
followed, as usual, by an hour of special study on the subject of the
lecture. On Sunday they are allowed to be absent almost the whole day
till ten P.M. There is no chapel, and apparently no common religious
observance of any kind in the school.

Such is a general sketch of the ordinary employment of the day; a couple
of hours of preparatory study before breakfast, a lecture on the
differential calculus, on descriptive geometry, on chemistry, or natural
philosophy, followed by an hour’s work at notes; scientific drawing till
dinner; recreation; and general study, or some lighter lecture in the
evening. Were we merely to count the hours, we should find a result of
eleven or eleven and a half hours of work for every day but Wednesday,
and of seven and a half hours for that day. It is to be presumed,
however, that though absolute idleness, sleeping, or reading any book
not authorized for purposes of study, is strictly prohibited, and when
detected, punished, nevertheless the strain on the attention during the
hours of drawing and the lectures of the evening is by no means extreme.
Landscape and figure drawing, the lecture in French literature, and
probably that in German, may fairly be regarded as something like
recreation. Such, at least, was the account given us of the lectures on
literary subjects, and it agrees with the indifference to literature
which marks the school. Of wholesome out-of-door recreation, there
certainly seems to be a considerable want. There is nothing either of
the English love of games, or of the skillful athletic gymnastics of the
German schools.

The method of teaching is peculiar. The plan by which a vast number of
students are collected as auditors of professorial lectures is one
pursued in many academical institutions, at the Scotch universities, and
in Germany. Large classes attend the lectures in Greek, in Latin, and in
mathematics at Glasgow; they listen to the professor’s explanations,
take notes, are occasionally questioned, and do all the harder work in
their private lodgings. Such a system of course deserves in the fullest
sense the epithet of voluntary; a diligent student may make much of it;
but there is nothing to compel an idle one to give any attention.

It seems to have been one especial object pursued in the Polytechnic to
give to this plan of instruction, so lax in itself, the utmost possible
stringency, and to accumulate upon it every attainable subsidiary
appliance, every available safeguard against idleness. Questions are
expressly put _vivâ voce_ by the professor before his lecture; there is
a subsequent hour of study devoted to the subject; there is the
opportunity for explanation to individual students; the exaction of
notes written out in full form; the professor also gives exercises to
the students to write during their hours of general study, which he
examines, and marks; general vivâ voce examinations (_interrogations
générales_,) conducted by the professors and _répétiteurs_, follow the
termination of each course of lectures; and lastly, one of the most
important and peculiar parts of the method, we have what are called the
_interrogations particulières_. After every five or six lectures in each
subject, each student is called up for special questioning by one of the
_répétiteurs_. The rooms in which these continual examinations are held
have been described. They occupy one entire story of the building; each
holds about six or eight pupils, with the _répétiteurs_. Every evening,
except Wednesday, they are filled with these little classes, and busy
with these close and personal questionings. A brief notice, at the
utmost of twenty-four hours, is served upon the students who are thus to
be called up. Generally, after they have had a certain number of
lectures, they may expect that their time is at hand, but the precise
hour of the summons can not be counted upon. The scheme is continually
varied, and it defies, we are told, the efforts of the ablest young
analysts to detect the law which it follows.

It will be seen at once that such a system, where, though nominally
professorial, so little is left to the student’s own voluntary action,
where the ordinary study and _reading_, as it is called in our English
universities (here such an expression is unknown) is subjected to such
unceasing superintendence and surveillance, and to so much careful
assistance, requires an immense staff of teachers. At the Polytechnic,
for a maximum of 350 pupils, a body of fifteen professors and
twenty-four _répétiteurs_, are employed, all solely in actual
instruction, and in no way burdened with any part of the charge of the
discipline or the finance, or even with the great yearly examinations
for the passage from the first to the second division, and for the
entrance to the public services.

With a provision of one instructor to every eight students, it is
probable that in England we should avoid any system of large classes,
from the fear of the inferior pupils being unable to keep pace with the
more advanced. We should have numerous small classes, and should
endeavor, above all things, to obtain the advantage of equality of
attainment in the pupils composing them.

The French, on the other hand, make it their first object to secure one
able principal teacher in each subject, a professor whom they burden
with very few lectures. And to meet the educational difficulty thus
created, to keep the whole large class of listeners up to the prescribed
point, they call in this numerous and busily employed corps of
assistants to _repeat_, to go over the professor’s work afresh, to whip
in, as it were, the stragglers and hurry up the loiterers. Certainly,
one would think, a difficult task with a class of 170 freshmen in such
work as the integral and differential calculus. It is one, however, in
which they are aided by a stimulus which evidently acts most powerfully
on the students of the Polytechnic School. During the two years of their
stay, the prospect of their final admission to the public services can
rarely be absent from the thoughts even of the least energetic and
forethinking of the young men. Upon their place in the last class list
will depend their fortune for life. A high position will secure them not
only reputation, but the certainty of lucrative employment; will put it
in their power to select which service they please, and in whichever
they choose will secure them favorable notice. Let it be remembered that
fifty-three of these one hundred and seventy are free scholars, born of
parents too poor to pay 40_l._ a year for their instruction; to whom
industry must be at all times a necessity, and industry during their two
years at the Polytechnic the best conceivable expenditure, the most
certainly remunerative investment of their pains and labor. The place on
the final class list is obviously the prize for which this race of two
years’ length has to be run. What is it determines that place? Not by
any means a final struggle before the winning-post, but steady effort
and diligence from first to last throughout the course. For the order of
the class list is not solely determined by success in the examination
after which it is drawn up, but by the result of previous trials and
previous work during the whole stay at the school.

For, during the whole time, every written exercise set by the professor,
every drawing, the result of every _interrogation particulière_ by the
_répétiteurs_, and of each general interrogation by the professors and
_répétiteurs_, is carefully marked, and a credit placed according to the
name of the student and reserved for his benefit, in the last general
account. The marks obtained in the examination which closes the first
year of study form a large element in this last calculation. It had been
found that the work of the first year was often neglected: the evil was
quickly remedied by this expedient. The student, it would seem, must
feel that he is gaining or losing in his banking account, so to call it,
by every day’s work; every portion of his studies will tell directly for
or against him in the final competition, upon which so much depends.

Such is the powerful mechanism by which the French nation forces out of
the mass of boys attending their ordinary schools the talent and the
science which they need for their civil and military services. The
efforts made for admission to this great scientific school of the public
services, the struggle for the first places at the exit from it, must be
more than enough, it is thought, to establish the habits of hard work,
to accumulate the information and attainment, and almost to create the
ability which the nation requires for the general good.

We may now follow the student through his course of two years’ study.
The first year’s work may be mainly divided into three portions of
unequal length; two of them of about four months each (with an
additional fortnight of private study and examination,) are mainly given
to hard lecturing, whilst the third portion of two months is devoted to
private study and to the examinations.

In accordance with this arrangement of the year, the four hardest
subjects are thus distributed. Analysis and descriptive geometry, the
staple work of the school--its Latin, as M. de Barante called it--come
in the first four months; there is then a pause for private study and a
general examination in these two subjects (_interrogations générales_ as
distinct from the _interrogations particulières_ of the _répétiteurs_.)
This brings us to the middle of March. Analysis and geometry are then
laid aside for the rest of the year, and for the next portion of four
months the pupils work at mechanics and geodesy, private study and a
general examination completing this course also. Important lectures on
physics and chemistry run on during both these periods, and are
similarly closed by private study and a general examination. The less
telling evening classes of French literature and German end at the
beginning of June, and landscape and figure drawing only last half the
year. It may be observed also, that, as a general rule, there is on each
day one, and only one, really difficult lecture. This is immediately
preceded and followed by private study, but then comes something
lighter, as a relief, such as drawing or work in the laboratories.

The chief feature in the third portion of the year is the complete break
in the lectures for general private study (_étude libre_,) a month or
six weeks before the closing examination at the end of the year. The
immediate prospect of this prevents any undue relaxing of the work; and
it is curious to observe here how private efforts and enforced system
are combined together, for even the private efforts are thus
systematized and directed. The closing examination of the first year
begins on the 1st and ends on the 25th of September.

The total number of lectures in each branch of study, with the dates
when they respectively commence and finish, and the period when the
general examinations (_interrogations générales_) take place, are
exhibited in the following tables, and we should add that the interval
between the close of each course and the commencement of the chief
yearly examination is devoted to free study.


  L  No. of Lectures
  C  Commenced.
  F  Finished.
  GE General Examinations _Interrogations Générales._

                    | L | Course of Lectures. |General Examinations.
                    |   |                     |  _Interrogations
                    |   |                     |     Gènèrales._
                    |   +----------+----------+----------+----------
  Subject of Study. |   |  C       |  F       |  C       |  F
  Analysis          | 48| 3rd Nov. |25 Feb.   |13th March|18th March
  Mechanics         | 40|21st March|29th June |24th July |2nd August
    & Machines      | 40|21st March|29th June |24th July |2nd August
  Descriptive       | 38| 3rd Nov. |3rd March |13th March|18th March
    Geometry        | 38| 3rd Nov. |3rd March |13th March|18th March
  Physics           | 34| 2nd  “   |28th June |10th July |19th July
  Chemistry         | 38| 5th  “   |17th  “   |10th  “   |19th  “
  Geodesy           | 35|20th March|30th  “   |24th  “   |2nd August
  French Literature | 30| 8th Nov. | 6th  “   |          |
  German            | 30| 2nd  “   |15th  “   |          |
  Figure and        | 50| 4th  “   |28th April|          |
    Landscape       |   |          |          |          |
    Drawing         |---|          |          |          |
  Total             |343|          |          |          |

  [Annual Examination begins on the 1st Sept., and ends on the 25th

The work of the second year is almost identical in its general plan with
that of the first. A continuation of analysis with mechanics in place of
descriptive geometry is the work of the first four months, then comes
the private study and the _interrogations générales_, and then again,
from the middle of March to the middle of July, work of a more
professional character, stereotomy, the art of war and topography, forms
the natural completion of the pupil’s studies. Chemistry and physics
follow the same course as during the first year, and terminate with the
private study and the general examination at the beginning of August.
The evening lectures in French literature and German end about the
middle of June, and those in figure and landscape drawing at the
beginning of May. The last portion is again given to private study and
the great Final Examination.


  L  No. of Lectures
  C  Commenced.
  F  Finished.

                   |  L  |Course of Lectures.|General Examinations.
                   |     |                   |  _Interrogations
                   |     |                   |     Gènèrales._
                   |     +---------+---------+----------+----------
  Subject of Study.|     |  C      |  F      |  C       |  F
  Analysis         |32   |11th Nov.|3rd March|13th March|18th March
  Mechanics and    |     |         |         |          |
    Machines       |42   |10th  “  |2nd   “  |13th  “   |18th  “
  Stereotomy       |32   |20th Mar.|26th June|10th July.|19th July.
  Physics          |36   |12 Nov.  |29th  “  |24th  “   |2nd Aug.
  Chemistry        |38   |14th “   |28th  “  |24th  “   |2nd   “
  Architecture and |     |         |         |          |
    Construction   |40   |10th “   |8th   “  |..........|..........
  Military Art and |     |         |         |          |
    Fortification  |20   |21st Mar.|21st  “  |10th  “   |19th July.
  Topography       |10   |3rd Jan. |21st  “  |          |
  French literature|30   |11th Nov.|9th   “  |          |
  German           |30   |14th “   |19th  “  |          |
  Figure and       |     |         |         |          |
  Landscape Drawing|48   |12th “   |2nd May. |          |
  Total            |358  |         |         |          |

  [Annual Examination Begins on the 10th Sept. and ends on the 10th


We have now brought the pupil nearly to the end of his career, but must
previously say a few words about his examinations, the chief epochs
which mark his progress, and the last of which fixes his position almost
for life. For this purpose it is necessary to recapitulate briefly what
has been said in different places of the whole examinatorial system of
the Polytechnic School.

1. All the professors require the students in their studying rooms, to
answer questions in writing on the courses as they go through them: a
different question is given to each student, and every third question is
of such a nature as to involve a numerical example in the reply.

These questions are given in the proportion of one to about every four
lectures, and the replies after being examined by the professor or
_répétiteur_, are indorsed with a credit, varying from 0 to 20, and the
paper is then given back to the student, to be produced at the close of
the year.

2. Credits are assigned to the students for their ordinary manipulations
in chemistry and physics, during the first year; and at the close of
each year, for their manipulations, in chemistry alone, before the

3. The _répétiteurs_ examine, (in the _interrogations particulières_,)
every ten or fourteen days, from six to eight students during a sitting
of two hours, on the subject of study lectured on since the previous
examination of the same kind. All these students must continue present,
and at the close the _répétiteur_ assigns to each a previous examination
of the same kind. All these students must continue present, and at the
close the _répétiteur_ assigns to each a credit entirely dependent on
the manner in which each has replied. The professors and captains
inspectors are occasionally present at these examinations, which are
discontinued at certain periods according to the instructions of the
director of studies.

4. At different intervals of time, from a fortnight to a month, as may
happen, after the close of the course in each branch of study, general
examinations (_interrogations générales_) are made by the professors and
_répétiteurs_. From four to six students are examined together for at
least two hours, and at the conclusion the professor makes known to the
director of studies the credit he has granted to each student for the
manner in which he has passed his examination.

Such may be called the minor or ordinary examinations. But there is an
annual closing examination at the end of each year, which we will now
describe. The first year’s annual examination commences on the 1st and
ends on the 25th September. It is carried on by special examiners,
(a different set from those who conduct the entrance examinations,) and
not by the professors. These give to every student a credit between 0
and 20 in each branch of study, according to the manner in which he

The following table shows the co-efficients of influence allowed to the
different studies of the first year, subdivided also among the
particular classes of examination to which the student has been
subjected. The component parts of the co-efficients as well as the
co-efficients themselves, slightly vary from year to year, dependent on
the number of examinations:--


  TC Total Co-efficients. (_repeated_)
  WA Written Answers to Professors’ Questions.
  ER Examinations by _Répétiteurs_. (_Int. Part._)
  GE General Examinations. (_Int. Gen._)
  Man. Manipulations.
  O Ordinary.
  Ex At Examination.
  SN Sheets of notes on descriptive Geometry.
  GD Graphical Representations and Drawing.
  1st First Annual Examination.

                   |    |Co-efficient of Influence awarded to|
                   |    +----+----+----+-------+---+----+----+
   Nature          |    |    |    |    |  Man. |   |    |    |
                   |    |    |    |    +---+---+   |    |    |
   of Study.       | TC | WA | ER | GE | O | Ex| SN| GD |1st | TC
  Analysis,        | 56 |  9 | 10 |  9 |.. |.. |.. | .. | 28 | 56
  Mechanics,       | 60 |  7 |  9 |  8 |.. |.. |.. | 14 | 22 | 60
  Descriptive      | .. | .. | .. | .. |.. |.. |.. | .. | .. | ..
   Geometry,       | 48 | .. |  7 |  7 |.. |.. | 4 | 12 | 18 | 48
  Geodesy,         | 39 |  6 |  5 |  7 |.. |.. |.. |  3 | 18 | 39
  Physics,         | 45 |  6 |  9 |  7 | 2 |.. |.. | .. | 21 | 45
  Chemistry,       | 45 |  5 |  9 |  7 | 4 | 2 |.. | .. | 18 | 45
  French           | .. | .. | .. | .. |.. |.. |.. | .. | .. | ..
   Literature,     | 12 | 12 | .. | .. |.. |.. |.. | .. | .. | 12
  German Language, | 10 |  2 |  3 | .. |.. |.. |.. | .. | 5  | 10
  Drawing,         | 10 | .. | .. | .. |.. |.. |.. | 10 | .. | 10
  Shading &        | .. | .. | .. | .. |.. |.. |.. | .. | .. | ..
   Tinting Plans,  |  3 | .. | .. | .. |.. |.. |.. |  3 | .. |  3

At the conclusion of this examination the director of studies prepares a
statement for each student, exhibiting the credits he has obtained at
each of the preceding examinations in each subject, multiplied by the
co-efficient of influence, and the sum of the products represents the
numerical account of the student’s credit in each branch of study.

As the process is somewhat intricate, we append the following example,
to show the nature of the calculation performed, in order to ascertain
the amount of credits due to each student:--


  [Outer Rows:]
  Subject of Examination,
    Co-efficient of Influence;
    Sum of Products,
    Mean Credit in each Subject of the Course
  [Inner Rows:]
  Nature of Examination or Proof;
    Credit obtained by the Student,
    Co-efficient of Influence,

  Analysis,             | 56 || 845.81| 15.00 |
    Written answers to Professors’ questions  | 17.16 |  9 | 154.44 |
    Examinations by _répétiteurs_             |       |    |        |
      (_interrogations particulières_)        | 15.47 | 10 | 154.70 |
    General Examination                       |       |    |        |
      (_interrogations générales_)            | 13.71 |  9 | 123.39 |
    Annual Examination                        | 14.75 | 28 | 413.28 |
  Mechanics,            | 60 || 664.13| 11.07 |
    Written answers to Professors’ questions  | 13.45 |  7 |  94.15 |
    Examinations by _répétiteurs_             | 12.72 |  9 | 114.48 |
    General Examination                       | 11.37 |  8 |  90.96 |
    Graphical representations and drawing     |  5.61 | 14 |  78.54 |
    Annual Examination                        | 13.00 | 22 | 286.00 |
  Descriptive Geometry, | 48 || 633.15| 13.19 |
    Examinations by _répétiteurs_             | 17.15 |  7 | 120.05 |
    General Examination                       | 11.72 |  7 |  82.04 |
    Sheets of notes                           | 12.45 |  4 |  49.80 |
    Graphical representation and drawing      | 11.88 | 12 | 142.76 |
    Annual Examination                        | 13.25 | 18 | 238.50 |
  Geodesy,              | 39 || 229.01|  5.87 |
    Written answers to Professors’ questions  |  9.16 |  6 |  54.96 |
    Examinations by _répétiteurs_             |  7.85 |  5 |  39.25 |
    General Examination                       |  5.74 |  7 |  40.18 |
    Graphical representation and drawing      |  4.36 |  3 |  13.08 |
    Annual Examination                        |  4.53 |  1 |  81.54 |
  Physics,              | 45 || 112.21|  2.49 |
    Written answers to Professors’ questions  |  2.76 |  6 |  13.56 |
    Examinations by _répétiteurs_             |  3.54 |  9 |  31.86 |
    General Examination                       |  5.74 |  7 |  40.18 |
    Ordinary manipulation                     |  1.55 |  2 |   3.10 |
    Annual Examination                        |  1.84 | 21 |  38.84 |
  Chemistry,            | 45 || 131.16|  2.91 |
    Written answers to Professors’ questions  |  2.46 |  5 |  12.30 |
    Examinations by _répétiteurs_             |  3.25 |  9 |  29.95 |
    General Examination                       |  2.47 |  7 |  17.29 |
    Ordinary manipulation                     |  2.26 |  4 |   9.04 |
    Manipulation at Exam                      |  1.58 |  2 |   3.16 |
    Annual Examination                        |  3.34 | 18 |  60.12 |
  French  Literature,   | 12 || 67.68 |  5.64 |
    Written answers to Professors’ questions  |  5.46 | 12 |  67.68 |
  German Language,      | 10 || 55.92 |  5.59 |
    Written answers to Professors’ questions  |  6.57 |  2 |  13.14 |
    Examinations by _répétiteurs_             |  4.86 |  3 |  14.58 |
    Annual Examination                        |  5.64 |  5 |  28.20 |
  Drawing,              | 10 || 43.60 |  4.36 |
    Graphical representation and drawing      |  4.36 | 10 |  43.60 |
  Shading and Tinting                         |
      Plans,            |  3 || 11.58 |  3.86 |
    Graphical representation and drawing      |  3.86 |  3 |  11.58 |

                               Sum  10)70.07
               General Mean Credit, = (7.00)

It is important to remark that any student whose _mean credit_, given in
the eighth column of the preceding table, in any branch of study does
not exceed _three_, or whose _general mean credit_ for the whole of the
studies being the arithmetical mean of all the values recorded in the
eighth column, and given at the bottom in the example, does not exceed
six, is _considered to possess an insufficient amount of instruction to
warrant his being permitted to pass into the first division for the
second year’s course_. He is accordingly excluded from the school,
unless he has been prevented from pursuing his studies by illness, in
which case, when the facts are thoroughly established, he will be
allowed a second year’s study in the second division, comprising the
first year’s course of study.

We now pass to the second annual or great final examination for
admission to the public services, remarking only that in the
_interrogations générales_ of the second year the principal subjects of
both years are included.

The final examinations for admission into the public service commence
about the 10th September, and last about one month. They are conducted
by the same examiners who examined at the close of the first year. These
are five in number, and appointed by the minister of war. One of these
takes analysis; a second, mechanics; a third, descriptive geometry and
geodesy; the fourth, physics; and the fifth, chemistry.

The examination in military art and topography is conducted by a captain
of engineers specially appointed for the purpose; and in the same manner
the examination in German is carried on by a professor, usually a
civilian, specially but not permanently appointed.

The questions are oral, and extend over the whole course of study
pursued during the two years. Each student is taken separately for one
hour and a quarter on different days by each of the five examiners; each
examiner examines about eight students daily.

A table, very similar to that already given, is prepared under the
superintendence of the Director of studies for every student, to
ascertain the numerical amount of his credits in each branch of study,
the co-efficients of influences for the particular subject of study and
nature of examination being extracted from a table similar to that in
page 80, and when these tables have all been completed, a general list
of all the students is made out, arranged in the order of their merits.

Formerly, conduct was permitted to exercise some slight influence on
their position, but that is no longer the case.

The same regulations exist, as regards the minimum amount of credit that
will entitle the students to enter into the public service, as have
already been stated above in reference to the passage from the first to
the second year’s course of study.


  RP Result of previous Year’s Examination.
  WA Written answers to Professors’ Questions.
  ER Examinations by _Répétiteurs_. (_Int. Part._)
  GE General Examinations. (_Int. Gen._)
  Man. Manipulations.
  O Ordinary.
  Ex At Examination.
  SN Sketches and Notes in Architecture
  GD Graphical Representations and Drawing
  EA Examination in Architecture
  2d 2d Annual or Final Examination.
  TC Total Co-efficients.

                |      Co-efficient of Influence awarded to     |
                |    |    |    |    | Man.  |    |    |    |    |
                |    |    |    |    +---+---+    |    |    |    |
                | RP | WA | ER | GE | O | Ex| SN | GD | EA | 2d | TC
  Analysis,     | 28 |  8 | 10 |  9 |   |   |    |    |    | 26 | 81
  Mechanics,    | 25 |  8 | 12 |  9 |   |   |    | 10 |    | 28 | 92
  Descriptive   |    |    |    |    |   |   |    |    |    |    |
   Geometry,    | 36 |    |    |    |   |   |    |    |    |    | 36
  Geodesy,      |    |  6 |  5 |  7 |   |   |    | 1  |    | 18 | 37
  Physics,      | 23 |  5 | 10 |  8 |   |   |    |    |    | 22 | 68
  Chemistry,    | 20 |  5 | 10 |  8 | 4 | 2 |    |    |    | 19 | 68
  Architecture, |    |    |    |    |   |   | 12 | 14 | 10 |    | 36
  Military      |    |    |    |    |   |   |    |    |    |    |
   Art and      |    |    |  3 |  5 |   |   |    |  9 |    |  8 | 25
   Tophography, |    |    |    |    |   |   |    |    |    |    |
  French        |    |    |    |    |   |   |    |    |    |    |
   Literature,  |  6 |  12|    |    |   |   |    |    |    |    | 18
  German,       |  5 |   2|  3 |    |   |   |    |    |    |    | 15
  Drawing,      |  5 |    |    |    |   |   |    | 10 |    |    | 15
  Shading and   |    |    |    |    |   |   |    |    |    |    |
   Tinting,     |  2 |    |    |    |   |   |    |  3 |    |    |  5

From the preceding tables and explanations, it will be apparent that, as
the whole of the students for each year are compelled to follow
precisely the same course of study, the system of professorial
instruction, combined with the constant tutelage and supervision
exercised by the _répétiteurs_, and the examinations (_interrogations
particulières_) of the _répétiteurs_, at short intervals of time, have
for their principal object the keeping alive in the minds of the
students the information which has been communicated to them. As a
stimulus to continuous and unceasing exertion, it will be seen by an
inspection of the tables of the co-efficients of influence, that the
manner in which the students acquit themselves from day to day, and from
week to week, is made an element, and a very important one, in
determining their final position in the list arranged according to
merit, exceeding as it does in most instances the influence exerted on
their classification by their final examination at the close of each
year. This principle thus recognizes not only their knowledge at the end
of each year, but also the manner in which they have proved it to the
professors and _répétiteurs_ in the course of the year; and with
reference to the second year’s study, the final result of the first
year’s classification exercises an influence amounting to about
one-third of the whole, in the final classification at the end of the
second year.

It follows also, that as the examinations at the end of each year are
made by examiners, otherwise unconnected with the school, and not by the
professors belonging to it, the positions of the students in the
classified list is partly dependent on the judgment of the professors
with whom they are constantly in communication, and partly on the public
examiners, whom they meet only in the examination rooms.[10]

    [Footnote 10: The influence exercised in the various branches of
    study, and consequently in the position of the students in the
    list classified according to merit, by the professors and
    _répétiteurs_ on the one hand, and by the examiners on the other,
    as in the table above.]

The examiners of the students are not frequently changed, and
practically the same may be said of the examiners for admission.

  PR By Professors and _Répétiteurs_.
  Ex By Examiners.
  Y1 By the results of the first Year’s Examination.

  Subjects of Study. |  Per-centage of influence exercised on the
                     |  position of the Students.
                     |During the || During the      ||In the Classified
                     | 1st Year. || 2nd Year.       ||List at the end
                     |           ||                 ||of 2nd year.
                     | PR  | Ex  || Y1  | PR  | Ex  || PR  | Ex
  Analysis,          | 50.0| 50.0|| 34.5| 32.5| 33.0|| 49.7| 50.25
  Mechanics,         | 63.2| 36.7|| 27.2| 42.4| 30.4|| 59.6| 40.40
  Descriptive        |     |     ||     |     |     ||     |
    Geometry,        | 62.5| 37.5||100.0|  0.0|  0.0|| 62.5| 37.5
  Geodesy,           | 53.8| 46.2||  0.0| 51.4| 48.6||*51.4| 48.6
  Physics,           | 53.3| 46.7|| 33.8| 33.8| 32.4|| 51.8| 48.2
  Chemistry,         | 60.0| 40.0|| 29.4| 43.2| 27.4|| 60.8| 39.2
  Architecture,      | ..  | ..  ||  0.0|100.0|  0.0||100.0|100.0
  Military Art and   |     |     ||     |     |     ||     |
    Topography,      | ..  | ..  ||  0.0| 68.0| 32.0|| 68.0| 32.0
  French Literature, |100.0|  0.0|| 33.3| 66.7|  0.0||100.0|  0.0
  German Language,   |100.0|  0.0|| 33.3| 33.3| 33.4|| 66.7| 33.3
  Drawing,           |100.0|  0.0|| 33.3| 66.7|  0.0||100.0|  0.0
  Shading and        |     |     ||     |     |     ||     |
    Tinting Plans,   |100.0|  0.0|| 40.0| 60.0|  0.0||100.0|  0.0
                     |     |     ||     |     | *   ||     |

  [* When taught in the 2nd year]

The students at the head of the list have generally since the wars of
the first Empire entered into the civil rather than into the military
services, the former being much better remunerated.

The services are usually selected by preference, nearly in the following

  The Roads and Bridges (_Ponts et chaussées_)} very nearly on an
    and Mines (_Mines_,)                       }   equality.
  Powder and Saltpetre (_Poudres et Salpêtres._)
  Naval Architects (_Génie maritime._)
  Engineers (_Génie militaire._)
  The Artillery (_Artillerie de terre._) }
    and the Staff Corps (_Etat Major_,)  } very nearly on an equality.
  The Hydographical Corps (_Ingénieurs Hydrographes._)
  Tobacco Department (_Administration des Tabacs._)
  Telegraph Department (_Lignes Télégraphiques._)
  Navy (_Marine._)
  Marine Artillery (_Artillerie de mer._)

Such, at least, is the result of a comparison of the selections made by
the students during eight different years.

This preference of the civil to the military services has been the
subject of frequent complaints on the part of the military authorities
to the minister of war.

No steps have, however, been taken by the French government to prevent
the _free_ choice of a profession being granted to the most successful

We have now followed the student at the Polytechnic to the end of his
school career. He is then to pass to his particular School of
Application, in which (as the name implies) he is taught to apply his
science to practice. It is difficult to state precisely the amount of
such science which the highest pupils may be thought to possess on
leaving; the best idea of it will be gained by reference to the
programmes of the most important of the lectures. It is also needless to
dwell again on the main features of the school--the emulation called
forth, the minute method, the great prizes offered for sustained labor.
We must, however, make some remarks on these points before concluding
our account, so far as they bear on the subject of military education.


  1. Keeping out of sight for the moment some defects both in the
principles and details of the education of this school, the method of
teaching adopted seems to us excellent, and worthy of careful study. In
this remark we allude principally to the skillful combination of two
methods which have been generally thought incompatible; for it unites
the well-prepared lecture of a German professor, with the close personal
questioning of a first-rate English school or college lecture. But
besides this, its whole system is admirably adapted for the class of
pupils it educates.

  These pupils are generally not of the wealthy classes; they are able,
and struggling for a position in life. On all these grounds their own
assistance in the work may be calculated upon. Yet they are not left to
themselves to make the most of their professors’ lectures. The aid of
_répétiteurs_, even more valuable in its constant “prudent
interrogations,” than in the explanations afforded, is joined to the
stimulus given by marking every step of proficiency, and by making all
tell on the last general account. But though the routine and method of
the school are so elaborate, play is given to the individual freedom of
the pupils in their private work, and this is managed so skillfully that
the private work is made immediately to precede the final examination,
on which mainly depends the pupil’s place for life. Thus from first to
last they are carried on by their system without being cramped by it;
every circumstance favorable to study is made the most of; rigorous
habit, mental readiness, the power of working with others, and the power
of working for themselves, the ambition for immediate and permanent
success, all the objects and all the methods which students ever have in
view, support and stimulate those of the Polytechnic in their two years’

  2. The mainspring, however, of the school’s energy is the competition
amongst the pupils themselves, and this could hardly exist without the
great prizes offered to the successful. This advantage, added to the
general impulse of the early days of the Empire, has no doubt powerfully
contributed to the great position of the school. It has made it a kind
of university of the _élite_ mathematicians, and as in England young men
look to the prizes of the universities, and the professions to which
they lead, as their best opening in life, so in France, ever since the
first revolution, the corresponding class has inclined to the active and
chiefly military career which is offered by the great competitive school
of the country.

  3. A preparatory school of this remarkable character can not but
exercise a very powerful influence over those three-fourths of its
pupils who leave it to enter the army. The obvious question is whether
the attempt is not made to teach more than is either necessary or
desirable for military purposes, and to this suspicion may be added the
fact that the civil prizes being more in request than the military, many
of those who enter the army do so in the first instance reluctantly, and
that the pupils at the bottom of the list appear to be often such marked
failures as to imply either great superficiality or premature

  4. In studying the Polytechnic School we have had these points
constantly brought before us, and feeling the difficulty of discussing
them fully, we beg to invite attention to the evidence sent us in reply
to some questions which we addressed on the subject to some
distinguished scientific officers and civilians connected with the
school. We will give briefly the result of our own inquiries.

  5. The complaint of General Paixhans has been quoted. He urges that a
considerable proportion of the army pupils are mere _queues de
promotion_, and quite insufficient to form _le corps et surtout la tête_
of troops _d’élite_.

  Other not inconsistent complaints we heard ourselves, of the mental
exhaustion and the excessively abstract tendencies of many of the
military pupils of the school.

  6. Such are the complaints. There is certainly reason to think that,
with regard to the twenty or thirty lowest pupils on the list, those of
General Paixhans are well founded. These are the _breaks down_, and we
are at first surprised that, entering as they must do,[11] with high
attainments, they should fall so low as the marks in the tables (with
which we are most liberally supplied) prove to be the case.

    [Footnote 11: The students are selected, by a competitive
    examination, out of a very large number of candidates, as will be
    seen from the following table, extracted from the yearly

           | Candidates |            |
           |    who     |            | Candidates
      Year.| inscribed  | Candidates |  admitted
           |   their    | examined.  |   to the
           |   Names.   |            | Polytechnic.
      1832 |    567     |    468     |     183
      1833 |    367     |    304     |     110
      1834 |    627     |    541     |     150
      1835 |    729     |    633     |     154
      1837 |    629     |    508     |     137
      1838 |    533     |    410     |     131
      1839 |    530     |    531     |     135
      1842 |    709     |    559     |     137
      1843 |    802     |    559     |     166
      1844 |    746     |    531     |     143
      1845 |    780     |    559     |     136

    Giving an average of one student for four candidates _examined_,
    so that it is impossible to imagine that there is any lack of
    ability in those selected.

    A similar result appears to follow from some other more recent

      Year.|  Number of    | Number declared |  Number
           |  Candidates   |   admissible    | admitted.
           | who inscribed | to the Second   |
           |  their Names. |  Examination.   |
      1852 |  510          |  216            |  202
      1853 |  494          |  222            |  217
      1854 |  519          |  238            |  170
      1855 |  544          |  232            |  170

    In judging, however, of these numbers, it should be borne in mind
    that, a very large number of the candidates who succeed have tried
    more than once; the successful of this year have been among the
    unsuccessful of last year, so that the proportion of individuals
    who succeed to individuals who fail, is, of course, considerably
    larger than one to four. Of the 170 candidates admitted in
    November, 1855, 117 had put down their names for the examination
    of 1854, and 53 only had not been previously inscribed. Of the 117
    who put down their names, 19 had withdrawn without being examined
    at all, 71 had been rejected on the preliminary examination, 27
    had been unsuccessful at that of the second degree; 98 of the 170
    came up for the second time to the examination.]

  At the same time, we believe that no teaching ever has provided or
will provide against many failures out of one hundred and seventy
pupils, even among those who promised well at first: and if the standard
of the majority of pupils is high at the Polytechnique, and the point
reached by the first few _very_ high, it is no reproach that the descent
amongst the last few should be very rapid.

  With regard to the assertion, that the teaching is excessive and leads
too much to abstract pursuits for soldiers, it may be partially true.
Perhaps the general passion for science has led to an overstrained
teaching for the army, even for its scientific corps; and yet would it
be allowed by officers of the highest scientific ability, either in the
French or the English army, that less science is required for the
greatest emergencies of military than for those of civil engineering, or
for the theory of projectiles than for working the department of

  It may, however, be true that an attempt is made at the Polytechnic to
exact _from all_ attainments which can only be reached by _a few_.

  7. With this deduction, we must express our opinion strongly in favor
of the influence of the Polytechnic on the French army. We admit that in
some instances pupils who have failed in their attempt at civil prizes
enter the army unwillingly, but they are generally soon penetrated with
its _esprit de corps_, and they carry into it talent which it would not
otherwise have obtained. Cases of overwork no doubt occur, as in the
early training for every profession, but (following the evidence we have
received) we have no reason to think them so numerous as to balance the
advantage of vigorous, thoughtful study directed early towards a
profession which, however practical, is eminently benefited by it. “It
can not be said,” was the verdict of one well fitted to express an
opinion, “that there is too much science in the French army.”

  8. Assuming, however, the value of the scientific results produced in
the French army by the Polytechnic, it by no means follows that a
similar institution would be desirable in another country. Without much
discussion it may be safely said that the whole history and nature of
the institution--the offspring of a national passion for system and of
revolutionary excitement--make it thoroughly peculiar to France.

  9. Some obvious defects must be noticed. The curious rule of
forbidding the use of _all_ books whatever is a very exaggerated attempt
to make the pupil to rely entirely on the professors and _répétiteurs_.
The exclusive practice of _oral_ examination also seems to us a defect.
Certainly every examination should give a pupil an opportunity of
showing such valuable qualities as readiness and power of expression;
but an examination solely oral appears to us an uncertain test of depth
or accuracy of knowledge; and however impartial or practiced an examiner
may be, it is impossible that questions put orally can present exactly
the same amount of difficulty, and so be equally fair, to the several

  At the same time, although in all great competing examinations the
chief part of the work (in our opinion) should be _written_, the
constant oral cross-questioning of the minor examinations at the
Polytechnic, appeared to be one of the most stimulating and effective
parts of their system,

  10. A more serious objection than any we have named lies against the
exclusive use of mathematical and scientific training, to the neglect of
all other, as almost the only instrument of education. The spirit of the
school, as shown especially by its entrance examinations, is opposed to
any literary study. This is a peculiar evil in forming characters for a
liberal profession like the army. Such a plan may indeed produce
striking results, if the sole object is to create distinguished
mathematicians, though even then the acuteness in one direction is often
accompanied by an unbalanced and extravagant judgment in another. But a
great school should form the whole and not merely a part of the man; and
as doing this, as strengthening the whole mind, instead of forcing on
one or two of its faculties--as giving, in a word, what is justly called
a _liberal_ education--we are persuaded that the system of cultivating
the taste for historical and other similar studies, as well as for mere
science, is based on a sounder principle than that which has produced
the brilliant results of the Polytechnic.

  11. It may be added, in connection with the above remark, that as the
entrance examination at the Polytechnic influences extensively the
teaching of the great French schools, and is itself almost solely
mathematical, it tends to diffuse a narrow and exclusive pursuit of
science, which is very alien from the spirit of English teaching.

  12. We may sum up our remarks on the Polytechnic School thus:--

  Regarded simply as a great Mathematical and Scientific School, its
results in producing eminent men of science have been extraordinary. It
has been the great (and a truly great) Mathematical University of

  Regarded again as a Preparatory School for the public works, it has
given a very high scientific education to civil engineers, whose
scientific education in other countries (and amongst ourselves) is
believed to be much slighter and more accidental.

  Regarded as a school for the scientific corps of the army, its
peculiar mode of uniting in one course of competition candidates for
civil and military services, has probably raised scientific thought to a
higher point in the French than in any other army.

  Regarded as a system of teaching, the method it pursues in developing
the talents of its pupils appears to us the best we have ever studied.

  It is in its studies and some of its main principles that the example
of the Polytechnic School may be of most value. In forming or improving
any military school, we can not shut our eyes to the successful working
at the Polytechnic of the principle, which it was the first of all
schools to initiate, the making great public prizes the reward and
stimulus of the pupil’s exertions. We may observe how the state has here
encouraged talent by bestowing so largely assistance upon all
successful, but poor pupils, during their school career. We may derive
some lessons from its method of teaching, though the attempt to imitate
it might be unwise. Meanwhile, without emulating the long established
scientific prestige of the Polytechnic, we have probably amongst
ourselves abundant materials for a military scientific education, at
least as sound as that given at this great School.


In addition to the Schools of Application for Artillery and Engineers at
Metz, and of Infantry and Cavalry at St. Cyr, of which a pretty full
account will be given, the following Public Services are supplied by the
Polytechnic School.

  GUNPOWDER AND SALTPETRE.--(_Poudres et Salpêtres._)

  In France the manufacture of gunpowder is solely in the hands of the
Government. The pupils of the Polytechnic who enter the gunpowder and
saltpetre service, are sent in succession to different powder-mills and
saltpetre refineries, so as to gain a thorough acquaintance with all the
details of the manufacture.

  On first entering the service they are named _élèves des poudres_.
They afterwards rise successively to the rank of assistant-commissary,
commissary of the third, of the second, and of the first class.


  A small number of the pupils of the Polytechnic enter the Navy. They
receive the rank of _élève de première classe_, from the date of their

  They are sent to the ports to serve afloat. After two years’ service
they may be promoted to the rank of _enseigne de vaisseau_, on passing
the necessary examinations, on the same terms precisely as the _élèves
de premiere classe_ of the Naval School.

  MARINE ARTILLERY.--(_Artillerie de la Marine._)

  The French marine artillery differs from the English corps of the same
name, in not serving afloat. Its duties are confined to the ports and to
the colonies. It is governed by the same rules and ordinances as the
artillery of the army.

  The foundries of La Villeneuve, Rochefort, Ruelle, Névers, and Saint
Gervais are under its direction.

  The officers of the marine artillery are liable to be sent on board
ship to study naval gunnery, so as to be in a position to report upon
alterations or improvements in this science.

  NAVAL ARCHITECTS.--(_Génie Maritime._)

  The naval architects are charged with the construction and repair of
vessels of war, and with the manufacture of all the machinery required
in the ports and dockyards. The factories of Indret and La Chaussade are
under their direction.

  The pupils of the Polytechnic enter the corps of naval architects with
the rank of _élève du Génie Maritime_. They are sent to the School of
Application of Naval Architects at L’Orient. After two years’
instruction they undergo an examination, and, if successful, they are
promoted to the rank of sub-architect of the third class, so far as
vacancies admit. They may be advanced to the second class after a
service of two years.

  HYDROGRAPHERS.--(_Ingénieurs Hydrographes._)

  The hydrographers are stationed at Paris. They are sent to the coast
to make surveys, and the time so spent reckons as a campaign in
determining their pension. On their return to Paris they are employed in
the construction of maps and charts.

  The hydrographers have the same rank and advantage as the naval

  On leaving the Polytechnic, the pupils enter the corps of
hydrographers with the rank of _élève hydrographe_. After two years’
service, and one season employed on the coast, they become
sub-hydrographers without further examination.


  The Polytechnic furnishes exclusively the pupils for the Government
Civil Engineer Corps. On leaving the Polytechnic, the pupils enter the
School of Application in Paris. The course of instruction here extends
over a period of three years. It commences each year on the first of
November, and lasts till the 1st of April. After the final examination,
the pupils are arranged according to the results of the examination and
the amount of work performed.

  The pupils enter the college with the rank of _élève de troisième
classe_. They rise successively to the second and to the first class, on
making the requisite progress in their studies.

  From the 1st of May to the 1st of November the _élèves_ of the second
and the third class are sent on duty into the provinces. The _élèves_ of
the first class who have completed their three years’ course of
instruction, are employed in the duties of ordinary engineers, or are
detached on special missions. In about three years after quitting the
college, they may be appointed ordinary engineers of the second class.

  The engineers of the _Ponts et Chaussées_ prepare the projects and
plans, and direct the execution of the works for the construction,
preservation, and repair of high roads, and of the bridges and other
structures connected with these roads, with navigable rivers, canals,
seaports, lighthouses, &c. They are charged with the superintendence of
railways, of works for draining marshes, and operations affecting
water-courses; they report upon applications to erect factories driven
by water. Under certain circumstances, they share with the Mining
Engineers the duty of inspecting steam-engines.

  Permission is not unfrequently granted to the engineers of the _Ponts
et Chaussées_ to accept private employment. They receive leave of
absence for a certain time, retaining their rank and place in their
corps, but without pay.


  The Mining School of Application is organized almost exactly on the
same plan as that of the _Ponts et Chaussées_: like the latter, it is in

  The course of instruction, which lasts three years, consists of
lectures, drawing, chemical manipulation and analysis, visits to
manufactories, geological excursions, and the preparation of projects
for mines and machines. Journeys are made by the pupils, during the
second half of the last two years of the course, into the mineral
districts of France or foreign countries for the purpose of studying the
practical details of mining. These journeys last one hundred days at
least. The pupils are required to examine carefully the railroads and
the geological features of the countries they pass through, and to keep
a journal of facts and observations. In the final examination, marks are
given for every part of their work.

  The mining engineers, when stationed in the departments, are charged
to see that the laws and ordinances relating to mines, quarries, and
factories are properly observed, and to encourage, either directly or by
their advice, the extension of all branches of industry connected with
the extraction and treatment of minerals.

  One of their principal duties is the superintendence of mines and
quarries, in the three-fold regard of safety of the workmen,
preservation of the soil, and economical extraction of the minerals.

  They exercise a special control over all machines designed for the
production of steam, and over railways, as far as regards the metal and

  The instructors in the School of Application in Paris, and in the
School of Mines at St. Etienne, are exclusively taken from the members
of the corps.

  Like the engineers of the _Ponts et Chaussées_, the mining engineers
obtain permission to undertake private employment.

  TOBACCO DEPARTMENT.--(_Administration des Tabacs._)

  The pupils who enter the tobacco service, commence, on quitting the
Polytechnic, with the rank of _élève de 2^{e} classe_. They study, in
the manufactory at Paris, chemistry, physics, and mechanics, as applied
to the preparation of tobacco. They make themselves acquainted at the
same time with the details of the manufacture and with the accounts and

  They are generally promoted to the rank of _élevè de 1^{re} classe_ in
two years. They rise afterwards successively to the rank of
sub-inspector, inspector, and director.

  After completing their instruction at the manufactory of Paris, the
_élevès_ are sent to tobacco manufactories in other parts of France.

  Promotion in the tobacco service does not follow altogether by
seniority. Knowledge of the manufacture and attention to their duties
are much considered, as the interests of the treasury are involved in
the good management of the service.

  TELEGRAPHS.--(_Lignes Telégraphiques._)

  On entering the telegraphic service the pupils of the Polytechnic
receive the rank of _élevè inspecteur_.

  They pass the first year at the central office. During the six winter
months they study, under two professors, the composition of signals, and
the regulations which insure their correctness and dispatch, the working
of telegraphs and the manner of repairing them, the theory of the mode
of tracing lines and of determining the height of the towers,
electro-magnetism and its application to the electric telegraph. During
the summer months they make tours of inspection. They assist in the
execution of works, and practice leveling and the laying down of lines.

  At the end of the year the _élevès inspecteurs_ undergo an
examination, and, if there are vacancies, are appointed provisional
inspectors. After a year in this rank they may be appointed inspectors
either in France or Algeria.

  Each inspector has charge of a district containing from twelve to
fifteen stations. He is obliged to make a tour of inspection once a
month of at least ten days’ duration.

  After a certain number of years’ service the inspector rises to the
rank of director. Besides their other duties, the directors exercise a
general superintendence over the inspectors.





LESSONS 1-9. _Derivatives and Differentials of Functions of a Single

Indication of the original problems which led geometers to the discovery
of the infinitesimal calculus.

Use of infinitesimals; condition, subject to which, two infinitely small
quantities may be substituted for one another. Indication in simple
cases of the advantage of such substitution.

On the different orders of infinitely small quantities. Infinitely small
quantities of a certain order may be neglected in respect of those of an
inferior order. The infinitely small increment of a function is in
general of the same order as the corresponding increment of the
variable, that is to say, their ratio has a finite limit.

Definitions of the derivative and differential of a function of a single
variable. Tangents and normals to plane curves, whose equation in linear
or polar coordinates is given.

A function is increasing or decreasing, according as its derivative is
positive or negative. If the derivative is zero for all values of the
variable, the function is constant. Concavity and convexity of curves;
points of inflection.

Principle of function of functions. Differentiation of inverse

Differentials of the sums, products, quotients, and powers of functions,
whose differentials are known. General theorem for the differentiation
of functions composed of several functions.

Differentials of exponential and logarithmic functions.

Differentials of direct and inverse circular functions.

Differentiation of implicit functions.

Tangents to curves of double curvature. Normal plane.

Differential of the area and arc of a plane curve, in terms of
rectilinear and polar co-ordinates.

Differential of the arc of a curve of double curvature.

Applications to the cycloid, the spiral of Archimedes, the logarithmic
spiral, the curve whose normal, sub-normal, or tangent, is constant; the
curve whose normal passes through a fixed point; the curve whose arc is
proportional to the angle which it subtends at a given point.

Derivatives and differentials of different orders of functions of one
variable. Notation adopted.

Remarks upon the singular points of plane curves.

LESSONS 10-13. _Derivatives and Differentials of Functions of Several

Partial derivatives and differentials of functions of several variables.
The order in which two or any number of differentiations is effected
does not influence the result.

Total differentials. Symbolical formula for representing the total
differential of the _n_^{th} order of a function of several independent

Total differentials of different orders of a function; several dependent
variables. Case where these variables are linear functions of the
independent variables.

The infinitesimal increment of a function of several variables may in
general be regarded as a linear function of the increments assigned to
the variables. Exceptional cases.

Tangent and normal planes to curved surfaces.

LESSONS 14-18. _Analytical Applications of the Differential Calculus._

Development of F(_x + h_,) according to ascending powers of _h_. Limits
within which the remainder is confined on stopping at any assigned power
of _h_.

Development of F(_x_,) according to powers of _x_ or _x - a_; _a_ being
a quantity arbitrarily assumed. Application to the functions sin(_x_,)
cos _x_, _a^{x}_, (1 + _x^{m}_) and log.(1 + _x_.) Numerical
applications. Representation of cos _x_ and sin _x_ by imaginary
exponential quantities.

Developments of cos^{m} _x_ and sin^{m} _x_ in terms of sines and curves
of multiples of _x_.

Development of F(_x + h, y + k_,) according to powers of _h_ and _k_.
Development of F(_x, y_) according to powers of _x_ and _y_. Expression
for the remainder. Theorem on homogeneous functions.

Maxima and minima of functions of a single variable; of functions of
several variables, whether independent or connected by given equations.
How to discriminate between maxima and minima values in the case of one
and two independent variables.

True values of functions, which upon a particular supposition assume one
or another of the forms

  0/0, ∞/∞, ∞ + 0, 0^0, 4^∞

LESSONS 19-23. _Geometrical Applications. Curvature of Plane Curves._

Definition of the curvature of a plane curve at any point. Circle of
curvature. Center of curvature. This center is the point where two
infinitely near normals meet.

Radius of curvature with rectilinear and polar co-ordinates. Change of
the independent variable.

Contacts of different orders of plane curves. Osculating curves of a
given kind. Osculating straight line. Osculating circle. It is identical
with the circle of curvature.

Application of the method of infinitesimals to the determination of the
radius of curvature of certain curves geometrically defined. Ellipse,
cycloid, epicycloid, &c.

Evolutes of plane curves. Value of the arc of the evolute. Equation to
the involute of a curve. Application to the circle. Evolutes considered
as envelops. On envelops in general. Application to caustics.

LESSONS 24-27. _Geometrical Applications continued. Curvature of Lines
of Double Curvature and of Surfaces._

Osculating plane of a curve of double curvature. It may be considered as
passing through three points infinitely near to one another, or as drawn
through a tangent parallel to the tangent infinitely near to the former.
Center and radius of curvature of a curve of double curvature.
Osculating circle. Application to the helix.

Radii of curvature of normal sections of a surface. Maximum and minimum
radii. Relations between these and that of any section, normal or

Use of the indicatrix for the demonstration of the preceding results.
Conjugate tangents. Definition of the lines of curvature. Lines of
curvature of certain simple surfaces. Surface of revolution. Developable
surfaces. Differential equation of lines of curvature in general.

LESSON 28. _Cylindrical, Conical, Conoidal surfaces, and Surfaces of

Equations of these surfaces in finite terms. Differential equations of
the same deduced from their characteristic geometrical properties.


LESSONS 29-34. _Integration of Functions of a Single Variable._

Object of the integral calculus. There always exists a function which
has a given function for its derivative.

Indefinite integrals. Definite integrals. Notation. Integration by
separation, by substitution, by parts.

Integration of rational differentials, integer or fractional, in the
several cases which may present themselves. Integration of the
algebraical differentials, which contain a radical of the second degree
of the form √(_c+bx+ax^{2}_). Different transformations which render the
differential rational. Reduction of the radical to one of the forms

  √(x^{2}+x^{2}), √(a^{2}-x^{2}), √(x^{2}-a^{2}).

Integration of the algebraical differentials which contain two radicals
of the form

  √(a+x), √(b+x),

or any number of monomials affected with fractional indices. Application
to the expressions

    x^{m} dx           dx          x^{m} dx
   ---------- , ---------------- , --------
   √(1-x^{2})   x^{m} √(1-x^{2})    √(ax-x)

Integration of the differentials

          dx                   dx
  F(log x)-- , F sin^{-1}x ---------- ,
          x                √(1-x^{2})

x(log x^{n})dx, x^{m} e^{ax}dx, (sin^{-1}x^{m})dx.

Integration of the differentials e^{ax} sin _bxdx_ and e^{ax} cos

Integration of (sin x^{m}.)(cos x^{n}) _dx_.

Integration by series. Application to the expression

  √(ax-x^{2}) √(1-bx)

Application of integration by series to the development of functions,
the development of whose derivatives is given: tan^{-1}_x_, sin^{-1}_x_,
log(1 + _x_.)

LESSONS 35-38. _Geometrical Applications._

Quadrature of certain curves. Circle, hyperbola, cycloid, logarithmic
spiral, &c.

Rectification of curves by rectilinear or polar co-ordinates. Examples.
Numerical applications.

Cubic content of solids of revolution. Quadrature of their surfaces.

Cubic content of solids in general, with rectilinear or polar
co-ordinates. Numerical applications.

Quadrature of any curved surfaces expressed by rectangular co-ordinates.
Application to the sphere.

LESSONS 39-42. _Mechanical Applications._

General formula for the determination of the center of gravity of
solids, curved or plane surfaces, and arcs of curves. Various

Guldin’s theorem.

Volume of the truncated cylinder.

General formula which represent the components of the attraction of a
body upon a material point, upon the supposition that the action upon
each element varies inversely as the square of the distance. Attraction
of a spherical shell on an external or internal point.

Definition of moments of inertia. How to calculate the moment of inertia
of a body in relation to a straight line, when the moment in relation to
a parallel straight line is known. How to represent the moments of
inertia of a body relative to the straight lines which pass through a
given point by means of the radii vectores of an ellipsoid. What is
meant by the _principal axes of inertia_.

Determination of the principal moments of inertia of certain homogeneous
bodies, sphere, ellipsoid, prism, &c.

LESSONS 43-45. _Calculus of Differences._

Calculation of differences of different orders of a function of one
variable by means of values of the function corresponding to equidistant
values of the variable.

Expression for any one of the values of the function by means of the
first, and its differences. Numerical applications; construction of
tables representing a function whose differences beyond a certain order
may be neglected. Application to the theory of interpolation. Formulæ
for approximation by quadratures. Numerical exercises relative to the
area of equilateral hyperbola or the calculation of a logarithm.

LESSONS 46-48. _Revision._

General reflections on the subjects contained in the preceding course.



LESSONS 1-2. _Definite Integrals._

Differentiation of a definite integral with respect to a parameter in
it, which is made to vary. Geometrical demonstration of the formula.
Integration under the sign of integration. Application to the
determination of certain definite integrals.

Determination of the integrals ∫{(sin _ax_)/_x_}_dx_, and ∫{(cos _bx_
sin _ax_)/_x_}_dx_, between the limits _0_ and _x_. Remarkable
discontinuity which these integrals present.

Determination of ∫e^{-_x_^{2}}_dx_ and ∫e^{-_x_^{2}}cos _mx dx_ between
the limits 0 and ∞.

LESSON 3. _Integration of Differentials containing several Variables._

Condition that an expression of the form M _dx_ + N _dy_ in which M and
N are given functions of _x_ and _y_ may be an exact differential of two
independent variables _x_ and _y_. When this condition is satisfied, to
find the function.

Extension of this theory to the case of three variables.

LESSONS 4-6. _Integration of Differential Equations of the First Order._

Differential equations of the first order with two variables. Problem in
geometry to which these equations correspond. What is meant by their
integral. This integral always exists, and its expression contains an
arbitrary constant.

Integration of the equation M _dx_ + N _dy_ = 0 when its first member is
an exact differential. Whatever the functions M and N may be there
always exists a factor _µ_, such that _µ_ (M _dx_ + N _dy_) is an exact

Integration of homogeneous equations. Their general integral represents
a system of similar curves. The equation (_a_ + _b x_ + _c y_) _dx_ +
(_a’_ + _b’ x_ + _c’ y_) _dy_ = _c_, may be rendered homogeneous.
Particular case where the method fails. How the integration may be
effected in such case.

Integration of the linear equation of the first order _dy_/_dx_ + P _y_
= Q, where P and Q denote functions of _x_. Examples.

Remarks on the integration of equations of the first order which contain
a higher power than the first of _dy_/_dx_. Case in which it may be
resolved in respect of _dy_/_dx_. Case in which it may be resolved in
respect of _x_ or _y_.

Integrations of the equation _y_ = _x_ _dy_/_dx_ + φ(_d y_/_d x_). Its
general integral represents a system of straight lines. A particular
solution represents the envelop of this system.

Solution of various problems in geometry which lead to differential
equations of the first order.

LESSONS 7-8. _Integration of Differential Equations of Orders superior
to the First._

The general integral of an equation of the _m_ order contains _m_
arbitrary constants.

(_The demonstration is made to depend on the consideration of infinitely
small quantities._)

Integration of the equation _d^{m}y_/_dx^{m}_ = φ(_x_.)

Integration of the equation _d^{2}y_/_dx^{2}_ = φ(_y_, _dy_/_dx_).

How this is reduced to an equation of the first order. Solution of
various problems in geometry which conduct to differential equations of
the second order.

LESSONS 9-10. _On Linear Equations._

When a linear equation of the _m_^{th} order contains no term
independent of the unknown function and its derivatives, the sum of any
number whatever of particular integrals multiplied by arbitrary
constants is also an integral. From this the conclusion is drawn that
the general integral of this equation is deducible from the knowledge of
_m_ particular integrals.

Application to linear equations with constant co-efficients. Their
integration is made to depend on the resolution of an algebraical
equation. Case where this equation has imaginary roots. Case where it
has equal roots. The general integral of a linear equation of any order,
which contains a term independent of the function, may be reduced by the
aid of quadratures to the integration of the same equation with this
term omitted.

LESSON 11. _Simultaneous Equations._

General considerations on the integration of simultaneous equations. It
may be made to depend on the integrations of a single differential
equation. Integration of a system of two simultaneous linear equations
of the first order.

LESSON 12. _Integrations of Equations by Series._

Development of the unknown function of the variable _x_ according to the
powers of _x-a_. In certain cases only a particular integral is
obtained. If the equation is linear, the general integral may be deduced
from it by the variation of constants.

LESSONS 13-16. _Partial Differential Equations._

Elimination of the arbitrary functions which enter into an equation by
means of partial derivatives. Integration of an equation of partial
differences with two independent variables, in the case where it is
linear in respect to the derivatives of the unknown function. The
general integral contains an arbitrary function.

Indication of the geometrical problem, of which the partial differential
equation expresses analytically the enunciation. Integration of the
partial differential equations to cylindrical, conical, conoidal
surfaces of revolution. Determination of the arbitrary functions.

Integration of the equation _d^{2}u/dy^{2} = a^{2}d^{2}u/dx^{2}_. The
general integral contains two arbitrary functions. Determination of
these functions.

LESSONS 17-23. _Applications to Mechanics._

Equation to the catenary.

Vertical motion of a heavy particle, taking into account the variation
of gravity according to the distance from the center of the earth.
Vertical motion of a heavy point in a resisting medium, the resistance
being supposed proportional to the square of the velocity.

Motion of a heavy point compelled to remain in a circle or cycloid.
Simple pendulum. Indication of the analytical problem to which we are
led in investigating the motion of a free point.

Motion of projectiles in a vacuum. Calculation of the longitudinal and
transversal vibrations of cords. Longitudinal vibrations of elastic
rods. Vibration of gases in cylindical tubes.

LESSONS 24-26. _Applications to Astronomy._

Calculation of the force which attracts the planets, deduced from
Kepler’s laws. Numerical data of the question.

Calculation of the relative motion of two points attracting one another,
according to the inverse square of the distance.

Determination of the masses of the earth and of the planets accompanied
by satellites. Numerical applications.

LESSONS 27-30.

Elements of the calculus of probabilities and social arithmetic.

General principles of the calculus of chances. Simple probability,
compound probability, partial probability, total probability. Repeated
trials. Enunciation of Bernouilli’s theorem (without proof.)

Mathematical expectation. Applications to various cases, and especially
to lotteries.

Tables of population and mortality. Mean life annuities, life interests,
assurances, &c.

LESSONS 31-32. _Revision._

General reflections on the subjects comprised in the course.


_General Arrangements._

The pupils take in the lecture-room notes and sketches upon sheets,
which are presented to the professor and the “répétiteurs” at each
interrogation. The care with which these notes are taken is determined
by “marks,” of which account is taken in arranging the pupils in order
of merit.

The plans are made according to programmes, of which the conditions are
different for different pupils. The drawings are in general accompanied
with decimal scales, expressing a simple ratio to the meter. They carry
inscriptions written conformably to the admitted models, and are, when
necessary, accompanied with verbal descriptions.

In the graphic exercises of the first part of the course, the principal
object is to familiarize the pupils with the different kinds of
geometrical drawing, such as elevations and shaded sections, oblique
projections and various kinds of perspective. The pupils are also
accustomed to different constructions useful in stereotomy.

The subjects for graphic exercises in stereotomy are taken from roofs,
vaults, and staircases. Skew and oblique arches are the subject of
detailed plans.



LESSONS 1-3. _Revision and Completion of the Subjects of Descriptive
Geometry comprised in the Programme for Admission into the School._

Object of geometrical drawing. Methods of projection. Representation of
points, lines, planes, cones, cylinders, and surfaces of revolution.
Construction of tangent planes to surfaces, of curves, of intersection
of surfaces, of their tangents and their assymplotes.

Osculating plane of a curve of double curvature. A curve in general cuts
its osculating plane.

When the generating line of a cylinder or a cone becomes a tangent to
the directrix, the cylinder or cone in general has an edge of regression
along this generating line. The osculating plane of the directrix at the
point of contact touches the surface along this edge.

Projections of curves of double curvature; infinite branches and their
assymplotes, inflections, nodes, cusps, &c.

Change of planes of projection.

Reduction of scale; transposition.

Advantage and employment of curves of error; their irrelevant solutions.

LESSONS 4-6. _Modes of Representation for the Complete Definition of

Representation by plans, sections, and elevation.

Projection by the method of contours. Representation of a point, a line,
and a plane; questions relative to the straight line and plane.
Representation of cones and cylinders; tangent planes to these surfaces.

LESSONS 7-11. _Modes of Representation which are not enough in
themselves to define objects completely._

Isometrical and other kinds of perspective.

Oblique projections.

Conical perspective: vanishing points; scales of perspective; method of
squares; perspective of curved lines; diverse applications. Choice of
the point of sight. Rules for putting an elevation in perspective. Rule
for determining the point of sight of a given picture, and for passing
from the perspective to the plan as far as that is possible. Perspective
of reflected images. Notions on panoramas.

LESSONS 12-13. _Representations with Shadows._

General observations on envelops and characteristics.

A developable surface is the envelop of the position of a movable plane;
it is composed of two sheets which meet. It may be considered as
generated by a straight line, which moves so as to remain always a
tangent to a fixed curve.

Theory of shade and shadow, of the penumbra, of the brilliant point, of
curves of equal intensity, of bright and dark edges.

Atmospheric light: direction of the principal atmospheric ray. Notions
on the degradation of tints; construction of curves of equal tint.

Influence of light reflected by neighboring bodies.

Received convention in geometrical drawing on the direction of the
luminous ray, &c.

Perspective of shadows.

LESSONS 14-15. _Construction of Lines of Shadows and of Perspective of

Use of circumscribed cones and cylinders, and of the normal parallel to
a given straight line.

General method of construction of lines of shadow and of perspective of
surfaces by plane sections and auxiliary cylindrical or conical

Construction of lines of shadow and perspective of a surface of

The curve of contact of a cone circumscribed about a surface of the
second degree is a plane curve. Its plane is parallel to the diametral
plane, conjugate to the diameter passing through the summit of the cone.
The curve of contact of a cylinder circumscribed about a surface of the
second degree is a plane curve, and situated in the diametral plane
conjugate to the diameter parallel to the axis of the cylinder.

The plane parallel sections of a surface of the second degree are
similar curves. The locus of their centers is the diameter conjugate to
that one of the secant planes which passes through the center of the

General study of surfaces with reference to the geometrical
constructions to which their use gives rise.

LESSON 16. _Complementary Notions on Developable Surfaces._

Development of a developable surface; construction of transformed curves
and their tangents. Developable surface; an envelop of the osculating
planes of a curve. The osculating plane of a curve at a given point may
be constructed by considering it as the edge of regression of a
developable surface; this construction presents some uncertainty in
practice. Notions on the helix and the developable helicoid.

Approximate development of a segment of an undevelopable surface.

LESSONS 17-18. _Hyperbolic Paraboloid._

Double mode of generation of the paraboloid by straight lines;
plane-directers; tangent planes, vertex, axis, principal planes;
representation of this surface. Construction of the tangent plane
parallel to a given plane. Construction of plane sections and of curves
of contact, of cones, and circumscribed cylinders.

Scalene paraboloid. Isosceles paraboloid.

Identity of the paraboloid with one of the five surfaces of the second
degree studied in analytical geometry.

Re-statement without demonstration of the properties of this surface
found by analysis, principally as regards its generation by the conic

LESSONS 19-20. _General Properties of Warped or Ruled Surfaces._

Principal modes of generation of warped surfaces. When two warped
surfaces touch in three points of a common generatrix, they touch each
other in every point of this straight line. Every plane passing through
a generatrix touches the surface at one point in this line. The tangent
plane at infinity is the plane-directer to all the paraboloids of

Construction of the tangent planes and curves of contact of
circumscribed cones and cylinders. When two infinitely near generatrices
of a warped surface are in the same plane, all the curves of contact of
the circumscribed cones and cylinders pass through their point of

The normals to a warped surface along a generatrix form an isosceles
paraboloid. The name of central point of a generatrix is given to the
point where it is met by the straight line upon which is measured its
shortest distance from the adjoining generatrix. The locus of these
points forms the line of striction of the surface. The vertex of the
normal paraboloid along a generating line is situated at the central
point. If the point of contact of a plane touching a warped surface
moves along a generatrix, beginning from the central point, the tangent
of the angle which the tangent plane makes with its primitive position
is proportional to the length described by the point of contact. The
tangent plane at the central point is perpendicular to the tangent plane
at infinity upon the same generatrix. Construction of the line of
striction by aid of this property.

LESSONS 21-22. _Ruled Surfaces with plane-divecters Conoids._

The plane-directer of the surface is also so to all the paraboloids of
“raccordement.” Construction of the tangent planes and curves of contact
of the circumscribed cones and cylinders.

The line of striction of the surface is its curve of contact with a
circumscribed cylinder perpendicular to the directer-plane.
Determination of the nature of the plane sections.

The lines of striction of the scalene paraboloid are parabolas; those of
the isosceles paraboloid are straight lines.

Construction of the tangent plane parallel to a given plane.

Conoid: discussion of the curves of contact of the circumscribed cones
and cylinders.

Right conoid. Conoid whose intersection with a torus of the same height,
whose axis is its rectilinear directrix, has for its projection upon the
directer-plane two arcs of Archimedes’ spiral. Construction of the
tangents to this curve of intersection.

LESSONS 23-25. _Ruled Surfaces which have not a Directer-Plane.
Hyperboloid. Surface of the “biais passe.”_

Directer-cone: its advantages for constructing the tangent plane
parallel to a given plane, and for determining the nature of the plane
sections. The tangent planes to the points of the surface, situated at
infinity, are respectively parallel to the tangent plane of the
directer-cone. Developable surface which is the envelope of these
tangent planes at infinity. Construction of a paraboloid of
_raccordement_ to a ruled surface defined by two directrices and a
directrix cone.

Hyperboloid; double mode of generation by straight lines; center;
assymptotic cone.

Scalene hyperboloid; hyperboloid of revolution. Identity of the
hyperboloid with one of the five surfaces of the second degree studied
in analytical geometry.

Re-statement without demonstration of the properties of this surface,
found by analysis, principally as to what regards the axis, the
vertices, the principal planes, and the generation by conic sections.

Hyperboloid of _raccordement_ to a ruled surface along a generatrix; all
their centers are in the same plane. Transformation of a hyperboloid of

Surface of the _biais passé_. Construction of a hyperboloid of
_raccordement_; its transformation into a paraboloid.

Construction of the tangent plane at a given point.

LESSONS 26-28. _Curvature of Surfaces. Lines of Curvature._

Re-statement without proof of the formula of Euler given in the course
of analysis.

There exists an infinity of surfaces of the second degree, which at one
of their vertices osculate any surface whatever at a given point.

In the tangent plane, at a point of a surface, there exists a conic
section, whose diameters are proportional to the square roots of the
radii of curvature of the normal sections to which they are tangents.
This curve is called the indicatrix. It is defined in form and position,
but not in magnitude. The normal sections tangential to the axes of the
indicatrix are called the principal sections.

The indicatrix an ellipse; convex surfaces; umbilici; line of spherical

The indicatrix a hyperbola; surfaces with opposite curvatures.

The assymplotes of the indicatrix have a contact of the second order
with the surface, and of the first order with the section of the surface
by its tangent plane.

A ruled surface has contrary curvatures at every point. The second
assymplotes of the indicatrices of all the points of the same generatrix
form a hyperboloid, if the surface has not directer-plane,--a
paraboloid, if it have one.

Curvature of developable surfaces.

There exists upon every surface two systems of orthogonal lines, such
that every straight line subject to move by gliding over either of them,
and remaining normal to the surface, will engender a developable
surface. These lines are called lines of curvature.

The two lines of curvature which cross at a point, are tangents to the
principal sections of the surface at that point.

Remarks upon the lines of curvature of developable surfaces, and
surfaces of revolution.

Determination of the radii of curvature, and assymplotes of the
indicatrix at a point of a surface of revolution.

LESSONS 29-30. _Division of Curves of Apparent Contour, and of
Separation of Light and Shadow into Real and Virtual Parts._

When a cone is circumscribed about a surface, at any point whatever of
the curve of contact, the tangent to this curve and the generatrix of
the cone are parallel to two conjugate diameters of the indicatrix.

Surfaces, as they are considered in shadows, envelop opaque bodies, and
the curve of contact of a circumscribed cone, only forms a separation of
light and shadow, for a luminous point at the summit of the cone, when
the generatrices of this cone are exterior. This line is thus sometimes
real and sometimes virtual.

Upon a convex surface, the curve of separation of light and shade is
either all real or all virtual. Upon a surface with contrary curvatures,
this curve presents generally a succession of real and virtual parts:
the curve of shadow cast from the surface upon itself presents a like
succession. These curves meet tangentially, and the transition from the
real to the virtual parts upon one and the other, take place at their
points of contact in such a way that the real part of the curve of
shadow continues the real part of the curve of separation of light and
shade. The circumscribed cones have edges of regression along the
generatrices, which correspond to the points of transition.

The lines of visible contour present analogous circumstances.

General method of determining the position of the transition points.
Special method for a surface of revolution.

LESSONS 31-34. _Ruled Helicoidal Surfaces._

Surface of the thread of the triangular screw; generation,
representation, sections by planes and conical cylinders.

Construction of the tangent plane at a given point, or parallel to a
given plane. The axis is the line of striction.

Construction of lines of shadow and perspective: their infinite
branches, their assymplotes. Determination of the osculating hyperboloid
along a generatrix.

Representation and shading of the screw with a triangular thread and its

Surface of the thread of the square screw; generation, sections by
planes and conical cylinders; tangent planes; curve of contact of a
circumscribed cone.

The curve of contact of a circumscribed cylinder is a helix whose _step_
is half that of the surface. Determination of the osculating paraboloid.
At any point whatever of the surface, the absolute lengths of the radii
of curvature are equal.

Representation and shading of the screw with a square thread, and of its

Observations on the general ruled helicoidal surface, and on the surface
of intrados of the winding staircase.

LESSON 35. _Different Helicoidal Surfaces._

Saint-Giles screw, worm-shaped screw and helicoidal surfaces to any
generatrix. Every tangent to the meridian generatrix describes a screw
surface with triangular thread, which is circumscribed about the
surface, along a helix, and may be used to resolve the problems of
tangent planes, circumscribed cylinders, &c.

Helicoid of the open screw, its generation, tangent planes.

LESSONS 36-37. _Topographical Surfaces._

Approximate representation of a surface by the figured horizontal
projections of a series of equidistant horizontal sections. This method
of representation is especially adapted to topographical surfaces, that
is to say, surfaces which a vertical line can only meet in one point.

Lines of greatest slope. Trace of a line of equal slope between two
given points.

Intersection of a plane and a surface, of two surfaces, of a straight
line and a surface.

Tangent planes, cones, and cylinders circumscribed about topographical

Use of a topographical surface to replace a table of double-entry when
the function of two variables, which it represents, is continuous. It is
often possible, by a suitable anamorphosis, to make an advantageous
transformation in the curves of level.

LESSON 38. _Revision._

Review of the different methods of geometrical drawing. Advantages and
disadvantages of each.

Comparison of the different kinds of surfaces, _résumé_ of their general

Object, method, and spirit of descriptive geometry.



LESSONS 1-4. _Generalities._

Notions on the mode of action of forces in carpentry. Resistance of a
piece of wood to a longitudinal effort and to a transversal effort.
Distinction between resistance to flexure and resistance to rupture.

Advantages of the triangular system, St. Andrew’s cross.

LESSONS 5-8. _Roofs._

Ordinary composition of roofs.

Distribution of pressures in the different parts of a girded roof.

Design of the different parts of roofs, &c., &c.

LESSONS 9-10. _Staircases._


LESSONS 11-12. _Generalities._

Notions on the settlement of vaulted roofs. Principal forms of vaults,
_en berceau_, &c., &c.

Distribution of the pressures, &c.

Division of the intrados. Nature of the surfaces at the joints, &c., &c.

LESSONS 13-15. _Berceaux and descentes._

LESSONS 16-22. _Skew Arches._

Study of the general problem of skew arches.

First solution. Straight arches _en échelon_.

Second solution: Orthogonal _appareil_. True and principal properties of
the orthogonal trajectories of the parallel sections of an elliptical or
circular cylinder. Right conoid, having for directrices the axis of the
circular cylinder and an orthogonal trajectory. The intersection of this
conoid by a cylinder about the same axis is an orthogonal trajectory for
a series of parallel sections.

Third solution: helicoidal. Determination of the angular elevation at
which the surfaces of the beds become normal to the head planes;
construction in the orthogonal and helicoidal _appareil_ of the curves
of junction upon the heads, and the angles which they form with the
curves of intrados. Cutting of the stones in these different
constructions. Broken helicoidal _appareil_, for very long skew arches.

Helicoidal _trompes_ at the angles of straight arches; _voussures_ or
widenings, which it is necessary to substitute near the heads at the
intrados of an arch with a considerable skew; case where the skew is not
the same for the two heads. Orthogonal trajectories of the converging
sections of a cylinder.

LESSONS 23-25. _Conical Intrados--Intrados of Revolution._

Skew _trompe_ in the angle. Suggestions on the general problem of
conical skew vaulted roofs.

Spherical domes, &c.

LESSONS 26-27. _Intrados, a Ruled Surface._

Winding staircases, &c., &c.

LESSON 28. _Helicodial Intrados._

Staircase on the Saint-Giles screw.

LESSONS 29-31. _Composite Vaulted Roofs._

Various descriptions of vaults.

Suggestions on vaulted roofs with polygonal edges and with ogival edges.

LESSON 32. _Revision._

Spirit and method of stereotomy.

Degree of exactness necessary. Approximate solutions. Case where it is
proper to employ calculation in aid of graphical constructions.

Review and comparison of different _appareils_.



The pupils execute during the two years of study:--

1. Various drawings or plans of models in relief representing the
essential and internal organs of machines, such as articulations of
connecting rods, winch-handles and fly-wheels, grease-boxes, eccentrics
worked by cams or circles giving motion to rods; the play of slides,
&c.; cylinders of steam-engines, condenser, pistons, and various
suckers; Archimedes’ screw, and other parts of machines.

The sketches of the plan drawings are traced by hand and figured. The
drawings in their finished state are washed and colored according to the
table of conventional tints; they all carry a scale suitably divided.

2. A drawing of wheel-work by the method of development, and tracing the
curves of teeth by arcs of circles from which they are developed. This
drawing represents, of the natural size, or on any other scale of size
considered suitable to show the nature of the partial actions only, a
small number of teeth either in development or projection; the entire
wheel-work is represented by the usual method of projection, where in
drawings on a small scale the teeth are replaced by truncated pyramids
with a trapezoidal base.

3. Finally, numerical exercises concerning the loss of work due to the
proejudicial resistances in various machines, the gauging of holes,
orifices, &c.

Models in relief or drawings on a large scale, of the machines or
elements of the machines mentioned in the course, assist in explaining
the lessons. They are brought back, as often as found necessary, under
the eyes of the students. When possible, lithographic sketches of the
machines, or the elements of the machines, which ought to enter into the
course, are distributed among the pupils.

The pupils, divided into sections, pay their first visit to the engine
factories towards the end of their first year of study; they make one or
more additional visits at the end of the second year.




Object of kinematics, under the geometrical and experimental point of
view. Its principal divisions.

Re-statement of the notions relative to the motion of a point, its
geometrical representation, and more especially the determination of its

_Simultaneous Velocities of a Point and the Increments of its

Ratio of the elementary displacement and the velocity of a point to the
displacement, and velocity of its projection upon a straight line or
plane. Use of infinitesimals to determine these ratios.
Example:--Oscillatory motion of the projection upon a fixed axis of a
point moving uniformly upon the circumference of a circle.

Analogous considerations for polar co-ordinates. Relations of the
velocity of a point, of its velocity of revolution and its angular
velocity about a fixed pole; of its velocity in the direction of the
radius vector; of the velocity of increase of the area which this radius

_Simple Motions of Solids, or Rigid Systems._

1. Motion of rectilinear or curvilinear translation; simultaneous
displacements, and velocities of its different points.

2. Motion of rotation about a fixed axis; relation of the velocities of
different points to the angular velocity.

Geometrical notions and theorems relative to the _instantaneous center_
of rotation of a body of invariable figure and movable in one plane, or
to the _instantaneous axis_ of rotation of a rigid system situated in
space, and movable parallel to a fixed plane. Relation of the velocities
of different points to their common angular velocity. Use of the
instantaneous center of rotation for tracing tangents; examples--and
amongst others--that of the plane curve described by a point in a
straight line of given length, whose extremities slide upon two fixed
lines. Rolling of a curve upon another fixed curve in a plane.
Descartes’ theorems upon the intersection of the normals at the
successive points of contact: cycloids, epicycloids, involutes, and
evolutes. Extension of the preceding motions to the instantaneous axis
of rotation of a rigid system movable about a fixed point.


LESSONS 3-6. _Composition of the Velocities of a Point._

Polygon of velocities. Example of movements observed relatively to the
earth. Particular cases; composition of velocities taken along three
axes; composition of the velocity of a point round a fixed pole, and its
velocity along the radius vector. Method of Roberval for tracing

_Composition of the Simple Motions of a Solid System._

Composition of any number of translatory displacements of a solid.
Composition of two rotations about two intersecting axes. Composition of
any number of rotations about axes cutting one another at the same
point; parallelopiped and polygon of rotations. Composition of two
simultaneous rotations about parallel axes; case where the rotations are
equal and of opposite kinds. Decomposition of a rotation about an axis
into an equal rotation about any axis whatever parallel to the first,
and a translation perpendicular to the direction of this axis. Direct
and geometrical decomposition of the most general motions of a body into
a rotation about, and a translation along, an axis called the
_instantaneous axis_. Composition of any two motions whatever. Every
movement of an invariable system is at each instant of time decomposable
into three movements of rotation, and three movements of translation
with respect to three axes, which are neither parallel nor lying in the
same plane, but otherwise arbitrarily chosen.

_Relative or Apparent Motions._

Relative motion of two points whose absolute motions are given
graphically _à priori_. Trajectory of the relative motions, relative
velocities, and displacements upon curves or upon the direction of the
mutual distance of the two points; use of the parallelogram to determine
its amount. Relative motion of a point in motion in respect of a body
turning about a fixed axis; relative motion of two bodies which turn
about parallel or converging axes, and in general of two rigid bodies or
systems impelled by any motions whatever. How this problem is
immediately reduced to that of the composition of given motions.

The most general continued motion of an invariable figure in a plane is
an _epicycloidal_ motion, in which the instantaneous center describes a
curve fixed in relation to absolute space, and traces relatively to the
proposed figure a movable curve, which is rigidly connected with that
figure and draws it along with it in its motion of rolling upon the
other fixed curve. Case of space or spherical figures.


LESSONS 7-9. _Accelerated Rectilinear Motion._

Re-statement of the motions acquired relatively to the acceleration in
the variable rectilinear motion of a point. Brief indication of the
solution of six problems arising out of the investigation of the laws of
the motion in terms of the space, time, velocity, and accelerating
force. For the most part these solutions may be brought to depend on
exact or approximate quadratures. Numerical exercises.

_Accelerated Curvilinear Motions._

Re-statement of the notions acquired relative to the composition of
accelerating forces; the resulting acceleration, the normal and
tangential acceleration animating a point in motion on a curve. The
total acceleration of a point upon an axis or plane is the projection
upon this axis or plane of the acceleration of the moving body in space.
In uniform curvilinear motion the total or resultant acceleration
becomes normal to the curve. Particular case of the circle; value of the
normal acceleration in terms of the velocity of revolution or the
angular velocity of the radius vector. Case of any curve whatever;
geometrical expression of the total or resultant acceleration.

_Accelerated Compound and Relative Motions._

Geometrical investigation of the simple and compound accelerations
arising out of the hypothesis in which the motion of any system of
points whatever is referred to another system of invariable form, but
also in motion. Geometrical and elementary explanations of the results
obtained by means of the transformation of co-ordinates.

_Examples or Exercises chosen from among the following Questions:_--

Projection of circular and uniform motion upon a fixed straight line or
plane; motion of a circle which rolls uniformly on a straight line;
comparison of the motions of the planets relatively to each other,
treating them as circular and uniform: comparison of the accelerating
force on the moon with that of bodies which fall to the earth.


LESSONS 10-19.

Succinct notions on the classification of elementary motions and organs
for transmission of motion in machines after Monge and Hachette, Lanz
and Bétancourt.

The most essential details upon this subject are set forth in the
following order, and made clear by outline drawings previously
distributed among the pupils.

_Organs fitted to regulate the direction of the circular or rectilinear
motion of certain pieces_.

Axle; trunnions, gudgeons; pivots and bearings; couplings of axes;
adjustment of wheels and of their arms. Joints with hinges, &c.; sheaves
and pulleys; chains, ropes, and straps; means of securing them to the
necks. Grooves and tongue-pieces. Eyelet-holes sliding along rectilinear
or curvilinear rods. Advantages and disadvantages of these different
systems of guides under the point of view of accuracy.

Rapid indication of some of their applications to drawbridges and to the
movable frames or wagons of saw-works and railways.

_Transmission at a Distance of Rectilinear Motion in a determinate
Direction and Ratio._

Inclined plane or wedge guiding a vertical rod. Wedge applied to
presses. Rods, winch-handles, &c. Disposition of drums or pulleys in the
same plane or in different planes; geometrical problem on this subject.
Fixed and movable pulleys. Blocks to pulleys. Simple and differential
wheel and axle moved by cords. Transmission through a liquid. Ratios of
velocities in these different organs.

_Direct Transformation of circular progressive motion into progressive
and intermittent rectilinear motion._

Rod conducted between guides: 1º, by the simple contact of a wheel; 2º,
by cross-straps or chains; 3º, by a projecting cam; 4º, by means of a
helicoidal groove set upon the cylindrical axis of the wheel. To-and-fro
movement, and heart-shaped or continuous cam, waves, and eccentrics.
Simple screw and nut. Left and right handed screws; differential screw
of Prony, called the micrometric screw. Ratio of the velocities in these
different organs.

The example of the cam and pile-driver will be particularly insisted
upon; 1º, in the case where this cam and the extremity of the rod have
any continuous form given by a simple geometrical drawing; 2º, in the
case where this form is defined geometrically by the condition, that the
velocity is to be transmitted in an invariable ratio, as takes place for
cams in the form of epicycloids or involutes of circles.

_Transformation of a circular progressive motion into another similar to
the first._

1º, by contact of cylinders or cones, the two axes being situated in the
same plane; 2º, by straps, cords, or endless chains, the axes being in
the same situation; 3º, by cams, teeth, and grooves, at very slight
intervals; 4º, by the Dutch or universal joint. Case, where the axes are
not situated in the same plane; use of an intermediate axis with beveled
wheels or a train of pulleys; idea of White or Hooke’s joint in its
improved form. Endless screw specially employed in the case of two axes
at right angles to one another. Combinations or groupings of wheels.
Idea of differential wheels. Relations of velocities in the most
important of these systems of transmission.

_Transformation of circular progressive Motion into rectilinear or
alternating circular motion._

Ordinary circular eccentric. Eccentrics with closed waves or cams.
Examples and graphical exercises in the class-rooms relative to the
alternate action of the traveling frames of saw-mills, of the slides or
entrance valves of steam-engines. Cams for working hammers and bellows.

_Transformation of alternating circular motion into alternating
rectilinear motion, or into intermittent and progressive circular

Pump rods with or without circular sectors, &c. Examples taken from
large exhausting pumps, fire-engines, and common pumps. Suggestions as
to the best arrangement of the parts. Lagarousse’s lever, &c.
Application of the principle relative to the instantaneous center of
rotation to give the relations of the velocities in certain simple

_Transformation of alternating circular or rectilinear motions into
progressive circular motion._

The knife-grinder’s treadle. System of great machines worked with
connecting rods, fly-wheel, &c. Watt’s parallelogram, and the simplest
modifications of it for steamboats, for instance. The most favorable
proportions for avoiding the deviation of piston-rods. Simplification of
parts in the modern steam-engines of Maudsley, Cavé, &c. Variable ratios
of the velocities.

_Of organs for effecting a sudden change of motion._

Suspendors or moderators, &c. Dead wheels and pulleys, &c. Mechanisms
for stretching cords or straps, and make them change pulleys during the
motion. Brakes to windmills, carriages, &c., &c. Case where the axes are
rendered movable. Means for changing the directions and velocity of the
motions. Coupled and alternate pulleys; alternate cones; castors moving
by friction and rotation upon a plate or turning-cone; eccentric and
orrery wheels. Means of changing the motion suddenly and by intervals;
wheels with a detent pile-drivers; Dobo’s escapement for diminishing the
shock, &c.

_Geometrical Drawing of Wheel-work._

General condition which the teeth of toothed wheels must satisfy.
Consequence resulting from this for the determination of the form of the
teeth of one of two wheels, when the form of the teeth of the other
wheel is given.

_Cylindrical action of toothed wheels_ or toothed wheels with parallel
axes. External engagement of the teeth; internal engagement. Particular
systems of toothed wheels; lantern wheels, flange wheels, involutes of
circles. Reciprocity of action; case where the action can not be
rendered reciprocal. Pothook action. Details as to the form and
dimensions given in practice to the teeth and the spaces which separate

_Conical action of toothed wheels_, or toothed wheels with converging
axes. Practical approximate method of reducing the construction of a
conical to that of a cylindrical engagement of toothed wheels.

_Means of observation and apparatus proper for discovering
experimentally the law of any given movement._

Simple methods practiced by Galileo and Coulomb in their experiments
relative to the inclined plane and the motion of bodies sliding down it.
Various means of observing and discovering the law of the translatory
and rotatory motion of a body according as the motion is slow or rapid.
Determination of the angular velocity, &c. The counter in machines.
Apparatus of Mattei and Grobert for assigning the initial velocity of
projectiles (musket balls.) Colonel Beaufoy’s pendulum apparatus.
Chronometrical apparatus for continuous indications by means of a
pencil. Eytelwein’s apparatus with bands, and its simplest
modifications. Apparatus with cylinders or revolving disks. Use of the
tuning-fork for measuring with precision very small fractions of time.

(The principal sorts of the apparatus above described are made to act
under the eyes of the pupils.)



_Résumé of the notions acquired upon the subject of forces, and their
effects on material points._

Principle of inertia, notion of force, of its direction, of its
intensity. Principle of the equality of action and reaction. What is
meant by the force of inertia? Principle of the independence and
composition of the effects of forces. Forces proportional to the
acceleration which they produce on the same body. Composition of forces.
Relation between the accelerating force, the pressure, and the mass.
Definition of the work done by a force. The work done by the resultant
is equal to the sum of the works done by the components. Moment of a
force in relation to an axis deduced from the consideration of the work
of the force applied to a point turning about a fixed line. The moment
of the resultant of several forces applied to a point is equal to the
sum of the moments of the components. Corresponding propositions of

LESSONS 22-25.

_Succinct Notions upon the Constitution of Solid Bodies._

Every body or system of bodies may be regarded as a combination of
material points isolated or at a distance, subject to equal and opposite
mutual actions. Interior and exterior forces. Example of two molecules
subject to their reciprocal actions alternately, attractive and
repulsive, when the forces applied draw them out of their position of
natural equilibrium. Different degrees of natural solidity, stability,
or elasticity; they can only be appreciated by experience.

_Equilibrium of any Systems whatever of Material Points._

General theorem of the virtual work of forces applied to any system
whatever of material points. It is applicable to every finite portion of
the system, provided regard be had to the actions exercised by the
molecules exterior to the part under consideration. Determination of the
sum of the virtual works of the equal and reciprocal actions of two
material points. Demonstration of the six general equations of
equilibrium of any system whatever. They comprise implicitly _every_
equation deduced from a virtual movement compatible with the
pre-supposed solidification of the system.

Theorem on the virtual work in the case of systems where one supposes
ideal connections, such as the invariability of the distance of certain
points of the system from one another, and the condition that certain of
them are to remain upon curves either fixed or moving without friction.

_Equilibrium of Solid Bodies._

The six general equations of equilibrium are sufficient as conditions of
the equilibrium of a solid body. Theory of moments and couples.


LESSONS 26-29. _Equilibrium of Heavy Systems._

Recapitulation of some indispensable notions for the experimental
determination of the center of gravity of solids when the law of their
densities is unknown. Re-statement of the theorem relative to the work
done by gravity upon a system of bodies connected or otherwise. In
machines supposed without friction submitted, with the exception of
their supports, to the action of gravity alone, the positions of stable
or unstable equilibrium correspond to the highest or lowest points of
the curve which would be described by the center of gravity of the
system when made to move. Influence of defect of centering in its
wheels, upon the equilibrium of a machine. Case where the center of
gravity always remaining at the same height the equilibrium is neutral.
Examples relative to the most simple drawbridges, &c.

_Equilibrium of Jointed Systems._

Equilibrium of the funicular polygon deduced from direct geometrical
considerations: Varignon’s theorem giving the law of the tensions by
another polygon whose sides are parallel and proportional to the forces
acting upon the vertices of the funicular polygon. Case of suspension
bridges; investigation of the curve which defines the boundary of the
suspension chain; tensions at the extremities.

Equilibrium of systems of jointed rigid bodies without friction.
Determination of the pressure upon the supports and the mutual actions
at the joints.

_Equilibrium and stability of solid bodies submitted to the action of
stretching or compressing forces._

Permanent resistance and limiting resistance of prisms to longitudinal
extension and compression. Equilibrium and stability of a heavy solid
placed upon a horizontal plane and submitted to the action of forces
which tend to overset it. Resultant pressure and mean pressure;
hypothetical distribution of the elements of the pressure on the base of
support. Conditions of stability, regard being had to the limit of
resistance of solid materials, co-efficient of stability deduced from


LESSONS 30-39. _General Notions._

Principle of work in the motion of a material point. Extension of this
principle to the case of any material system whatever in motion.
Considerations relative to mechanical work in various operations, such
as the lifting of weights, sawing, planing, &c. It is the true measure
of the productive activity of forces in industrial works. It may always
be calculated either rigorously or approximately when the mathematical
or experimental law which connects the force with the spaces described
is given. Uniform work, periodical work, mean work, for the unit of
time. Horse-power unit. Examples and various exercises, such as the
calculation of the work corresponding to the elasticity of gases on the
hypothesis of Mariotte’s law, the elongation of a metallic prism, &c.

_Dynamometrical Apparatus._

Dynamometer of traction by a band or rotating disc or register.
Dynamometer of rotation with simple spring, with band or register.
Dynamometer of rotation with multiple springs and with register for the
axles of powerful machines. Improved indicator of Watt.

(These pieces of apparatus are made to act under the eyes of the

_Work of Animal Prime Movers upon Machines._

Results of experience as to the values of the daily work which animal
motors can supply under different circumstances without exceeding the
fatigue which sleep and nourishment are capable of repairing.

_Theory of the Transmission of Work in Machines._

Principal resistance. Secondary resistances. Two manners in which bodies
perform the duty of motors. Ratio of work done to work expended always
inferior to unity. Different parts of machines; receiver; organs of
transmission; tools as machines.

_Calculation of the Work due to the passive resistances in machines._

_Résumé_ of the notions previously acquired on friction. Application to
the inclined plane, to the printing-press, to guides or grooves, to the
screw with a square thread; different cases of uniform motion being
impossible under the action of forces of given directions. Friction of
trunnions, pivots, eccentrics, and insertions of winch-handles. Prony’s
dynamometrical brake; conditions of its application. Resistance to
rolling; its laws according to experiment. Use of rollers and
friction-wheels; their practical inconveniences.

Mixed friction of toothed wheels; the Dobo escapement: friction of the
teeth in the endless screw.

Stiffness and friction of cords. Results of experience. Friction of
cords and straps running round drums. Different applications; brakes;
transmission by cords, endless straps, or chains.

Examples and exercises; effects of passive resistances in the capstan,
the crane, pulleys, &c.

LESSON 40. _Revision._



LESSONS 1-2. _Completion of the Notions acquired on this Subject._

Differential equations of the motion of a material point submitted to
the continued action of one or more forces. The acceleration of the
projection of a point upon any axis or plane is due to the projection of
the forces on this axis or plane. The acceleration along the trajectory
is due to the tangential force. Relation of the curvature to the
centripetal force. Introduction of the force of inertia into the
preceding enunciations.

The increase of the quantity of motion projected upon an axis or taken
along the trajectory is equal to the impulsion of the projected
resultant, or to that of the tangential force. The total impulsion of a
force is got by methods of calculation and of experiment analogous to
those which relate to _work_. The increase of the moment of the quantity
of motion in relation to any axis is equal to the total moment of the
impulsions of the forces during the same interval of time; direct
geometrical demonstration of this theorem. In decomposing the velocity
of the moving body into a velocity in the plane passing through the axis
of the moments, and a velocity of revolution perpendicular to this
plane, we may replace the moment of the quantity of motion in space by
the quantity of motion of revolution. Particular case known under the
name of the principle of areas.

Extension of the preceding theorems to the case of relative motions.
Apparent forces which must be combined with the real ones that the
relative motion of a point may be assimilated to an absolute motion.
Particular case of relative equilibrium. Influence of the motion of the
earth upon the accelerating force of gravity.



_Principle or general rule_ which reduces questions in dynamics to
questions in equilibrium by the addition of the forces of inertia to the
forces which really act on the system. Equation of virtual work which
expresses this equilibrium; it comprises in general the external and
internal forces.

_General Theorems._

These theorems, four in number, are founded upon the principle of the
equality of action and reaction applied to internal forces. They may be
deduced from the preceding rule, but the three last are obtained more
simply by extending to a system of material points analogous theorems
established for isolated material points.

General theorem of the motion of the center of gravity of a system.
Particular case called _principle of the conservation of the motion of
the center of gravity_.

General theorem on the quantities of motion and impulsions of exterior
forces projected on any axis.

General theorems of moments of quantities of motion and impulsions of
exterior forces, projected on any axis whatever.

General theorems of the moments of quantities of motion and impulsions
of exterior forces about any axis. Analogy of these two theorems with
the equations of the equilibrium of a solid, in which the forces are
replaced by impulsions and quantities of motion.

Composition of impulsions, of quantities of motion, or the areas which
represent them. All the equations which can be obtained by the
application of the two theorems relative to quantities of motion and
impulsions, reduce themselves to six distinct equations. Particular case
called _principle of the conservation of areas_. Fixed plane of the
resulting moment of the quantities of motion called _plane of maximum

General theorem of work and _vis viva_. Part which appertains to the
interior forces in this theorem. Particular case called principle of the
conservation of _vires vivæ_, where the sum of the elements of work done
by the exterior and interior forces is the differential of a function of
the co-ordinates of different points of the system. Application of the
theorem of work to the stability of the equilibrium of heavy systems.

Extension of the preceding theorems to the case of relative motions.
Particular case of relative equilibrium. Motion of any material system
relative to axes always passing through the center of gravity, and
moving parallel to themselves. Invariable plane of Laplace. Relation
between the absolute _vis viva_ of a material system, and that which
would be due to its motion, referred to the system of movable axes above

_Examples and Applications._

The following examples, amongst others, to be taken as applications or
subjects of exercises relative to the general principles which precede.

Walking. Recoil of guns. Eolypile. Flight of rockets.

Pressure of fluid veins, resistance of mediums, &c. Direct collision of
bodies more or less hard, elastic, or penetrable. Exchange of quantities
of motion. Loss of _vis viva_ under different hypotheses. Influence of
vibrations and permanent molecular displacements.

Pile driving; advantage of large rammers. Comparison of effects of the
shocks and of simple pressures due to the weight of the construction.
Oblique collision, and ricochet. Data furnished by experiment.

Oscillations of a vertical elastic prism suspended to a fixed point, and
loaded with a weight, neglecting the inertia, and the weight of the
material parts of this prism. Case of a sudden blow. What is meant by
the “_resistance vive_” of a prism to rupture? Results of experiments.

Work developed by powder upon projectiles, estimated according to the
_vis viva_ which it impresses on them, as well as upon the gun and the
gases upon hypothesis of a mean velocity.


LESSONS 9-12. _Simple Rotation of an invariable Solid about its Axis._

In applying to this case the first general rule of dynamics, the theorem
of the moments of the quantities of motion, and the theorem of work, we
are led to the notion of the moment of inertia; explanation of the
origin of this name. The angular acceleration is equal to the sum of the
moments of the exterior forces divided by the moment of inertia about
the axis of rotation. Sum of the moments of the quantities of motion
relative to this axis. _Vis viva_ of a solid simply turning about an
axis. What is meant by _radius of gyration_?

_Remind_ of the geometrical properties of moments of inertia, of the
ellipsoid which represents them, of the principal axes at any point, of
those which are referred to the center of gravity.

Pressure which a rotating body exercises on its supports. Reduction of
the centrifugal and tangential forces of inertia to a force which is the
force of inertia of the entire mass accumulated at the center of
gravity, and a couple.

Particular case where the forces of inertia have a single resultant;
different examples. Center of percussion. Compound pendulum; length of
the corresponding simple pendulum. Center of oscillation; reciprocity of
the centers or axes of suspension and oscillation. Pressure upon the
axis. Influence of the medium; experience proves that the resistance,
varying with the velocity, changes the extent of the oscillations, but
does not sensibly affect the time. Experimental determination of the
center of oscillation and the moment of inertia about an axis.

_Motion of an invariable Solid subject to certain Forces._

General notions on this subject. Motion of the center of gravity; motion
of rotation about this point.

LESSONS 13-19. _Various Applications._

Motion of a homogeneous sphere or cylinder rolling upon an inclined
plane, taking friction into account.

Motion of a pulley with its axis horizontal, solicited by two weights
suspended vertically to a thread or fine string passing round the neck
of the pulley, the axle of which rests upon movable wheels. Atwood’s
machine serving to demonstrate the laws of the communication of motion.

Motion of a horizontal wheel and axle acted on by a weight suspended
vertically to a cord rolled round the axle, or upon a drum with the same
axis, and presenting an eccentric mass. To take account of the variable
friction of the bearings, and the stiffness of the cord, with recourse,
if necessary, to approximation by quadratures. Oscillations of the
torsion balance.

Balistic pendulum. Condition that there may be no shock on the axis.
Experimental determination of the direction in which the percussion
should take place.

Theory of Huyghen’s conical pendulum considered as a regulator of
machinery. How to take account of the inertia and friction of the
jointed rods, as well as of the force necessary to move the regulating
lever, &c.; appreciation of the degree of sensibility of the ball
apparatus with a given uniform velocity.

Windlass with fly-wheel. Dynamical properties of the fly-wheel. Reduced
formulæ for a crank with single or double action. Advantages and
disadvantages of eccentric masses. Tendency of the tangential forces of
inertia to break the arms. Numerical examples and computations.

Mutual action of rotating bodies connected by straps or toothed wheels
in varying motion.

The wedge and punching-press. Stamping screw or lever used in coining,
cams, lifting a pile or a hammer. To take account of the friction during
the blow, and afterwards to estimate the loss of _vis viva_ in cases
which admit of it.


LESSONS 20-22.

Principle of the equality of pressure in all directions. Propagation of
the pressures from the surface to the interior of a fluid, and upon the
sides of the vessel. Equations of equilibrium for any set of forces.
Pressure exerted in the containing orifices. Measure of the pressure
upon a plain portion of surface inclined or vertical (sluice-gate,
embankments, &c.) Center of push or pressure. Pressure against the
surfaces of a cylindrical tube. Effect, and resistance to oppose to the
pressure. Manometer and piezometer. Equilibrium of a body plunged in a
heavy fluid or floating at its surface. Stability of floating bodies.
Metacenter. Laws of the pressure in the different atmospheric strata.


LESSONS 23-27. _Flow of Fluids through small Orifices._

Study of the phenomena which accompany this flow in the case of a thin
envelop and a liquid kept at a constant level. Conditions of this
constancy in the level, and the permanence of the motion in general.
Motion of the lines of fluid; form; contraction; reversal and
discontinuity of liquid veins. Fundamental formulæ for liquids and gases
based upon the principle of _vis viva_, and Bernoulli’s hypothesis of
parallel sections or Borda’s of contiguous threads. Torricelli’s theorem
relative to small orifices. What is called the theoretical expenditure,
effective expenditure, and co-efficient of geometrical contraction.
Co-efficient deduced from the effective expenditure. Its variations with
the volume of the fluid contents, and the form of the inner surfaces of
the reservoir. Results of the experiments of Michelotti, Borda, Bossut,
&c. Phenomenon of adjutages. Venturi’s experiments; influence of
atmospheric pressure; loss of _vis viva_; reduction of the velocity and
augmentation of the expenditure. Results of experience relative to the
co-efficient of expenditure, the form and range of the parabolic jets,
showing the initial _vis viva_, and the loss of _vis viva_.

_Large orifices._--Sluice holes and floodgates; reservoirs or open
orifices; expenditure; practical formulæ and results of experiment.
Influence of the proximity of the sides and the walls. Arrangement to
avoid the effects of contraction or the losses of _vis viva_.

_Flow through conducting Pipes and Open Canals._

Practical formulæ relative to the case of uniform sections of great
length. Measure of the pressures at different points of a conduit-pipe.
Expression for the losses of effect due to corners and obstructions.
Flow of gases. Principal methods of measuring the volume consumed
adopted in practice. Floats. Pitot’s tube. Woltman’s mill. Register mill
in air or gas. Waste in such instruments. Modulus and scale for


LESSON 28. _General Considerations. Résumé of the Notions acquired on
this Subject._

Equation of _vis viva_, and transmission of work in machines, account
being taken of the different causes of power and resistance. Physical
constitution of machines; _receiver_, _communicators_, and _operator_.
Influence of the weights, of frictions, of shocks, and any changes in
the _vis viva_. Parts with continuous or uniform motion, with
alternating or oscillating motion. Laws of the motion on starting from
rest, and when the stationary condition is established. The positions to
which the maximum and minimum of the _vis viva_ correspond are those in
which there is equilibrium between all the forces, exclusive of the
forces of inertia. Advantage of uniform or periodic motion. General
methods for regulating the motion; symmetrical distribution of the
masses and strains; flys and various regulators. Brakes and moderators;
their inconveniences. Object and real advantages of machines.

LESSONS 27-35. _Hydraulic Wheels._

Vertical wheels with float-boards, with curved ladles, and with spouts.
Figure of the surface of the fluid in these latter. Horizontal wheels
working by float-boards, buckets, and reaction. Turbines. Description,
play, and useful effects compared according to the results of
experiment. Vertical wheels of windmills and steamboats. Screw


Description. Result of Coulomb’s observations.

_On the principal kinds of Pumps._

Special organs of pumps. Valves and pistons, force pump, sucking pump;
limit to the rise of the water. Sucking and force pump. Dynamical
effects. Indication as to the losses of _vis viva_ and the waste in
different pumps. Explanation of the hydraulic ram. Air vessel. Fire
pumps. Double action pumps.

_Various Hydraulic Machines._

Hydraulic press. Water engine. Exhausting machines; _norias_; under and
overshot wheels; Archimedes’ screw, construction and experimental data.

LESSONS 36-39. _Steam Engines._

Succinct description of the principal kinds of steam-engine with or
without detent. Effects and advantages of the detent. Condenser. Air
Pump. Furnace and feeding-pump.

Variable detent. Formulæ and experimental results.

LESSONS 40-42. _Revision._

Reflections on the totality of the subjects of the course.



LESSONS 1-5. _Preliminary Notions._

Definitions of physics. Phenomena. Physical laws. Experiments are
designed to make them spring out of the phenomena. Method of induction.
Physical theories; different character of the experimental and
mathematical methods.

_General Properties of Bodies._

Extension. Measure of lengths. Vernier. Cathetometer. Micrometer screw.
Spherometer. Dividing engine.

Divisibility. Porosity. Ideas generally received on the molecular
constitution of bodies. These conceptions, which are purely
hypothetical, must not be confounded with physical laws. Elasticity.
Mobility. Inertia. Forces; their equilibrium, their effects, their
numerical estimation.

_Weight or Gravity._

Direction of gravity. Plumb-line. Relation between the direction of
gravity and the surface of still water.

Weight. Center of gravity.

Experimental study of the motion produced by weight. In vacuum, all
bodies fall with the same velocity. Disturbing influence of the air.
Inclined plane of Galileo. Atwood’s machine. To prove by experiment; 1º
the law of the spaces described; 2º the law of velocities. Morin’s
self-registering apparatus with revolving cylinder.

Law of the independence of the effect produced by a force upon a body,
and the motion anteriorily acquired by this body. Law of the
independence of the effects of forces which act simultaneously upon the
same body. Experimental demonstration and generalization of these laws.
Law of the equality of action and reaction.

Mass. Acceleration. For equal masses the forces are as the accelerations
which they produce. Relation between the force, mass, and acceleration.

General laws of uniformly accelerated motion. Formulæ.

Pendulum. Law of the isochronism of small oscillations and law of the
lengths deduced from observation.

Method of coincidences or beats. Use of the pendulum as the measure of
time. Simple pendulum; formulæ. Compound pendulum: the laws of the
oscillations of a compound pendulum are the same as the laws of the
oscillations of a simple pendulum whose length may be calculated.

Determination by means of the pendulum of the acceleration produced by
gravity. This acceleration is independent of the nature of the body.

Remark that the formulæ for the motion of oscillation apply to the
comparison of forces of any kind, that may be regarded as constant and
parallel to themselves in all positions of the oscillating body.

Identity of gravity and universal attraction.

Measure of weights. Balance. Conditions to be attended to in making it.
Absolute sensibility; proportional sensibility. Method of double
weighing. Details of the precautions necessary in order to obtain an
exact weight.

_Different States of Bodies. Hydrostatics._

Solids. Cohesion. Transmission of external pressures.

Elasticity. The true laws of elasticity are unknown. Empirical laws in
certain simple cases, and for a very small action. Elasticity of
compression, extension, torsion. Experimental determination of the
co-efficients of elasticity. Limits of elasticity. Limits of tenacity.

Ductility. Temper. Cold hammering. Annealing.

Liquids. Fluidity. Viscosity. Physical laws which form the basis of
hydrostatics:--1º the transmission of external pressures is equal in all
directions; 2º the pressure exercised in the interior of a liquid upon
an element of a surface is normal to that element, and independent
(as to amount) of its direction. These principles are demonstrated by
the experimental verification of the consequences drawn from them.

Application to heavy liquids. Free surface, and surface _de niveau_.
Pressure upon the parts of the containing vessel, and upon the bottom in
particular; hydrostatic paradox; verificatory experiments. Haldat’s
apparatus. Hydrostatic press.

Application to immersed or floating bodies (principle of Archimedes;)
verificatory experiments. (In treating of the equilibrium of floating
bodies, the conditions of stability are not gone into.)

Superposed liquids.

Communicating vessels. Water level. Spirit level; its use in

Densities of solids and liquids. Anemometers.

Compressibility of liquids. Piezometer. Correction due to the
compressibility of the solid envelop.

Gas. Expansibility. Other properties common to liquids and gases.
Principle of the equal transmission of pressures in all directions.
Weight of gases. Pressure due to weight (principle of Archimedes.)
Weight of body in air and in vacuum. Aerostation.

Superposed liquids and gases.

Communicating vessels. Barometer.

Detailed construction of barometer. Barometers of Fortin, Gay-Lussac,
Bunten. Indication of the corrections necessary.

Mariotte’s law. Regnault’s experiments.

Manometer with atmospheric air--with compressed air. Bourdon’s

Law of the mixture of gases.

Air pump. Condensing pump.

_Primary Notions of Hydrodynamics._

Toricelli’s principle. Mariotte’s vessel and syphon. Uniform flow of
liquids. The same of gases.

_Molecular Phenomena._

Cohesion of liquids. Adhesion of liquids to solids. Capillary phenomena.
Apparent attractions and repulsions of floating bodies.

Adhesion of drops.

Molecular actions intervene as disturbing forces in the phenomena of the
equilibrium and motion of liquids.



LESSONS 6-9. _Generalities._

General effects. Arbitrary choice of one of these effects to define the
thermometric condition of a body. Conventional adoption of a
thermometer. Definition of temperature.

_Dilating Effects._

Definition of the co-efficients of linear, superficial, and cubic
dilatation. Approximate relation between the numerical values of these
three co-efficients. The value of the co-efficient of dilatation depends
upon the thermometric substance and the temperature selected as the zero
point. It becomes nearly independent of the zero point when the
co-efficient is very small.

Relation between volume, density, and temperature. Linear dilatation of
solid bodies. Ramsden’s instrument. Cubical dilatation of liquids.
Dulong and Petit’s experiments on mercury. Discussion. Regnault’s

Cubical dilatation of solids and of other liquids when that of mercury
is given.

Relations between the volume, density, and elasticity of a gas, and its

Cubical dilatation of gases. Experiments of Gay-Lussac, Rudberg, and M.
Regnault. Advantage of varying the methods of experimenting in these
delicate researches.

Methods based upon the changes of volume under a constant pressure, and
upon the changes of pressure for a constant volume.

The disagreement of these two methods is due to deviations from the law
of Mariotte.

The constancy of the co-efficients of dilatation previously defined is
only approximately true.

Necessity of employing two different co-efficients of dilatation
according as consideration is being had to the variations of volume to a
given pressure, or of pressure to a given volume.

Empirical formulæ for the dilatation of liquids.

Graphical constructions.

LESSON 10. _Thermometers._

Construction of thermometers. Mercurial thermometer. Details of
construction. Fixed points. Different scales; their relation. Arbitrary
scales. Change which takes place in the zero point. Different
precautions to be observed in using the mercurial thermometer.

General want of comparability of mercurial thermometers with tubes of
different material.

Air thermometers. They are comparable with one another within the limits
of the errors of experiment, whatever the nature of the tube employed.
This property entitles the air thermometer to a preference for all
accurate measures. Comparison of the air and mercurial thermometers.


LESSONS 11-13. _Changes of State produced by Heat._

Exposition of the phenomena which accompany the liquefaction of solids
and the solidification of liquids. Constancy of the temperature whilst
the phenomenon is going on.

Sudden melting and freezing. Persistance of the liquid state beneath the
melting point.

Influence of pressure.

Exposition of the phenomena which accompany the conversion of liquids or
solids into vapor, and the inverse passage from the gaseous to the
liquid or solid state. Constancy of the temperatures whilst the
phenomenon is going on.

Influence of pressure.

Phenomena of ebullition in free space. Augmentation of the temperature
and pressure in a confined space. Papin’s digester.

Properties of vapors in spaces and in gases. Saturated vapors. Their
tension does not depend upon the space which they occupy, but only upon
their temperature.

Effects of a diminution or increase of pressure without change of
temperature; the same without change of pressure. Effects of lowering
the temperature in a limited region of space occupied by vapor.

Tension of a saturated vapor at the boiling point of its liquid.

Measure of the tensions of the vapor of water. Experiments of Dalton,
Gay-Lussac, Dulong, and Arago, and of M. Regnault.

Tables of the tensions of steam. Empirical formulæ. Graphical

It is assumed that non-saturated vapors are subject to the same laws as


LESSONS 14-16. _Various Applications of the Laws previously

A phenomenon can not always be separated from the accessory phenomena
which concur with it in producing the final result. Necessity of
corrections to render complex results comparable _inter se_.

Density of solids when regard is had to the temperature and weight of
the gases displaced by them.

Precautions to be attended to in the experiments. Empirical formulæ for
the density of liquids. Maximum density of water. The temperature
corresponding to the maximum must be determined graphically, or by

Corrections for measures of capacity, for barometric measures.

The uncertainty of the corrections can not, in any considerable degree,
affect the densities of solids and liquids.

Density of gases. Biot and Arago’s experiments. Special difficulties of
the question. The uncertainty of the corrections may sensibly affect the
results. Regnault’s method.

The same method may be applied to the determination of the co-efficient
of dilatation for gases.

Density of vapors. Definition founded on the hypothetical application of
the same laws to gases and vapors. Formulæ. Experimental method of
Gay-Lussac and of Dumas. Corrections. Comparison of the two methods.
Necessity of conducting the experiments at a distance from the
saturation point. Latour’s experiments. Relations between the weight and
volume of a gas, and its temperatures; between the weight and volume of
a gas mixed with vapors, and its temperature. Various problems.

Hygrometry. Chemical hygrometry. Hygrometry by the dew-point.


LESSONS 17-18. _Propagation at a Distance._

Rapid propagation of heat at a distance, in vacuum, in gases, in certain
liquid or solid mediums. Experiments which establish this.

Rays of heat. Velocity of propagation. Intensity of heat received at a
distance. Intensity of heat received or emitted obliquely. Emitting
power, power of absorption, reflection, diffusion. The emitting and
absorbing power are expressible by the same number in terms of their
proper units respectively.

Analysis of calorific radiations by absorption. Different effects of
deathermanous or thermochroic medium. Different influences of increasing
thicknesses of the combination of different mediums. Radiations
proceeding from different sources, various effects of different mediums
on these radiations.

The calorific radiations emanating from different sources, have all the
characters of differently colored heterogeneous rays of light.


LESSON 19. _Law of Cooling._

Definition of the rate of cooling. Many causes may conspire in the
cooling of a body.

Cooling in space. Newton’s law only an approximation. Experimental
investigation of the true law. Method to be followed in this
investigation. The velocity of cooling is not a _datum_ directly
observable. It must be deduced provisionally from an empirical relation
between the temperature and the time. Preliminary experiments. Course of
the definitive experiments. Elementary experimental laws.

Hypothetical form of the function which expresses the velocity of
cooling. To determine by means of the preceding experimental laws the
unknown form of the function which expresses the law of radiation.
Relation between the temperatures and the times. This relation only
contains data immediately observable, and may be verified _à

The contents which enter into the preceding relation depend upon
thermometric constants and the nature of the radiating surface.

The contact of a gas modifies the law of cooling.

LESSONS 20-21. _Propagation by Contact._

Slow propagation of heat in the interior of bodies, in solids, liquids,
and gases. Confirmatory experiments. Hypothesis of partial radiation.
Theoretical law resulting from this hypothesis upon the decrease of
temperatures in a solid limited by two indefinite parallel planes
maintained at constant temperatures. Determination of the co-efficient
of conductibility by the experimental realization of these conditions.
This experiment determines a numerical value of the co-efficients; it is
not of a nature to serve as a check upon the theoretical principles.
Enunciation of the law resulting from the same theoretical principles
upon the decrease of temperatures in a thin bar heated at one end.


LESSONS 22-23. _Specific Heats._

Comparison of the quantities of heat. The quantities of heat are not
proportioned to the temperatures. Definitions of the unity of heat.
General method of mixtures to estimate the quantities of heat.
Experimental precautions and corrections.

Application of the general method of mixtures. Specific heats of solids
and liquids. Law of the specific heat of atoms. Heat absorbed by
expansion, restored by the compression of bodies. Experiments on gases.
Specific heats of gases under constant pressure. Measure of specific
heats of gases under constant pressure. Special difficulties of the
question. Succinct indication of one of the methods. Specific heats to a
constant volume.

LESSON 24. _Latent Heat._

Component heat of liquids absorbed into the _latent_ state during
fusion, restored to the _free_ state during solidification.

Influence of the viscous state. Latent heat of ice. Ice calorimeter; its

Component heat of vapors, absorbed into the latent state during
vaporization, restored to the free state during condensation. Measure of
the latent heat of vapors. Regnault’s experiments.

Empirical laws on the latent heat of vaporization.

_Applications of Calorimetry._

Means of producing heat or cold; 1, by changes in density; 2, by changes
of state. Freezing mixtures. Vaporization of liquids. Condensation of

Steam-boilers. Warming by hot air and hot water. Various problems.
Sensations produced by a jet of vapor.

Different physical and chemical sources of heat; percussion, friction,
chemical combinations, animal heat, natural heat of the globe, solar
heat, &c. It will be remarked that mechanical work may become a source
of heat, and heat a source of mechanical work.


LESSONS 25-27.

General phenomena. Distinction of bodies into conductors and
non-conductors. Distinction of electricity into two kinds. Separation of
the two electricities by friction. Hypothesis of electric fluids.
Effects of vacuum of gases and vapors of points. Electrical attractions
and repulsions. Electrization by influence. Case where the influenced
body is already electrized. Sparks; power of points. Electrization by
influence preceding the motion of light bodies.


Electrical machines of Van-Marum, Nairne, Armstrong.

Condenser. Accumulation of electricity upon its surface. Leyden jar.
Batteries. Electrical discharges. Effects of electricity.

Condensing electroscope. Electrophorus.

Velocity of statical electricity.

Atmospherical electricity. Phenomena observed with a serene sky.
Electricity of clouds. Storms. Lightning. Thunder. Effects of thunder.
Return-shock. Lightning conductor.

Different sources of statical electricity.


LESSONS 28-30.

Natural magnets. Action upon iron and steel. Artificial magnets. The
attractive action appears as if it were concentrated about the
extremities of magnetic bars. First idea of poles.

Direction of a magnetized bar under the earth’s action. Reciprocal
action of the poles of two magnets. Names given to the poles.

Phenomena of influence. Action of a magnet upon a bar of soft iron; upon
a bar of steel. Coercive force. Effects of the rupture of a magnetized
bar. Theoretical ideas on the constitution of magnets. More precise
definition of the poles.

Action of the earth upon a magnet. The earth may be considered as a
magnet. Its action may be destroyed by means of a magnet suitably
placed. Astatic needles. The magnetic action of the earth is equivalent
to a _couple_. Three constants define the couple of terrestrial action.
Declination. Inclination. Intensity. Measure of the declination; of the

Magnetic metals. Influence of hammering, tempering, &c. Methods of
magnetizing. Saturation. Loss of magnetism. Influence of heat. Magnetic
lines. Armatures.

Magnetization by the earth’s influence. Means of determining the
magnetic state of a body.

_Measure of Magnetism and Electricity._

LESSONS 31-32.

Coulomb’s balance. Distribution of magnetism on a magnetized bar;
distribution of electricity at the surface of isolated conductors.
Comparative discussion of the conditions of the two problems and the
methods of experiment.

Laws of the magnetic attractions and repulsions. Law of electric
attractions and repulsions. Comparative discussion of the conditions of
the two problems, and the methods of experiment.

Determination of the law of magnetic attractions and repulsions by the
method of oscillations.

Comparison of the magnetic intensity at different points of the earth’s

LESSONS 33-34. _Revision._

Considerations on the totality of the subjects of the course.




Chemical sources of electricity. Experimental proofs. Arrangement
devised by Volta to accumulate, at least in part, at the extremities of
a heterogeneous conductor the electricity developed by chemical actions.

Pile. Tension at the two isolated extremities; at one single isolated
extremity; at the two extremities reunited by a conductor. Continuous
current of electricity. Poles. Direction of the current, &c.

Various modifications of the pile of Volta. Woollaston’s pile, Münch’s
pile, &c. Dry piles; their application to the electroscope.

Principal effects of electricity in motion, and means of making the
currents perceptible. Experiment of Oersted. Galvanoscopes.

Currents produced by heat in heterogeneous circuits. Thermo-electric
piles. Thermometric graduation of thermo-electric piles.

Currents produced by the sources of statical electricity.


LESSON 3.   1. _Chemical Actions._

Definitions. Phenomena of decomposition and transference. Reaction of
the elements transferred upon electrodes of different kinds.

Principles of electrotyping.

Causes of the variation of the current in ordinary piles; means of
remedying this; Daniell’s pile. Bunsen’s pile.

LESSONS 4-8.   2. _Mechanical Properties._

Reciprocal actions of rectilinear or sinuous currents parallel or
inclined. Reaction of a current on itself.

Reciprocal actions of helices or solenoids. Continuous rotation of
currents by their mutual action; by reaction. Analogy of magnets and
solenoids. Electro-dynamical theory of magnetism. Action of magnets upon
currents and solenoids. Action of currents upon magnets. Experiments of
Biot and Savart. Continual rotation of a current by a magnet; of a
magnet by a magnet.

Action of the earth upon currents; it acts as a rectilinear current
directed from east to west, perpendicularly to the magnetic meridian.

Continual rotation of a current by the action of the earth.

Astatic conductors.

LESSONS 9-10.   3. _Magnetic Properties._

Action of an interposed conductor upon iron filings.

Electro-magnets. Magnetization temporary or permanent. Principles of the
electric telegraph. Electrometers. Reference to diamagnetic phenomena.

4. _Electro-motive Properties._

Phenomena of induction by currents, by magnets. Phenomena of magnetism
in motion. Induction of a current upon itself.

Induction of different orders.

Interrupted currents. Clarke’s machine.

LESSON 11.   5. _Calorific Properties._

Influence of the nature of the interposed conductor; of its section; of
the intensity of the current. Unequal temperatures at the different
junctions of a heterogeneous circuit.

6. _Luminous Properties._

Incandescence of solid conductors. Spectrum of the electric light.
Voltaic arc. Transfer of ponderable matter. Action of the magnet upon
the Voltaic arc.

7. _Physiological Action of Currents._

Some words on this subject. Muscles and nerves. Actions of discontinuous
currents. Reotomic contrivances.


Compass of sines, of tangents. Experimental graduation of galvanometers.

The dynamical intensity of a current diminishes when the length of a
current increases. Reostat.

Laws of the dynamical intensity of a current in a homogeneous circuit.
Reduced length and resistance of a circuit. Specific co-efficients of
resistance. Laws of the dynamic intensity of a current in a
heterogeneous circuit.

The intensity of currents is in the inverse ratio of the total reduced
length, and proportional to the sum of the electromotive forces.
Formula of the pile. Discussion of the case of hydro-electric piles--
thermo-electric piles. Conditions for the construction of a pile,
with reference to the effects to be produced. Conditions for the
construction of a galvanometer with reference to its intended

Laws of secondary currents in the simplest cases. The chemical intensity
of a current is proportional to its dynamical intensity.


LESSONS 12-15.

Noise, sound, quality of the sound, pitch, intensity, _timbre_. A state
of vibration in a solid, liquid, or gaseous body is accompanied with the
production of sound.

The pitch depends on the number of vibrations. Unison. Instruments for
counting the vibrations:--1st. Graphic method. 2nd. Toothed wheels. 3rd.
Lever. Feeling of concord. Musical scale. Gamut. Limit of appreciable

Study of vibrating motions in solids. Vibrating cords. Vibrations
transversal, longitudinal. Experimental laws. Sonometer.

Spontaneous division of a cord into segments. Fundamental sounds.
Harmonic sounds.

Straight and curved rods. Transversal and longitudinal vibrations.
Experimental laws. Division into segments. Nodes. Ventral segments.

Plane and curved plates. The vibrations divide them into
“_concamerations_.” Nodal lines. Harmonic sounds.

Study of the vibrations in liquids and in gases.

Theoretical ideas upon the propagation of a vibratory motion in
indefinite elastic media, on an indefinite cylindrical tube. Waves of
condensation of dilatation. Progressive nodes and ventral divisions.
Laws of the intensities of sound. Direct measure of the velocity of the
propagation of sound in water. Measure of the velocity of the
propagation of sound in air. Formulæ without demonstration. Comparison
of the formulæ with experiment.

Sonorous waves reflected in an indefinite medium.

Fixed nodes and ventral divisions. Sonorous waves reflected in closed
and open tubes. Fixed nodes and ventral divisions; the vibratory state
and density thereat.

Series of sounds afforded by the same tube. Effect of holes.

Sonorous reflected waves in rods. Series of sounds afforded by the same
rod vibrating longitudinally. Indirect measure of the velocity of sound
in gases, liquids, and solids.

Experiments on the communication of vibrating motion in heterogeneous
mediums, on the general direction of the vibrating motion communicated.

Intensification of sounds. Interferences. Beats. Different stringed and
wind instruments. Means of setting them in vibration.

A few words on the organs of voice and hearing. Incompleteness of our
knowledge on this subject.


LESSONS 16-17. _Propagation of Light._

Propagation of light in a straight line. Rays of light. Geometrical
theory of shadows. Velocity of light. Rœmer’s observations. Laws of
intensity of light. Photometers of Bouguer, Rumford. Intensity of
oblique rays. Comparison of illuminating powers. Total brightness.
Intrinsic brightness.


Reflection of light: its laws. Experimental demonstration. Images formed
by one or more plane mirrors. To ascertain if a looking-glass has its
two faces parallel.

Spherical mirrors. Foci, formulæ. Discussion. Images by reflection.
Measure of the radius of a spherical mirror.

Definition of caustics by reflection. Definition of the two spherical
aberrations in mirrors.

Woollaston’s goniometer.

LESSON 18. _Refraction._

Refraction of light in homogeneous mediums. Descartes’ law. Experimental
demonstration for solids and liquids.

Inverse return of the rays. Successive refractions. Indices of
transmission in terms of the principal indices. Consequences of
Descartes’ law. Total reflection. Manner of observing it.

Irregular refractions. Mirage.

Refraction is always accompanied with the accessory phenomenon of

Geometrical consequences of the law of refraction. Focus of a plane
surface. Focus of a medium bounded by two parallel plane surfaces; by
two plane surfaces inclined in the form of a prism.

Foci of a spherical surface; of a medium limited by two spherical
surfaces. Lenses.

Formula for lenses. Discussion. Varieties of lenses. Optic center.
Images. Measure of the focal distance of lenses.

Definition of caustics by refraction. Definition of the two spherical
aberrations of a lens.

LESSONS 19-20. _Dispersion._

Unequal refrangibility of the differently colored rays which compose
white light. Analysis of heterogeneous light by the prisms. Newton’s
method. Solar spectrum. Homogeneity of the different colors. Second
refraction of a homogeneous pencil. Experiment with crossed prisms.
Precautions to be attended to in the experiments. The spectrum, obtained
by Newton’s method, differs from the spectrum produced at the focus of a
lens placed between the prism and the picture, according to the method
of Fraunhofer. Reasons of the comparative purity of this latter
spectrum. Fraunhofer’s lines. Different spectra of different sources of
heterogeneous light. Marginal iridescence of a large pencil of natural
light traversing a prism. Dispersion of light by lenses. Iridescence of
focal images. Recomposition of light, by means of a prism at the focus
of a spherical mirror or a lens, by the rapid rotation of a plane
mirror, by the rotation of a disk with party-colored sectors. Compound

Chemical and calorific radiations accompany luminous radiations.

Analysis of light by absorption. Characteristic action of transparent
colored mediums upon different sorts of compound light. Different
influences of increasing thickness. Effects of differently colored
mediums upon heterogeneous light. Effects of differently colored mediums
upon homogeneous rays separated by the prism.

LESSON 21. _Measure of the Indices of Refraction._

Determination of the indices of refraction.

1. In solids. Measure of the refracting angles. Minimum of deviation.
Measure of the corresponding deviation. Use of Fraunhofer’s lines.

2. In liquids.

3. In gases. Special difficulties of the question. Experimental method.
Biot’s and Arago’s experiments.

Any power whatever of the index of refraction diminished by unit is
sensibly proportional to the density of the gas. Method of Dulong
founded on this remark.

LESSONS 22-23. _Application of the preceding Laws._

Rainbow. Different orders of bow.


Achromatic prisms. Diasperometer achromatism of lenses; how to verify
it. Definition of secondary spectra: their nature gives the means of
recognizing, whether flint or crown glass predominates, in an
imperfectly achromatic lens.

Instruments essentially consisting of an achromatic lens. Magic lantern;
megascope; solar microscope; camera obscura; collimators.


Summary description of the principal optical parts of the eye. They act
like the lens of a camera obscura to form an image upon the retina.
Distinct vision; optometers; short sight; long sight; spectacles.

Binocular vision; perspective peculiar to each eye; estimation of
distances; sensation of solidity; stereoscope; estimation of magnitudes.


LESSONS 24-26. _Optical Instruments._

_Camera lucida._ A lens is necessary to reduce to the same apparent
distance the two objects seen simultaneously. Instruments to assist the
sight; simple microscope; the magnifying power; distinctness; field;
advantage of a diaphragm; it modifies the field and the brightness
variously according to its position.

Woollaston’s double glass; its advantages.

General principle of compound dioptrical instruments.

Compound microscope; experimental measure of its magnifying power, by
means of the diaphragm, by means of the camera lucida.

Astronomical telescope; object glass; simple eye-glass. Necessity for a
diaphragm; its place; the wires, their place; optic axis of a telescope.
Parallax of the threads of the wires; magnifying power of the
object-glass; of the eye-glass; field of view of a telescope.

Optic ring; different methods of measuring the magnifying power.

Distinctness of a telescope; night-glass.

Different distances of drawing out the eye-glass for short-sighted and
long-sighted observers.

Different sorts of eye-pieces; positive eye-pieces; ordinary double
eye-piece of the astronomical telescope. Ramsden’s eye-piece; treble
eye-piece of the terrestrial telescope. Negative eye-pieces; simple
eye-piece of Galileo. Compound _ditto_ of Huyghens; advantages and
disadvantages of these different combinations; general principle of
catadioptrical instruments.

LESSONS 27-29. _Double Refraction._

Crystallized mediums do not all act upon light like homogeneous mediums.

Double refraction of Iceland spar: the extraordinary image turns round
the ordinary image. The ordinary and extraordinary rays cross at the
interior of the crystal.

Huyghens’ construction; measure of the ordinary and extraordinary
indices of refraction; attractive and repulsive crystals; a ray falling
perpendicularly does not always bifurcate in a camera with parallel
faces, nor in a prism. Definition of uniaxial and biaxial crystals.

The dispersion of the ordinary ray differs from that of the
extraordinary ray.

The two rays are unequally absorbed in many colored mediums. Tourmaline.

Doubly-refracting prisms; their construction. Use of doubly-refracting
prisms to measure apparent diameters, &c.

LESSONS 30-31. _Polarization._

Successive refractions in doubly-refracting prisms. Special properties
of the two rays emerging from the first doubly refracting crystal.
Polarization by double refraction.

Reflection from transparent media polarizes the light partially or
wholly according to the incidence. Brewster’s law. Reflection of
polarized light from a transparent medium.

Simple refraction partially polarizes the light. Many successive
refractions polarize it almost totally. Piles of glasses.

Different methods to obtain a ray of polarized light, 1st, by
reflection; 2nd, by simple refraction; 3rd, by double refraction, by
eliminating one of the refracted pencils;--by a screen,--by total
reflection, Nicol’s prism, by absoption, tourmaline.

Distinctive characters of light completely or partially polarized.

LESSONS 32-34. _Theory of Undulations._

Hypothesis of luminous undulations.

Vibratory state of a simple ray of homogeneous light. Vibratory state at
the intersection of two simple rays of homogeneous light intersecting at
a very small angle.

Experimental proofs in support of this hypothesis:

1st. Experiment with interferences, fringes. Their breadth is different
for different colors; they give the various colors of the prism in white
light. The alternately bright and dark sheets are hyperboloids of
revolution. The measure of the fringes give the means of estimating the
lengths of the undulations corresponding to different colors.

2nd. Colored rings of Newton, observed by reflection, by refraction. Law
of the diameters; these vary in absolute length for different colors.
Variously colored rings with white light. Reflected rings with a white
spot at the center.

The theory of the undulations does not apply merely to theses phenomena.
Explication of the laws of reflection and refraction. Definition of
polarization in the system of waves. Elementary application of double
refraction and the polarization which accompanies it in uniaxial
crystals when the face of the crystal is parallel to the axis, and the
plane of incidence normal or parallel to this axis.

_Chemical and Calorific Radiations._

Chemical and calorific radiations are subject, like luminous radiations,
to the laws of reflection, refraction, dispersion, double refraction,
polarization, interferences.

LESSONS 35-36. _Revision._

Considerations on the totality of the subjects of the course.


The practical exercises which constitute the subject of this programme
will be performed in part by the pupils under the direction of the
professors and _répétiteurs_, in part by the professors and
_répétiteurs_, with the coöperation of the pupils.


Use of various instruments, designed for measuring lengths. Experiments
on weight with Atwood’s machine, the inclined plane, Morin’s apparatus,
and the pendulum.

Some experiments on elasticity.

Various verifications of the principles of hydrostatics and

Construction of aerometers.

Construction of a barometer, of a manometer. Various verifications of
the law of Mariotte.

Various experiments with the air-pump.

Determination the density of solids or liquids by different methods.

Construction of a thermometer.

Experiments on the dilatation of liquids and solids by means of the
ordinary thermometer and by means of the statical thermometer.

Experiments upon the dilatation of air by various methods.

Experiments upon the tension of vapors by different methods.

Determination of the density of vapors and gases by various methods.

Leading experiments on calorific radiation.

Experiments on cooling.

Determination of specific heats, heats of fusion, heats at which bodies
pass into vapor.

Cooling mixtures.

Use of the chemical hygrometer, the wet bulb hygrometer.

Rehearsal of the leading experiments on magnetism.

To magnetize a needle, to reverse its poles.

Rehearsal of the principal experiments of statical electricity.

Experiments verificatory of the laws of electricity and magnetism.

Use of compasses.


Experiments upon the chemical actions of poles.

Leading experiments in electro-dynamics.

Leading experiments upon the magnetic properties of currents.

Experiments on induction.

Experiments on the calorific and luminous actions of currents.

Quantitative experiments on the laws of currents.

Experiments on the propagation of sound; on the vibrations of rods of
plane or curved plates, membranes, sonorous tubes.

Experiments on mirrors, plane or curved.

Experiments on lenses. Experiments on the decomposition of light by the
prism--by absorption. Measures of the indices of the refraction of
solids. Use of the magnifying glass and microscope; measure of the
magnifying power. Use of different telescopes, with and without
corrections. Measure of the magnifying power. Experiments on double
refraction and polarization. Experiments on interferences and colored


The organization of the school, which is fixed by a Decree dated Nov.
30th, 1863, is of a military character. There is a staff of military
officers in addition to, and quite separate from, the staff employed in
the duties of instruction. The pupils wear uniform, which, however, is
more civil than military in appearance. They are formed into four
companies which together constitute a battalion; and, although they are
not actually subject to the penal code of the army, the discipline
maintained and the punishments inflicted are entirety military in

The military establishment remains exactly as it was in 1856, and
consists of:

The Commandant, a General Officer, usually of the Artillery or the
Engineers, at present a General of Artillery.

A Second Commandant, a colonel or lieutenant-colonel, chosen from among
the former pupils of the school; at present a colonel of Engineers.

Three captains of Artillery and three captains of Engineers, as
inspectors of studies, chosen also from former pupils of the school.

Six adjutants (_adjudants_), non-commissioned officers, usually such as
have been recommended for promotion.

Slight changes have been made in the civil establishment; it now
consists of:--

1. A Director of Studies, at present a colonel of Engineers.

2. Seventeen professors,[12] (two additional professors for history)
seventeen _Répétiteurs_ and assistant _Répétiteurs_, and five drawing
masters. Of the 17 professors, two are at present officers of Engineers,
and one an officer of Artillery; the remainder are civilians, of whom
three are members of the Academy of Sciences.

    [Footnote 12: In 1856 there were only 15 professors; there are now
    two additional professors for history, the study of which has been
    recently introduced at the school.]

3. Five examiners for admission, and five for conducting the
examinations at the school. All of these at present are civilians.

4. An administrative staff consisting of a treasurer, librarian, &c.;
and a medical staff.

The general control or supervision of the school is vested, under the
War Department, in four great boards or councils, viz.:--

1. A Board of Administration, composed of the Commandant, the Second
Commandant, the Director of Studies, two professors, two captains of the
military staff, and two members of the administrative staff. This board
has the superintendence of all the financial business, and all the
minutiæ of the internal administration of the school.

2. A Board of Discipline, consisting of the Second Commandant, the
Director of Studies, three captains of the Military Staff, and one major
of the army, selected from former pupils of the school.[13] The duty of
this board is to decide upon cases of misconduct.

    [Footnote 13: Formerly two professors of the school were also
    members of the Council of Discipline, but the professors have now
    no voice in matters of discipline.]

3. A Board of Instruction, whose members are, the Commandant, the Second
Commandant, the Director of Studies, the Examiners of Students, the
Professors, and two captains of the Military Staff; and whose chief duty
is to make recommendations relating to ameliorations in the studies and
the programmes of admission and of instruction in the school to--

4. A Board of Improvement (_Conseil de Perfectionnement_), charged with
the general control of the studies, and formed of:--

  The Commandant, president,
  The Second Commandant,
  The Director of Studies,
  Two delegates from the Naval Department,
  Two delegates from the Department of Public Works,
  One delegate from the Home or Finance Department,
  Three delegates from the War Department,
  Two members of the Academy of Sciences,
  Two examiners of students,
  Three professors of the school.

The delegates from the public departments are appointed by the
respective ministers; the members of the Academy, the examiners, and the
professors are selected by the Minister of War. The real management of
the school, so far as the course of instruction is concerned, is in the
hands of the _Conseil de Perfectionnement_; it will be seen that of the
18 members composing it more than half are entirely independent of the
school, and are men of eminence in the various public services for which
the instruction at the Polytechnic is preparatory. One of the chief
duties of the Council is to see that the studies form a good preparation
for those of the more special schools (_Ecoles d’ Application_) for the
civil and military services; and the eminent character of its members
gives great weight to the recommendations they make to the Minister of

The annual expenses of the school, as extracted from the Budget for
1869, are as follows:--

  Pay of staff, professors, &c.,                                 331,850
  Instruction, maintenance, examination of candidates,
      clothing, books, &c.,                                      321,073
  Outfits for 30 new pupils at 600 francs each          18,000
  Allowances (_premières mises_) to 25
      exhibitioners on admission to the military
      services at 750 fr. each                          18,750
                                                        ------    36,750
  Maintenance and repair of buildings,                            30,000
  Total sum charged in the schools estimate,                     719,673
  Add regimental pay of 28 officers and non-commissioned
      officers employed at the school,                            85,515
  Total expenditure                                              805,188
  Deduct repayments from pupils,                                 237,000
  Cost to the State,                                             568,188

  Or about 22,720_l._

The chief changes that have been made in regard to the course of
instruction since 1856, may be summarized as follows:

1. The more elementary portions of chemistry and physics which are
required in the entrance examination, but which were formerly repeated
at the school, have been omitted. The course of instruction in these
subjects is now confined to the more advanced portions which do not
enter into the entrance examination.

2. The mathematical courses have in some points been slightly curtailed,
and the number of lectures in French literature and German have been
diminished. By the modifications thus made in the programmes, it has
been found possible to shorten the whole course of study and to increase
the length of the vacations.

3. The subject of “Military Art,” which formerly entered into the final
examination is no longer taken into consideration in determining the
order of merit of the pupils. In this respect the course of instruction
may be said to have even less of a military character than formerly.
Topographical drawing is the single military subject which has any
influence on the final classification of the pupils, and this only to a
very slight extent.

4. History has been introduced as a subject of instruction. This change
was made in 1862. The course comprises general history, both ancient and
modern, but more especially the history of France in modern times. The
introduction of this subject appears to have arisen partly from a
feeling that an acquaintance with history was a necessary element of a
liberal education, and partly from a wish to meet, to some extent, an
objection often made to the Polytechnic course of instruction, that it
was too deficient in studies of a literary character. History, however,
like military art, is evidently still regarded as a subject of only
secondary importance and has no influence on the final classification.

5. A diminution has been made in the number of examinations during the
course, by the suppression of one of the half-yearly examinations by the
professors (_interrogations générales_, as distinct from the
_interrogations particulières_) in each year. Further reference will be
made to this point when speaking of the examinations at the school.

6. The importance of written exercises in determining the respective
merits of the pupils has been decreased, apparently from the difficulty
of establishing a security that such compositions were the unaided work
of the individual.

The following table shows the present course of instruction during the
two years, and the alterations which have been made in the number of
lectures in each subject since 1856:--

  _Subject._--_First Year’s Course._       _Lectures in_--1868. 1856.

  Analysis {Differential calculus,                          25    28
           {Integral calculus,                              18    20
  Descriptive geometry and geometrical drawing,             32    38
  Mechanics and machinery,                                  40    40
  Physics, comprising heat and electricity,                 30    34
  Chemistry:--The metals,                                   30    38
  Astronomy and geodesy,                                    30    35
  French composition and literature,                        25    30
  History,                                                  25     0*
  German,                                                   25    30
  Figure and landscape drawing,                             48    50

   _Second Year’s Course._

  Analysis:--Integral calculus,                             32    32
  Stereotomy:--Geometrical drawing of constructions
      in timber and masonry,                                28    32
  Mechanics:--Dynamics, hydrostatics, and machinery,        40    42
  Physics:--Acoustics, optics, and heat,                    30    36
  Chemistry:--Continuation of the metals and organic
      chemistry,                                            30    38
  Architecture and buildings, construction of roads,
      canals, and railways,                                 40    40
  French composition and literature,                        25    30
  History,                                                  25     0*
  German,                                                   25    30
  Military art,                                             20    20
  Topography,                                                2    10
  Figure and landscape drawing,                             48    48

  [* Introduced in 1862.]

In connection with several of the courses, such as descriptive geometry,
stereotomy, machinery, and architecture, much drawing is done by the
pupils; hand sketches are taken of the diagrams shown in the
lecture-room, and finished drawings are afterwards executed in the
_salles d’étude_. In addition to this, 30 attendances of two or three
hours each, distributed over the two years, are especially devoted to
drawing more elaborate plans and elevations of architectural
constructions and machinery. The practical applications of the
theoretical instruction are limited to manipulations in the laboratory
in connection with the course of lectures on chemistry and physics.
Towards the close of the second year the pupils are also taken to visit
some of the large manufacturing establishments in Paris, in order to
gain a practical acquaintance with machinery.

All the subjects taught at the school are obligatory, but history and
military art, as already stated, have no influence in determining the
order of merit of the pupils in the final result.

The only instruction in practical military exercises, which is
compulsory upon all, is that in drill. The pupils are exercised under
arms in company drill, and are also occasionally drilled as a battalion;
but very little importance is attached to this point--the only really
military portion of their training. Drill goes on only for about three
months in each year during the spring and summer, and even during this
brief period only takes place about twice a week. By the regulations of
the school the pupils should be exercised in musketry practice, but
although they are armed with the Chassepot rifle this regulation is
never carried out. Instruction is given in fencing and gymnastics, but
attendance at both is voluntary, and scarcely more than half the pupils
take advantage of it. Neither riding nor swimming are taught at the

The school year commences about the 1st of November, and terminates
about the first of August. Some seven months of the year are given up to
lectures and the ordinary routine of study; about two months are
occupied with the annual examinations and private preparation for them;
the remaining three months--August, September, and October--are the
vacation. In addition to this long vacation, from eight to twelve days
are allowed after the periodical examination, which takes place near the
end of February, at the close of the first portion of each year’s study.

One peculiarity in the arrangements of the school is that the subjects
of each year’s course are not all studied simultaneously. The lectures
in the main subjects of instruction--those which, as a rule, present the
most difficulty--are divided into courses which continue only during a
certain portion of each year. Thus in the junior division, analysis and
descriptive geometry are the mathematical subjects studied during the
first three months, or three months and a half. The course in them is
then concluded; an examination by the professors (_interrogation
générale_) is held in these subjects, and they are laid aside for the
remainder of the year, though they enter into the examination at the
close of the year. Their place is then taken by a course of lectures in
mechanics and geodesy. Similarly in the second year, analysis and
mechanics are the subjects of the first course of lectures, at the
termination of which there is an examination; and for the remainder of
the year no further lectures in them are given, stereotomy and military
art taking their place.

The subjects involving as a rule less difficulty--such as history,
French literature, German, and drawing--are spread over the whole year,
forming generally the evenings’ occupation.




The first French Artillery School was founded in the time of Louis XIV.
(in 1679) at Douai. It had but a short existence: and it was only in
1720 (under the Regency,) when the Royal Regiment of Artillery received
a new organization, that schools of theory were permanently founded in
each of the seven towns where there were garrisons of artillery. But no
academy properly so called was established before that founded by
D’Argenson at La Fère, in 1756, with a staff of two professors of
mathematics, and two of drawing. This was transferred to Bapaume, near
the Flemish frontier, in 1766, re-transferred to La Fère, and
suppressed, among other schools, at the beginning of the Revolution.

Of early Engineer Schools there was only one, the very distinguished
School of Mézières, near the northern frontier. This was founded in
1749, also under the ministry of D’Argenson; Monge was a professor
there; and it had a very high reputation down to its suppression in the

When the wars of the Revolution broke out, Provisional Schools for
giving a brief course of rapid instruction was established at Metz for
the engineers, and at Chalons-sur-Marne for the artillery. These had to
supply, at a great disadvantage, the officers needed for the protection
of the invaded frontier.

It was intended originally that the Polytechnic, established in 1794,
should send engineers direct to the army; but it was quickly found to be
a better plan to allow the pupils destined for this service first to
spend some little time at Metz; which thus, in October, 1795, became a
School of Application for Engineers. The artillery pupils in like manner
went to Châlons. This separate system of two Schools of Application
continued till 1802, when the establishment at Châlons was united with
that of Metz, and Metz became what it has since continued to be, the
seat of the United School of Application for the two services. The
Polytechnic students who select the _Artillerie de terre_, _Artillerie
de mer_, or the _Génie militaire_, enter here to receive the special and
professional instruction deemed requisite to fit them for actual

The students quitting the Polytechnic in the manner described in the
account of that school, at the average age of twenty-one, enter the
School of Application, with the provisional rank, the uniform, and the
pay of sub-lieutenants (_sous-lieutenants_.) The ordinary term of
residence is two years. Under special circumstances this may be
shortened; and in case of illness or want of application individual
students are occasionally retained for a third year. Each new body of
students, each _admission_ or _promotion_, is classified at the end of
the first year, and the students composing it are arranged in order of
merit in accordance with the reports of the professors, but without an
examination; at the close of the second year they pass a final
examination before the Board of Officers, and are definitively placed in
the corps they have chosen, the artillery or engineers, according to the
order of merit. They are allowed to count, as regards retirement from
the service and towards military decorations, four year’s service on
account of the two years passed at the Polytechnic School, and of the
time passed in preparing for admission to it, reckoning from the day of
their admission to the School of Application.

Metz is a fortified place on the Prussian frontier, the seat of war at
the time of the school’s first foundation; it is on the line of railway
to Mannheim, about thirty miles from the point where this branch
diverges from the main line to Strasburg. The Moselle flows through the
town, and is employed, with its little affluent the Seille, in the
military defenses. The garrison numbers 10,000 men; there is an Arsenal,
a school of Pyrotechny for the manufacture of rockets, two Regimental
Schools, one of Artillery and the other of Engineers. The School of
Application occupies buildings erected on the site, and partly the
original buildings themselves, of a suppressed Benedictine monastery.
Three sides of the cloistered monastic quadrangle are devoted to the
offices, lecture-rooms, galleries and halls of study. A fourth, formerly
the ancient church, is converted into a _salle des manœuvres_. There is
an adjoining residence for the commandant; and a separate modern
building, four stories in height, affords lodging to the young men.

The _salle des manœuvres_ is a large area under a lofty roof, rising to
the whole height of the buildings of the quadrangle; it contains
artillery of various descriptions, mortars, field and siege guns placed
as in a battery, and is amply large enough to allow cannon to be moved
and exercises performed when the state of the weather may make it

The amphitheaters or lecture rooms, much on the same system as those at
the Polytechnic, are two in number, one for each of the two divisions.
Officers of the artillery and engineers who are in garrison, are
entitled, if they please, to attend the lectures, and other officers
also may be admitted by permission.

The galleries, partly on the ground floor, partly on the first floor,
contain very good collections of models of artillery, ancient and
modern, of sets of small arms, of tools, of locks, barrels and other
portions of muskets in various stages of the process of their
manufacture, of specimens of carpentry and roofing, of minerals, of
models of fortifications, bridges, coffer-dams, locks, &c.

The library on the first floor has an adjoining reading room; and near
it is the examination room, of which further mention will be made. The
three halls of study (_salles d’étude_) on the first floor are on a
different plan from those of the Polytechnic, each one being large
enough to accommodate a whole division (seventy students.) Three rooms
are also provided for the professors to prepare their lectures in.

The barracks, on the opposite side of the open space used for drill and
exercises, form a lofty and handsome building, entered by separate
staircases, the ground-floor rooms of each being assigned to a servant,
who undertakes to provide attendance for all the young men lodging in
the rooms above. The rooms are comfortable, mostly double-bedded, the
bedroom serving also as a sitting room, and a small adjoining closet
being used for washing, &c. Twenty or twenty-two appear to be thus
accommodated on each staircase; there are lodgings altogether for one
hundred and forty-five. A certain number of the senior sub-lieutenants
would, probably, on the arrival of the new cadets from the Polytechnic,
be removed to lodge in the town.

There is a riding-school adjoining the court; stables, for thirty-three
horses, which are kept for the use of the pupils, and lodgings for the
attendants are provided in the neighborhood.

The mere description of the buildings shows at once that the system is
different in many respects from that of the Polytechnic. Young men of
twenty-one and twenty-two years of age, already holding provisional
commissions in the service, receiving the pay and wearing the uniform of
sub-lieutenants, are naturally allowed much greater freedom of action.
They live, and partly also study, not in the halls of study, but in
their own rooms; they take their meals in the town, where they frequent
the _cafés_ and _restaurants_ of their choice. The _rappel_ summons them
every morning to rise and attend a roll-call at half-past five or six;
military exercises, riding, or interrogations, similar to the
_interrogations particulières_, require the presence of a portion of the
number, but the rest are free to return to their rooms. At ten they have
to attend either the day’s lecture, followed by employment in the halls
of study, till four o’clock P.M., or they proceed at once to the halls
of study, and set to work on the drawings, designs, projects, &c., which
are described hereafter in the account of the studies. From four to
half-past five P.M.; drill, exercises, and riding occupy a portion of
the number, probably those who were not called for in the morning. After
half-past five they are left to themselves.

This ordinary routine of studies is interrupted in the summer months by
the occurrence of expeditions for making surveys, and for measuring and
sketching machines in manufactories. The young men are sent, two
together, to survey (_lever à boussole_;) singly for the reconnaissance
sketch _(lever à vue _;) and generally, a certain number are distributed
about a district not too large for an officer to make his round in it,
and see each day that all are at work. The railways afford considerable
facilities; the expeditions never occupy more than ten days at a time,
but they may be extended as far as Strasburg.

There are no _répétiteurs_ in the school; but the system of
_interrogations particulières_ is carried on; and an examination by the
professor and an assistant professor takes place after, about, every
eight or ten lectures.


The Staff of the Institution consists of--

  1 General Officer, at present a General of Brigade of Artillery,
      as Commandant.
  1 Colonel or Lieutenant-Colonel, Second in Command and Director
      of Studies, at present a Lieutenant-Colonel of Engineers.
  1 Major of Artillery.
  1 Major of Engineers.
  5 Captains of Artillery.
  8 Captains of Engineers.
  1 Surgeon (_Médecin-Major_.)

The Commandant is taken alternately from the Artillery and Engineers,
and the command lasts for five years only.

The Second in Command is always chosen from that arm of the service
which does not supply the Commandant.

The inferior officers of each rank are taken in equal numbers from the
two arms.

The Staff of Instructors is as follows:--

  1 Professor of Artillery, at present a Captain of Artillery.
  1 Assistant     ditto     also a Captain of Artillery.
  1 Professor of Military Art, charged also with the Course
      of Military Legislation and Administration
      (a Captain of Engineers.)
  1 Professor of Permanent Fortification and of the Attack
      and Defense of places (a Captain of Engineers.)
  1 Assistant    ditto     ditto  (a Captain of Engineers.)
  1 Professor of the Course of Topography and Geodesy
     (a Captain of Engineers.)
  1 Professor of Sciences applied to the Military Arts.
  1 Professor of Mechanics applied to Machines (a Captain of Artillery.)
  1 Professor of the Course of Construction (a Captain of Engineers.)
  1 Assistant            ditto.
  1 Professor of the German language (a civilian.)
  1 Professor of Veterinary Art and Riding (a Captain of Artillery.)
  1 Assistant      ditto  (a civilian.)
  1 Drawing Master, Chief of the Drawing Department (a civilian.)

In all, nine Professors, four Assistant Professors, and one Drawing

The School employs in addition an administrative staff, consisting of--

  A Treasurer, } both of whom must have been Officers in the
  A Librarian, }   Artillery or Engineers.
  A Principal Clerk.
  An Assistant Librarian.
  Two Storekeepers, intrusted with the _materiel_ belonging to
    the two arms.
  One skilled Mechanic.
  One skilled Lithographer.
  One Fencing Master.

Clerks and draughtsmen are provided as required.

The school is under the general superintendence of two hoards or
councils, the Superior Council and the Administrative Council.

The Superior Council consists of the General Commandant, as President,
the Second in Command, the Director of Studies, as Vice-President; the
Major of Artillery, and the Major of Engineers, as permanent members;
two Captains of the Establishment, one of each arm; two Military
Professors, one of each arm; and one Captain of the Establishment; these
five last being all removable at the General Inspections.

The Superior Council has the duty of drawing up the programme of the
studies of the year, of suggesting changes in the regulations relating
both to studies and discipline, all subject to the approval of the
Minister of War; of preparing at the end of the year the classified list
of the students, drawn up according to their conduct and progress in
their studies, and of pointing out to the Jury of Examiners any students
who should go again through the courses of the year, and stay in
consequence an additional year at the school.

When questions relating to the instruction are brought before the
Superior Council, the whole body of military professors attend and take
part in the proceedings, and the Council is thus said to be constituted
as a Board or Council of Instruction. Improvements are here suggested,
and are subsequently submitted to the Jury of Examiners, and to the
Minister of War; the value to be attached, in the system of marks or
credits, to each particular course of study is determined; a statement
is drawn up showing what printed works, models, &c., are wanted. The
budget itself, to be submitted to the Minister of War, is finally drawn
up by the Superior Council in its ordinary sittings.

The Administrative Council, composed of the Second in Command as
President, the two Majors of Artillery and of Engineers, one Captain and
one Military Professor, and the Treasurer as Secretary without the right
of voting, takes cognizance of all the financial and other business
matters of the school.


The studies at Metz consist of topography and geodesy, including
military drawing and surveying under special circumstances; field
fortification, military art and legislation, permanent fortification,
and the attack and defense of fortified places, accompanied by a sham
siege, without, however, executing the details practically on the
ground; architecture, as applicable to military buildings and
fortifications; the theory and practice of construction, and artillery.
The programmes of these studies are inserted at length in the Appendix.

The instruction is given principally (as at the Polytechnic) by means of
a series of lectures, and the knowledge which the students have acquired
is first directly tested by requiring them to execute various kinds of
surveys of ground, either with or without the use of instruments; to
prepare drawings of buildings, workshops, and machines in full detail
(plan, elevation, and sections) from the measurements they have recorded
in their note-books or on their sketches, and to accompany such drawings
with descriptive memoirs of all particulars and calculations that may be
necessary to exhibit their purpose or efficiency; to draw up projects
and lay out works of field and permanent fortification, or of those of
attack or defense of a particular place on certain given data, or
according to the nature of the ground; to design a military building,
bridge, machine, or piece of ordnance, accompanied by estimates and
descriptive memoirs, showing in what manner the instructions and
conditions under which it was drawn up have been complied with; and to
prepare a project for the amelioration of the works of defense of a
specified portion of a fortified place known to be defective in some

The instruction during the first year’s residence is common to the two
arms; and the time is appropriated in the following manner, namely:--

  Military art and legislation,             33
  Topography and geodesy,                   47
  Field fortification,                      39
  Permanent fortification,                  88
  Theory and practice of construction,      77
                                Total,     284

The _sous-lieutenants_ who complete their first year’s work are allowed
nearly a month’s vacation during November.

The instruction given to the Artillery and Engineers during the second
year’s residence is not entirely the same, as will be seen by comparing
the accompanying table of the year’s study:--

                                      Artillery. Engineers.
                                        Days.       Days.
  Military art and legislation,           2           2
  Topography and geodesy,                28          28
  Attack and defense of places,          44          44
  Permanent fortification,               44         129
  Artillery, machines, &c.,              81          --
  Theory and practice of construction,   46          42
                                        ---         ---
                                        245         245
  Brought forward from first year,      284         284
                                        ---         ---
  Total,                                529         529

We should not omit to state that there is a short course on the
Veterinary Art.

The lectures, as before said, begin at 10 A.M., and they last usually an
hour and a half, and are followed by work in the halls of study. It
would appear, however, that very frequently the day’s occupation
consists simply of work in the halls of study (or occasionally out of
the school buildings, when the students are sent on some excursion;)
and, accordingly, in giving the account of the studies, a _day_ or day’s
work will sometimes mean a lecture followed by drawing or other
employment, sometimes this drawing or other employment without any
lecture preceding. Taking a general average, the proportion appears to
be about two lectures to five _séances_, _i.e._, sittings without

The system will be better understood by referring to the accompanying
tables, which are translated from the Project for the Employment of Time
for the year 1851-2, submitted for the approval of the Minister of War.
The dates in the first column indicate the days of the commencement of
each particular study. The school year, it should be said, begins on the
1st of December.


  Att Attendances.
  LbW Lectures before Work.
  TL  Total of Lectures.

  Month and  |  Second Division.                        |  Number of
    Date.    |                                          +----+----+----
             |  First Year’s Instruction.               | Att| LbW| TL
  December 1 | Lectures on Military Art in              |    |    |
      “    2 |   Topography--Conventional Tints,        |  2 |....|....
      “    4 | Study of Hill Drawing                    |    |    |
             |   (in sepia with contour lines,)         |  2 |....|....
             |              { Plate 1 .. 5}             |    |    |
             |              { Plate 2 .. 5}             |    |    |
      “    6 | Military Art,{ Plate 3 .. 5}             |    |    |
             |              { Plate 4 .. 5}             |    |    |
             |              { Plate 5 .. 9}             | 29 |  4 | 39
  January 12 | Front of Cormontaige                     | 24 |  3 | 13
             |                                          |    |    |
  February 9 | Project of Field Fortification,          |    |    |
             |   { Plate 1. Plan of the whole,       3} |    |    |
             |   { Plate 2. Organization of a work,  8} |    |    |
             |   { Plate 3. Details of Construction, 4} |    |    |
             |   { Memoir                            4} | 19 |  5 |  7
  March    3 | Plan of Stability of Revetments, &c.,    |  9 |  9 |  9
    “     13 | Study of the Drawing showing the effect, |  8 |  1 |  1
    “     23 | Plan of a Building,                      |    |    |
             |   { Out-of-door work,                 9} |    |    |
             |   { Laying down and drawing, Memoir, 23} | 32 |....|....
  April   29 | Topographical Triangulation,             |  4 |  4 |  6
  May      5 | Defilement and Profiling on the Ground,  |  3 |....|....
             | Project of a Building,                   |    |    |
             |   { Sketches,         14}                |    |    |
             |   { Drawing,          24}                |    |    |
             |   { Memoir,            4}                |    |    |
             |   { Estimate,          3}                | 45 | 12 | 22
  June    28 | Survey with a plane-table,               |    |    |
             |   { Out-of-door work   0}                |    |    |
             |   { Laying down and drawing, 3}          | 13 |  1 |....
             | One day free in case of bad weather,     |  1 |....|....
  July    14 | To find the Variation of the Needle,     |  1 |  1 |....
   “      17 | Survey of Ground with the Compass,       |    |    |
             |   { Out-of-door work,        8}          |    |    |
             |   { Laying down and drawing, 2}          | 10 |  1 |....
             | One day free in case of bad weather,     |  1 |....|....
  August   2 | Reconnaissance Plan--Out-of-door work,   |  6 |  1 |....
             | One day free in case of bad weather,     |  1 |....|....
    “     10 | Study of Shaded Drawing                  |    |    |
                 (_Hachures_ and colored.)              |  8 |  1 |....
    “     18 | Laying down and drawing the Survey       |    |    |
                 made with the Compass,                 |  2 |....|....
             | Project of Fortification on Level Ground,|    |    |
             |   { Plate 1  6}                          |    |    |
    “     20 |   { Plate 2 30}                          |    |    |
             |   { Memoir,  6}                          | 42 |  3 | 19
  September  |                                          |    |    |
  October  8 | Project of Fortification on Hilly Ground,|    |    |
             |   { Plate 1        19}                   |    |    |
             |   { Memoir,         3}                   | 22 |  8 | 10
  Nov.     3 | Last day of week,                        |    |    |
    “      6 | Leave for their Vacation,                |    |    |
  There remains therefore in this division:--1st. Three free days in
  case of bad weather; one after each survey. 2nd. Two days at the end
  of the year, the 4th and 5th November. Total five free day.
  Total of the days employed 279 + 5 days free,         |284 |    |


  Month and  |  First Division.                         |  Number of
    Date.    |                                          +----+----+----
             |  Second Year’s Instruction.              | Att| LbW| TL
             |             Brought forward,             |284 |....|....
  December 6 | Laying down the First Survey             |    |    |
             |   by Reconnaissance,                     |  8 |....|....
      “   16 | Attack and Defense:--Plate,              |    |    |
             |   Batteries, with Plan and               |    |    |
             |   Sections of Detail,                    |  4 |  5 |  6
             | Ditto, { Plate 1,  25 }                  |    |    |
      “   20 |        { Journal,   2 }                  |    |    |
             |        { Plate 2   13 }                  | 40 |  6 | 20
  January    |                                          |    |    |
  February 7 | Designs and Constructions of             |    |    |
             |   Revetments, Arches, &c.,               |  9 |  9 |  9
      “   18 | Project and Permanent Fortification      |    |    |
             |   in Hilly Ground, { Plate 1  19 }       |    |    |
             |                    { Memoir,   3 }       |    |    |
             |                    { Plate 2   8 }       | 30 |  8 | 19
             |                                          |    |    |
             | SPECIAL WORKS:                           |    |    |
             | Artillery.                               |    |    |
             |     Engineers.                           |    |    |
             |                                          |    |    |
  March   25 | Measurement and Drawings                 |    |    |
             | of a Cannon,                          12 | 12 |....|....
             |     Project of  Fortification in         |    |    |
             |     hilly ground, Plate 2 _cont._,    12 |    |    |
  April    8 | Measurement of a Workshop,               |    |    |
             |     Out-of-door Work,                    |  9 | 30 | 30
    “     19 | Laying down the Measurement,          28 |    |    |
             |     Laying down the Measurement,      24 |    |    |
  May     18 |     Project of Fortification in hilly    |    |    |
             |       ground, Plate 3,                14 |    |    |
      “   24 | Project for  Machines,                14 |    |    |
  June     4 |     Abstracting and calculating          |    |    |
             |       Measurements,                    3 |    |    |
      “    8 |     Plate 4,                          11 |    |    |
      “    9 | Questions in Artillery,                5 |    |    |
             | 1st. Measurement of  _Matériel_,         |    |    |
             | Gun Carriages, &c.,                    8 |    |    |
             |     Register of the removal of Earth,  3 |    |    |
             | Laying down ditto,                    10 |    |    |
             |     Estimate,                          2 |    |    |
             |     Memoir,                            2 |    |    |
             |     Project for Improvements,            |    |    |
             |       {Plate 1,                       30 |    |    |
             |       {Plate 2,                        6 |    |    |
             |       {Memoir,                         2 |    |    |
  July     6 | 2nd. Measurement of _Matériel_,        8 |    |    |
       “  15 | Project for a Cannon,                 24 | 97 |  2 |  2
             |                                          |    |    |
  August  12 | Second Reconnaissance Survey,            |    |    |
             | Out-of-door Work and Tracing of the      |    |    |
             |    Lines on the Reconnaissance Plan,     |  7 |....|....
             | One day free in case of bad weather,     |  1 |....|....
       “  21 | Geodetical Calculations,                 |  4 |....|....
       “  26 | Laying down the Reconnaissance Survey,   |  8 |....|....
  September  |                                          |    |    |
           4 | Memoir on Entrenched Lines,              |  1 |....|....
       “   6 | Tracing or laying out Camps,             |  1 |....|....
       “   7 | Operations of a Sham Siege,              | 13 |....|....
             | One day free,                            |  1 |....|....
       “  19 | Preparing for the Examination,           |....|....|....
  October    |                                          |    |    |
  November 1 | Examination for leaving,                 |....|....|....
             |                                          |----|....|....
  Total of the days employed, 522 + 7 days free         |529 |    |



About six weeks of free or voluntary study is allowed, immediately prior
to the Final Examination, for the sub-lieutenants to prepare for their
last effort.

The examination which takes place prior to their leaving the School of
Application, is entirely conducted by a board of six officers, under the
presidency of a general officer alternately of the artillery or
engineers, the remaining members of the board consisting of a general
officer of each corps and three field officers of these corps; the last
three being specially charged with the duty of examining. It takes place
in a room set apart for the purpose, with a small interior room in
connection with it, into which the members of the board retire to
deliberate at the end of each student’s examination. The jury assembles
each year at the period fixed by the minister of war.

The three examining members conduct the examination of the students in
three different branches of study; the first more particularly relating
to artillery science, the second to engineering science, and the third
to mechanical science in its connection with the art of war. The whole
of the students who are to leave the school are first examined in such
one or other of these branches of study as may be determined on.

The student under examination is specially questioned by the examining
officer in his subject, and occasionally by the president or any other
member of the board that may wish to do so, for three-quarters of an
hour. As soon as the examination of the student has been concluded, the
board retire to the adjoining room and compare their notes of the
credits they have severally awarded to the student under examination,
and they also examine his drawings, sketches, and memoirs relating to
the subjects on which he has been questioned, and prepared during his
two years of residence in the school. They severally note the credits to
which they consider him to be entitled for them, and adopt the general

As soon as the examination of the whole of the students in this
particular study has been finished, the examination in the next branch
is commenced, so that five or six days elapse between the first and
second examinations of the same student; and the same interval of time
occurs between the second and third examinations.

The credit allotted to each student by the board of examiners
represents, on the scale of 0 to 20, the manner in which he has replied
to the questions, or executed the drawings, sketches, memoirs, &c.,
belonging to each course. The importance attached to each particular
branch of study is estimated very nearly by the amount of time allowed
for its execution divided by 20; and the definitive marks which each
student obtains for that branch of study is obtained from the products
of the numbers respectively representing the credit for answering, and
that for the importance of the subjects on which he has been examined.

The final classification of the order of merit, in each arm of the
service, is arranged after a comparison of the total of the marks
obtained by each student. This total is the sum of the definitive marks
gained by each student in the sciences bearing on artillery,
engineering, and mechanics in connection with the art of war, for the
talent displayed in drawing, sketching, and writing memoirs, and for
skill in practical exercises, as determined by the results of the
examination conducted by the jury of examiners, added to the marks due
to the previous classification in the school, with the weight or
influence equal to one-third of that allowed for the examination by the

The co-efficients of influence for the present year are--

  For those particularly relating to Artillery Science,        39.29
        “          “            “    Engineering Science,      53.75
        “          “            “    Mechanical Science,       43.00
  For talent in drawing, sketching, writing memoirs, &c.,       6.80
  For practical exercises,                                     16.75
  Previous classification in the school,                       45.30

So that the examination conducted by the jury of examiners exercises an
influence on the position of the students very nearly approaching to
two-thirds of the whole amount.

It is this final classification which determines their seniority in the
respective services. We were permitted to be present during the
examination, which was entirely oral, of two of the _sous-lieutenants_,
before the jury of examiners.

The questions were replied to with great fluency and readiness, but it
seemed to us that the examination was somewhat limited for the object in
view, viz., that of awarding a credit representing the progress which
each student had made in the particular science on which he had been
questioned, especially as that credit would have very great weight in
determining the candidate’s future position.[14]

    [Footnote 14: The examination chamber is a small room in the
    school buildings, near the library, ornamented with portraits of
    Vauban, and of D’Argenson, under whose ministry the original
    schools at La Fère and Mézières were founded. At a large table
    under these portraits, and extending across the room, General
    Morin, President, and four officers, members of the jury, were
    seated. The sixth member sat at a small table in front, near the
    blackboard, at which the student stood. The Commandant, the
    Director of Studies, and the other officers of the school were
    seated also in this part of the room.

    The student who was first examined was questioned partly by the
    examiner, partly by the president, and gave his answers, working
    problems and drawing illustrations on the board as he went on. He
    was asked questions as to the details of the steam-engine, and as
    to the method of casting cannon. The German teacher of the School
    put him on to construe from a German book, and tried him in
    speaking; he succeeded just passably in both. The whole occupied
    about three-quarters of an hour.

    The second student, after answering similar scientific questions,
    had opportunity given him to show his knowledge, which was
    considerable, of the geology of the neighborhood; and having lived
    in foreign countries, he was able to make a very good display of
    his knowledge of German, Spanish, Italian, and English.

    After each examination the jury retired into the inner cabinet, by
    a door opening to it from behind their seats.]

On quitting the School of Application at Metz, the sub-lieutenants of
artillery and engineers respectively join the regiments, to which they
are then definitely assigned as second lieutenants, and continue to be
employed in doing duty, and in receiving practical instruction with
them, until they are promoted.


The lieutenants of the artillery are employed on all duties that will
tend to make them efficient artillery officers, and fully acquainted
with all details connected with the drill, practice, and manœuvres of
the artillery, and also with the interior economy and discipline of a
regiment of artillery.

After the officers of artillery are promoted to the rank of second
captain, but not before, they are detached from their regiments and
successively sent into the various arsenals, cannon foundries, powder
mills, and small arm manufactories, pyrotechnic establishments, and
workshops, in order that they may become practically acquainted with the
whole of the processes connected with the manufacture and supply of
artillery, rockets, small arms, powder, material of all kinds, tools,
&c., and also with the construction and repair of the buildings and
factories required for these purposes. Sometimes they are employed as
assistants in these establishments. The inspectors of the arms of
regiments are selected from among those who have become acquainted with
the manufacture of small arms.

When promoted to first captains they again rejoin their regiments, so
that they may not lose the qualifications and knowledge required from a
good practical artillery officer.

Field-officers of artillery are employed as superintendents and
directors, and captains as sub-directors, of the important works
intrusted to their arm.

In time of war, the officers of artillery have the construction of their
own batteries, and the direction of the ordnance in battles and sieges,
together with the formation of movable bridges and passages by boats.

It must be noticed, in contradistinction to the practice which prevails
in England, that the artillery and engineer services manufacture their
own tools.

The young engineer officers are employed with the men of their
regiments, and with them pass through courses of practical instruction
in the field, in sapping, mining, field fortification, sham-sieges,
bridges, and castrametation. During this practical instruction one of
the lieutenants belonging to each company is always present, and the
captain of the company visits the work once in the course of the day.

The duties of the officers of engineers in time of peace are the
construction, preservation, and repairs of fortresses and military
buildings, and the command and instruction of the engineer soldiers.

In time of war, the officers of engineers are intrusted with the
construction of works of permanent fortification, of the general works
in the attack and defense of fortresses, and the reconnaissance
connected therewith.

They _may_ also be charged--

With the construction of such works of field fortifications as the
commander-in-chief or the generals of division consider necessary; such
as _épaulments_, trenches, redoubts, forts, blockhouses, bridgeheads,
intrenched camps, as well as the opening of communications, the
establishment of bridges resting on fixed supports, and the formation
and destruction of roads.

After the officers of engineers have been promoted to the rank of second
captain, and not before, they are mostly employed apart from their
regiments, on the _état major_ of the engineers in fortified towns and
places, either in charge of the existing military buildings and
fortifications, or with the duty of carrying on, or assisting to carry
on, such new works as are in course of construction from time to time.

We have already stated that by the law in France one-third of the
officers of the army is obtained from the military schools; one-third
from the non-commissioned officers who have been raised to that grade
from the ranks; while the remaining third is placed at the disposal of
the supreme executive power. As regards the artillery and engineers this
last third is in actual practice obtained, like the first third part,
from the Polytechnic School, so that only one-third of the officers of
those arms are promoted from among the non-commissioned officers, and
these seldom rise above the rank of captain. Much attention is, however,
paid to the improvement of the education of these latter officers, and
we found that _four_ officers of engineers and _one_ officer of
artillery so promoted were, by order of the minister of war, on the
recommendation of the inspectors-general, passing through the School of
Application at Metz, the course of instruction for them being modified
on their account. And it was confidently expected that a large number of
those officers who had been promoted in this way during the war would be
ordered to the School of Application at Metz.

We should not omit to mention that occasional exchanges of service take
place, during the first year of residence at Metz, among the pupils
destined for the artillery, and those destined for the engineers.

The pay of officers of the artillery and of the engineers is the same.
A small additional allowance is granted to officers of artillery when



There are ten regimental artillery schools established in places or
towns that are usually garrisoned by the troops of this arm, and one of
these schools exists at Metz.


The soldiers of the engineers appear to be very well taught in their
regimental schools, of which there are three, one for each regiment,
established at Metz, Arras, and Montpellier, where the regiments are
usually in garrison. The strength of each regiment is 4,500 men.

The instruction given in these schools has for its object to afford, to
its full extent, to the officers, _sous-officiers_, and soldiers of the
engineers, the requisite theoretical and practical knowledge to enable
them satisfactorily to fulfill the duties of their various ranks, and to
qualify them for promotion to higher rank.

It is so regulated that at the end of the first year the men have learnt
the nature of the service and duties of a soldier; and that at the close
of the second year, the practiced sapper is cognizant of mining, and the
practical miner is acquainted with sapping.

In the lowest classes the men begin with learning to read and write;
this if followed by arithmetic, grammar, writing from dictation, and
composition. The next subjects are special mathematics, landscape, plan,
topographical and architectural drawing. We attended a class in which a
corporal of sappers was explaining to the mathematical teacher
(a civilian) the theory of the inclined plane, and we saw a large number
of their drawings, topographical and architectural, many of which were
very well executed.

The theoretical instruction is given between the months of November and
March, the practical instruction in the field, (already noticed)
occupies the rest of the year. The combined courses are completed in two






The chief Regulations for the Police of the Establishment are as

I. BARRACKS.--The Students are lodged in Barracks in the School, under
the command of a Captain of the Staff, with the title of Commandant of
the Quarter. They take their meals, however, out of the Barracks, in the
town. They are allowed free egress and ingress from and to their
Barracks, from the call at 6 in the morning to 10 at night, excepting
during the hours devoted to lectures and the studies in the rooms.
During these hours they must give special notice o£ their times of going
out and coming in.

in Brigades of thirty Students at the utmost, and each Brigade in two
sections. The Students of Artillery and those of the Engineers
constitute, as far as possible, separate Brigades. A Captain of the
Staff is attached to each Brigade for its superintendence. The students
in these Brigades and Sections are arranged in the order of merit which
they held on entrance, and the first Student on the list of each Brigade
and of each section of a Brigade is called its Chief. This arrangement
is preserved at their messes, which are held at the Restaurateurs’, each
section of fifteen having its own table, and its chief being the head of
the mess. Private bills or private additions to the mess are forbidden,
the maximum price for the daily fare being fixed by the Commandant of
the School.

III. CONDUCT OF THE STUDENTS.--All games of chance are forbidden; and
any debts discovered are punished. If a Student continues long without
paying such, he is reported to the Minister of War.

done out of the rooms of study, except in cases of illness.

All works to be executed by the Students are considered as service
ordered to be done, which must be completed at the hours and within the
period fixed in the order of the day. Students who are in arrears of
work at the end of their first year are required to finish them during
the time of vacation.

V. SUPERINTENDENCE OF OUT-OF-DOOR WORK.--After describing facilities
afforded to the Students for working in the country, and stating
minutely the method to be followed, the directions add that “on bringing
back their plans, Students must present their sketches, and all the
notes taken by them, in their rough state, to the Officer of the Staff
intrusted to inspect them. They can not begin to put their work into
shape till this Officer’s visa has been affixed to the sketches, notes,”

VI. VACATION.--There is one vacation at the end of the first year. Any
class, or any single student, under punishment, may be deprived of this.
Any work to which the Professor gives a mark below 7, must be considered
incomplete, and to be done again. Students are kept up in vacation to
finish their work; but if it is done within fifteen days, and marked by
the Professor’s visa, they are allowed to go away for the rest of the

Young Officers, after their final examination, are subject to all the
Regulations of the School, down to the moment of their leaving the town.


The time devoted to each of the courses in the School, to the works of
every kind which belong to it, to the exercises, drill, theoretical
instructions, &c., is fixed in accordance with programmes approved by
the Minister of War; and the Table similar to that given at pages
180-181, exhibiting the employment, is each year submitted for his
approbation by the Superior Council of the School.

Every kind of work, such as the out-door operations, sketches, drawings,
memoirs, calculations, interrogations, manipulations, manœuvres, drill,
&c., is valued by the Professor or Officer of the Staff charged with its
direction, by the product of two numbers, one representing the merit of
its execution, and the other the importance of the work.

The numbers representing the merit of the execution or instruction are
regulated by the scale of 0 to 20, as at the Polytechnic School.

The co-efficient of importance is found by dividing the number
representing the maximum value allowed for the execution of any work by
20, the maximum credit for merit; and the number representing the
maximum value, allowed for the execution of any work has reference to
all the circumstances bearing upon its execution. It is regulated by the
number of hours appropriated to its execution; and in estimating this
number of hours, regard is had, not only to the time occupied in making
the drawing, but also to that which is necessary for the calculations,
essays, and sketches indispensable to its execution. The lectures are
reckoned at one and a half hours, and the sittings in the Halls of Study
at four and a half hours.

The number of hours inserted in the Table giving the distribution of the
time employed, being insufficient for the composition of the memoirs,
specifications, estimates, &c., the value given for this kind of work,
of which a great part is performed out of the Halls of Study, is fixed
at twice the number of hours inserted in the Table showing the
distribution of the time employed.

The interrogations are the subject of a special credit, the maximum
being equal to the number of hours devoted to the lectures, multiplied
by one and a half hour, the length of each lecture.

The credit given for a work performed outside the school is divided into
two parts: one, equal to one-third of the total credit, is in the hands
of the Officer charged with the superintendence of the work, who
estimates the zeal and aptitude of the student; the other, equal to
two-thirds, is applied by the Professor, and given according to the
merit of the work.

The sum of the credits, given for work of all kinds in a course of
study, forms the maximum credit for the course.

The method of fixing the credit for the execution of works, according to
the time devoted to them, is equally applicable to the exercises,
practice, and drill.

When the time granted for the execution of any work has expired, the
Director of Studies sends this work to the Professor for his
examination, who establishes the number or credit, showing its
importance, and returns it to the Director of Studies.

Every work which has been finished and examined, is marked by the
Professor by a number representing its merit, which number may be

This is multiplied by the number representing its importance, and the
nearest whole number resulting from this product expresses the value of
the examined work.

Every unfinished work receives a provisional value, and is then returned
to the person executing it, and as soon as it has been completed a
second evaluation is made, but only two-thirds of the difference between
the first and second evaluations is added to the first; the same
principle is applied to the works which have been valued below seven, or
to those which have been amended or recommenced.

Every work which has not been executed by the student is marked 0; but
the grounds for its non-execution are placed before the Jury of

In the event of two papers being so similar that it is evident one must
have been copied from the other, and that it is not possible to decide
which has been copied from the other, both are marked 0.

And on the other hand, if it is proved that there was no complicity
between the authors of the two papers, the copied paper is the only one

At the end of each year’s study, the Council of the School makes a
classification of the students of the two divisions.

Each of these classifications is formed of the following elements:--

1st. Notes of conduct given by the General commanding and the Colonel
Second in Command.

2nd. Notes of appreciation given by the General Commanding, and the
Colonel Second in Command, and by the Officers of the Staff of the

3rd. Tables of credits given by two Field Officers of the Artillery and
Engineers on the theoretical and practical instruction with which they
are charged.

4th. Tables of credits given by each Professor for the works of all
kinds, interrogations, &c., of his course.

The classification of the first year comprehends all the works, drill,
and practice, executed during the first year, which have been valued, as
well as the notes of appreciation and of conduct.

The number appropriated to these notes at the end of the first year is
equal to the moiety of the total number allowed for the two years of

The classification of the students of the second year presents the
reunion of the works executed by them since their entrance into the

The maximum number of credits appropriated to all the Officers of the
Staff, as a note of appreciation, is equal to one-sixth of the total of
all the courses taken together.

The same number, divided into two equal parts, is assigned to the notes
of appreciation given by the General commanding and the Second in

Lastly, the notes of conduct given by the General commanding and the
Second in Command form one-fiftieth of the total value.

For the classification of each division the Director of Studies
abstracts into a Table, for each arm, all the elements which should
enter into this classification. Below the name of each student are
inserted all the credits which belong to him, and the total, reduced in
the ratio of the maximum 20, is the definitive number of the
classification of each student.

The Director of Studies appends to these Tables a report containing
everything which affords a means of estimating the work, the conduct of
each student, the delays, and the causes, &c. In giving the names of the
students whose credits are less than 7, he proposes, conformably with
the Regulations, the measures that should be taken with regard to them.

The Superior Council of the School being assembled, the different Tables
furnished by the Professors and by the Officers of the Staff, as well as
those in which they are summed up, are collated, and the list of
classifications for each division and for each arm is fixed separately,
with the definitive numbers representing the credits.

These classified lists indicate for each arm the new rank of the
Students, their rank at admission to the School of Application and of
passage to the first division, the sum of the values for the works
executed by them, and all the elements which would tend to enable a
proper judgment to be formed of their merits and conduct.

The Superior Council adds to it, if there be any necessity for it,
notes, exposing the grounds which have contributed to the principal
alterations in the relative position of the Student, and points out
those whose credit is less than 7, as well as those who by their bad
conduct deserve to become the object of exceptional measures.

_Examination for Leaving._

Each year the General commanding the School determines by lot, at least
one month in advance, the order in which the examinations for the
promotions in the Artillery and Engineers are to take place. The
Students belonging to the same arm can change among themselves, but
eight days after the lots have been drawn the list of the order of
examination is definitely closed. The General commanding the School
makes known at the same period the order of the examinations and the
division of the subjects between these examinations.

The General commanding the School places before the General of Division,
President of the Jury of Examination, the following:--

1st. The division of the subjects between the three examinations.

2nd. The order of examination of the Arms, and of the students of each

3rd. The provisional classification of the students of the first
division made by the Superior Council.

4th. The particular reports relating to each student made by the General
commanding the School.

5th. The list of the propositions made by the Superior Council and the
proceedings of the sitting at which it was agreed to.

6th. The classification of the Students of the second Division.

7th. Tables of questions established for each course.

8th. The abstracts of the sittings of the Superior Council held since
the last examination.

The Student Sub-lieutenants are successively examined in all the
branches composing the theoretical and practical instruction of the
School. The theoretical knowledge is grouped in three series, each of
which is the object of a particular trial.

The drill and practice are executed in the presence of the Jury, who
cause the command to be given to the Sub-lieutenant, in order to satisfy
themselves of the amount of their instruction, and to assign marks of
merit to them individually.

The subjects of the three examinations are divided in the following

First. Examination, made by the Field Officer of Artillery in the--

  Course of Military Art.
  Course of Artillery.
  Course of Veterinary Art.
  Sham Siege (part relating to Artillery.)
  Course of Military Law and Administration.

Second. Examination, held by the Field Officer of Engineers.

  Course of Permanent Fortification and the Attack and Defense
    of Places.
  Course of Construction.
  Sham Siege (part relating to the Engineering.)

Third. Examination, held by the third Examiner, taken either from the
Artillery or Engineers, in the--

  Course of Mechanics.
  Course of Applied Sciences.
  Course of Topography and Geodesy.
  German Language.

Every Student, on presenting himself before the Examiners, submits for
their approbation the drawings and manuscripts relating to the subjects
on which the examination is to bear. Independent of the questions which
are placed before him by the Examiners, the Student Sub-lieutenant must
reply to any objections or questions which the members of the Jury may
think fit to address to him.

The German Master directly questions the Students, if the Jury wish it.
The Professors or their Assistants must be present at the examinations
relating to their course.

As soon as the examination is ended, the members of the Jury retire to
an adjoining room with closed doors, to determine on the amount of marks
to be given to the Student examined.

When the trials of all kinds are finished, the Jury proceed to the
definitive classification of the Students belonging to each arm. In
making this classification, regard is had to the following

1st. Each examination has a co-efficient of importance equal to the sum
of all the different courses which are included in it.

2nd. The co-efficient of importance for drawing is equal to the 1/20 of
the sum of the co-efficients of the three examinations.

3rd. The co-efficient of importance of the practice, drill, &c., is, as
for the courses, the sum of the co-efficients appropriated to the works
taught in the School.

By multiplying the co-efficients of importance by the mean number of
marks of merit obtained by the Students in the different examinations,
the definitive credit which must be assigned to each Student in the
Table of Classification is obtained.

The classification of the School enters into the definitive
classification for a value equal to one-third of the total number of the
three examinations, without comprising the valuation of the drawings;
this value is added to the credits determined above.

The Jury give an account of the proceedings of the examinations in a
“_procès-verbal_” addressed to the Minister by the General acting as



_Twenty-six Lectures common to Students of both Arms._

_First Lecture._--(1.) Definition of the word Artillery. Material,
personnel, science. Object and division of the course.


Ideas on the origin of powder and its use in fire-arms; mealed or
pulverized powder; powder in grain. General conditions which powder
ought to satisfy; action of each of its component parts. Proportion of
component parts used in France. _Fulmi-ligneux._

Considerations on the physical properties of powder. Size of the grains
expressed by the number of grains to the gramme. Density of the grains
and specific density of the powder; circumstances causing them to vary.
Effects of damp upon powder.

_Second Lecture._--(2.) Combustion of powder. Different modes of
ignition of powder. Research respecting the laws of its combustion,
process of observation employed, laws discovered. Influence of the
density, the composition, the mode of manufacture, the damp, the tension
and temperature of the surrounding gases.

Combustion of the grains of powder. Calculation applied to the spherical
grain. The formula is applicable to the irregular grains of ordinary

Calculation of the density of the gases of powder in a fixed space, on
the hypothesis of a simultaneous ignition of the grains. Discussion of
the formula obtained; influence of the density of the grains, of the
duration of their combustion and of the space in which the powder is

Inquiry into the rapidity of ignition of charges of powder. Experiments
made upon trains of powder, and upon gun-barrels filled with powder.
Conclusions drawn from the results obtained.

_Third Lecture._--(3.) Calculation of the density of the gases of the
powder on the hypothesis of successive ignition.

Results of the application of the formula to charges of a spherical and
a truncated form.

Tension of the gases of powder. Impossibility of determining it by
considerations of a purely theoretical nature. Experimental solution of
this question. Experiments by Rumfort; description of his apparatus.
Results obtained. Formula representing them. Observations on these

_Fourth Lecture._--(4.) Effects of powder in a fixed space.

Hollow projectiles. The readiest bursting of a hollow sphere takes place
in the direction of the plane of a great circle. Determination of the
minimum bursting charge; law by which this charge varies with the
thickness of the envelope. Influence of the fuse-hole of hollow
projectiles; weakening of the envelope of the shell, diminution of the
charge; loss of gas, increase of the charge. Effects of the shock of the
exploding gases; means of estimating it. Influence of the vivacity of
the powder in burning. Number and rapidity of the explosions.

Hollow cylinders burst more easily longitudinally than transversely.
Consequences of this principle relatively to the employment of a fibrous
metal for the manufacture of arms. Thickness necessary to resist

_Fifth Lecture._--(5.) Effects of powder in cannon.

Analytical theory of the effects of powder in cannon.

Equation of the problem. General expressions of the quantity of force
exercised by the expansion of the gases,--of the density of the
different sections of gas and of their tension. Differential equations
of the motion of the gases, of the projectile, and of the gun. Equation
of condition leading to the establishment of the general formula which
determines the position of a stratum of gas in the terms of the function
of its original position, and of the other data of the question. General
relations between the velocity of the projectile and that of the gun.

Density of the stratum of gas at a given moment. Position of the stratum
which has a maximum density.

_Sixth Lecture._--(6.) Approximative solution applicable to the cases
ordinarily met with in practice. Hypothesis relating to the velocity and
the tension of different strata of gas.

Relations between the velocity of the projectile and that of the gun.
Approximate expression of the amount of force due to the expansion of
the gases; line to be followed in the execution of the arithmetical
calculations. Formula serving to determine the velocity of the
projectile. General considerations on the state of the gases of powder
during the burning of the charge. Influence of the motions of the
projectile and of the bottom of the bore on the distribution of the
gases at each instant. Influence of the successive generation of the
gases combined with the enlargement of the space which incloses them on
their density throughout the whole duration of the phenomenon.

_Seventh Lecture._--(7.) Influence of the vent and of the windage of the
projectile on the effects of powder in cannon.

Determination of the loss of velocity occasioned by the windage of the
projectile. Influence of the weight of the piece upon the velocity of
the projectile. Influence of the weight of the projectile on tension of
the gases and upon the velocities of the two bodies set in motion.
Influence of the weight of the charge of powder. Charge giving the
maximum of velocity. Influence of the size and density of the grains of
the powder as well as other circumstances which cause a variation in the
law of generation of the gases. Advantage of very rapid combustion in
short pieces and of slower combustion in long ones.

_Eighth Lecture._--(8.) Influence of the length of bore; circumstances
which modify it; length corresponding to the maximum of velocity.
Comparison of the quantities of motion of the projectile and of the gun.
Trial of a formula fitted to represent their relation. Determination of
this relation with the help of the balistic pendulum.

Mean pressure exercised on the projectile during its passage through the
bore. Injuries produced in guns by firing; enlargement of metal and
cracks; lodgment and percussion of the projectile.

Different effects of the percussion; means tried to prevent injuries
(in general.) Considerations on the metals employed in the manufacture
of ordnance. Charging with elongated cartridge; use of wooden bottoms
and wads.

_Ninth Lecture._--(9.) Examination of the proper means for measuring the
effects of powder. Eprouvettes of different sorts. Experimental
processes founded on the measure of the velocity of the projectile.
Grobert’s rotatory machine. Process of Colonel Debooz. Process based on
the employment of an electric current. Method by ranges (mentioned here
by way of note.)

Balistic pendulum. Pendulum of Robins, of d’Arcy, of Hutton.
Improvements introduced in France into the construction of these
apparatus. Description of the pendulums in use at the present day;
cannon pendulum; musket pendulum.

_Tenth Lecture._--(10.) Analytical theory of the balistic pendulum.

  1. Receiver pendulum; formula which gives the velocity of the
projectile. Determination of the elements which enter into the formula,
and the degree of approximation necessary. Simplification of the
calculation of the velocities in the case of firing several times

  2. Cannon pendulum. Amount of recoil in the gun. Percussion of the
knife-edges of the pendulum. Case where there is none. Means of
correcting the position of the center of percussion.

_Eleventh Lecture._--(11.) Examination of the effects of the recoil upon
guns and their carriages. The question may be considered as resolving
itself into two others.

  1. Percussions of the carriage upon the points supporting it;
analytical solution. Determination of the percussions and of the force
of the recoil in the case of carriages on wheels, and that of mortar
beds. Graphic solution of the same question by an analysis of the force
which acts upon the bottom of the bore. Modification of the sketch
according to the different cases presented by the direction of fire
relatively to the ground.

_Twelfth Lecture._--(12.) Discussion of points relating to the
percussion of the carriage upon its supports, and to the force of the
recoil. Influence of the elevation of the line of fire; of the
inclination of the ground or of the platform; of the length of the
carriage in proportion to its height and of the friction which results
from the contact of the trail with the ground. Velocity of recoil of the
collective apparatus. Determination of the extent of the recoil on a
given ground. Recoil of the different pieces of ordnance in use. Case in
which the forepart of the carriage has a tendency to be lifted up;
velocity of this motion; determination of the effect resulting from it.

_Thirteenth Lecture._--(13.)

  2. Percussions produced by the gun upon its carriage. Determination of
the amount of percussion of the breech upon the elevating screw, and of
that of the trunnions upon the trunnion holes. Discussion of points
relative to the effects produced. Influence of the elevation; of the
dimensions of the gun, and of the proportion of its weight to that of
the entire apparatus.

Effect of the elasticity of the different parts of the apparatus. It
diminishes the wear of the parts struck, and renders it necessary to
take into account the velocity of the parts striking.

_Fourteenth Lecture._--(14.) Effects of powder in mines. Historical
notices. Dimensions of the boxes containing the powder. Considerations
on the effects of the expansion of the gases in an indefinite or limited
compressible medium.

Definitions having reference to craters and chambers of mines. Ordinary
charge of the chamber. The old rule for miners; its entire alteration.
Table relating to different kinds of medium. Overcharged chamber.
Overcharged chamber or “camouflet.” Limit of the effects of compression
which result from the action of the chambers. Use of gun cotton.
Considerations on the effects of the petard. Dimensions of the cavity
reserved for the powder. Means employed or proposed to diminish the
charge of powder proportioned to a given effect.


_Fifteenth Lecture._--(15.) Science of projectiles. Historical notices.
Utility of an acquaintance with the laws of the motion of projectiles in
a vacuum. Definitions relating to the trajectory. Differential equations
of the motion in vacuo. Equation of the trajectory. Inclination of its
elements. Velocity of the projectile at any one point. Duration of its
passage. Determination of the range and of the angle of greatest range.
Relations between the ranges; the initial velocities; and the angles of
projection. Examination of the cases where the theory of the parabola is

Preliminary ideas on the resistance of fluids; difficulties inherent in
this question. Approximative formula of the resistance, established by
the help of the principle of active forces; circumstances not taken into
consideration by it.

_Sixteenth Lecture._--(16.) Experiments relating to the determination of
the resistance of the air.

  1. Case of small velocities. Rotatory apparatus; results furnished by
them in the case of thin planes; their essential defect. Apparatus with
rectilinear movement. Mean value of the co-efficient of the theoretical
resistance in the case of thin planes; modification of this value for
the case of spheres, &c.

  2. Case of great velocities. Direct determination of the resistance of
the air by the aid of the balistic pendulum. Experiments of Hutton,
their results. Experiments made at Metz in 1839 and 1840. General
expression of the resistance based upon the total of the results
obtained, and containing a function of the velocity in three terms.
Search after a function in two terms fit to replace in each particular
case the general expression.

_Seventeenth Lecture._--(17.) Theory of the motion of projectiles in the
air. Differential equations of the motion. Hypothesis on the relation of
the element of the trajectory to its projection. Calculations based on
this hypothesis, and leading to the final equation of the arc of the
trajectory. Inclination of the element of the trajectory. Velocity of
the projectile at a given point. Duration of the passage.

_Eighteenth Lecture._--(18.) Examination of the functions employed in
the formulas of the science of projectiles. Formation of the balistic
co-efficient, and the series contained in the functions. Relations of
the series and the functions to each other. Arithmetical tables designed
to give their values. Determination of the relation of an arc of the
trajectory to its projection. Error resulting from the introduction of
the constant relation in balistic calculations.

_Nineteenth Lecture._--(19.) Application of balistic theories to the
movement of projectiles thrown at great angles. Analysis of the
trajectory, and determination of all the circumstances of the movement.
Trajectory of shells considered as a single arc. Solution of several
problems involved in this hypothesis. Determination of the range.
Velocity corresponding to a given range and angle of projection. Angle
of projection corresponding to a known initial velocity and range. Angle
of greatest range. Variation of the velocity of the projectile during
the whole of its passage. Limit of velocity of projectiles falling
vertically in the air.

_Twentieth Lecture._--(20.) Application of balistic theories to the
motion of projectiles thrown at low angles. Case where the relation of
the arc to its projection can be supposed sensibly equal to unity.
Problems relative to direct fire; distinction established between the
angle of projection and the angle of fire. In ordinary cases in practice
the angle of fire is very nearly independent of the height of the object
aimed at. Relations between the angle of projection, the angle of
elevation of the object aimed at, and the angle of descent. Problems
relating to plunging fire. (Ricochet fire.) Determination of the initial
velocity and the angle of projection for a projectile which has to pass,
firstly, through two given points; secondly, through one given point,
the trajectory having at this point a known direction. Case of practical

_Twenty-first Lecture._--(21.) Relations between the velocities, the
spaces traversed, and the durations of passage in the rectilinear
movement of projectiles. They are applicable to direct fire, and are
independent of the function of the velocity which enters into the
expression of the resistance of the air. Case where the resistance of
the air can be supposed proportional to the square of the velocity.
Establishment of balistic formulas in this hypothesis. Application of
the formulas to the resolution of one of the problems connected with a
plunging fire. Comparison of the results obtained with those arrived at
by the use of general formulas. Indication of methods applicable to the
resolution of several questions in projectiles.

_Twenty-second Lecture._--(22.) Examination of disturbing causes which
influence the motion of projectiles.

  1. Disturbing causes acting on the projectile during its passage
through the bore. Imperfections of form, such as want of straightness in
the bore, faulty position of the line of sight and the trunnions.

  Influence of the windage of the projectile and of the percussions
which result from it. Deviation from the original direction; its
consequence in the different kinds of fire. Effect of the recoil and the
vibrations of the barrel in the fire of small-arms.

  Influence of the various causes which are capable of modifying the
initial velocity.

  2. Disturbing causes acting upon the projectile during its passage
through the air. Influence of the rotatory motion which results from the
last percussion within the bore. Effects of the eccentricity of
projectiles. Case where the rotation occasions no deviation. Influence
of the proximity of the ground. Deviation produced by the wind (air in
motion.) Influence of atmospheric changes.


_Twenty-third Lecture._--(23.) Importance of the question. Preliminary
ideas. Resistance due to the motion of a carriage and determination of
the effort necessary for drawing it in the case of uniform motion.
Two-wheeled carriage on level ground; the effort of draught in a
direction parallel to the ground; first, resistance referable to the
friction of the wheels on the axle; secondly, resistance referable to
their revolution upon the ground. Influence of the weight of the
carriage. Advantage of large wheels over small ones, demonstrated in the
two cases of a yielding soil and a hard soil scattered over with
obstacles. Expression of the power of draught necessary to overcome the
two resistances united.

_Twenty-fourth Lecture._--(24.) General expressions of the effort of
draught necessary for two-wheeled and four-wheeled carriages; case of a
locked wheel. Influence of the direction of the traces and of the
inclination of the ground upon the draught. Advantage of rolling over
dragging for the transport of burdens. Examination of resistances which
are developed in the passage from repose to motion. Considerations on
the position of the fillet in the box, and determination of the
co-efficient of friction for the case of the revolution of the wheel
about the axle.

Influence of the length of the nave on the frictions when the axle is
thrown out of a horizontal position.

_Twenty-fifth Lecture._--(25.) Turning of carriages considered
successively in the case of two-wheeled and four-wheeled carriages.
Center and angle of the turn in four-wheeled carriages. Calculations of
the angle of the turn and of the space required by the carriage to
execute a half turn. Examination of the dimensions of the carriage which
influence the angle of the turn. Diameter of the fore-wheels and height
of the body of the carriage; distance between the wheels and breadth of
the body of the carriage; position of the point of reunion of its fore
and hind parts. Examination of the circumstances favorable or
unfavorable to the action of the horse. Relation between the forces to
which he is subjected, and the pressure of his feet on the ground.
Sliding of the feet; influence of the weight of the animal; of the
co-efficient of friction; and of the direction of the traces. Lifting of
the fore-hand; influence of the weight of the horse, and of the
increased distance between the points on which he rests; of the position
of his center of gravity; and of the direction of the traces.

_Twenty-sixth Lecture._--(26.) Considerations on the mode of action of
the draught-horse. Effect of his weight, and of the inclination of the
traces. Effort of draught of which the horse is capable, both
momentarily and continuously; results of experiments. Composition of
artillery harness. Harness à limonière (with shafts and cross-bar,) or
on the French system; on the German system, with pole and support. Use
and discontinuance of swing bars. Arrangement of the traces. General
arrangement of harness. Bât-saddle.



_Twenty Lectures, of which Fourteen are common to the Students of both
Arms and Six confined to Artillery Students._


_Twenty-seventh Lecture._--(1.) Classification of small arms. Arms not
fire-arms. Classification of hand-weapons. Considerations on the profile
and outline of cutting weapons. Effect of the curve. Division of the
mass. Form of the hilt.

Considerations on the profile and outline of thrusting weapons.

Position of the center of gravity; form of the point. Description of
arms other than fire-arms now in use. Sabres and swords. General ideas
respecting their component parts; blade, hilt, and scabbard. Regimental
arms. Infantry sword. Sword-bayonet of the artillery and chasseurs,
cavalry sword; peculiar requisites. Sword of cavalry of reserve, of
cavalry of the line, and of light cavalry. Horse artillery sword.

Officers’ and non-commissioned officers’ arms. Cavalry lance. Camping
axe. Side-arms in use in the navy. Sword, pike, boarding-axe, dirk.

Defensive armor. Cuirassiers and carabineers’ cuirasses. Cuirass and
helmet of the sapper.

_Twenty-eighth Lecture._--(2.) Fire-arms. Historical notices. First
attempts in fire-arms. Hand cannons. Arquebuses, culverines, &c.
Poitrinal, matchlock, firelock, pistol, and blunderbuss.

Means employed successively for loading and ignition of the charge.
Twisted match, wheel-lock, flint-lock, percussion-lock, (the two last
mentioned here by way of note.) Classified account of fire-arms now in
use. Muskets. Considerations on the weight and principal dimensions of
muskets. Detailed description of the infantry musket. Action of the
flint and the percussion lock.

_Twenty-ninth Lecture._--(3.) Comparison of the flint and the percussion
musket. Voltigeur’s, dragoon’s, and double-barreled musket. Gendarmerie
and cavalry carbine. Cavalry and gendarmerie pistol. Arms in which
precision of aim is studied. Means employed to prevent the deviations
caused by the windage of the projectiles and their rotatory-movement in
the air. Diminution and suppression of the windage; straight grooves in
the barrel, spiral grooves, rifled arms. Rotation of the ball about its
axis of flight.

Principles of arrangement of rifled arms. Charge of powder and
inclination of the grooves; two modes of solution, powerful charge and
long spiral, weak charge and short spiral. Length of the barrel:
conditions which determine it; number and form of the grooves.

_Thirtieth Lecture._--(4.) Loading of rifled arms; ramming the ball
home; loading at the breech. Different methods tried. Loading with a
flattened ball; effect of the flattening of the ball. Examination of the
successive improvements to which this idea has served as a basis.
Chambered arms; use of the short bottom and the patch. Arms _à tige_.
Elongation of the ball; shortening of the spiral groove; diminution of
the charge: advantages resulting from it. Pointed cylindrical ball;
principles of its outline; effect of the notches of the ball;
superiority of this projectile over the spherical balls. Summary
examination of the different models of rifled arms which have been
successively in use. Versailles rifles.

Wall-piece, pattern 1831. Common rifle, pattern 1842. Wall-piece,
pattern 1840. Bored-up wall-piece, pattern 1842. Pistols for officers of
cavalry and gendarmerie. Rifles _à tige_, pattern 1846, and artillery
carbine _à tige_. Description of these two arms. Superiority of the
rifle _à tige_ over the arms for precise aim previously adopted. Trial
relating to a new improvement in the construction of rifled arms. Disuse
of the “_tige_.” Ball with cup. Comparative notice of the fire-arms of
the different European powers.


_Thirty-first Lecture._--(5.) Principles of construction of projectiles.

Considerations on the substances which may be chosen for the manufacture
of projectiles. Essential conditions, density, hardness, tenacity,
cheapness. Projectiles of stone, lead, cast-iron, iron, copper,
gun-metal. Forms of projectiles.

Exterior form; conditions which serve to determine it. The spherical
form preferable to any other in the actual state of artillery. Advantage
of elongated projectiles. Conditions relating to their use. First
attempts. Interior form of hollow projectiles; howitzer shells, bombs,
and grenades. Thickness of the metal; fuse-hole; charging-hole of naval
hollow projectiles; lugs or handles of shells. Density of projectiles.
Recapitulation of the balls; howitzer shells; shells and grenades in
use, their nomenclature, dimensions, weight. Cannon-balls. Choice of
metal and weights. Different arrangements for the use of shot,
case-shot, canister or naval grape-shot. Spherical case; conditions
relating to their use. Charge of spherical case. Bar-shot. Rescue

_Thirty-second Lecture._--(6.) Cannon. Historical ideas on the subject.
Principle of arrangement of ancient arms and machines of war. Motive
force employed; its inferiority compared to that furnished by the
combustion of powder. Earliest cannon.

Historical view of the different systems of ordnance which have been
successively in use in France.

1. Cannon. Calibres in use in the 16th century. Edict of Blois, 1572.
Cannon employed in the reign of Louis XIV. Regulation of 1732. System of
Vallière. Modifications introduced by Gribeauval in 1765. Cannon of the
year XI. Cannon in use at the present day.

2. Ordnance adapted to hollow projectiles. Difficulties inseparable from
the throwing of hollow projectiles; first attempts. Mortars. Double
fire. Ancient calibres. Mortars in use at the present day. Stone mortar.
Howitzers, their first use in the French artillery; howitzers of 1765;
of the year XI. Calibres in use at the present day. Considerations on
the calibres of different kinds of cannon. Siege, garrison, field,
coast, and naval ordnance. Siege, garrison, field, mountain, coast, and
naval howitzers. Mortars and stone mortars. Considerations on the metals
which may be employed in the manufacture of cannon for siege, garrison,
field, coast, and naval purposes. Interior form of ordnance.

  1. Part of the bore traversed by the projectile, transverse section;
trial of rifled cannon, longitudinal section.

  2. Part of the bore occupied by the charge; influence of its form; the
spherical, cylindrical, truncated form. Chambers of mortars; reason for
their adoption. Cylindrical and truncated chambers; comparison of their
effects. Spherical chamber; pyriform chamber: interior form of the naval
mortar _à semelle_ (cast in one piece with the bed.) Chamber of
howitzers; experiments with reference to their adoption for field
howitzers. Dimension. Howitzers without chamber. Chamber of carronades.
Junction of the chambers with the rest of the bore: form of the bottom
of the bore or of the chamber.

_Thirty-third Lecture._--(7.) Vent; its object, its dimensions. Bushes
inserted before casting, (_masses de lumière_;) after casting, (_grains
de lumière_.) Considerations on the position of the vent relatively to
the charge. Experiments made with the infantry musket, and with 24 and
16 pounder guns.

Arrangement of the vent in guns of 1732; portfire chamber. Vent of
mortars. Priming pans. Windage of projectiles; conditions which
determine it for the different services. Rules received with respect to
ancient guns. Dimensions in use at the present day. Different
characteristics resulting from the windage of projectiles. Length of the
bore. Question of the length of the bore considered with reference to
the projectile effect of the powder. The length of ordnance is
determined by considerations unconnected with this effect.

Length of bore of siege and defensive artillery, of field, coast, and
naval guns. Length of bore of mortars, and of the stone mortar. Length
of bore of howitzers. Thickness of metal and external outline.
Cannon:--Theoretical determination of the external outline necessary for
resistance to the effect of the gases of the powder. Co-efficient of
resistance, its value in the guns in use. Thickness in the chase
necessary for resistance to the percussions of the projectile.

Swell or moulding of the muzzle. Thickness at the position occupied by
the trunnions. Thickness of metal of the different systems of cannon
which have been successively in use in France. Thickness of metal in
howitzers. Form resulting from the diminution of internal diameter, at
the position occupied by the chamber. Exceptional form of the siege
howitzer. Outline of the interior of mortars.

_Thirty-fourth Lecture._--(8.) Line of sight; its object and
arrangement. Considerations on the inclination of the line of sight
relatively to the axis of the gun. Trunnions; object and arrangement of
trunnions and their shoulders. Position of trunnions relatively to the
center of gravity of the gun. Preponderance of the breech over the
chase; manner of estimating it; preponderance allowed in the different
guns in use. General principle serving as the basis for its adoption.
Position of trunnions relatively to the axis of guns. Reasons for their
depression; circumstances which cause it to vary. Trunnions of mortars;
their reinforces. Dolphins of ordnance. Weight of ordnance; necessary
relation between the weight of a gun, and the quantity of movement of
its projectile. Conditions serving to determine the weight of the
different species of cannon, howitzers, and mortars in use. Examination
of the weights adopted for the pieces of ordnance of all sorts, which
have been successively employed. General recapitulation of the different
species of ordnance in use. Nomenclature. Dimensions, weight. Land
artillery. Siege, garrison, and field guns. Siege, garrison, field, and
mountain howitzers, mortars, and stone mortars. Naval artillery. Cannon,
carronades, howitzers, mortars, stone mortar, blunderbuss. Observations
on ordnance. Exceptional ordnance. Villantroy’s howitzers. Belgian
mortar of 60 c., &c. Description of the artillery petard.


_Thirty-fifth Lecture._--(9.) Historical ideas on the subject. Cause of
the motion of rockets. Their exterior and interior form. Relation which
should exist between the law of generation of the gases and the orifice
for their escape. Measure of the tension of the gases in rockets.
Results of experiments. Motion of the rocket. Variation of the velocity
during its passage. Means of regulating the motion; effect of the
directing stick. Influence of the wind upon the trajectory of the

Description of rockets in use.--1st. War rockets; calibres employed;
body of the rocket; arrangement of the stick. Projectiles fitted to the
head of the rocket; rockets without stick. 2d. Signal rockets; their
calibres and composition.


_Thirty-sixth Lecture._--(10.) Historical ideas on the subject.
Arrangements originally in use for the service of ordnance. Successive
improvements. Carriages on wheels. Introduction of limbers. General
conditions which gun-carriages should satisfy.

General principles of their construction:--1st. With reference to the
act of firing. 2dly. With a view to transport.

Mortar carriages. Particular requisites. Description of the carriages in
use. Siege carriages; particular conditions. General arrangement of
ancient siege carriages. Detailed description of the present siege
carriage and its limber; its weight and different characteristics. Field
carriage; particular requisites; general arrangement of the carriages
employed before 1765. Field carriages of the system of Gribeauval; its
defects. General arrangement and detailed description of the present
field carriage and of its limber. Weight and different characteristics.
Mountain carriages; particular requisites; description of the carriage
and of the arrangement of its shafts (_limonière_.)

_Thirty-seventh Lecture._--(11.) Garrison and coast carriages;
particular requisites; object of the platform for the two systems; its
principal dimensions; position of the pintle or working bolt (_cheville
ouvrière_.) General arrangement of ancient garrison and coast
gun-carriages. Description of the present garrison carriage; change of
the carriage into a movable one on four wheels; weight and different
characteristics. Replacement of the platform by a directing transom bed
under certain circumstances of the service. Casemate carriage. Iron
carriages; inconveniences of this kind of construction for siege
purposes and on the field of battle; its advantages for the armament of
coasts. Description of the coast carriage actually in use; weight and
different characteristics. Naval carriages; particular requisites.
General arrangement of naval carriages in use. Carriage on four small
wheels for cannon. Bracket carriage (_à échantignolle_,) and carriage
with double pivot platform for howitzers. Carronade carriage. Mortar
bed, cast in one piece with the mortar, (_à plaque_.) Exceptional
methods of construction. Depressing gun carriages for a very plunging
fire. Villantroy’s howitzer beds, those of the Belgian mortar of 60 c.,


_Thirty-eighth Lecture._--(12.) Battery carriages. Ammunition wagon.
Historical ideas on the subject. Requisites for carriages used for the
transport of munitions of war. General arrangement and description of
the present ammunition wagon. Principles of arrangement of the
ammunition chest. Loading of the chest with munitions of various kinds.
Mountain ammunition chest. Loading of the chest with howitzer ammunition
and infantry cartridges.

Battery wagon; object of this carriage; patterns successively adopted.
Description of the wagon, pattern 1833. Field forge; object of this
carriage. Description of the forge in use. Arrangement and play of the
bellows. Mountain forge. Description and loading of it.

_Thirty-ninth Lecture._--(13.) Park carriages and machines.

Park wagon. General arrangement and description of the park wagon and
its limber. Carriages destined to the transport of heavy burdens.
Ancient gun wagon. Truck. Block carriage. General arrangement and
description of the carriage. Siege cart; its object and description.
Devil carriages. Arrangement of the ancient devil carriages with perch
and with screw. Devil carriage with roller. Description of the carriage
and of its mechanism. Gin. General arrangement of the different patterns
successively employed. Description of the gin at present in use.
Handscrew; its use, general arrangement, and description.

_Fortieth Lecture._--(14.) Pontoon equipages. Conditions which military
pontoon equipages should satisfy. Considerations on the nature of the
supports to be employed. Reserve pontoon equipage. Boat of the reserve
equipage; its general form and dimensions. Description of the boat and
skiff; use of the boat for navigation; its weight and different

Tackle and machines employed for bridge-making. Balks, moorings,
chesses, blocks, and balk collar. Framework, with movable head;
different kinds of piles. Means of anchorage. Common anchor; its
properties. Anchor basket and chest. Buoy. Cordage. Ideas on its
arrangement and on the measure of its resistance. Capstan. Windlass.
Tackling. Handscrew. Pile driver. Hand rammer. Grapnel and hooks.

General arrangement of the boat carriage. Description. Its weight and
properties. Light equipage.

_Forty-first Lecture._--(15.) General ideas on the artillery of the
different European powers, and comparison with the French material.

Ordnance; description, species, and calibres. Gun-carriages, carriages,
and other parts of the train. General arrangement; facility of movement;
modes of harnessing, &c.


_Forty-second Lecture._--(16.) Knowledge of woods. Preliminary ideas.
Structures and general properties of woods. Diseases and defects of
woods. Description and properties of the principal substances employed
in the construction of the material; uses to which the different kinds
of wood are specially destined. Selection of standing timber; felling;
transport; reception of woods; cubature. Cutting up in large and small
sizes. Observations on the shrinking of wood. Preservation of woods.
Drying in the air. Round, squared, and blocked-out timber. Preservation
in store; preservation in water. Steeping. Influence of the contact of
woods with other woods, and with metals.

_Forty-third Lecture._--(17.) General considerations on the substances
employed in the manufacture of gun and artillery carriages. Different
properties of metals. Choice of kinds of wood; effects of their being
dried. Classified account of axles and wheels. Axles; substance
employed, their forms and dimensions. Wheels; essential requisites.
Importance of the elasticity of wheels. Effects of the dishing of a
wheel, form of the spokes, coupling of the spokes with the nave and the
felloes. Tires. Form and number of the felloes determined by the effects
of the drying. Form of the nave. Wheel-boxes.

_Forty-fourth Lecture._--(18.) Means employed for the connection of the
pieces which enter into the composition of gun-carriages, carriages, and
other furniture of the train. Nails, clinch nails, rivets, bolts,
screws, &c. Examination of the joinings employed in the construction of
gun-carriages, carriages, and other furniture of the train.

General principles. Joinings of gun-carriages. Joint plates (“_rondelles
d’assemblage_.”) Mortar beds, siege, field, and garrison carriages.

_Forty-fifth Lecture._--(19.) Joining of other carriages and furniture.
Hind parts, ammunition wagon, battery wagon, forge, park wagon, block
carriage, cart, devil carriage, and drays. Boat and wherry. Fore parts,
particular requisites. Fore parts of the field and siege carriage, of
the park wagon, devil carriage, and drays. Barrels and cases.

_Forty-sixth Lecture._--(20.) Means employed for the preservation of the
material. Cost price of the principal parts of the material. Ordnance,
projectiles, powder, carriages, and other furniture of the train.
Small-arms. Preservation of ordnance in gun-metal and cast-iron.
Preservation of projectiles. Formation and counting of piles.
Rust-cleaning machine. Preservation of gun-carriages, carriages, and
other furniture of the train. Different methods of stacking in use.
Preservation of powder and made-up ammunition; stacking in powder
magazines. Means proposed for avoiding the danger of explosion.
Preservation of small-arms. Armories. Preservation of iron and cut wood.



_Forty-seventh Lecture._--(1.) Fire of ordnance. Kinds of fire in use
with ordnance. Choice of charges of powder. Charges of powder formerly
in use; their progressive reduction. Charges of field, siege, garrison,
coast, and ships’ cannon; of howitzers and mortars.

Arrangement of the charge. Shot cartridge for field guns. Loading of the
other kinds of guns, of howitzers, mortars, and the stone mortar.
Loading for fire with red-hot shot. Armaments for the service of
ordnance. Methods of igniting the charges of powder; tubes formerly in
use, friction tubes. Percussion system; Swedish tube. Ignition of the
charge of hollow projectiles, fuses of hollow projectiles, fuse with
several pipes for the fire of spherical case, hand grenade fuse.
Rapidity of fire. Laying of ordnance. Principal methods of laying guns;
laying them by the help of the line of sight. Determination of the
elevation. Instruments in use to obtain elevations. Negative elevations,
means of using them. Laying guns for fire parallel to the ground; for
breaching fire at a short distance.

_Forty-eighth Lecture._--(2.) Determinations of elevations by
experiment; construction of practice tables. Laying guns when the axis
of the trunnions is not horizontal. Laying guns with the help of the
plumb-line and quadrant; plunging fire, rectification of the aim.

Fire of mortars, means for directing it in use; use of pickets, of the
line, of the quadrant. Laying pieces in the case of a defective
platform. Means of laying them for night-firing. Laying naval ordnance;
use of the front sight. Initial velocities of projectiles with the
different charges in use. Angles of sight, and point-blank ranges of
ordnance. Ranges at different sights. Maximum ranges.

_Forty-ninth Lecture._--(3.) Probabilities in the fire of ordnance;
known laws, facts ascertained by experiment. Distribution of projectiles
over an object aimed at of indefinite extent. Mean point of impact. Fire
of canister; effects of the dispersion.

Fire of spherical case. Effects of the bursting of the projectile;
dispersion of the balls and of the explosions. Fire of the stone mortar;
use of mortars for the same purpose.

Fire of small arms: charges of powder adopted. Ball cartridge. Initial
velocities of balls with the different arms. Angles of sight and
point-blank ranges. Rules for fire according to distances, for muskets,
carbines, and pistols. Fire of rifled arms; use of the tangent scale.
Probability of the fire of small-arms; comparison of arms with
smooth-bored and rifled barrels. Different means employed for the
estimation of distances.

_Fiftieth Lecture._--(4.) Effects of projectiles on the different
substances fired at. Effects of concussion and penetration. Effects on
earth. Theory of the penetration of a projectile into a resisting
medium. Formula to express the penetration, based on the results of
calculation and experiment. Effects of penetration into wood. Effects on
metals, cast-iron, iron, lead. Effects on masonry and on rock.
Application to a breaching fire delivered in a regular direction
relatively to the revetment. Effects of the shock of projectiles upon
living bodies. Effects of hollow projectiles bursting in different
media; earth, wood. Method of bursting employed against troops.

Effects of spherical case. Incendiary effects. Effects of war rockets.
Explosive rockets. Incendiary rockets. Effects of concussion.



_Six Lectures, common to the Students of both Arms._

_Fifty-first Lecture._--(1.) Definitions. Meaning attached to the word
“battery.” Different denominations given to batteries: first, according
to the circumstances of the war in which they are employed; secondly,
according to their mode of construction; thirdly, according to the kind
of ordnance with which they are armed; fourthly, according to the kind
of fire for which they are intended; fifthly, according to the direction
of their fire.

Principles of construction. General considerations on the elements which
constitute the different kinds of batteries which have reference to
them. Epaulment; its length, height, and thickness in different cases.
Section of the epaulment. Ground-plan of the epaulment of the different
kinds of batteries; returns at its extremities. Case where the battery
is in advance of a parallel. Epaulment with redans; its trace.

_Embrasures_ opened in the epaulment; their construction in different
cases; slope of the bottom; interior opening; exterior opening; form of
the cheeks.

_Genouillère_; fixing of its height for the different kinds of fire.
Limit of the obliquity of the embrasures.

_Fifty-second Lecture._--(2.) _Terre-Plein_; its position relatively to
the ground; its length for the different kinds of batteries. Disposition
of the part unoccupied by the platforms. Terre-plein of garrison, field,
coast, and barbette batteries.

_Ditch_; cases in which it is employed. Its position with reference to
the epaulment. Depth, breadth, section, and plan of the ditch.

_Communications_ between the battery and the works, in its neighborhood;
parallels or trenches; plan and construction. Communication between the
battery and its ditch.

_Powder magazines:_ their object. Discussion respecting their site and
capacity with a view to the different kinds of batteries, viz., siege,
garrison, and field batteries.

_Traverses_ of _crownwork_ and garrison batteries. Width between them
and dimensions.

_Fifty-third Lecture._--(3.) Details of construction. Different
materials employed in the construction of batteries. First, materials
for revetments, fascines, gabions, hurdles, sods, bags of earth,
withy-bands, stakes, &c. Secondly, materials for platforms; hurtoir,
sleepers, planks, beams, pickets. Construction of revetments of
different kinds employed in batteries. First, revetment of the interior
slope of a battery upon the natural ground. Secondly, revetment in use
when the terre-plein is more or less sunken. Ordinary siege battery,
battery in a parallel, battery in a crownwork. Third, revetment of the
checks of embrasures in the different cases met with in practice; direct
batteries with point-blank range; ricochet, breaching, garrison, and
field batteries.

_Fifty-fourth Lecture._--(4.) Construction of platforms. Ordinary siege
platforms, movable platforms (_à la Prussienne_,) garrison and coast
platforms, ordinary mortar platforms, platforms for coast mortars of
great range. Peculiar case where the fire has to be elevated or greatly
depressed. Construction of the communications from the battery to the
parallel and to its fosse. Construction of powder magazines in
batteries. Magazines of siege batteries, Nos. 1, 2, 3, 4. Case of
breaching batteries; garrison battery and field battery. Magazines.
Degree of resistance offered by blinded magazines. Modifications adopted
for the strengthening of magazines whose construction is already fixed.

_Fifty-fifth Lecture._--(5.) Number of workmen to be employed on the
construction of the different parts of batteries: revetments, platforms,
communications, powder magazines. Earthworks.

Duration of the total labor necessary for the construction of each kind
of battery. Duration of the duty for the different parts of the
_personnel_ employed upon the construction; officers, gunners,
assistants. Definitive number of workmen necessary for the construction
of the different kinds of batteries. Tools of different kinds.

Simultaneous execution. Preliminary operations. Reconnaissance.
Prolongations. Sketch of the plan of a battery. Formation of the working
party. Transport of materials. Plan of the battery. First, battery
having its terre-plein on the level of the ground. Disposition of the
working party. Work of the first night, of the following day, of the
second night. Second, a battery sunk outside a parallel. Third, battery
in a parallel or trench of some kind already established. Day labor,
night labor.

(4.) Particular case of crownwork batteries.

_Fifty-sixth Lecture._--(6.) Exceptional constructions. Blinded
batteries for cannon or howitzers; for mortars. Batteries of earth-bags.
Batteries on stony ground, on the rock, or marshy soil. Floating
batteries. Construction on sites deficient in space. Case where the fire
of the place is too dangerous. Coast batteries. General arrangement.

Instruction preparatory to working at the plans of batteries. (Course.)



_Ten Lectures common to Students of both Arms._


_Fifty-seventh Lecture._--(1.) Historical résumé. Progress of modern
artillery, from its origin down to our time. Artillery of Charles VII.
and of Louis XI. Progress under Francis I. Effects of the wars of
religion. Edict of Blois, 1572. Improvements by Sully. Creation by
Gustavus Adolphus. State of the artillery under Louis XIV. Employment of
artillery on the field of battle at the commencement of the 18th
century. Regulation of 1732. Introduction of howitzers into the French
artillery. Regimental pieces. Progress of the artillery in Prussia and
in Austria in the Seven Years’ War. Reorganization of the French
artillery in 1765. Résumé of the improvements owing to Gribeauval.
System of the year XI. Present system.

Historical ideas on the personnel of the artillery. State of the
personnel at the commencement of the use of fire-arms. Masters and
grand-masters of the artillery, &c. Personnel employed originally on the
service, and the guard of ordnance. Creation by Louis XIV. Account of
the successive modifications in the personnel from this epoch down to
1765. Organization of 1765. Horse artillery. Pontoneers. Artillery
train. Artillery of the Imperial Guard. Organization of 1829. Present
state of the personnel. Regiments of artillery. Composition of the
personnel of the different kinds of batteries. Companies of pontoneers,
workmen, armorers, veteran gunners. Driver-corps (“_train de pare_.”)
Naval artillery.

_Fifty-eighth Lecture._--(2.) Committee and central depôt of artillery.
Organization of artillery commands. Establishments for the instruction
of the personnel; artillery schools. Creation in 1679. Present schools;
personnel attached to them. Central school of military pyrotechnics.
Establishments for the preservation of the material. Importance of the
material of artillery. Its state in France at different epochs.
Artillery directions. Division of the territory of France. Personnel of
the directions.

Establishments for the manufacture of the material. Ideas on the subject
of their management. Arsenals; their object, management, number,
personnel. Forges; their object, management, districts, personnel,
inspection. Foundries for land artillery; their number, management,
personnel, inspection. Naval foundries. Manufactures of arms; their
special management, number, personnel, inspection. Branch of the service
connected with gunpowder and saltpetre. Powder manufactories and
refineries; management, personnel. Direction of the service.
Establishments existing in France. Percussion cap manufactory.


Selection of ordnance, conditions which determine it; cannon, howitzers,
relation between them. Proportion of the number of pieces of ordnance to
that of the combatants. Mean proportion received in France;
circumstances which may lead to a modification of it. Organization of
ordnance in batteries. Account of the arrangements formerly adopted.
Present system. Distribution of the batteries in the army. Principles
received. Application of these principles to the artillery train of an
army of a given strength. Infantry divisional batteries; cavalry
divisional batteries; reserve batteries. Case of the formation of army
corps. Composition and supply of batteries. Principles and details of
the supply of batteries with ammunition for the guns and for the troops.
Second supply distributed amongst the parks.

_Fifty-ninth Lecture._--(3.) Field parks. Their composition, in
carriages of all kinds. Application of the principles to the artillery
train of an army of a given strength. Approximate relation of the number
of the carriages and of the horses of the train to that of the pieces of
ordnance. Means of renewing the supply of the parks.

Personnel of the field train. Personnel of the batteries; working
companies. Companies forming part of the train. Personnel attached to
the parks. Staff. Particular conditions, having reference to war in a
mountainous country. Selection of pieces of ordnance. Proportion between
their number and that of the combatants. Composition of some artillery
trains employed in our African expeditions. Composition and supply of
the mountain battery. Lading of the mules. Composition of pontoon
trains. Reserve train, boats, wherries, tackle, carriages, and horses.
Personnel of the train. Light train: material, personnel.

_Sixtieth Lecture._--(4.) Marches of the artillery. Reception of a
battery or of a park. Precautions to be taken before the departure.
March at a distance from the enemy. Order of march. Distribution of the
personnel; halts. Case of an accident to a carriage; ascents; descents;
deep-bedded roads; passage through inhabited places; passage of bridges;
of fords. Passage over ice. Night march. Transport of mountain
artillery. March of pontoon trains. Transport of the trains by water;
navigation by convoys; by isolated boats. Transport of ordnance, powder
and projectiles in the boats. Transport of artillery trains by sea.

March in the vicinity of the enemy. Isolated convoys; rule with
reference to their command; order of march; general measures of
security; precautions to be taken during halts; manner of receiving an
attack. Case where resistance becomes impossible; arrangements for the

Artillery in the march with other troops. Order of march. Relation of
the different corps to each other. Exceptional difficulties which may
occur on marches; privations of all kinds; bad weather; bad state of the
roads; instances. March among high mountains; passes strongly occupied
by the enemy; examples.

Encampments and bivouacs. Choice of ground convenient for a camp;
disposition of the artillery camp. Establishment of artillery bivouacs.
Disposition of the park; precautions relating to the superintendence.
Different measures to be taken on arriving on the place of encampment or
of bivouac. Attention to be paid to the horses: special precautions for
the mules of the mountain artillery. Precautionary measures variable
according to circumstances.

_Sixty-first Lecture._--(5.) Artillery on the field of battle. Measures
to be taken on arriving in the neighborhood of the enemy.

Choice of positions adapted for artillery.

  1. Different considerations relative to the ground to be occupied;
form of the ground; cultivated lands; nature of the ground;
communications, &c.

  2. Position of the artillery relatively to the enemy.

  3. Position of the artillery relatively to the troops to be supported.

Execution of the fire. Choice of the different kinds of fire according
to the nature of the object aimed at and the distance. Fire of cannon,
with ball, with shot. Fire of field and mountain howitzers. Fire
parallel to the ground.

Use of war rockets. General principles relating to the effects to be
produced by artillery, and to the warmth of the fire. Proper use of
stores; their replacement. Use of the prolong. Arrangements to be made
after the engagement. Spiking and unspiking of ordnance.

Use of artillery in the principal circumstances of a campaign. General
case of an offensive engagement. Part played by the artillery in
supporting infantry and cavalry marching to the attack. Importance of
the artillery for following up a first advantage which has been
obtained. Examples. Use of the artillery in masses to strike a decisive
blow. Examples. Defensive engagement.

Disposition and use of the artillery for the defense of fortified
positions. Attack of entrenchments. Reconnaissance. Disposition and use
of artillery; attack of lunettes by the gorge. Examples. Attack and
defense of villages; disposition of the artillery under these two
circumstances. Attack of squares. Importance of artillery towards
preparing for it. Examples. Defense of squares; disposition of
artillery. Examples. Case of a charge of cavalry upon artillery. Use of
artillery in the advanced guard, in the rearguard, in a retreat.

Use of artillery in the passage of streams. Examples. Use of artillery
to defend or force the passage of valleys or defiles. Examples.


_Sixty-second Lecture._--(6.) Object to be attained with the use of
artillery in the attack of places. Selection of ordnance, cannon,
howitzers, mortars. Composition of the siege train. Method to be
followed in order to determine it. Examples of trains employed in
different sieges. Carriages of the train. Supply of the siege train with
projectiles, powder, &c.

Personnel of the siege train; troops and staff. Transport of the siege
train. Horses to be employed. Limit in either direction. Employment of
watercourses. Examples. Establishment of the train before the place.
Encampment of the artillery force. Organization of the parks. Workshops,
powder magazines, trench-depots. Rules relating to the direction of
artillery works.

Commanding officers of attack.

_Sixty-third Lecture._--(7.) Considerations on the different kinds of
batteries to be employed in the attack of fortified places. Position of
the batteries relatively to the point to be breached. Direct battery
within point-blank range; enfilading battery, for a plunging fire, for
direct fire within point-blank range, for plunging fire. Mortar
batteries. Composition of the different kinds of batteries. Position of
the directing lines of an enfilading battery, relative positions of the
cannon, the howitzers, or the mortars. Position of the batteries
relatively to the parallels and the rest of the trenches. Examination of
the circumstances which affect the power of a plunging fire, command of
the work over the battery; distance between the height of the traverses.
Slope of the crests of the work.

General principles relating to the order of the works of the artillery,
commencing from the opening of the trenches.

Times for the construction of the first batteries. Batteries of the
first and second parallels. Use of field artillery to defend the flank
of the attacks. Replacement of the fire covered by the advance of the
works; batteries of the third parallel. Use of vertical fire. Mortars of
15c. Throwing of grenades. Breaching and counter batteries.
Considerations relating to their position. Batteries in the covered way.

Case of a breach into an interior work. Composition of the breaching and
counter batteries. Calibres to be used. Number of pieces of ordnance.

Ideas upon the operation of arming batteries. Precautions to be taken.
Passage out of the parallels or trenches. March in the trenches;
examples of some operations of this kind. Supply of the different kinds
of batteries. Rule relating to their daily service. Firing of siege
batteries. Opening of the fire. Direct fire within point-blank range.
Plunging fire. Fire of mortars. Warmth of the fire by day and by night;
mean consumption of material. Fire of breaching batteries. Effects to be
produced. Height of the horizontal cutting, number of the vertical ones.
Execution of the fire; fall of the revetment. Fire upon the counter
forts. Fire to render the breach practicable; balls, shells,
war-rockets, facts ascertained by experiment.

Consumption of powder and projectiles, length of the operation.
Breaching fire in a very oblique direction. Fire upon masked masonry.
Breach into an unreveted work. Fire of counter-batteries. Bombardment.
Case where it can be employed; manner of executing it.

Occupation of the place; arrangements which must be made by the
artillery. Case of raising the siege. Case of its transformation into a

_Sixty-fourth Lecture._--(8.) Service of artillery in the defense of
places. Object to be attained with artillery. Selection of ordnance,
guns, howitzers, mortars. Use of war-rockets and arms of precise aim.
Field artillery. Basis of the supply of fortified places. Projectiles,
powder, small-arms, various carriages. _Personnel_ of the artillery.
Troops. Staff.

Measures to be taken before the siege. Reconnaissances. Arrangement of
the material. Organization of the _personnel_, of the duty by local
divisions, of the workshops of all sorts. Precautionary armament. Basis
of its organization. Supply of ordnance. Defensive armament. General
principles relating to the armament of different kinds of works.
Bastions, cavaliers, demilunes, approaches, &c. Organization of the
armament. Traverses, embrasures, gun-carriages to be employed. Powder
magazines. Supplies. Service of pieces.

Employment of the artillery against the first works of the besiegers,
against the construction and armament of batteries; against the
besieging artillery. Partial disarmament in case of inferiority. Part
played by artillery in sorties. Modification of the defensive armament
in proportion to the progress of the attack. Last defensive armament.
Principles relating to its disposition. Armament of the flanking part of
the fortification. Increased use of vertical fire. Use of war-rockets
against works in close proximity. Crowning batteries, cavaliers of the
trenches. Heads of saps, &c. Blinded batteries. Conditions of the
establishment. Defense of breaches.

Service of artillery in the defense of coasts. General considerations on
the degree of extension admissible in the armament of coasts. Principal
points to be defended. Selection of ordnance intended for the armament
of coast. Objects to be effected. Effects of balls (utility of large
calibres;) of howitzer shells and of shells. Fire with red-hot balls.
Material appropriated to the defense of coasts.

Position of coast batteries, conditions which determine it. Composition
of coast batteries; their supply. Ideas upon the organization of the
batteries and their small redoubts (_réduits_.) Use of the fleet and of
field artillery. _Personnel_ allotted to the service of artillery on the


_Sixty-fifth Lecture._--(9.) Composition of the siege train necessary
for the attack of Metz. Carriages of the train.

Supply of the train with projectiles, powder, &c. Personnel of the
train, troops and staff. Transport of the siege train. Establishment of
the train before the place; encampment of the artillery force.
Organization of the parks. Work-shops, powder magazines and depôts.

_Sixty-sixth Lecture._--(10.) Object, disposition, and armament of all
the batteries from the first opening of the trenches to the capture of
the place. Use of field artillery to flank the batteries, &c.

Service of artillery in the defense of the place. Supply of ordnance,
projectiles, powder, small-arms, and different carriages.

Personnel of the artillery. Troops, staff. Organization of the personnel
and of the duties by local divisions. Precautionary armament; supply of
ordnance. Defensive armament. Armament of the different works. Service
of the pieces. Last defensive armament.

  _Lectures Preparatory to the Labors of the Course._

  1. Drawing and tracing of ordnance,             3 lessons.
  2. Design for ordnance,                         4    “
  3. Application of the theories of the course,   1    “
  4. Drawing of artillery material,               1    “
  5. Tracing of batteries,                        1    “

The sixth lecture of the fourth part of the course (the fifty-sixth) is
partly devoted to the communication of the instructions necessary for
the execution of the work of tracing plans of batteries.

  _Studies in connection with the Artillery Course._

  The practical studies which are connected with the artillery
    course, are,--

  1. Drawing of ordnance,                                    12 days.
  2. The designs for ordnance,                               24   “
  3. The application of the theories of the artillery course, 6   “
  4. The drawings of artillery material,                     26   “
  5. The tracing of batteries,                                4   “
          Total,                                             72 days.

The tracing of batteries is executed by the students of both arms, the
other tasks by the artillery students alone.


The survey of ordnance consists in constructing accurate sketches of a
gun, howitzer, and mortar, in measuring their dimensions, and in giving
a description of each of the pieces drawn. It is on this occasion that
the students are practiced in the management of instruments to insure
precision, such as the _étoile mobile_, and the sliding compass, &c. One
day is devoted to this work.

The tracing of ordnance consists in the execution of a drawing upon
colombier paper, containing an exact and detailed representation of a
gun, a howitzer, and a mortar, with their projectiles.

This work is performed with the help of the tables for the construction
of ordnance. Eleven days are devoted to it.

_Detailed Programme of the Drawing._

1. For each gun, howitzer, or mortar, a longitudinal section in the
direction of the axis, and at right angles to the axis of the trunnions,
and a plan parallel to the axis of the bore and of the trunnions.

Besides this, for those cannon and howitzers which have dolphins, a
transverse section taken across the middle of the dolphins and the axis
of the trunnions. For mortars, a transverse section made by a plane
passing in front of the dolphins, the whole on a scale of one-fifth.

2. Detail of the button (comprising the cascable and breeching loop for
naval ordnance) on a scale of two-fifths.

3. Detail of the tracing of a dolphin, on the scale of two-fifths.

4. Tracing of the bush of a gun, on a scale of two-fifths, and tracing
of a priming-pan at the real size.

5. For garrison ordnance, in cast-iron, detail of the widening of the
base ring on a scale of two-fifths.

6. Tracing of a cannon-ball, of a howitzer-shell, and of a shell, on a
scale of one-fifth.

Tracing of the lugs of a shell, ring and lug at the real size.

All the parts of the drawing must be colored in uniform tints in
conformity to the table of conventional colors; the annexation of the
figures of measurement is not required.

This work is preceded by three or four lectures intended to make the
students familiar with the tracings which they have to execute, and the
solution of the problems in geometry and descriptive geometry, to which
the representation on paper of pieces of ordnance and their projectiles
give rise.


The design for ordnance has for its object the complete determination of
the nature of a projectile, and of a piece of ordnance in accordance
with certain special conditions, inquiring into the laws of the motion
of the projectile, and into its principal destructive effects, and the
settlement of practice-tables for the gun. The general case for
treatment is that of a howitzer, which comprehends the gun and the
mortar as particular cases.

The data usually adopted are,--

  1. For the projectile, its weight and the quantity of powder which it
is capable of containing.

  2. For the piece, the initial velocity of its projectile. This
operation comprises calculations, a drawing, and a memoir.

The drawing, on colombier paper, which must be figured in all its parts,

  1. The tracing of the profile of the piece, as it is determined by
calculation, so as to satisfy the different conditions of resistance, on
a scale of one-fifth.

  2. The complete tracing of the piece executed in conformity with the
rules laid down for the tracing of ordnance on a scale of one-fifth.

  3. Tracing of the projectile on a scale of one-fifth.

  4. Tracing of the wooden bottom and of the fuse of the projectile,
executed in the case of each of these objects in two figures--the one on
a large scale (two-thirds, or even the size of nature,) representing the
inquiry into their forms and dimensions, the other giving on a scale of
one-fifth the results of this inquiry. To this is added, for the
mountain howitzer, or any other howitzer for which it is admissible, a
tracing of the mounted howitzer carriage.

  5. The representation in drawing of the laws of the motion of the
projectile, the trajectory, inclinations, remaining velocities,
durations of the passage.

  In addition, the scale of the elevations and that of the angles of
fire, for an object of aim placed at different distances.

  6. An inscription showing all the essential elements by which the
projectile and the piece are distinguished.

The final tracings of the gun, the projectile, the bottom, and the fuse,
must be colored in uniform tints conformably to the table of
conventional colors.

As to the tracing of the profile founded upon the calculation, it should
receive merely an edging of the color which represents the metal used.



_Object of the work. Data of the Question._


_First Section.--Substance, Forms, and Dimensions._

1. Choice of the metal employed in the manufacture of this projectile.

2. Forms of the projectile.

3. Internal diameter.

4. External diameter.

5. Dimensions of the vent.

6. Diameters of the high and low gauges.

7. Densities of the projectile empty and filled with powder.

8. Weight of the cast-iron ball of the same calibre as the howitzer

_Second Section.--Minimum Bursting Charge._

9. Theoretical bursting charge for the hollow sphere.

10. Effect of the shock of the gases, and of their loss through the

11. Résumé of the results arrived at in this chapter.


_First Section.--Metal, Calibre, and Length of Bore._

12. Choice of the metal of which the piece is to be formed.

13. Windage of the projectile and diameter of the bore.

14. Effect of the windage on the velocity of the projectile.

15. Length of the bore and charge of powder which satisfy the data of
the programme.

16. Résumé of the results arrived at in this section.

_Second Section.--Thickness of Metal necessary in order that the Piece
may resist the Expansion of the Gases._

17. Explanation of the method employed to resolve the question of the
thicknesses of metal.

18. First propulsion of the projectile, mean density of the gases after
this propulsion.

19. Second propulsion of the projectile, mean density of the gases after
this propulsion.

20. Third, fourth, &c., propulsions of the projectile, mean density of
the gases after each of them.

21. Density and position of the strata (of gas) at the moment of the
maximum of mean density.

22. Density of the last stratum for the positions which come after that
of the maximum of mean density.

23. Tensions which result from the densities found.

24. Corresponding thicknesses of metal.

25. Résumé of the results obtained.

_Third Section.--Profile of the Piece._

26. Inclosing curve, resulting from the calculations of the second

27. Modification rendered necessary by the form of the posterior part of
the projectile.

28. Utility of the chamber and its dimensions.

29. Tracing of the chamber and of its junction with the bore.

30. Thickness of metal around the chamber.

31. Chase and reinforce.

32. Determination of the angle of sight.

33. Vent and base ring.

34. Minimum weight of the piece for the resistance of the carriage.

35. Approximate calculation of the weight given by the profile
previously obtained. Modification of this profile, if there is any.

_Fourth Section.--Trunnions, Breech, and Handles._

36. Dimensions of the trunnions and of the shoulders.

37. Tracing of the breech.

38. Base rings and other moldings.

39. Object and fixing of the preponderance of the breech.

40. Exact settlement of the position of the trunnions, definitive length
of the reinforce.

41. Center of gravity of the piece; dimensions and position of the

42. Means of executing the calculations indicated in the two preceding

43. Table of the dimensions of the piece.


_First Section.--Elements of the Charging of a Howitzer._

44. Tracing of the shot bottom.

45. Tracing of the fuse.

46. Diameter of the cartridge (or of the bag.)

47. Charge of powder for firing with ball.

_Second Section.--Laws of the Motion of the Projectile. Establishment of
Practice Tables._

48. Preliminary calculations.

49. Trajectory.

50. Curve of the inclinations.

51. Curve of the remaining velocities.

52. Curve of the durations of the passage.

53. Determination of the elevations for the fire at different distances.

54. Angle of fire, corresponding to the different distances of the
object aimed at.

55. Angles of descent.

56. Résumé of the laws of the motion and of the practice tables.

_Third Section.--Effects of the Projectile._

57. Depth of penetration in the media indicated by the programme.

58. Effects of explosion in earth.

59. Résumé of the results relating to the effects of the projectile.

NOTE.--The formulas cited in the memoir need not be accompanied by their
demonstration, except in the case of the latter not having been already
developed in the lessons of the artillery course. It will be sufficient
to insert in this notice only the final result of the calculation
relating to each formula, without entering into the details of such

The study of the design for ordnance is preceded by four lessons
intended to make the students acquainted with all the details of its
execution, and the substance of which is indicated in the programme of
the memoir.


This study is intended to apply to the students those theories of the
course which have not found their application in the design for
ordnance. It comprises the solution by arithmetical calculations of
certain questions on the effects of powder, the balistic pendulum, the
effects of recoil, the science of projectiles, the draught of carriages,
&c. The number of the questions may vary according to their nature and
the time which their solution requires. The stating of the questions and
the results of the calculations are inscribed on separate papers. This
study is preceded by a lesson in which the students have recalled to
them the formulas which they have to employ.


The drawing of artillery material has for its object the representation
by figured sketches of a gun-carriage, carriage, or other furniture of
artillery material. The sketches, on paper put together in the form of a
book, and headed by a special programme for the object to be drawn,
consist of plans, sections, or elevations of the object, executed on
certain scales, and of detailed projections of the principal iron-work
and joints. The whole fixed by the special programme in question.

All the simultaneous projections of any one part of the object drawn
(fore part or hind part for carriages) must be completely figured; they
are accompanied by explanatory inscriptions, with letters of reference
to show the names of the pieces in wood or metal which they comprise.

Each collection of sketches must contain as well a notice in
confirmation of the drawing, giving the complete description and the
properties of the object to which it refers.

The students make two surveys of the same kind; eight days are allowed
for each of these surveys, including the composition of the confirmatory

The first survey is followed by the execution of an unfigured drawing,
containing a complete representation of the object surveyed (elevation
and plan,) obtained by the combination of the partial projections
contained in the sketch. The drawing should be colored in the
conventional uniform tints, and accompanied by an explanatory
inscription, with letters of reference. Ten days are devoted to this
work of composition.


This work consists in executing sketches showing, each in accordance
with a separate programme, the complete plan of a battery and the
essential data having reference to its construction and to its armament.
The sketches, made by scale and completely figured, must comprise in the
case of each battery to be represented--

  1. The general plan of the battery, on the scale of 1/200.

  2. The sections or elevations necessary for the understanding of this
plan, including the detail of the powder magazines, lines of
communication, &c., on the scale of 1/100.

  3. An inscription giving the object of the battery, its armament, its
general arrangement (_terre-plein_, embrasures, revetment,
communications, magazines, &c.,) the workmen, materials, and tools
necessary for its construction, and finally the duration of the labor
and its distribution by day and night.

  Four days are devoted to this work, which must be executed on a half
sheet of colombier paper. The separate programmes relating to each of
these batteries are shown on the study orders of the rooms.


  NL Number of the Lectures.
  CG Credits given for the Lectures.
  +A With application at 1h 50m.
  -A Without application at 3h.
  TC Total Credits.
  Q  Number of the Questions.

    LECTURES                       |    |     CG     |        |
                                   |    +-------+----+        |
                                   | NL | +A    | -A |   TC   |  Q
  Division of the Course--         |    |       |    |        |
  First Part. Theory,              |    |       |    |        |
    Sections 1, 2, 3,              | 26 | 18    | 42 |  60    |  4
  Second Part. Description of the  |    |       |    |        |
    Material, Sections             |    |       |    |        |
    1, 2, 3, 4, 5, 6,              | 20 | 30    | .. |  30    |  3
  Third Part. Fire of Ordnance,    |  4 | ..    | 12 |  12    |  1
  Fourth Part. Construction        |    |       |    |        |
    of Batteries,                  |  6 |  9    | .. |   9    |  2
  Fifth Part. Organization and     |    |       |    |        |
    Service of the Artillery,      |    |       |    |        |
    Sections 1, 2, 3,              |  8 | ..    | 24 |  24    |  1
  Sham Siege,                      |  2 |  3    | .. |   3    | ..
  Lectures in preparation          |    |       |    |        |
    for the Studies,               |  9 | 13 50 | .. |  13 50 | ..
  Totals,                          | 75 | 73 50 | 78 | 151 50 | 10

  S   Sketches
  D   Drawings.
  M   Memoirs.
  Inv Inventories.
  ID  In-door Attendance. 1½ hours.
  OD  Out-door Attendance. 1½ hours.
  C   Credits in round Numbers.

  STUDIES.                   | Number of
                             | S  | D  | M  | Inv| ID | OD |  C
  Survey of Ordnance,        |  1 | .. | .. | .. | .. |  1 |  5
  Tracing of Ordnance,       | .. |  1 | .. | .. | 11 | .. | 50
  Design for Ordnance--      |    |    |    |    |    |    |
    Calculations,            | .. | .. | .. |  1 | 10 | .. | 45
    Drawings,                | .. |  1 | .. | .. |  8 | .. | 35
    Memoir,                  | .. | .. |  1 | .. |  6 | .. | 55*
  Application of Theories--  |    |    |    |    |    |    |
    (Artillery Question)     | .. | .. |  1 | .. |  6 | .. | 55†
  First Survey of Material-- |    |    |    |    |    |    |
    Sketch,                  |  1 | .. | .. | .. | .. |  8 | 35
    Composition of Notice,   | .. |  1 | .. | .. | 10 | .. | 45
  Second Survey--            |    |    |    |    |    |    |
    Sketch,                  |  1 | .. | .. | .. | .. |  8 | 35
  Sketch of Batteries,       |  1 | .. | .. | .. |  4 | .. | 20
        Totals,              |  4 |  3 |  2 |  1 | 55 | 17 | ..

  [* The time is doubled for the memoirs.]

  [† Ditto.]


  Lectures,      150}
  Studies,       380} 530


  Cr Credits given for the Lectures.
  L  Number of the Lectures.
  +A With application at 1h 50m.
  -A Without application at 3h.
  T  Total Credits.
  Q  Number of the Questions.
    LECTURES                       |    |    Cr    |        |
                                   |    +-----+----+        |
                                   | L  | A   | -A |    T   |  Q
  Division of the Course--         |    |     |    |        |
                                   |    |     |    |        |
  First Part. Theories,            |    |     |    |        |
    Sections 1, 2, 3,              | 24 | ... | 72 |   72   |  4
  Second Part. Description         |    |     |    |        |
    of the Material,               |    |     |    |        |
    Sections 1, 2, 3, 4, 5, 6,     | 14 | ... | 42 |   42   |  2
  Third Part. Fire of Ordnance,    |  4 | ... | 12 |   12   |  1
  Fourth Part. Construction        |    |     |    |        |
    of Batteries,                  |  6 |  9  | .. |    9   |  1
  Fifth Part. Organization         |    |     |    |        |
    and Service of the             |    |     |    |        |
    Artillery, Sections 1, 2, 3,   |  8 | ... | 24 |   24   |  1
  Mock Siege,                      |  2 |  3  | .. |    3   | ..
       Totals,                     | 58 | 12  |150 |  162   |  9

                          |       Number of        |        |
                          +-----------+------------+        |
       STUDIES            | Sketches. | In-door    | Credit |
                          |           | Attendance |        |
  Sketches of Batteries,  |     1     |     4      |   20   |


  Lectures,                    162 }
  Studies,                      20 } 182. Round number, 180.


The course is divided into six parts, and is made up of lectures and
works of Application in the Halls of Study and on the ground.


  The 1st part contains sundry historical notices on the
  Organization of Armies,                                 6 Lectures.
  2d part is on Tactics,                                  3    “
  3d      “     Castrametation,                           2    “
  4th     “     Field Fortification,                     16    “
  5th     “     Military Communication,                  10    “
  6th     “     Strategy,                                 6    “
                                    Total                43


The first lecture commences with explanations relating to the Greek and
Roman armies; their order of battle, mode of marching; comparison of the
Roman Legion with the Greek Phalanx, and of the Roman Legion under
Marius and under the Emperors.

2. Military organization of the Franks under the Kings of the first
race. Consequences of the feudal system, acting on the military
organization. Feudal armies. Chivalry. Crusades, and war against
England. Establishment of the first standing armies. Results dependent
on the introduction of fire-arms. Progress made in the Art of War and in
the organization of armies, from the sixteenth century to the present

3. Necessity for standing armies. Their proper character. Recruiting.
Promotion. Degrees of rank. Station of the officers. Various positions
of military men. On the composition of armies, Infantry, Cavalry,
Artillery, Engineers. _Corps d’Etat-Major._ Composition of the army
during the Revolution and during the Empire. Actual formation of a
French army.

General Staff. Commissariat. (_Intendance._)--Different services
dependent on it.

Relations between the strength of each of the arms that make up an army.
On other corps which are not classed among the principal arms.

4, 5, 6. Summary relating to the military organization of the principal
Powers of Europe.


1. Definitions. Formations. Manœuvers; character of a good manœuver.
Order of battle: first, of the Infantry; second, of Cavalry; third, of
the Artillery; relating to Sharpshooters (_tirailleurs._)

2. Brief summary of the principal movements in battalion drill to pass
from line to the order in columns and reciprocally. Movements in column.
Movements in battle. Dispositions to be made against Cavalry.

3. Of the principal movements in line. Order of battle. Line of battle.
Formation of Infantry to advance against the enemy. Action of Cavalry.
Principal formations. Charges of Artillery. Use of the Three Arms.


1. General principles of castrametation. Situation. Construction and
disposition of barracks. Camp of a Regiment of Infantry, of Cavalry, and
of a Battery of Artillery.

2. Manner of tracing a camp on the ground. Huts; details relating to
their construction. Tents. Bivouacs. Screens. Kitchens and camp ovens.
Choice of the site of a camp; precautions to be taken for its security.
Main guards. Advanced posts. Patrols and sentinels.


1. Definition of fortification in general. Object and character of field
fortification; its utility demonstrated by historical examples.
Napoleon’s opinion. Essential principle of field fortification.
Discussion on the ordinary profile of earthen entrenchments; on the
dimensions to be given to the ditch in level ground.

2. Definitions relating to the trace; general principles. Redoubts.

3. On the elements of lines. Relation that should exist between the
crest and the internal size of a closed work. Maximum and minimum of the
sides of a square redoubt. Defects inherent to the trace of this kind of
redoubt. Circular redoubts. Redoubts _en crémaillères_. Star forts.
Lines with bastions.

4. Revetments of various kinds; case in which the slope of the ditch
should be reveted; choice to be made of the different kinds of

5. Exterior dispositions; accessories to the defense; abattis; _trous de
loups_; palisades; _chevaux de frise_, &c. Precautions to be adopted
with reference to such accessories.

6. Interior dispositions; armament of musketry, artillery, barbettes,
and embrasures; their advantages and disadvantages; construction of.

7. Powder magazines of different kinds. Small earthen entrenchments;
palisades, carpentry, or blockhouses; advantages and disadvantages of
blockhouses. African blockhouse. Closing of field-works.

8. Artificial inundations; under what circumstances they can be
considered as obstacles. Positions and dimensions of dikes. Details of
their execution; what advantage can be drawn from an inundation having
less than five feet depth of water.

9. What is understood by the defilading of a work. The defilading of
fieldworks should, above all things, be made to depend on their trace
and situation. Definitions: dangerous ground; dangerous points.
Defilement of an isolated and closed work; in what case it is
practicable. Use of traverses. A partial defilement may sometimes be

10. Continuous lines. Broken lines. Traces of redan, tenailles,
cromailleres. Bastioned lines. Comparison between continuous and broken
lines. Principal objections to their use. Utility of each demonstrated
under certain circumstances.

11. Lines in broken ground: their form should depend on the nature of
the ground. On the manner of fortifying a table-land. Expedients for
defilading portions of lines. On the manner of making use of the natural
obstacles of the ground; forests, scarps, marshes, water-courses, &c.
Method of fortifying a house, village, an open town. Defense of a bridge
or road.

12. _Têtes de pont_. Utility of small earthen entrenchments in these
cases to facilitate the passage of a retreating army. Traces of a large
_tête de pont_. Principal circumstances relating to the use of lines in
war. Lines of circumvallation and countervallation. Frontier lines.
Retrenchments against a descent. Lines that an army should make in an
enemy’s country, far from its base of operations. Entrenchment on the
field of battle. Lines, mixed, proposed by General Rogniat.

13. Attack and defense of entrenchments, of a continuous line; of a line
at intervals; of an isolated work, &c. Examples of the attack and
defense of lines.

14. Instruction relating to the operations for profiling and defilading
on the ground.

15. Instruction on the project of field fortification. Calculation of
the dimensions of a ditch corresponding to the face of a work of a
variable relief, and to be constructed in level or other ground. Details
relating to traverses, small entrenchments; defensive caponnieres, and
accessories to defense, &c.

16. On the construction of entrenchments. Practical operations and
organization of workshops to obtain durable and solid work. Necessity,
in most cases, for accelerating the construction of entrenchments.
Vauban’s precepts. In what manner the work must proceed to obtain a
useful result; and, in the event of plenty of hands, how to finish it


1. On roads. 1 and 2, Classification of roads. Section and trace of
roads in level and mountain country. Details connected with the study of
a project for a road. Particular conditions relating to military roads.
Execution of paved and macadamized roads. Roads for passing difficult
places by the use of fascines, logs, &c. Maintenance and destruction of

2. On military bridges.

3. Observations on the currents and change of form in the bed of rivers.
Fords. Transverse sections, &c. Reconnaissances of rivers. Properties
essential to military bridges. Relation between the buoyancy and the
load in the case of floating supports. Anchorage. Construction of the
abutments. Means of rendering bridges stable.

4. Construction of a bridge of boats in different ways. Bridges made of
ordinary boats. Method of withdrawing a bridge of boats.

5. Raft bridge. Relation between the weight and the extrinsic load of a
raft. Number of trunks of trees required for a raft bridge on a river of
given dimensions. Weight of the trunk of a tree. Number and space
between rafts. Construction of a raft and a bridge of rafts. Bridges of
casks and trestles.

6. Rope bridges; their use. Calculations respecting the tension and
diameters of ropes. Construction of a suspension bridge, and
calculations relating to it.

7. Bridges on piles, carriages, gabions, &c.

8. Measures to be taken for the preservation of military bridges.
Destruction of military bridges; also of masonry bridges.
Reëstablishment of bridges.

9. Flying bridges. Ferry-boats, tubs, passage by fords, on the ice, by

10. Execution of the passage of rivers. Advancing and in retreating.


1. Definition. Fundamental principles of all operations in war. In all
cases there are--first, the base of operations; second, the point to be
arrived at; third, the line of operations. Strategetical points and

2. On marching. Preparatory and manœuvering marches. Advanced and rear
guard. On provisions. System of magazines. Requisitions. Invasions.
Battle. Examples.

3. On positions. War in a mountainous district. Retreats. Pursuit.
Convoys. Partizans.

4. Winter quarters. Cantonments. War against irregular bands. Military

5. Precis of the campaigns of the French armies.

6. Analysis of the principal campaigns of great captains.


These works consist of four Plates of Drawings, two Memoirs, and a
Project, of Field Fortification. Of the four Plates of Drawings, two
relate to Field Fortification, and two, accompanied by Memoirs, relate
to Military Communications.

Plate 1--Elements of lines. Tracing, on the scale of 1/1000 of the
interior crest (only) of a redan, lunette, redoubt, star fort, bastioned
fort, according to particular data given to each Sous-Lieutenant.
Construction on the scale of 1/200 of a complete profile for each of
these works, supposed to be established on level ground. Complete
calculation of the deblais and remblais for one of the preceding works,
according to the instructions of the Professor.

Plate 2.--Details of a field-work. Trace on the scale of 1/200 of a
portion of the work of which the deblais and remblais has been
calculated. Graphic construction of a barbette and of a direct or
oblique embrasure. Details of revetments in fascines, hurdles, turf.
Pisé. Drawing of a blockhouse.

Plate 3.--Accompanied by a Memoir. Project of a portion of road on
ground represented by certain lines, according to certain data.

Plate 4.--Accompanied by a Memoir. Military bridges.

  1. Drawing of a portion of a bridge of boats, three openings being
shown; the two first relating to the successive construction of the
bridge, and the third, of the construction by portions.

  2. Project for establishing a raft bridge; the width of the river; the
kind of troops to pass over the bridge; the length; mean diameter of the
available trunks of trees and the length and scantling of the joints
being given. The drawing to exhibit a plan of two openings of the
bridge, and a transverse section.

  3. Tressel bridge. To draw a longitudinal elevation and a transverse
section of a tressel bridge, being given the length of the top and of
the feet of the tressels up and down the stream.

  4. Project for the repair of a broken arch; being given the opening of
the head, the elevation of the roadway of the bridge above the level of
the water; the depth of the water, the rapidity of the current, the kind
of troops to pass over the bridge, and the available time and the
resources as regards men and materials which can be had recourse to.

_Programme of the Project of Field Fortification._

This project is made by the Sub-Lieutenants, according to certain data
given to each of them. It has for its object to cause them to
study:--1st. The trace. 2d. The complete organization necessary for its
defense. 3d. The details of construction of a field-work. In
consequence, the work comprises three Plates of Drawings and a Memoir
divided into three parts.

_Programme of the Drawings._

Plate 1.--Plan of the whole. This plate has for its object the research
of a trace and of a combination of suitable works for the fortification
of a certain portion of ground under certain circumstances of war
defined by particular data. Each Sub-Lieutenant receives a lithographed
sheet representing the ground to be fortified, and he has to exhibit on
this sheet the works he proposes, in tracing in plain lines the
horizontal projections of the interior crests and superior limits of the
ditch, and in dotted lines the stockades or palisades; to show in black
figures at the angles of the works the relief of the interior crests;
the sites of barbettes, embrasures, traverses, barriers, &c., being
indicated by reference letters and explanatory notes, the lines in red
showing the directions and objects of the line of fire.

Plate 2.--Organization of a work.

This plate has for its object the study of the details of the interior
and exterior organization of a work of a certain form, in order to
render it susceptible of making a good defense.

Each Sub-Lieutenant will draw a complete plan of such one of the works
shown on Plate 1, as may be pointed out by the Professor. He will
represent the ditches, parapets, embrasures, accessory defenses, small
entrenchments, descents into the ditch, &c., according to the particular
data furnished to him; the figures of the relief of the crests of all
kinds, the deblais and remblais being marked at all the angles. The
figures of the natural ground will be underlined. The same plate will
contain figured profiles which have served for the determination of the
complete projection of the work. Scale 1/250.

Plate 3.--Details of construction.

The object of this plate is to show the composition of workshops and the
manner that should be adopted in the construction of field-works,
according to circumstances, for the execution of the deblais and

Each Sub-Lieutenant will indicate the manner in which the work drawn on
Plate 2 should be constructed:--1st. To render it durable and solid. 2d.
To arrive rapidly at a useful result, even with limited resources of
workmen and tools. 3d. To finish the work in the shortest possible time,
by making use of all the necessary means. A plan will show the
composition of the workshops under each of these hypotheses, and the
successive advancement of the work will be represented by certain
profiles supposed to be made at certain periods of the construction
through the center of one of the faces of the work. In these profiles a
firm trace, figured with altitudes, will show the limits of the deblais
and remblais at the period represented by the profiles; and in addition
by dotted lines, the final results proposed to be obtained. All these
projects must be accompanied by a figured plan, showing the principal
altitudes in meters. The remblais will be colored with gamboge, the
undisturbed earth in bistre, and the deblais will be left white.

_Programme of the Memoir._

Each Sub-Lieutenant will write at the head of his Memoir the text of the
particular programme, to which he is obliged to conform in the
preparation of his project, and he should add to the text of the Memoir
all the sketches properly figured, which are necessary for the proper
appreciation of the dispositions which are not sufficiently detailed on
the Drawings.

The Memoir is divided into three parts, corresponding to the three
Plates of Drawings.


1st. General principles, according to which it would be proper to trace
the works indicated in the particular programme, such as lines at
intervals, continuous lines, têtes de pont, &c.

2d. Description of the tracing in Plate 1. Reasons deduced from the form
of the ground or the nature of the military operations that led to the
adoption of the trace. Object of the works, and their connection with
each other.

3d. Number, description, and position of the pieces of artillery
composing the armament.

4th. Maximum and minimum of troops that could be employed in the defense
of these works.

5th. Dispositions which should be adopted (relatively to the necessary
preparations in materials and to the separation and movement of troops)
for the attack and for the defense.


1st. Particular object of the work shown in Plate 2. Trace of the
complete projections of the parapets, barbettes, ramps, embrasures,
traverses, &c.

2d. Conditions that should be fulfilled by the ditch. Approximate
calculation of dimensions which should be given to it, taking into
account the increased means of providing for an excess or defect of the

3d. Discussion on the site and the part which might be expected from
small entrenchments, accessory defenses, shutters, descents of ditches,

4th. Site of powder magazines; capacity that should be given to them,
suitable to the state of the munitions necessary for the armament of the


1st. Means of ascertaining the nature of the earth; considerations
respecting relays for the transport of earth with the shovel.

2d. Description, number and disposition of the workmen in a shed for
deblai and remblai, according to the nature of the ground and number of

3d. Explanation of Plate 3. Organization of the sheds and conduct of the
work where the duration and solidity of the work are the greatest
essentials; where, on the other hand, rapidity of execution is the
principal thing to be fulfilled.

4th. Which of the modes of construction exhibited in Plate 3 it would be
desirable to employ for the proposed works, according to the
circumstance specified in the particular programme. Calculation for this
mode of construction, of the time and of the numbers of men and tools
necessary for the execution of the deblais and remblais of the work
given in the plate.

5th. Details of construction of the revetments, magazines, shutters,
accessory defenses, artillery platforms, &c.


These works consist of an exercise in tracing out a camp, and an
exercise on the profiling and defilement of field-works.

The exercise on tracing camps has no particular programme, but is
preceded by a lecture given by the Professor.

_Programme of Practical Exercises on the Defilement and Profiling of
Field Works._

This exercise comprehends: 1st, work on the ground; 2d, a Memoir.

The work on the ground has for its object: 1st, the trace of the
projections of the interior crest of a work, whose position and form are
known; 2d, the determination of the relief of the interior crest; 3d,
the profiling of the different parts, so that the relief of the
different parts of the parapet, barbettes, traverses, &c., may all be

The Sub-Lieutenants for this kind of work are divided into groups of six
or eight, employed together on the same work, each group being divided
into two squads. The work may be a lunette or a redan of given
dimensions, having a parapet of three meters thick, and a natural slope
of one to one.

1st. The direction of the capital will be marked out in front by two
numbered pickets.

2d. The tracing will be executed by means of poles or pickets placed at
all the angles, and at the extremities of the gorge; the relief will be
determined by the practical methods of defilement adverted to in the
lecture which preceded the work.

3d. The relief obtained by the defilement will be marked on all the
poles or pickets placed at the angles, and at the extremities of the
sides of the work.

4th. On each face two vertical profiles will be executed, perpendicular
to the horizontal projections of its interior crest. In order that these
profiles shall not interfere with those placed at the angles, they must
be established at several meters distant from the extremity of each

5th. The profiles of the angles will be deducted by simple
prolongations, and the same for the profiles of the gorge. If the
homologous crests of two contiguous faces do not meet each other, they
should be reconciled by joining two points taken on each of them at half
a meter from the intersection of their projections.

6th. On the traverse, designed to secure the defenders from a reverse
fire, two profiles are constructed, near to its extremities if its crest
is a right line, but if it is bent, another profile must be set up at
the junction.

7th. The data of all these profiles are, the relief of the interior
crest at the point where it is encountered by the profile, the thickness
of the parapet, the constant parts of every profile, and the natural
slope of the ground; the portion of the slope of the traverses exposed
to the view of the dominant heights should not be reveted, the others
should be.

8th. At the points of intersection of the profiles with the projections
of the ridges of the works, as well as at the points used for adjusting,
poles or pickets are placed, on which the points belonging to the ridges
are marked. These points will be joined together in each profile by
twine, indicating the different planes of the work.

9th. The form and dimensions of the batteries, either of barbettes or
embrasures, will be equally determined by poles or pickets placed at all
their angles, and united together by twine in the manner that will be
subsequently explained.

10th. For the barbette batteries, the first thing to be done is to
establish and to construct the front coupé of the salient of the
interior crest, and substitute an interior horizontal crest throughout
the extent of the barbette for that situated in the plane of defilement.
The necessary adjustments are then made between the slope of the parapet
of the barbette and that of the rest of the face, and indicate by means
of twine the intersections of the terre-plein of the barbette and of its
slope with the different planes of the work.

11th. For the embrasures, after having determined their direction, the
intersections of the cheeks and bottom, with the interior and exterior
slope of the parapet, and with its slope; also the slope which
terminates the interruption of the banquette throughout the extent of
the battery. In the case where the platform is formed more than 0^m 4
elevated above the soil, a ramp is constructed with its slope, and the
intersections with the slope from the platform are shown.

12th. After the batteries, the slope of the ends of the traverses and of
the passages for entry and exit are constructed.

13th. The traverse will be finished by adjusting its different planes
with those of the parapet. In the particular case, where it was
interfered with to make a passage over the banquette, it is finished by
reveting the slope passing by the crest of the banquette of the work.

14th. At the passages of entry and exit from the work, the parapets will
be finished by the slope of the revetment, whose intersections with the
different planes of the parapets must be determined.

15th. For each squad of workmen, the distance of the salient of the work
to the point on which it will be defiladed must be determined.


1st. Object of defilement--which is considered to be dangerous ground,
dangerous point, plane of defilement.

2d. Position of the dangerous point relatively to the work which is to
be defiladed. Practical method on the ground. Results to which it leads.

3d. On the field this method is not always applicable to an isolated
work, and never is so to entrenchments of a great development, such as
lines, large têtes-de-pont, &c. By what proceeding is it generally
expedient to attempt to fulfill in war the indisputable condition of


  NL Number of the Lectures.
  +A With application.
  -A Without application.
  I  No. of Interrogations.

  First Lectures.--                |    |Credits for Lectures.
                                   |    +----+----+-------+---
  Parts of the Course.             | NL | +A | -A | Total | I
  1st Part. Historical notions     |    |    |    |       |
    on the Organization of Armies  |  6 |    | 18 |   18 }|
  2nd Part. Tactics                |  3 |    |  9 |    9 }| 1
  3rd  “  Castrametation           |  2 |    |  6 |    6 }|
  4th  “  Field Fortification      | 16 | 24 |    |   24  | 2
  5th  “  Military Communications  | 10 | 15 |    |   15  | 1
  6th  “  Strategy                 |  6 |    | 18 |   18  | 1
    Totals                         | 43   39   51     90*   5

[* The number 90 is applied to the interrogations and to the obligations
of the notes.]

  D Drawings
  M Memoirs
  I In the Halls
  O Outside
  C Credits

                                       |          Number of
    EXECUTION OF WORK.                 |D | M |Attendances |  C
                                       |  |   +-----+------+
                                       |  |   | I   |  O   |
  Drawings of Military Art,--          |  |   |     |      |
   Plate 1. Elements of Lines          | 1|.. |  4  |  ..  |  20
   Plate 2. Details of a Field-work    | 1|.. |  8  |  ..  |  35
   Plate 3. Project of a Road          | 1|.. |  8  |  ..  |  35
   Memoir                              |..| 1 |  2  |  ..  |  20
   Plate 4. Military Bridges           | 1|.. |  8  |  ..  |  35
   Memoir                              |..| 1 |  2  |  ..  |  20
  Project of Field Fortification,--    |  |   |     |      |
   Plate 1. Plan of the whole          | 1|.. |  3  |  ..  |  15
   Plate 2. Organization of a work     | 1|.. |  8  |  ..  |  35
   Plate 3. Details of Construction    | 1|.. |  5  |  ..  |  20
   Memoir                              |..| 1 | ..  |   3  |  30
  Tracing of Camps                     |..|.. | ..  |   1  |   5
  Tracing on the Ground                |..|.. | ..  |   2  |  10
  Memoir                               |..| 1 |  1  |  ..  |  10
           Totals                      | 7| 4 | 51  |   3  | 280


  Lectures,            90
  Execution of Work,  280
      Totals          370

4th. Methods of defilement employed. Determination of the different
planes of barbettes, of their ramps, of the profiles of the gorge, &c.
Construction of embrasures.

5th. Means made use of in practice for determining the distance of the
salient of the work to the dangerous point on which it is defiladed.


The course of instruction in Permanent Fortification and the Attack and
Defense of Places, is divided into three parts, viz:--

  Art. Artillery.
  Eng. Engineers.

                                                      | No. of
                                                      | lectures to
                                                      | Art. | Eng.
  The first part consists of the study of the         |      |
    Construction of existing Fortifications,          |      |
    and it is common to the two services;             |      |
    it comprises,                                     |  10  |  10
  The second part contains principles                 |      |
   of the Art of Fortification, divided into          |      |
   three sections, of which the                       |      |
     {1st section relates to                          |      |
        Fortification on level ground                 |  19  |  19
     {2nd section relates to                          |      |
        Fortification on hilly ground                 |  19  |  26
     {3rd section relates to general                  |      |
        questions of Fortifications                   |   4  |   5
  Third part relates to the Attack                    |      |
    and Defense of Places,                            |  24  |  24
              Total number of Lectures,               |  76  |  84

The first part contains a description of the various works of permanent
fortification, their respective uses, and the changes that have been
successively made in them, together with a short history of ancient
fortification prior to the invention of powder, and the changes
introduced by the use of fire-arms.

The systems of Errard, Beville, Pagan, Vauban, Cochorn, and

The first section of the second part describes the principles on which
the various parts of a front of fortification on level ground, and
according to Cormontaigne’s system, are regulated, such as the command,
relief, defilement, form, length, and material of which the various
parts should be constructed; the modifications required by the absence
or presence of water; the changes which are necessary as regards
exterior or advanced works, and ending with a comparison of a front of
fortification according to Cormontaigne, with a modification of the same
system introduced by the French engineers.

The second section commences with the principles of defilement and its
application under various given circumstances, proceeds with the
description of an imaginary work founded on certain given data, and
furnishes the data of its proposed construction. It then supplies the
theory relating to mines, and their use in the attack, defense, and
destruction of places, and points out the particular duties of engineers
in fortified places, and the proper and most efficient manner of
carrying them on.

The third section relates to the preparation of projects for the
improvement of inefficiently fortified places, and to the utility,
particular organization, and proper position of fortified places on a
frontier line. It then explains the necessity for military law in
providing for the security of fortified places and districts along the
frontiers of a state.

The third part describes the various operations connected with the
attack and defense of a bastioned fortification, commencing with the
operations preliminary to the siege and investment of the place, and
continuing to describe the several processes to be employed in the
attack of the place, with the corresponding efforts that should be made
during its defense, and ending with an historical account of certain

This course requires the practical completion of the following:

  Nature of the Work; Time allowed for its completion.
    Subject of the Work.

    1st Part.--On existing fortifications.

  Single Plate,  20 days,
    Complete projection of the front of Cormontaigne without
    counterguard or cavalier,
    Three profiles of the front,

    2d Part.--Principles of the Art of Fortification.

  Plate, No. 1,  8  “
    1st Section: Fortifications on level ground.--Principal graphical
    constructions of the front on level ground according to particular
    data given to each Student
  Plate, No. 2,  28  “
    Complete projection of the whole of the visible and underground
    parts of the same front,
    Three profiles of the front,
  Memoir,  6  “
    Description of the principles of the Fortification, with a
    detailed discussion of the dispositions adopted in the particular
    case treated by the Students.
  Plate 3,  20  “
    2d Section: Fortification on hilly ground.--Drawing of the ideal
    fortress and of its Tête-du-pont, with the interior entrenchments,
    inundation, sluices, and all necessary details to enable a proper
    comprehension to be had of the action of the water.
    Drawing complete of one of the fronts of the place and its
    outworks, described by a particular programme. Defilement of all
    the works of this front and of the masonry of one of its faces,
  Memoir,  3  “
    On the situation of the fortification; description of the
    imaginary fortress, and of the management of the water;
    explanation of the operations of defilement drawn on Plate 3.
  Plate 4, (Artillerie.)  10  “
    Plan and profile of a full revetment of the escarp with its
    Plan, profiles, and elevation of a revetment “en décharge.”
    Detail of a gallery and small chamber of a mine, of its tamping
    and mode of firing,
  Plate 4, (Engineers.)  20  “
    Detailed project of one of the parts of the front of fortification
    defiladed in Plate 3. Plans at different height; disposition of
    the galleries and small chambers of mines required for blowing up
    the whole of the ground between two listening galleries.
  Plate 5,  10  “
    Sections and elevations of the preceding project. Foundations,
    coping of vaults, dressing of cut stones, &c.,
    Detail of a small gallery and chamber of a mine, comprised in
    the dispositions of Plate 4. Tamping and mode of firing.
  Avant,  3  “
    Abstractions of measurement of a part of the preceding project,
  Plate 6,  11  “
    Study of the alterations in the earth of the same part of the
    projects, representing the four principal periods of the work,
    by a plan and section, with an elevation of the 4th period,
  Memoir,  2  “
    General theory of the removal of earth. Application to a
    particular project,
  Register,  3  “
    Register of the removal of earth as represented in Plate 6.
  Estimate,  1  “
    Estimate of the part of the project to which the abstraction of
    measurements has been applied.
    3d Section: Projection of the improvement of an existing
    fortified place.
  Plate 7,  30  “
    Complete projection of the project for improving an existing
    fortified place,
  Plate 8,  6  “
    Details of the most interesting parts of the project, in plans,
    sections, and elevations,
  Memoir,  2  “
    Marginal notes on the defects presented by the existing system,
    and on the means employed for correcting them.
  Calculation,  5  “
    Balance of the “deblais” and “remblais” of the project.

    3d Part.--Attack and Defense of Places.
  Single Plate,  30  “
    Project of attack of a front of fortification on level ground,
    Details of the attack,
  Journal,  4  “
    Journal of the siege. Details relating to the composition of
    the garrison and of the besieging army; also on the material for
    the Artillery and Engineers required for the attack and defense.
    Pen sketch of the most elementary works of attack.

  [Transcriber’s Note:
  The “Observations” column is divided into four sections:
    Through Plate 3: Common to Students of Both Services.
    Plate 4: Artillery.
    Plate 4 (Engineers), through end of 2nd Part:
      Special to Engineer Students.
    3d Part: Common.]


  NL Number of Lectures.
  Cr Credits for the Lectures.
  +A With application (_a._)
  -A Without application (_b._)
  T  Total.
  I  Number of Interrogations.

  I. LECTURES.                   |    |        Cr         |
    PARTS OF THE COURSE.         |    +------+------+-----+
                                 | NL |  +A  |  -A  |  T  |  I
  First Part. Study of           |    |      |      |     |
    existing Fortifications,     | 10 |  4.5 |  21  |  26 |  1
  Second Part. Principles        |    |      |      |     |
    of the Art of Fortification, |....| .... | .... | ....| ...
   First Section. Fortification  |    |      |      |     |
     on level ground,            | 19 | 24.0 |   9  |  33 |  2
   Second Section. Fortification |    |      |      |     |
     on hilly ground,            | 19 | 19.5 |  18  |  38 |  2
   Third Section. General        |    |      |      |     |
     questions of Fortification, |  4 | .... |  12  |  12 | ....
  Third Part. Attack and         |    |      |      |     |
    Defence of Places,           | 24 | 24   |  24  |  48 |  2
      Totals,                    | 76 | 72   | 84   | 157 |  7

  [(_a._) The lectures with application count for 1 hour 5 minutes.]

  [(_b._) Those without application for 3 hours.]

  D  Drawings.
  M  Memoirs.
  V  Various.
  S  Sitting in the Halls of Study.
  Cr Credits.

  II. EXECUTION OF WORK.              |    Number of     |
                                      |  D | M | V |  S  |   Cr
  First Part.                         |    |   |   |     |
    Front of Cormontaigne             |  1 |   |   |  20 |    90
  Second Part.                        |    |   |   |     |
    Plate 1. Construction of Project  |    |   |   |     |
      on Level Ground                 |  1 |   |   |   8 |    35
    Plate 2. Project on Level Ground  |  1 |   |   |  28 |   125
    Memoir on ditto                   |    | 1 |   |   6 |    55
    Plate 3. Project on Hilly Ground  |  1 |   |   |  20 |    90
    Memoir on ditto                   |    | 1 |   |   3 |    30
    Plate 4. Project of Details. Plan |  1 |   |   |  20 |    90
    Plate 5. Project of Section. Plan |  1 |   |   |  10 |    45
    Abstraction of Measurements       |    |   | 1 |   3 |    25
    Plate 6. Removal of Earth         |  1 |   |   |  11 |    50
    Memoir on ditto                   |    | 1 |   |   2 |    20
    Register of ditto                 |    |   | 1 |   3 |    25
    Estimate of the Project           |    |   | 1 |   1 |    10
    Plate 7. Project of Improvements  |  1 |   |   |  30 |   135
    Plate 8. Details of ditto,        |  1 |   |   |   6 |    25
    Memoir on ditto                   |    | 1 |   |   2 |    20
    Balance of Deblais and Remblais   |    |   | 1 |   5 |    45
  Third Part.                         |    |   |   |     |
    Project of Attack                 |  1 |   |   |  30 |   135
    Journal of the Siege              |    | 1 |   |   4 |    35
                Totals                | 10 | 5 | 4 | 212 | 1,085


    Lectures,                          165 }
    Execution of Works,              1,085 } 1,250

  II. STUDIES AND EXECUTION           |  Number of   |
      OF WORK.                        +----+---+-----+
                                      |  D | M |  V  |  Cr
  First Part.                         |    |   |     |
    Front of Cormontaigne,            |  1 |   |  20 |  90
  Second Part.                        |    |   |     |
    Plate 1. Construction of the      |    |   |     |
    Project on Level Ground,          |  1 |   |   8 |  35
    Plate 2. Project on Level Ground, |  1 |   |  28 | 125
    Memoir,                           |    | 1 |   6 |  55
    Plate 3. Project on Hilly Ground, |  1 |   |  20 |  90
    Plate 4. Details of the Project,  |  1 |   |  10 |  45
    Memoir,                           |    | 1 |   3 |  30
  Third Part.                         |    |   |     |
    Plate. Project of Attack,         |  1 |   |  30 | 135
    Journal of Attack,                |    | 1 |   4 |  35
             Totals                   |  6 | 3 | 129 | 640


  Lectures,                      160 }
  Studies and Execution of Work, 640 } 800.


  Cr Credits for Lectures.
  NL Number of Lectures.
  +A With application.
  -A Without application.
  T  Total Credits.
  I  Number of Interrogations.

                                      |    |        Cr       |
  I. LECTURES.                        |    +-----------------+
                                      | NL |  +A  | -A |  T  | I
  First Part.                         |    |      |    |     |
    Study of Existing Fortification,  | 10 |  4.5 | 21 |  26 | 1
                                      |    |      |    |     |
  Second Part.                        |    |      |    |     |
    Principles of the Art             |    |      |    |     |
      of Fortification,               |    |      |    |     |
    First Section. Fortification      |    |      |    |     |
      on Level Ground,                | 19 | 24.0 |  9 |  33 | 2
    Second Section. Fortification     |    |      |    |     |
      on Hilly Ground,                | 26 | 36.0 |  6 |  42 | 2
    Third Section. General Questions  |    |      |    |     |
      on Fortification,               |  5 |  1.5 | 12 |  13 |
  Third Part.                         |    |      |    |     |
    Attack and Defense Places,        | 24 | 24.0 | 24 |  48 | 2
                Totals                | 84 | 90.0 | 72 | 162*| 7

[* The number 162 is applicable to the Interrogations.]


The course of Topography comprehends two parts.

The first relates to the art of topographical drawing, and the second
to the art of making topographical surveys. Both parts are carried on
_pari passu_; but as the order in which the different branches of the
instruction can be given depends very much on the other works carried on
in the School, it will be more convenient to give the programme for each


The instruction in topographical drawing comprehends lectures and
exercises in graphical representation. It is based on a complete
exposition of the conventional principles of this species of drawing,
and it is illustrated by engraved examples of the characteristics
adopted for the representation of the various details.

_First Section.--Lectures._

The lectures have for their object the explanation of the general
principles of the instruction in topographical drawing, and the
geometrical conditions which should regulate the shading of maps and
their reduction. They immediately precede the exercise to which they

Lecture 1 relates to small maps, copies, and reductions of these; and it
explains the object of topographical maps, the various kinds and the
different scales generally used. The manner in which the form of the
ground is represented by equi-distant contour or level lines is also
explained, and mention is made of the conventional tints used, and the
species of writing and value of the scale employed.

Lectures 2 and 3 relate to the execution of shaded plans by the brush
and the pen, under different circumstances of light and shade.

Lecture 4 explains the different methods for reducing topographical
maps, also the description, mode of using, and verification of

_Second Section.--Exercises._

These exercises are intended to teach the students the conventional
signs used in topographical drawing, and to give them facilities with
the pencil and brush for producing shaded maps, and in reducing them
from one scale to another.


This instruction comprises:

  1st. Lectures given in amphitheatre.
  2d. Practical lectures or exercises.
  3d. The execution of topographical surveys.

_First Section.--Oral Lectures._

These lectures are divided in two classes, which comprehend:--

  1st. Those relating to the description of the instruments, and of the
methods used in topography.

  2d. Those which have reference to the manner in which the students
should proceed in the execution of the work, and principally of surveys
of limited extent.

Eight lectures are devoted to the description of the various
instruments, the method of adjusting their errors, and the manner of
using them, as well as to the different ways of proceeding in
topography; touching also on the various modes of measuring distances,
with descriptions of the compass, plane table, and instruments used for
leveling, and on the taking observations for and preparation of
sections, and the orientation of maps.

Four preparatory lectures are given, showing the manner in which the
students should proceed when on the ground to make a survey of small

Two lectures relate to the methods that should be employed in making a
survey of considerable extent, and on the appropriate scales.

Two lectures on military reconnaissance plans; instruments and scales

Two preparatory lectures relate to the execution of a reconnaissance
plan, in which the operations of a sham siege are intended to be

_Second Section.--Practical Lectures or Exercises._

The object of these lectures, which take place on the glacis of the
fortification, is to show the students the practical modes of using the
instruments, and the precautions which must be taken, together with the
most elementary proceedings in topography. They are given to ten or
twelve students at the same time, and the Professor is assisted by an
officer of the staff. Each lecture lasts two and a half hours.

_Third Section.--On the Execution of Topographical Surveys._

The object is to familiarize the students with the use of the principal
instruments and the principal operations, and they comprehend
out-of-door work, of which the results are sketches, registers, and
minutes made in pencil, and in the construction of plans, and inking in
of the minutes in the Halls of Study.

The out-of-door work is performed under the superintendence of officers
of the staff, who assist the students in their work. The construction of
the plans is not commenced until the pencil minutes have been examined
by the Professor.

These exercises comprise:--

  1st and 2d. Construction of plans by the aid of the compass.
  3d. The plan of a fortification made with the plane table.
  4th. The determination of the variation of the compass.
  5th. The execution of a second survey by the aid of the compass.
  6th.         “       “  rapid survey by pacing the distances.
  7th.         “       “  reconnaissance survey.
  8th.         “       “  an itinerary and reconnaissance sketch.
  9th. The preparation of a plan on which the whole of the operations
    of a sham siege may be laid down, as the works of attack and
    defense proceed.


  Cr Credits for Lectures.
  NL Number of Lectures.
  +A With application.
  -A Without application.
  T  Total Credits.
  I  Number of Interrogations.

                                      |    |        Cr        |
                                      |    +------------------+
  I. LECTURES.                        | NL |  +A  | -A |   T  | I
  1st part:                           |    |      |    |      |
  Topographical drawing,              |  4 |   6  |....| }    |
  Art of Surveying--                  |    |      |    | } 36 |
    On the instruments and            |    |      |    |      |
      Topographical processes,        | 8  | 12   |....| }    |
    On Surveys of considerable        |    |      |    |      |
      magnitude,                      | 2  | .... |  6 | }    | 2
    On Reconnaissance Plans,          | 2  |  1.5 |  3 | }    |
    Preparatory to out-of-door work,  | 5  |  7.5 |....| }    |
               Total,                 |21  | 27   |  9 |  30* | 2

[* The credit is diminished here and carried forward to the exercises,
which serve for the interrogations of many lectures. These lectures have
therefore really three series of interrogations.]

  D  Drawings.
  M  Memoirs.
  V  Various.
  +H In the halls.
  -H Out of the halls.
  O  Out of doors.
  C  Credits.

                                |    |    |    | Attendances  |
    EXECUTION OF WORK.          |    |    |    +----+----+----+
                                |  D |  M |  V | +H | -H |  O |  C
  1st Part:--                   |    |    |    |    |    |    |
  Topographical Drawing:        |    |    |    |    |    |    |
    Conventional Tints,         |  1 |....|....|  3 |....|....|  10
    Study of Maps,              |  4 |....|....| 26 |....|....| 120
    Reduction,                  |  1 |....|....|  2 |....|....|  10
    Construction of a           |    |    |    |    |    |    |
      Triangulation with the    |    |    |    |    |    |    |
      Compass,                  |  1 |....|....|  3 |....|....|  15
    1st Survey with the Compass:|    |    |    |    |    |    |
      Out-of-door work,         |....|....|  1 |....|....|  6 |  50
      Laying down,              |  1 |....|....|  4 |....|....|  20
    Survey of Fortifications    |    |    |    |    |    |    |
      with the Plane-Table:     |    |    |    |    |    |    |
      Out-of-door work,         |} 1 |....|  1 |....|....| 10 |  80
      Laying Down,              |}   |  1 |....|  4 |....|....|  25
    Determination of the        |    |    |    |    |    |    |
      Variation of the Compass, |  1 |....|....|  1 | 1h |....|   5
    2d Survey with the Compass: |    |    |    |    |    |    |
      Out-of-door work,         |  1 |....|  1 |....|....|  8 |  65
      Laying down,              |  1 |....|....|  2 |....| 10 |
    Rapid Survey:               |    |    |    |    |    |    |
      Out-of-door work,         |} 1 |....|  1 |....|....|  6 |  50
      Laying down,              |}   |  1 |....|  4 |....|....|  25
    Reconnaisance survey:       |    |    |    |    |    |    |
      Out-of-door work,         |} 1 |....|  1 |....|....|  4 |  30
      Laying down,              |}   |  1 |....|  3 |....|....|  20
    Itinerary and               |    |    |    |    |    |    |
      Reconnaissance,*          |  1 |....|....|....|....|  1 |  10
    Topographical operations    |    |    |    |    |    |    |
      relative to sham siege†   |....|....|....|....|....|....| ....
    Topographical exercises,    |    |    |    |    |    |    |
      4 each of 2½ hours        |    |    |    |    |    |    |
      duration,                 |....|....|....|....|  6 |....|  20‡
         Total                  | 15 |  3 |  5 | 52 |  7 |  35| 565

[* The description Itinerary is reckoned with the simulated siege

[† For a memoir.]

[‡ This number is formed with 5 taken from it for the credit of the
interrogations because the exercises serve for the interrogations of
several lectures.]


  Lectures,                          30}
  Execution of work,                565} 595.


This course is divided into two parts--the one part special for the
engineers, and the other common to the artillery and engineers.

The first comprises:--

  1st. The study of the execution of a triangulation of some extent, and
of its connection with the general triangulation of France, executed
under the superintendence of the Dépôt de la Guerre, and

  2d. Leveling with the barometer.

The second contains:--

  1st. The study of reflecting instruments.

  2d. The principles of dialling.

Each of these parts comprehend:--

  1st. Lectures given in the amphitheatre.

  2d. Practical lectures or exercises.

  3d. An application.


1st Section--Lectures.

These Lectures include:--

  1st. A description of the principal geodesical instruments.

  2d. The establishment of the triangulation.

  3d. The survey and the calculations connected with it.

  4th. The orientation of the triangulation.

  5th. The calculation of the co-ordinates of the points and their
construction from the minutes of the survey.

  6th. The geodesical and barometrical leveling.

The first lecture is devoted to the explanation of the different kind of
signals used under various circumstances; on the method of measuring
bases and angles, and the principles on which these operations are
performed; and concluding with the description and mode of using certain
instruments for measuring angles.

The second lecture continues and enlarges on the subject of the
measurement of angles, horizontal and vertical, with different kinds of

The third lecture relates to the corrections and reductions which must
be made to observed angles, such as the correction for the eccentricity
of the instruments, to the reduction of the angles to the horizon, and
to the center of the station, and also on the adjustments of the
instruments, or the application of corrections for certain errors.

The fourth lecture discusses the calculation of the triangles and their
errors, and points out the best organization that can be given to the
triangulation, and the exactitude which can be expected from it.

The fifth lecture also relates to the calculation and the development of
the triangulation, and explains the nature of the geodesical operations
for the map of France.

The sixth lecture explains the manner of observing for, and
determination of the azimuthal bearing, for the orientation of the

The seventh lecture has reference to the convergence of meridians,
calculation of rectangular co-ordinates, sundry problems, and geodesical

The eighth lecture shows in what manner the barometer is made use of for
the determination of differences of altitude, the nature of the
corrections to be applied to the instrument, and the degree of
exactitude to be found in the results of this process.

The ninth lecture points out the order in which geodesical calculations
should be performed and the verifications which should be exacted.

The Second Section contains five lectures or exercises, and they have
for their object to familiarize the students with the use of the various
kinds of instruments employed in carrying on the operations which have
been shortly described in the first section.

The Third Section relates to the practical application of the preceding
principles, and mostly consists of geodesical applications.


The First Section consists of lectures given in the amphitheatre, and
relates to reflecting instruments, such as the sextant, reflecting
circle, and the method of using them, and also on the principles of
dialling, and its connection with various problems in astronomy;
describes also the different kinds of dials.


In which the students are called upon, in the presence of the Professor,
to adjust the sextant, and to use it in connection with an artificial
horizon for the measurement of the angle between any two objects of the
altitude of these objects above the horizon, and also the same altitude.

Third Section contains the practical application of the principles
enunciated in the preceding sections, in the preparation by the students
of two drawings, in which they will exhibit the graphical representation
of the hour in terms of the altitude of the sun previously observed, and
show the various constructions of a sun-dial, according to the specified
conditions based on the observation of the hour angle.


  Cr Credits for Lectures.
  L  Number of Lectures.
  +A With application.
  -A Without application.
  I  Number of Interrogations.
    LECTURES.                      |    |        Cr         |
                                   |    +------+----+-------+---
                                   |  L |  +A  | -A | Total | I
  First Part:--Geodesy:            |    |      |    |       |
    Lectures with application,     |  4 |   6  |....|} 21   | 1
    Lectures without application,  |  5 | .... | 15 |}      |
  Second Part:                     |    |      |    |       |
    Reflecting Instruments,        |  1 |  1.5 |}...|       |
    Dialling,                      |  2 |    3 |}   |  4.5  | 1
        Total,                     | 12 | 10.5 | 15 | 25.5  | 2

  Att Attendances
  D  Drawings.
  M  Memoirs.
  V  Etats Divers.
  +H In the halls.
  -H Out of the halls.
  C  Credits.

                                |    |    |    |   Att   |
    EXECUTION OF WORK.          |    |    |    +----+----+
                                |  D |  M |  V | +H | -H |  C
  First Part:                   |    |    |    |    |    |
    Geodesical calculations,    |....|....|  1 |  4 |....| 20
    Exercises of 2½ hours,      |....|....|  1 |....|  5 | 10
                                |    |    |    |    |    |
  Second Part:                  |    |    |    |    |    |
    Drawings of Dialling,       |  2 |....|....|  4 |....| 20
    Exercises of 2½ hours,      |....|....|....|....|  1 |  5
      Total                     |  2 |....|  2 |  8 |  6 | 55


  Lectures,                           25 }
  Execution of Work,                  55 } 80.


  Cr Credits for Lectures.
  L  Number of Lectures.
  +A With application.
  -A Without application.
  I  Number of Interrogations.
    LECTURES.                      |     |        Cr         |
                                   |     +------+----+-------+
                                   |  L  |  +A  | -A | Total | I
  Reflecting Instruments,          |  1} |  4.5 |....|   5   | 1
  Dialling,                        |  2} |      |    |       |
      Total,                       |  3  |  4.5 |....|   5   | 1

  D  Drawings.
  M  Memoirs.
  +H In the halls.
  -H Out of the halls.
  C  Credits.

                                |  Number of        |
                                |    | Days    |    |
    EXECUTION OF WORK.          |    +----+----+    |
                                |  D | +H | -H |  M | C
  Drawings of Dialling,         |  2 |  4 |....|....| 20
  Exercises of 2½ hours,        |....|....|  1 |....|  5
      Total,                    |  2 |  4 |  1 |....| 25


  Lectures,                            5 }
  Execution of Works,                 25 } 30.


  1st part--Geology,                                       12
  2d    “   On the Metallurgy of Iron, on Working in Iron,  6
  3d    “   Applications of the Working in Iron,            3
  4th   “   On the Manufacture of Small-arms,               4
  5th   “      “         “     of Ordnance,                 5
  6th   “      “         “     of Powder,                   5
  7th   “   On Pyrotechny,                                  2
                                   Total,                  37


_Lecture_ 1.--Preliminary notions. Definition of geology expressed from
its applications. Division in four sections:--1st. Mineralogy. 2d.
Paleontology. 3d. Geognosy. 4th. Geogeny. (Only the three first are here
treated of.)

First Section.--Mineralogy. Generalities. Distinctive characters of
minerals. Fundamental principle of a mineralogical classification.
Minerals are distinguished as having characters either exterior,
crystalline, chemical, or physical; classification of minerals.

_Lecture_ 2.--First class: Simple bodies forming one of the essential
principles of minerals. Genus silica, quartz, sulphur. Second class:
Alkali and alkaline salts, potass, soda, &c. Third class: Alkaline
earths, and earths. Genus lime. Fourth class: Metals. Iron of various
kinds; copper, lead, tin, zinc.

_Lecture_ 3.--Fifth class: Silicates of various kinds. Sixth class:
Combustibles, minerals.

_Lecture_ 4.--Description of various rocks. Classification of rocks.

_Lecture_ 5.--Use of rock and stone in the arts, and particularly in the
art of construction.

_Lecture_ 6.--On the calcination of calcareous stones, lime-kilns.

_Lecture_ 7.--Manufacture of artificial hydraulic lime, manufacture of
bricks, stucco, or cements.

_Lecture_ 8.--Second Section: Paleontology. General division established
in zoology and botany. General notions relating to the different kinds
of animals and vegetables, of which the remains are found in various
geological formations. Third section: Geognosy. Lectures 9, 10, 11, 12,
occupied with the explanation of the various formations.


_Lecture_ 13.--Preliminary notions. Definitions and general
considerations. Characteristics of iron, steel, cast-iron, &c.

_Lecture_ 14.--On iron ore and the various kinds of fluxes.

_Lecture_ 15.--On combustibles. Vegetable combustibles, mineral

_Lecture_ 16.--Manufacture of cast-iron. High furnaces, different modes
of proceeding with vegetable and mineral combustibles.

_Lecture_ 17.--Manufacture of iron and steel and the different kinds of


_Lecture_ 19.--Making of projectiles, carriages for guns and mortars,
axle-trees and anchors. Use of cast-iron for artillery. General notions
in moulding. Use of wrought-iron and steel. Materials first made use of
for the making of projectiles, and in the casting of cannon-balls, &c.

_Lecture_ 20.--On the manufacture of hollow projectiles and the
carriages for guns and mortars.

_Lecture_ 31.--On the manufacture of axles and anchors.


_Lecture 22._--Preliminary considerations. Assay of metals. Fire-arms,
manufacture of gun-barrels, describing the various details.

_Lecture_ 23.--Bayonets, locks, &c.

_Lecture_ 24.--On the making of stocks. Finishing. Rifling small-arms.

_Lecture_ 25.--Manufacture of sabres, swords, lances, hatchets,
cuirasses, and on the preservation, maintenance, and repair of arms.


_Lecture_ 26.--Preliminary notions. Metals proper for the manufacture of
ordnance. Composition and properties of gun-metal. Wrought and cast-iron
ordnance. Moulding generally. Moulding of cannons.

_Lecture_ 27.--Moulding of howitzers. Foundries. Fusion of the metals.

_Lectures_ 28, 29.--Boring. Turning. Carving. Turning of the trunnions,
&c. Manufacture and reception of bushes. Insertion and replacement of

_Lecture_ 30.--Last operations. Proofs and reception of cannon. Chemical
operations. Assay and analysis of the metals employed in the casting of
gun-metal; proportion of the several ingredients.


_Lecture_ 31.--General notions. Various kinds of powder, &c. On
saltpetre and sulphur.

_Lecture_ 32.--Charcoal; wood employed; various kinds of charcoal;
proceeding followed in making powder in various ways by the pestle.

_Lecture_ 33.--Manufacture by mills, &c.

_Lecture_ 34.--Influence of the proportion of the several ingredients,
and of the manner of making it on its various properties. Preservation,
inflammation, and combustion.

_Lecture_ 35.--Proofs and reception of powder. Proof of its projectile
force. Mortar proof, and various kinds of other proofs to which it is
subject. Reception and analysis of powder.


_Lecture_ 36.--Preliminary ideas. Objects of the course. Precautions
that should be adopted to prevent accident. Mixture of the materials.
Manufacture of leaden balls of various kinds. Caps. Fireworks for
warlike purposes, used for setting buildings, &c., on fire. Firing
cannon and exploding mines.

_Lecture_ 37.--Fireworks employed under various circumstances in war.
Signal rockets. For illuminating or setting on fire. For explosions.
Petards. On ordinary fireworks.

_Works of Application._--The works of application which are connected
with the course of science applied to the military arts are as

  1st. Study of samples of mineralogical specimens.
  2d. Study of geological maps to be followed by a memoir.
  3d. Memoirs on:
         1st. Iron and its applications.
         2d. Manufacture of cannon.
         3d. Manufacture of small-arms and powder.
  4th. Out-of-door geological excursions to be followed by memoirs.
  5th. Manipulations relative to moulding in earth or sand.
  6th. Chemical manipulations.
  7th. Pyrotechnic manipulations.

_First.--Study of Samples of Mineralogical Specimens._

This study has for its object the determination of the kind of minerals
described in the course. It is made in sections of ten or twelve
Sub-Lieutenants and by attendances of one hour, each Sub-Lieutenant
being called upon to reply at least three times.

_Second.--Study of Geological Maps, followed by a Memoir._

The study of geological maps will consist in indicating, by conventional
colors, the different geological formations of a lithographical map, and
to make a section in a particular direction. The map will be the same
for all, and it will be conceived so as to correspond with the
geological formation of France, but the sections will differ for each

An explanatory memoir will have for its object to call the attention of
the Sub-Lieutenants to the most salient facts which will be placed in
relief by this study.

One attendance in the halls of study will be devoted to this work.

_Third.--Three Memoirs._

Three memoirs on different parts of the course, other than the
geological, will be made immediately after the interrogations relative
to each section. Particular data will be furnished to each
Sub-Lieutenant. Three attendances in the halls of study will be allowed
for these memoirs.

_Fourth.--Geological Excursions._

Three geological excursions will be made in the environs of Metz by
groups of ten or twelve Sub-Lieutenants under the direction of the
Professor, and at the period of the out-of-door work, so as not to
interfere with the current work in the halls. The first excursion will
have for its object the study of the lias and lower oolite, met with in
the vicinity of Metz. If the time will admit of it, a reconnaissance
will be made to the great oolite at Taumont or at Amanvillers.

The second excursion will be made in the direction of Gorze for the
study of the lower oolitic formation and to trace it up to Bradford
clay, where an important fault occurs in this direction near to Metz.
The study of this fault will be the great object of this excursion.

The third excursion will be made in the direction of Forbach, meeting
with the lias, chalk-colored freestone, &c.

Three entire days will be devoted to these excursions, and each
Sub-Lieutenant will enter his observations in a note-book, and make a
certain number of sections, and report the results of these excursions
in three memoirs in a specified time.

_Fifth.--Manipulations relative to Moulding in Earth or Sand._

These mouldings of projectiles will be made by sections of ten or twelve
Sub-Lieutenants, two attendances of three hours each being devoted to
them, one for ordinary and the other for hollow projectiles.

The manipulations for the moulding of cannon will be executed by the

All the Sub-Lieutenants will be successively called by sections a
certain number of times, in order that they may be enabled to render an
account of the different states of advancement of the work.

Programme of practical instruction for the casting of projectiles.

  1st attendance.   Making shot, &c.
  2d attendance.    Making hollow projectiles.

Programme of the moulds to be executed by the Professor.

Manufacture of cannon; moulding in earth and the various processes to be
carried on.

_Sixth.--Chemical Manipulations._

The chemical manipulations are made by sections of ten or twelve

Nine attendances of three hours each are employed.

  1st. To the determination of the specific gravity and real density
    of gunpowder and to its analysis.
  2d. To two other analyses of gun-metal, iron-ore, &c.

_Seventh.--Manipulations in Pyrotechny._

The manipulations in pyrotechny will be made by the whole division,
divided into three brigades. Each brigade will be assembled in one of
the halls at the School of Pyrotechny, and will execute the different
manipulations indicated in the following programme, under the direction
of the Professor, and with the assistance of the master artificers of
the School of Pyrotechny. Five attendances of three hours will be
employed at these manipulations.


  1st Attendance. Munitions for small-arms.
                          {Construction of bullets.
    Infantry cartridges,  {      “      of pouches and caps.
                          {      “      of cartridges.
    Cartridges with oblong bullets.
  2d Attendance. Ammunition for field guns.
    Construction and filling of pouches, packing in wood, &c.
  3d Attendance. Ammunition for siege artillery, &c.
    Construction and filling of cartridges, &c.
    Charging hollow projectiles.
  4th Attendance. Fireworks for war purposes.
    Construction of matches, quick matches, tubes, fusees
      for shells and grenades.
    Construction of signal rockets.
  5th Attendance. Carriage of field ammunition.
    Loading and unloading field ammunition chests for cannons,
      howitzers, and infantry wagons.
    Construction of ornamental lances and Roman candles.


  NL No. of Lectures.
  +A With Application, 1h. 5m.
  -A Without Application, 3h. 0m.
  T  Total Credits
  I  No. of Interrogations

     Lectures.--                      |    | Credits for   |
                                      |    |  Lectures.    |
                                      |    +-----+----+    |
    Parts of the Course.              | NL | +A  | -A |  T | I
  1st Part, Geology,                  | 12 | 15  |  6 | 20 | 2
  2d   “   on Working in Iron,        |  6 |     | 18 | 20}| 1 *
  3d   “   Applications of            |    |     |    |    |
             working in Iron,         |  3 | 15  |  6 | 10}|   †
  4th  “   Manufacture of Small Arms, |  4 |     | 12 | 10 | 1
  5th  “   Manufacture of Cannon,     |  5 |     | 15 | 15 | 1
  6th  “   Manufacture of Powder,     |  5 |     | 15 | 15}| 1
  7th  “   Pyrotechny,                |  2 |  3  |    |  5}|
                                      | -- +-----+----+----+----
                                      | 37 |19.50| 72 | 95 | 6

  [* The first series of interrogations relates to mineralogy.]
  [† The second to geognosy.]

  [Transcriber’s Note:
  The printed Observations column (shown here as footnotes) is
  ambiguous; the best guess is that both items refer to Geology.]

  St Studies.
  Sk Sketches.
  M  Memoirs.
  E  Exercises.
  Mp Manipulations.
  H  Attendances in halls, 4h. 5m.
  OD Attendances out of doors, 6h.
     Attendances at the Laboratory:
  L1 1h. to 2h.
  L3 of 3h.
  P  Attendance at the School of Pyrotechny 3h.
  Cr Credits.

         Works of                   |       Number of             |
       Application.                 |St|Sk|M |E |Mp|H |OD|L1|L3|P | Cr
  Study of Mineralogical Specimens, | 3|..|..|..|..|..|..| 3|..|..|  5
  Study of Geological Map,          |..|..|..|..|..|..|..|..|..|..| ..
    followed by a Memoir Map,       |..| 1|..|..|..| 1|..|..|..|..|  5
  Memoir,                           |..|..| 1|..|..|..|..|..| 1|..| 10
  Memoirs on the Metallurgy         |..|..|..|..|..|..|..|..|..|..| ..
    of Iron, and its--              |..|..|..|..|..|..|..|..|..|..| ..
    1. Application,                 |..|..| 1|..|..| 1|..|..|..|..| 10
    2. Manufacture of cannon,       |..|..| 1|..|..| 1|..|..|..|..| 10
    3. Manufacture of small arms    |..|..|..|..|..|..|..|..|..|..| ..
       or powder,                   |..|..| 1|..|..| 1|..|..|..|..| 10
  Geological Excursions,            |..|..|..|..|..|..|..|..|..|..| ..
    followed by Memoirs:            |..|..|..|..|..|..|..|..|..|..| ..
      Excursions,                   |..|..|..| 3|..|..| 3|..|..|..| 20
      Memoirs,                      |..|..| 3|..|..|..|..|..|..|..| 20
  Manipulations in--                |..|..|..|..|..|..|..|..|..|..| ..
      Moulding,                     |..|..|..|..| 2|..|..|..| 2|..|  5
      Chemistry,                    |..|..|..|..| 9|..|..|..| 9|..| 25
      Pyrotechny,                   |..|..|..|..| 5|..|..|..|..| 5| 15
    Total,                          | 3| 1| 7| 3|16| 4| 3| 3|12| 5|135


  Lectures,               95 }
                             } 230.
  Works of Application,  135 }



_Lectures_ 1 and 2.--Short account of the general principles which serve
as a base for the application of mechanics to machines, under the
compound ratio of their establishment and of the calculation of their

_Lecture_ 3.--General composition of a factory; power, recipient,
transmission of movement, tools. General method of calculating the
effect of forces in a complete factory.

_Lectures_ 4, 5, and 6.--Theoretical rules and the results of
experiments concerning the flow of liquids. (Particular reference is
made to the principles which relate to the large orifices of machines
moved by water.)

_Lecture_ 7.--Gauging of the volumes and valuation of the dynamical
power of water-courses which feed machines.


_Lecture_ 8.--Theory of the effect of water on hydraulic wheels.
Determination of the elements of the calculation.

_Lectures_ 9 to 13.--Application of the general theories to the
principal hydraulic recipients. Conditions of the maximum, relative to
the useful effect of each kind. Results of experiments, &c. (With
reference to turbines, those which are most generally employed in the
artillery workshops must be adverted to.)

_Lecture_ 14.--Comparative abstract of the usual properties of various
hydraulic “recepteurs.” Operations that must be carried on in order to
arrive at their results and to their reception in manufactories.

_Lecture_ 15.--Physical ideas relative to the use of the vapor of water
as a motive power. Theoretical bases of the calculation of the effects
of steam-engines. Force exerted by the compression and expansion of
elastic fluids.

_Lectures_ 16 to 18.--Practical notions and results of experiments
relating to the effects and to the usual properties of the principal
systems of steam-engines in use, as to the employment, reception, and
maintenance in workshops.


_Lecture_ 19.--Resistance to compression: 1st, by gradual pressure; 2d,
by shock. Results of experience. Application to wooden and cast-iron
supports, and to the foundations of machines. Stocks of hammers.

_Lecture_ 20.--Resistance to traction. Application to the shank of a
piston, to bolts, chains, cordage, and leather straps. Resistance to
flexure. Practical formulæ for calculating the transverse dimensions of
the wooden or cast-iron arms of hydraulic wheels, of the catches or

_Lecture_ 21.--Continuation of the resistance to flexure. Practical
formula for calculating the dimensions of the several parts of such
machines. Cranks, winches, and handles in wood or in metal.

_Lecture_ 22.--Resistance to torsion. Practical formulas. Results of
experiments relative to the resistance of wood and metals to boring and
turning. Resistance of cast-iron plates to clipping.


_Lectures_ 23 and 24.--Of blowing machines. General expression of their
useful effect. Conditions of the maximum effect. Ventilators; their use
in workshops and galleries of mines. Practical bases of their
construction. Blowing machines with a piston. Description. Calculation
of the effects and results of experiment.

_Lectures_ 25 and 26.--Description and properties of alternative and
circular sawing machines. Practical rules for their establishment.
Results of experiments concerning the motive power they require, the
useful effect obtained, and the resistance of various kinds of wood to
the action of the tool. Results of observation relative to the work in
shops by hand-saws.

_Lectures_ 27 and 28.--Machines which act by shocks. Practical formula
for the calculation of the loss of acting force in the shock.
Description and usual properties of various kinds of hammers employed in
workshops. Results of experiments proper for serving as the base for the
establishment of lever hammers and pestles in powder manufactories.
Results of calculation and observation relative to hammers and pestles
moved directly or by the transmission of a movement by steam.

_Lecture_ 29.--Grindstones for powder manufactories. Rapidity suitable
to the different parts of the work. Means of obtaining it. Calculation
of the necessary motive power. Sharpening grindstones for the
manufacture of arms. Ventilation.

_Lecture_ 30.--Lathes and drilling bits. Description. Rapidity of
movement and form of the tools, according to the nature of the matter
and kind of work. Results of experiments concerning the motive force
required, and its relation to the useful effect obtained. Composition of
a workshop of turning-lathes for an arsenal of artillery.

_Lecture_ 31.--Boring. Machines for cutting and boring. The form of the
tool and the rapidity of its action must depend on the nature of the
material and the kind of work. Results of experience concerning the
motive power required, and its relation to the useful effect obtained,
principally for the boring machines of the manufactories of arms and of
foundries. Boring machines, disposal of them in an arsenal.

_Lecture_ 32.--Flatteners. Machines for centering, for making screw
holes. Descriptions. Different rapidity of the work, dependent on its
nature and that of the material. Results of experiments concerning the
amount of the motive power and its relation to the useful effect


_Lecture_ 33.--Proceeding to be followed in the preparation of the
sketches of a machine. Observations on the effects of machines, their
duration, original cost, and cost of maintenance, mode of making, &c.
Indications of the difficulties which are met with, and means which
should be employed.

_Lecture_ 34.--Project of a factory (specially for the sub-lieutenants
of artillery.) Legal conditions respecting the erection of factories.
General mode of proceeding with the project. Choice of motor machines
dependent on local circumstances and the nature of the work to be

_Lecture_ 35.--(Special for the sub-lieutenants of artillery.)
Determination of the effects supported by the pieces, whose dimensions
should be calculated in applying the practical formula of the resistance
of materials. Selection of materials.

_Lecture_ 36.--(Special for the sub-lieutenants of artillery.) Principal
assemblages of various pieces of machines. Building, foundations,
supports of trunnions and pivots.


_Survey of Workshops._

This survey of workshops comprehends:--

1st. Figured sketches and observations made on the ground.

2d. Drawing of the whole and of details shaded.

3d. A memoir containing an accurate description of the machines and
workshops, the calculation of the dynamical effect, the exposition of
the mode of fabrication, and, in general, the results and consequences
of the observations made on the spot. It must be executed by each,
conformably with the particular programme, and to the instruction which
will be given to him. He is allowed for this work thirty-four days.

_Project of Machines._

This work, executed immediately following the preceding, by the
sub-lieutenants of artillery only, has exclusively for its object the
establishment of a workshop for the service of the artillery,
comprehending the driving machines and the principal operators; or, if
there be time, the improvement of the workshops of the same arm,
described in the preceding work. This project must be executed
conformably to the particular programme given to each sub-lieutenant. It
comprehends; 1, sheet of drawings: 2, a memoir. Twenty-six days are
allowed for this work,


  NL No. of Lectures.
  CL Credits for Lectures.
  +A With application.
  -A Without application.
  C  Total Credits.
  I  No. of Interrogations.

                    |      Artillery.       |        Engineers.
  Oral Instruction  +----+----+----+----+---+----+-----+----+-----+---
    --Parts of      |    |   CL    | C  | D | A  |    CL    |     | D
    the Course.     |    +----+----+    |   |    +-----+----+     |
                    | NL | +A | -A | TC | I | NL |  +A | -A |  TC | I
  1st Section--General Principles, |    |   |    |     |    |     |
                    |  7 |  6 |  9 | 15 | 1 |  7 |   6 |  9 |  15 | 1
  2d Sec.--Driving Machines,  |    |    |   |    |     |    |     |
                    | 11 | 12 |  9 | 21 | 1 | 11 |  12 |  9 |  21 | 1
  3d Sec.--Resistance of materials,|    |   |    |     |    |     |
                    |  4 |  5 |  3 |  8 |...|  4 |   5 |  3 |   8 |...
  4th Sec.--Working Machines, |    |    |   |    |     |    |     |
                    | 10 | 15 |....| 15 | 1 | 10 |  15 |    |  15 | 1
  5th Sec.--Lectures preparatory to the works of application,     |
                    |  4 |  6 |....|  6 |   |  1 | 1.50|....| 1.50|...
     Total          | 36 | 44 | 21 | 65 | 3 | 33 |39.50| 21 |60.50| 3


  D  Sheets of drawings.
  M  Memoirs.
  Att Attendances.
  H  In the halls.
  O  Out-of-doors.
  C  Credits.

                       |    Number of         |    Number of
  Works of application |   |   |  Att   |     |   |   |   Att   |
                       |   |   +----+---+     |   |   +----+----+
                       | D | M |  H | O |  C  | D | M |  H |  O |  C
  Survey of workshops: |   |   |    |   |     |   |   |    |    |
    Figured sketches   |   |   |    |   |     |   |   |    |    |
      and observations,| * |...|....| 8 |  65 | 1 |...|....|  8 |  65
    Shaded drawings,   | 1 |...| 22 |...| 100 | 1 |...| 22 |....| 100
    Memoir,            |...| 1 |  4 |...|  40 |...| 1 |  4 |....|  40
  Project of machines: |   |   |    |   |     |   |   |    |    |
    Calculations       |   |   |    |   |     |   |   |    |    |
      and drawings,    | 1 |...| 20 |...|  90 |...|...|....|....|....
    Preparation        |   |   |    |   |     |   |   |    |    |
      of memoir        |...| 1 |  6 |...|  60 |...|...|....|....|....
          Total,       | † | 2 | 52 | 8 | 355 | † | 1 | 26 |  8 | 205

  [* 1 note book.]

  [† 1 note book 2 sheets]


                                         Artillery.        Engineers.
  Credits for lectures assigned to the
    interrogations,                          65                60
  Credits for works of application,         355               205
                                            ---               ---
                                            420               265


The course on construction is divided into four parts.

The first part relates to the elements of masonry and the principles
which should regulate the form, dimensions, and the construction of
walls, and the different parts of buildings; it contains eighteen

The second part is devoted to the architecture of military
buildings--twelve lectures.

The third part supplies the theory of the stability of construction, and
is divided into--

1st section, relating to the resistance of materials--six lectures.

2d     “     to the stability of walls of revetments and arches--nine

The fourth part applies to constructions in water--twenty lectures.

The course is very nearly the same for the Artillery as for the


_Lectures_ 1, 2, and 3.--Relate to the elements of which masonry is
composed, such as the different kinds of stones, usual dimensions,
manner in which good stone may be known; bricks, lime, cement, sand,
mortar, stucco, mastic plaster, asphalte, &c., and to the general
considerations relating to foundations, and the different kinds of walls
under various circumstances.

_Lecture_ 4.--Treats of sustaining walls and the probable effects of the
pressure of the earth. Of the conditions which must be fulfilled to
insure stability. Various formulæ on the subject. Details of
construction and on the proper material to be used.

_Lecture_ 5.--Refers to the manner of facing masonry. Openings in walls,
windows. Partition-walls.

_Lecture_ 6.--On cylindrical arches, vaults, key-stones. Formulæ for the
calculation of the thickness of piers of an arch or vault. Construction
and use of tables for the calculation of the thickness. Construction of
arches and vaults in different materials.

_Lecture_ 7.--Arches continued, flat arches, plate bands, &c.

_Lecture_ 8.--On the woods used in construction. On the influence of the
soil on its quality. Characteristics of good wood. Preservation of wood.
Proper wood for constructions.

_Lecture_ 9.--Flooring. Beams. Girders. Joists. Ceilings.

_Lecture_ 10.--Staircases, conditions respecting. Construction of
different kinds of staircases, part of masonry, wood, &c.; steps.
Construction of landing-places, &c.

_Lectures_ 11 and 12.--Roofs in carpentry. Conditions which should be
satisfied. Composition of the roof of a building. On the different kinds
of roofs.

_Lecture_ 13.--On the different ways of joining pieces of wood or timber

_Lecture_ 14.--On permanent kinds of roofing. Conditions which should be
fulfilled by good roofing. Composition of roofing. Tiles, lathing, cut
slates, ridge tiles, hollow tiles, Dutch tiles. On slate roofing.
Metallic roofing. Metal mostly used. Precautions to be taken with
reference to all metal roofing.

_Lecture_ 15.--Details relating to inhabited buildings. Cellars.
Privies. Drainage. Chimneys; cause of their smoking. Most favorable
forms of the flues, pipes. Bake-house, hearth.

_Lecture_ 16.--On joinery and locksmiths’ work. Flooring of different
kinds. Doors. Camp-beds. Racks and mangers in stables. Shutters.

_Lecture_ 17.--Apparatus for heating and for cooking food. Hearth,
ash-pan. Grate-flues. Amount of surface to be given to heating
apparatus. Furnace of kitchens in barracks. Summary notions on the
heating and ventilating of buildings. Calorifiéres with hot air, steam,
and hot water.

_Lecture_ 18.--Plan of a building. Projections adopted for the
representation of a building. Plans, sections, and elevations. Order in
which the measurements should be made, and the sketch prepared. Height
at which the horizontal plane of projections should pass, &c.


_Lecture_ 1.--Decoration, without making use of the orders of
architecture. Principal conditions relating to decoration. Symmetry,
regularity, simplicity, unity, and apparent soliditity. Proper
character. Proportions of the façades. Height of the stories. Basements.
Horizontal chains or fillets. Vertical chains and pilasters. Proportions
of the doors and windows. Arcades and arched windows. Cornices,

_Lecture_ 2.--Distribution of buildings. Considerations that should have
weight in the distribution. Number composing the edifice. Circumstances
that guide in the disposal of masses. Conditions that should be
satisfied in placing a building. Locality and suitable dimensions.
Relations that should exist between them. Interior and exterior
communications. Stories on the same floor. Position of the large rooms.
Separation of the rooms. Position and arrangement of staircases.
Verification of stability.

_Lecture_ 3.--Conditions to be fulfilled in the distribution of the
principal military establishments. Arsenals. Polygons for drill.
Military establishments to the School of Bridges.

_Lecture_ 4.--Foundries. Manufacture of arms.

_Lecture_ 5.--Refining saltpetre. Powder. Powder magazines. Details
relative to the construction of lightning conductors.

_Lecture_ 6.--Infantry and cavalry barracks.

_Lecture_ 7.--Hospitals. Military prisons and penitentiaries.

_Lecture_ 8.--Storehouse for corn. Store-pits. Storehouse for fodder.
Preserving houses.

_Lecture_ 9.--Cisterns. Filtration.

_Lecture_ 10.--Military tribunals. Guard-house. Gates of cities. Hotels
and dwelling-houses. Officers’ quarters.

_Lecture_ 11.--Preparatory to the execution of a project for a building.
Method of proceeding. Composition of the sketch; approximate surface of
all the locality; separation into symmetrical groups in the case of
several buildings; number of stories; surface of the ground floor;
length and breadth of the building between its walls; distribution of
each story; verification of the relation between the stories. Elevation
of the building. Sketches. Memoir. General details, and details of

_Lecture_ 12.--Discussion before the abstraction of the measurements and
the preparation of the estimate of the building.


1. Resistance of prismatic bodies to extension and compression.
Elasticity of bodies. Modulus of elasticity. Limits of permanent
efforts. Resistance to extension and compression of stone, bricks, and
analogous materials; also of wood and metals. Applications.

2. Transverse resistance. Some cases in which it is brought into play.
Results of experience. Resistance of bodies submitted to the effects of
transversal flexure. Results of experience and conventions. Conditions
of equilibrium of bodies submitted to efforts directly transversal to
their length. Direction and value of molecular efforts. Equation of the
axis of the body. Equation of the squaring. Discussion of these

3. Geometrical method for determining the inertia. Application to the
research for the inertia of various sections. Applications of general
equations of equilibrium and of squaring to straight pieces.

  1st. A horizontal piece set in a frame at one extremity, and subjected
to a weight acting at the other extremity, with a uniform vertical

  2d. Horizontal beam placed upon two supports, and subjected to a
weight acting at its center, and with a uniform vertical effect.

  3d. Beam placed horizontally on two supports, and having two equal
weights symmetrically placed with respect to its center.

  4th. Beam placed horizontally on two supports, and subjected to a
weight acting at any point whatever throughout its length.

  5th. Horizontal beam fixed at both its extremities, and subjected to a
weight acting at its center with an equal vertical effect.

  6th. Horizontal beam placed on three points of support, at unequal
distances, and weighted with two weights acting at the middle of the
intervals between the supports.

  7th. Vertical beam fixed at the foot, and charged with a weight acting
at a certain distance from the axis of the beam.

5. Solids of equal resistances. Most suitable form for cast girders.
Applications of the formula of equilibrium and squaring to various kinds
of carpentry.

6. On polygonal roofs. Conditions respecting them. Arched roofs,
pressure, &c. On the stability of walls required to resist the pressure
of roofs.


7. On the pressure of earth. Explanation of the theory on Coulomb’s
system. Investigation of the pressure of earth by analysis. Hypothesis
necessary in order to simplify the calculations. General formula of the
value of the pressure, &c. Equations of stability and equilibrium under
the hypothesis of slipping and rolling.

8. Simplification of the general equations of equilibrium in three
particular cases. Determination of the co-efficient of stability in
Vauban’s profile. M. Poncelet’s formula for calculating the thickness of
revetment walls with perpendicular face. Transformation of the profile
of a revetment to another of equal stability. Vauban’s counterforts, &c.

9. Geometrical method for determining the pressure of earth, whatever
may be the profile of the wall and of the earth, taking into account the
friction of the earth on masonry. Geometrical determination of the
amount of the pressure. Proceeding for the determination, by geometry,
of the thickness of a revetment wall at the level of the exterior

10. On buttresses. Geometrical determination of the buttressing of
earth, and of its momentum. Simplification of the geometrical
constructions of the pressure, of the buttressing, and of their momenta
under certain hypotheses.

11. Points of application of the pressure and of the buttress. 1st. In
the case of a terrace sloping less than the natural slope of the ground.
2d. In the case of the ordinary revetments of fortification.

On the stability of the foundations of revetment walls.

Compressible soil. The resultant of all the forces should pass through
the center of the base. Size of the footing of the wall or depth of the
foundations to arrive at the result. Possibility of the wall slipping
over the base of the foundations. Use of the buttress to prevent this
movement. Graphical method to determine the depth of the foundations.
Depth of the foundations in unstable soil.

12. Pressure of arches. Case of cylindrical arches. Explanation of the
theory of the pressure of arches. Point of application of the pressure
in the five modes of possible rupture. Expression for the pressures and
resistances by rolling or slipping. Proceeding to be followed to find by
calculation the pressures and resistances.

13. Geometrical determination of the pressures and resistances by
rolling. Explanation of the solution of this question. Construction of
lines proportional to the surfaces of the voussoirs. 1st. In the case of
an arch. Extrados without coping or additional weight. 2d. In that of an
arch with extrados in the form of coping, and with or without additional
weight. Construction of the verticals passing through the center of
gravity of the voussoirs. Abstract of the operations to be performed.
Determination by geometrical means of the pressure and resistance
against slipping.

14. Co-efficient of stability of arches from the springing. Manner of
finding the outline of an arch for a certain given co-efficient.
Stability of a cylindrical arch on its piers. Thickness of the piers.
Considerations relative to the value of the co-efficient of stability.
Stability of an arch on the base of its foundations. Filling in and
depth of the foundations of piers.

Extension of the geometrical methods serving for the determinations of
the pressures and thicknesses of piers in case of cross vaulting,
arcades, and spherical vaulting.

15. Investigation by analysis of the pressures and resistances of an

1st. Hypothesis of a plat-band; stability at the springing charge
necessary on the coussinet; stability of the plat-band on its piers;
thickness of the piers. Squaring of a tie-beam of iron which annihilates
the pressure.

2d. Hypothesis of a semicircular vaulting with arched extrados.
Pressures and resistances. In similar arches the pressure is
proportional to the square of the radius.


1st. Classification of ground on which it may be necessary to place a
foundation. Soundings. Their object. Various kinds of sounding line.
Dams in earth, and in wood and earth combined. Case of an unstable
foundation. Construction on rock. Thickness of dams and of the clay
work. General disposition of a dam. Bottom-springs. Means of choking or
smothering them or of diverting them. Use of sunk dams. Service bridges.
Their height and disposition. Railways in great constructions. Their

2d. Summary review of draining or pumping machines. Choice between the
different methods of draining. Table of the useful effect of such

Pile driving. Pile driving machine with band ropes. Preparation of the
pile and operation of driving. Pile driving machine with catch. Choice
between the two kinds of pile driving machines. Precautions to be taken
in the driving of piles. Distribution of piles, the space to be left
between them, and the squaring of them. Disposition and driving of
planks. Method of drawing up piles and planking. Execution of a
foundation on piles. Driving stakes out of water. Machine for squaring

3d. Parafouilles. Their object and construction.

Foundations in mortar under water. Preparation and immersion of the
mortar. Examples.

Thickness of sunk dams with the enceint in mortar.

4th. Foundation frames and platforms. Their object and their
construction. Preparation of the foundation frames in masonry.

Foundation by packing.

Foundation by coffer-dams. Details of a coffer-dam.

5th. Foundations on solid gravel. Properties of gravel. Case where it is
advantageous to make use of gravel. Examples.

Foundations on sunk wooden piles, in gravel, and in gravel and mortar.

Foundation on pillars built in masonry.

Foundations on quicksand.

Species of foundation to adopt according to the nature of the ground.

6th. Banks of reservoirs. Conditions which should be fulfilled in their
establishment. Banks in earth; their profile; revetments to protect
them; the wet slope; sort of remblai; precautions which exact a large
remblai. Banks in remblai and sustaining walls combined. Banks entirely
in masonry; movements observed in walls; most suitable profile.
Comparison between banks in earth and masonry. Works which are employed
in connection with banks of reservoirs. Dikes of inundations. Their
profile; defense of their slope against the action of water; their
establishment and works in connection with them.

7th. Batardeaux in the ditches of strong places. Situation; profile;
details of construction. Weirs. Their object; effect of a weir in a
current. Advantages of the wedge or circular form. Height to give to a
weir; and longitudinal form of the swelling occasioned by a horizontal
dam. Construction of weirs with vertical walls, with a long slope down
the stream. Injuries to which weirs are liable. Profile to adopt
according to the nature of the ground.

8th. Sluice-dams, their object; form of the piles; distance apart, and
dimensions. Details of construction. Various kinds of apparatus for
opening and shutting sluice-dams. Play of a revolving gate. Calculation
of the dimensions of the two half sluice gates and of the wicket.
Carpentry of a revolving gate. Movable dams with iron wickets.
Modifications to render them applicable to the retention of water at a
greater height than 2.80 meters.

9th. Navigable locks. Canal lock; its management; form of the chamber;
profile of the cheeks. Trace of the pier on which the gates work. Means
of filling and emptying the chambers. Means of raising the
paddle-valves. Wood-work of the gates sheathed in timber. Planes.
Details of the pivots, collars and rollers. Arrangements for the
management of the sheathed gates.

10th. Gates sheathed in wood; curves. Ties of cast-iron, and lining in
wood or sheet-iron. Cast-iron gates.

_River Navigation._--Advantages and disadvantages of water transit.
Conditions of a navigable river. Works for the improvement of the
navigation on a river.

_Artificial Navigation._--Classification of canals. Conditions which
determine the best position for a summit level. Search after a minimum
of elevation. Expenditure of water at the summit level.

11th. Principal processes employed to economise the water in passing
through a lock. Profile of a navigable canal.

Deep cuttings; their profile. Great landslips and means of remedying

Tunnels; their profile. Piercing of a tunnel.

12th. Bridges in masonry. Position; breadth of the roadway; outlet to be
left for the water; size and form of the arches; trace of the surbased
arches on more than five centers. Expansion of the bridge-heads. Profile
of the arch. Thickness of the piles and abutments. Apparatus for the
arches and bridge-heads. Parts above the arches. Leveling with the
banks. Fixed and movable centerings. Removal of the centerings of

13th. _Wooden Bridges_ composed of straight pieces. Arrangement of the
stakes and starlings. Different construction of the openings according
to their span. Arrangement of the platform.

_American Bridges._--Arrangement of the earliest form of bridge on
Town’s system. Height of the trusses constructed in the form of
trellis-work. Modifications introduced to increase the resistance of the
bridge. Calculation of the resistance of the trusses.

Arched frame-work of bridges. Composition of the arches. Junction of the
straight beams with the arches.

_Cast-iron Bridges._--Different systems. General principles of their

_Aqueducts_ in masonry; in cast-iron.

14th. _Suspension Bridges._--Equation of the curve of the chains and
construction of this curve. Tension supported by the suspension cables,
their thickness. Influence of the length of the flèche upon the tension
of the cables. Inconveniences resulting from a long flèche. Vibrations
and means of diminishing them. Limits of length of the flèche. Length of
the curve of suspension. Causes operating to vary this length; means of
obviating the effects produced by them. Length of the suspension rods.
Number of supports to be adopted. Thickness of the piles. Points at
which the fixing cables are to be attached. Advantages and disadvantages
of chains composed of bars and of cables of iron wire. Some details of

15th. _Drawbridges._--Conditions which they must satisfy. General
principle of their balance.

_Drawbridges with Plyers._--Special theory of this bridge. Reduction of
it to practice. Alteration of equilibrium and means of remedying it.

Disadvantages of the drawbridge with plyers.

16th. Spiral drawbridge of Captain Berché. Trace of the spiral.
Determination of the radius of the chain-roller, and of the greatest
radius of the spiral.

17th. Drawbridges with variable counterbalances, invented by M.
Poncelet. Construction of the chains of the counterbalance.
Establishment of the leverage. Calculation of the counterbalances for
the special case of the pulleys in front corresponding to the axis of
the platform. Influence of the nature of the chains. Method of allowing
for the weight of the small chains. Definitive construction of the
chains of the counterbalance. Provision of loose cords.

18th. Succinct ideas upon the motion of the sea, and its action on the

Undulating movement. Height of the waves, and depth at which the
agitation is perceptible. Effects of the waves on the coasts. Tides;
spring-tides; neap-tides. Height of tides and hour of flood. General
currents. Action of the sea on its shores. Protection of level and steep

19th. Sea-ports. Requisites of a good port. Ports in the Mediterranean.
Conditions of a good roadstead. Moles and breakwaters. Ocean ports,
channel tide-dock, floating dock, and sluice of floating dock, laying-up
dock, and sluice for the ditch of fortifications. General arrangement of
a harbor.

20th. Construction of moles. Stones dropped for foundations. Profile of
a loose heap. Volume of the materials which insure their stability.
Settling of masonry resting on a heap. Instances of masonry constructed
at sea. 1. Wall of Cherbourg. 2. Fort Boyard.

_Piers._--Direction, length, form of interval between, and profile of
piers. Their construction. Passages reserved through piers.


  First Part.--Parts of Buildings                            18
  Second Part.--Architecture of Military Buildings           12
               { First Section. Resistance of Materials, 6}
  Third Part.--{                                          }  15
               { Second Section. Stability of             }
               {   Constructions,                        9}
  Fourth Part.--Hydraulic Constructions,                     20
    Total                                                    65


  Name of work.
    No. Days allowed for execution of work to Students of
    Artillery. / Engineers.
      Subject employed on.

  Survey of a Building:
    31 // 31
  Sketch (out-of-door work,)
     8 /  8
    21 / 21
     2 /  2
      Representation of an existing building or a part of a building
      by means of plans, sections, and elevations.
      The memoir contains an accurate and critical description of the
      distribution, construction, and decoration of the building.
        Each day is equivalent to 4½ hours’ work.
        The sketches are executed to scales approximating to
        one-fiftieth for the whole drawing, of one-twentieth for the
        large details, and of ¼ to ½ for the minute details.
        The drawing prepared from the sketches is made on the scale
        of 1-100th.

  Project for a Building:
    42 // 42
  Sketch, (first study in pencil.)
    12 / 12
  Drawing, (fair copy)
    18 / 18
     4 / 4
     4 / 4
  Abstraction of Measurements and Estimates
     4 / 4
      Study and preparation of a project of a building, in accordance
      with certain given data.
      The sketches, the result of the first study, are made in pencil;
      the drawing is the fair copy of the sketch, modified as may be
      The memoir contains an explanation of the rules and principles
      which must be observed in the construction of buildings, and the
      grounds on which the dispositions contained in the building have
      been adopted.
      The abstraction of the measurements and their reduction to the
      proper elements, and the estimates, are prepared in conformity
      to the instructions laid down for the Engineer Service in towns:
      these supply the estimated cost of the construction of the
      building according to the project.
        This work, common to the students of the two arms, is an
        application of the first part of the course.
        The scale for the drawing is in general 1-200th for the plans
        and elevations, and 1-100th for the sections. It is restricted
        by the condition that the whole of the drawings should be
        given on a single sheet of paper.
        The details need only occupy half a sheet of paper, and its
        scales must depend on the size of the objects to be represented.
        The details need only occupy half a sheet of paper, and its
        scales must depend on the size of the objects to be represented.
        The project for a building is an application of the first two
        parts of the course, as well as of the 1st section of the 3d

  Diagram of the Stability:
    9 // 9
    6 / 6
    3 / 3
      Determination of the profile for a revetment wall, according to
      certain conditions.
      Verification of the stability of an arch, and calculation of the
      pier supporting this arch. In the memoir a short explanation is
      given of the theory relating to the strength of the revetment
      walls and arches, as well as the results of the application of
      these principles to the particular case.
        The drawing is executed to the scale of 1-100th.
        This work is an application of the 2d section of the 3rd part.

  Project for an Hydraulic construction:
    28 // 34
    10 / 12
    15 / 18
     3 / 4
      Study and composition of a project for a great work of art on
      certain given data.
      In the memoir an explanation is given of the principles and the
      results of the theories which are to be applied in making this
      The arrangements adopted in the project are discussed for the
      foundation and all other parts of the construction.
        The scale of the drawing is chosen in such a manner that the
        project may be placed on a single sheet; generally it is
        1-200th, or smaller.
        The project of a hydraulic construction is an application of
        the 1st section of the 3rd part as well as of the 4th part of
        the course.

    Total, 110 // 116

  NL No. Lectures
  CL Credits for Lectures
  +A With application
  -A Without application
  T  Total
  I  No. Interrogations

  1st. Lectures.--  |       Artillery.      ||       Engineers.
    Parts of        |   |      CL       |   ||   |      CL       |
    the Course.     |   +------+---+----+   ||   +------+---+----+
                    |NL |  +A  |-A |  T | I || NL|  +A  | -A|  T | I
  1st Part:         |   |      |   |    |   ||   |      |   |    |
    Elements of Masonry, form and dimensions of  |      |   |    |
    the different parts of buildings,   |   ||   |      |   |    |
                    | 18|   24*|  6|  30|  2|| 18|   24*|  6|  30|  2
  2d Part:          |   |      |   |    |   ||   |      |   |    |
    Architecture of military buildings, |   ||   |      |   |    |
                    | 12|   18 |...|  18|  1|| 12|   18 |...|  18|  1
  3d Part:          |   |      |   |    |   ||   |      |   |    |
    Theory respecting stability:   |    |   ||   |      |   |    |
    1st section--Resistance of materials,   ||   |      |   |    |
                    |  6|    6 |  6|  12|  1||  6|    6 |  6|  12|  1
    2d section--Stability of revetment walls and arches,|   |    |
                    |  9| 10.5 |  6|16.5|  1||  9| 10.5 |  6|16.5|  1
  4th Part:         |   |      |   |    |   ||   |      |   |    |
    Hydraulic Constructions,   |   |    |   ||   |      |   |    |
                    | 20|   24 | 12|  36|  1|| 20|   24 | 12|  36|  1
       Total,       | 65|   82 | 30| 112|  6|| 65|   82 | 30| 112|  6

[* A lecture with application is equivalent to 1½ hours of work, and a
lecture without application is equal to 3 hours.]

  D Drawings and Sketches.
  M Memoirs.
  V Various.
  H Attendances in halls 4½ hours.
  O Attendances out of doors, 6 h.
  C Credits.

  2d. Execution of  | Artillery. Number of  || Engineers. Number of
    the Work.       +---+---+---+---+---+---++---+---+---+---+---+----
                    | D | M | V | H | O | C || D | M | V | H | O | C
  Plan of a Building:   |   |   |   |   |   ||   |   |   |   |   |
    Sketches (pen,) | 1 |...|...|...|  8| 50|| 1 |...|...|...|  8| 50*
    Drawing,        | 1 |...|...| 21|...| 95|| 1 |...|...| 21|...| 95
    Memoirs,        |...| 1 |...|  2|...| 20||...| 1 |...|  2|...| 20†
  Project of a Building:|   |   |   |   |   ||   |   |   |   |   |
    Sketch,         | 1 |...|...| 12|...| 55|| 1 |...|...| 12|...| 55
    Drawing,        | 1 |...|...| 18|...| 80|| 1 |...|...| 18|...| 80
    Detail,         | 1 |...|...|  4|...| 20|| 1 |...|...|  4|...| 20
    Memoir,         |...| 1 |...|  4|...| 35||...| 1 |...|  4|...| 35
    Abstraction of quantities and estimates,||   |   |   |   |   |
                    |...|...| 1 |  4|...| 20||...|...|  1|  4|...| 20
  Diagram of Stability. |   |   |   |   |   ||   |   |   |   |   |
    Drawing,        | 1 |...|...|  6|...| 25|| 1 |...|...|  6|...| 25
    Memoir,         |...| 1 |...|  3|...| 25||...| 1 |...|  3|...| 25
  Project of an Hydraulic construction. |   ||   |   |   |   |   |
    Sketch,         | 1 |...|...| 10|...| 45|| 1 |...|...| 12|...| 55
    Drawing,        | 1 |...|...| 15|...| 70|| 1 |...|...| 18|...| 80
    Memoir,         |...| 1 |...|  3|...| 25||...| 1 |...|  4|...| 35
      Total,        | 8 | 4 | 1 |102| 8 |565|| 8 | 4 | 1 |108| 8 |595

[* Of which 20 is for the out-of-door work, and 30 for the sketch.]

[† The time allowed for the preparation of the memoirs in the halls
should be doubled, in order to take an account of the correction out of
the halls of study.]


  Artillery, {Lectures,           112}  677, or about 680.
             {Execution of Work,  565}

  Engineers, {Lectures,           112}  707, or about 710.
             {Execution of Work,  595}



_Number of Lectures_, 50.

Grammar and composition during the 25 Lectures forming the odd numbers.

Oral translations of German authors. Phraseology. Lecture on idioms,
founded on the passages which have been translated and given in the form
of conversation during the first half of the 25 Lectures forming the
even numbers.

Dialogues and conversations, on various subjects of every-day life, such
as are particularly useful to an officer traveling in Germany, carried
on during the second half of the Lectures of the even numbers.


_Number of Lectures_, 100.

Translations of German authors, and conversations in German on the
passages translated, during fifty Lectures, reckoning the odd numbers.

Military reconnaissances, in the form of a dialogue in German and in
French, during the first half of the fifty Lectures, even numbers.

Translation of French into German: 1st, Narratives; 2d, Historical and
descriptive fragments; 3d, Dramatic scenes; 4th, Epistolary style,
during the second half of the fifty Lectures, even numbers.

At the close of the second year, the Sub-Lieutenants give in a
composition on a certain subject.

The Sub-Lieutenants most advanced are not obliged to follow the course
in German, but they should make translations of articles taken from
German military works. These translations, after having been corrected,
are deposited in the Library of the School.

Abstract of the course in German:--

  1st year’s study,        50 Lectures.
  2d   “       “          100    “
         Total,           150 at ½ hour each--112. 3 0.
  Credits of influence,                         110.

XII.--PROGRAMME OF A SHAM SIEGE.--(Common to the Artillery and


ART. I.--_Commission charged to study the Project for a Sham Siege._

A Commission is charged with drawing up and presenting to the General
commanding the School a project for a sham siege. This is composed of:--

  The Colonel second in command of the School, President.
  The Major of Artillery,          }
  The Major of Engineers,          } Members.
  The Professor of Artillery,      }
  The Professor of Fortification,  }

The Professors of Artillery and Fortification may be replaced by the
Assistant Professors.

The General Commandant of the School decides in a Council of Instruction
on the dispositions to be adopted for the project of a sham siege.

ART. II.--_Preparatory Lectures._

  By the Professor of Military Art,                                  2
    1st. Considerations relating to the fortress of Metz.
      Circumstances which might bring on a siege of it. Force of
      the garrison and of the besieging army. Investment.
    2d. Trace of the lines of circumvallation and of
  By the Professor of Topography,                                    1
    Execution of the second reconnaissance plan (_memoire_,)
      (1 lecture.)
    1st. Measure of the base. Plan of the ground of the attack.
      Construction of the plans. Plans of the work executed.
  By the Professor of Permanent Fortification,                       2
    1st. Discussion on the points of attack. Organization of the
      _personnel_ and _matériel_ of the Engineers of the besieging
      army and of the garrison.
    2d. General progress of attack, and general dispositions of
  By the Professor of Artillery,                                     2
    1st. Composition of the personnel and matériel of the
      Artillery of the besieging army. Transport of the siege
    2d. General dispositions of the artillery in the attack
      and defense.


Director of the Siege.--The General Commandant of the School.

Chief of the Staff.--The Colonel second in command of the School.

Chief of the Artillery Service.--The Major of Artillery attached to the

Director of the Park of Artillery.--This may be given to the preceding.

Chief of the Engineer Service.--The Major of the Engineers attached to
the Staff of the School.

Director of the Engineer Park.--This may be given to the preceding.

Major of the Trenches.--A Captain. Chiefs of Attacks. Captains.

Chiefs of Brigades.--Named by the General Commandant of the Siege.


Before proceeding to the ground, the sub-lieutenants assist at
conferences which are held for the purpose of explaining to them the
successions of the several operations of the siege, as well as upon the
traces which they have to execute. These conferences, eight in number,
are divided as follows:--

  The Chief of the Artillery Service will hold 4 conferences, and
  The Chief of the Engineer Service       “    4        “


1st. The second reconnaissance survey (comprised in the course of
topography.) Tracing of lines; one day is allowed for this work.

2d. “Director” plan. The execution of this plan comprises out-of-door
work and drawing. The out-of-door work includes the measurement of one
or many bases, the observation of the angles which are formed by this
base, and the direction of certain remarkable points in the city and
fortification, and the formation of a net-work of triangulation,
intended to co-ordinate the surveys of the details.

The work of constructing the plan consists in laying down, day by day,
the surveys of the details of the ground, as well as of the traces
executed. Five days are allowed for the execution of the topographical
work, which precedes the opening of the trenches. The Director Plan is
kept close up during the whole duration of the siege.

3d. Itineraries and sketches (comprised in the course of topography.)

The Professor of Topography directs the whole of the surveys and the
execution of the Director Plan.


The sub-lieutenants, divided into brigades, trace the works of the
siege, under the direction of the officers of the staff, and take part
in the superintendence of the works executed in full relief when the
exigencies of the service will permit the chief of the Artillery Service
and the Colonel of the Regiment of Engineers to place workmen at the
disposal of the General Commandant of the School. Six days are
appropriated to this work.


The work in the Halls of Study consists of:--

1st. A memoir on the sham siege, which memoir must be approved by the
General Commandant of the School.

2d. Of a sketch representing one of the works traced or executed in full
relief. These works in the Halls are performed during the interval of
the attendances devoted to out-of-door work. Two days are appropriated
to the preparation of the memoir, and two to the execution of the
sketch. This time is included in the eleven days allowed to the sham


  NL No. of Lectures or Conferences.
  CL Credits for Lectures or Conferences.
  L  Lectures.
  Cf Conferences.
  T  Total.
  Q  No. of Questions.

                        |    |       CL       |    |
     Lectures and       |    +-----+----+-----+    |
     Conferences.       |    |     |    |     |    |
                        | NL |  L  | Cf |  T  | Q  |
  By the Professor      |    |     |    |     |    | *
    of Military Art,    |  2 |  3  |....|  3  |}   |
    “  Topography,      |  1 |  1½ |....|  1½ |}   |
    “  Permanent        |    |     |    |     |    |
         Fortification, |  2 |  3  |....|  3  |}   |
    “  Artillery,       |  2 |  3  |....|  3  |} 2 |
  Conferences by the Chief of the Service,    |    |
   } of Artillery,      |  4 | ... |  6 |  6  |}   |
   } of Engineers,      |  4 | ... |  6 |  6  |}   |
          Total,        | 15 | 10½ | 12 | 22½ |  2 |

[* One series of questions by the Chief of the Artillery Service, as to
what relates to that arm.

One series of questions by the Chief of the Engineer Service, as to what
relates to that arm.

A Credit of 11 is assigned to each series of questions.]

  D Drawings.
  M Memoirs.
  H Attendances in the Halls.
  I Credits.

                      |            Number of           |
                      |   |   |Attendances |      |    |
                      |   |   |  out of    |      |    |
                      |   |   |   doors.   |      |    |
                      |   |   +-----+------+      |    |
         Works of     |   |   |  of |  of  |      |    |
     Application.     | D | M |4½ h.|  8 h.|  H   | I  |
  2nd Reconnaissance Plan (Memoir.) |      |      |    |
  Topographical Work, |   |   |   4 |      |      | 20}| *
  Itinerary and Sketch (Memoir,)    |      |      |   }|
  Plan “Director,”    |   |   |     |      |  1   |  5}|
  Tracing of Lines,   |   |   |     |   1  |      |{10 | †
  Tracing of Works of Attack and of Defense,      |    |
                      |   |   |   6 |      |      |{25 |
  Sketch,             | 1 |   |     |      |  2   |  1}| ‡
  Memoir,             |   | 1 |     |      |  2   |  2}|
                      +---+---+-----+------+------+ 90 |
       Total,         | 1 | 1 |  10 |   1  |  5   |----|

[* Credits given by the Professor of Topography.]

[† Credits given by the Captains of the Staff, Chiefs of Brigades.]

[‡ Credits given by the Chiefs of the Service of the Artillery and



_Lecture 1_.--Classification and nomenclature of the various matters
which constitute the horse. Skeleton (head and body.)

_Lecture 2_.--Skeleton (limbs.) Mechanical importance of the skeleton.
Nomenclature and use of the muscles. Cellular and fatty tissues, grease,
skin. Insensible perspiration.

_Lecture 3_.--Functions for maintenance. Arteries of the nerves. Animal

_Lecture 4_.--On various functions.


_Lecture 5_.--Proportions. Equilibrium. Description and importance of
the natural beauties and defects of the head and region of the throat.

_Lecture 6_.--Description and importance of the other parts of the
horse. Blemishes. Soft tumors.

_Lecture 7_.--Osseous tumors. Various accidents. Temperaments.
Description of clothing, &c.

_Lecture 8_.--Data respecting horses.

_Lecture 9_.--To know the age. On various bad habits. Examination of the
eyes; their diseases.

_Lecture 10_.--Defective paces, &c. Draught and pack horses. Mules.

_Lecture 11_.--Stud and remounts. Races.

_Lecture 12_.--Vicious horses, and different bits. Manner of bitting a
horse. On grooms and punishment.


_Lecture 13_.--Examination of the foot, and shoeing with the hot shoe.

_Lecture 14_.--Shoeing with the cold shoe. Different kinds of
horse-shoe, &c.

_Lecture 15_.--On stables. Food. Rations.

_Lecture 16_.--Description and nomenclature of the saddle. Harness and
pack. Various saddles.

_Lecture 17_.--On work and rest. Horse and mule on the road and in
bivouac. On diseases and accidents.

  Abstract of the course:--

  Interior of the horse, 4 } 17 lectures at 1½ hours.
  Exterior,              6 } Total time, 25½ hours.
  Health,                7 } Credits, 25.

The instruction on horseback can, under certain circumstances, be
considered as connected with this course; and questions are asked during
the time when the sub-lieutenants are not engaged in actual riding
exercise. This instruction is described under the head of Practical
Military Instruction; it comprises at the maximum 272 attendances, and
its credit of influence is valued at 240.



These are intended for the theoretical and practical instruction of
officers, _sous-officiers_, and gunners.

Each School is under the orders of the General of Brigade commanding the
Artillery in the military division in which it is situated.

Independent of the general officer, the school has the following

  A Lieutenant (associated assistant to the General.)
  A Professor of Sciences, applying more particularly to the Artillery.
  A Professor of Fortification, of drawing, and construction of
  Two _Gardes_ of Artillery (one of the first, and the other of the
    second class.)

There are, in addition, attached to each school the number of inferior
officers (captains, lieutenants, or _sous-lieutenants_) required for
carrying on the theoretical courses, which are not placed under the
direction of the professors.

A captain of the first class, assisted by two first lieutenants, is the
director of the park of the school. Another captain, also of the first
class, but taken from the regiment of Pontooneers, has the direction of
that portion of the bridge equipage necessary for the special
instruction of this corps, as well as of the material of the artillery
properly belonging to this instruction.

The lieutenant-colonel, assistant to the general, fulfills, independent
of every other detail of supervision with which he may be charged, the
functions of _ordonnateur secondaire_, in what concerns the expenses of
the school and their propriety (_justification_.) He corresponds with
the minister of war for this part of the service.

The instruction is divided into _theoretical_ and _practical_, and the
annual course is divided into half-yearly periods, or into summer and
winter instructions.

The summer instruction commences, according to different localities,
from the 1st of April to the 1st of May, and that of the winter from the
1st of October to the 1st of November.

The winter and summer instruction is subdivided into school and
regimental instruction.

The school instruction comprehends all the _theoretical_ and _practical_
instruction common to the different corps which require the assistance
of the particular means of the school, the employment of its professors,
locality, and material, as that of the practical instruction in which
the troops belonging to the different corps of the army are united to
take part.

The regimental instruction is that which exists in the interior of the
regiments and the various bodies of the artillery. It is directed by the
chiefs of these corps, who are responsible for it, with the means placed
at their disposal, under the general surveillance of the commandant of
the school.

The special instruction of the Pontooneers not admitting of their
following the same instruction as the other regiments of artillery, the
chief of this corps directs the special instruction according to certain
bases prescribed by the regulations.

There are for the captains of artillery, each year during the winter
half-year, six conferences for the purposes of considering and
discussing projects for the organization of different equipages and
armaments for the field service, and for attack and defense of places.

In a building belonging to each school of artillery, under the name of
the hotel of the school, are united the halls and establishments
necessary for the theoretical instruction of the officers and
sous-officers, such as halls for _théorique_ drill and drawing, library,
depots of maps and plans, halls for machines, instruments and models,

Each school is provided with a physical cabinet and a chemical
laboratory. There is also a piece of ground, called a polygon, for
exercising artillerymen to the manœuvers of cannon and other firearms of
great range. Its extent is sufficient in length to furnish a range of
1,200 meters, and in breadth of 600 meters.

Permanent and temporary batteries are established on this ground, and
they seem not only for practice, but also to accustom the men to the
construction of fascines, field batteries, &c.

The administration of each school, and the accounts relating to it, are
directed by an administrative council, consisting of--

  The General Officer commanding the Artillery (President.)

  The Colonels of the regiments of Artillery in the towns where two
regiments of the Artillery are quartered, and in other towns, the
Colonel and Lieutenant-Colonel of the regiment.

  The Colonel of the regiment of Pontooneers in the town where the
principal part of the corps may be stationed, and in any other town the
Lieutenant-Colonel or the Major.

  The Lieutenant-Colonel associated assistant with the General

The functions of secretary of the council are intrusted to a _grade_ of
the first class.

The functionaries of the corps of intendants fulfill, in connection with
the administrative councils of the artillery schools, the same duties as
are assigned by the regulations relating to the interior administration
of bodies of troops. They will exercise over the accounts, both of money
and material of the said schools, the same control as over the
administration connected with the military interests of the state.


The colonel of each regiment has the superior direction of the

The lieutenant-colonel directs and superintends, under his orders, the
whole of the details of the regimental instruction.

A major, selected from among the officers of this rank belonging to the
_état-major_ of this arm, directs and superintends, under the orders of
the colonel, the whole of the details of the special instruction.

The complete instruction consists of--

General instruction, or that of the regiment, by which a man is made a

Special or school instruction, having for its object the training of the
miner or sapper.

The instructions are each separated into _theoretical_ and _practical_

The theoretical instruction of the regiment comprehends the theories:--

  On the exercises and manœuvers of infantry. On the interior service.
On the service of the place. On field service. On the maintenance of
arms. On military administration. On military penal legislation.

The practical instruction of the regiment comprises:--

  The exercises and manœuvers of infantry. Practice with the musket.
Military Marches. Fencing.

The teaching of these various duties is confided to officers,
_sous-officiers_, and corporals of the regiments, as pointed out by the
regulation, and the orders of the colonel.

The fencing school is organized in a similar manner to those of the
infantry, and the military marches are also made in the same way as in
those corps.

The _special_ and _theoretical_ instruction consists of:--

  Primary instruction. Mathematics. Drawing. Geography. Military history
of France. Fortification and the various branches of the engineering

Three civil professors (appointed by competition) are attached to each
regimental school, for the special theoretical instruction, as regards
the primary instruction, drawing, and mathematics.

The courses are distributed and taught in the following manner:

  Primary instruction for the Soldiers.  }
  French grammar for the Corporals.      }
  Book-keeping for the _Sous-Officiers_. }
      By the Professor of Primary Instruction.

  Elementary arithmetic for the Corporals. }
  Complete arithmetic }                    }
  Elementary geometry }                    }
    for the Serjeants.                     }
  Complete geometry }                      }
  Trigonometry      }                      }
    for the Serjeant-Major.                }
  Surveys for the _Sous-Officiers_.        }
  Special mathematics for the Officers.    }
      By the Prof. of Mathematics.

  Drawing for the Corporals and _Sous-Officers_.
      By the Professor of Drawing, who is also charged with
      completing the collection of models which relate to it.

  The elements of fortification for the Serjeant-Majors. }
  Construction, and theories on practical schools        }
    for the _Sous-Officiers_.                            }
  Permanent fortification          }                     }
  The attack and defense of places }                     }
  Mines                            }                     }
  Bridges                          }                     }
  Ovens                            }                     }
  Topography                       }                     }
    for the Officers.                                    }
  Geography                        }                     }
  Military history of France       }                     }
    for the _Sous-Officiers_.                            }
      By the Officers of the regiment, named by the Colonel,
      independently of those appointed by the regulations

At the end of each course the colonel of the regiment causes a general
examination to be made in his presence of the whole of the men who have
followed this course, and has a list made out in the order of merit,
with notes of the capacity and aptitude of each.

These lists are consulted in the formation of tables of promotion, and
placed with the said tables before the inspector-general.

Each captain and lieutenant are obliged to give in at least a single
treatise on five different projects, consisting of a memoir discussing
or the journal of a siege, with drawing of the whole, and of details in
sufficient number to render them perfectly intelligible.

The _special practical_ instruction is composed of seven distinct
schools, relating to:--

  Field Fortification. Saps. Mines and Fireworks. Bridges. Ovens.
Topography. Gymnastics.

And they comprehend, in addition, sham sieges, and underground war. Each
of these seven schools is taught in accordance with the special
instructions annexed to the regulation, which, however, are not

Winter is more especially devoted to the course of special theoretical
instruction, which commences on the 1st November, and usually finishes
on the 15th March, and the course of _special practical_ instruction is
carried on during the summer from the 15th March to the 15th September.
The second fortnight of September and the month of October are devoted
to sham sieges and underground war, to the leveling of the works
executed, and to the arrangement of magazines.




It will have been seen in the accounts of the Polytechnic School and the
School of Application at Metz, in what manner young men destined for
commissions in the artillery and engineers receive their previous
education, and under what conditions appointments as officers in these
two services are made in France. The regulations for the infantry, the
cavalry, and the marines are of the same description. There are in these
also the same two ways of obtaining a commission. One, and in these
services the more usual one, is to rise from the ranks. The other is to
pass successfully through the school at St. Cyr. Young men who do not
enter as privates prove their fitness for the rank of officers by going
through the course of instruction given, and by passing the examinations
conducted in this, the principal, and putting aside the School of
Application at Metz, the one Special Military School of the country.

The earliest foundation of the kind in France was the Ecole Royale
Militaire of 1751. Like most other similar institutions of the time, it
was intended for the young nobility. No one was to be admitted who could
not prove four generations of _Noblesse_. The pupils were taught free of
charge, and might enter at eight years old. Already, however, some marks
of competition are to be discerned, as the best mathematicians were to
be taken for the Artillery and Engineers. Buildings on the Plain of
Grenelle (the same which still stand, occupying one end of the present
Champs de Mars, and retaining, though only used as barracks, their
ancient name,) were erected for the purpose. The school continued in
this form till 1776, when it was dissolved (apparently owing to faults
of discipline,) and replaced by ten Colleges, at Sorrèze, Brienne,
Vendôme, and other places, all superintended by ecclesiastics. A new
Ecole Royale Militaire, occupying the same buildings as the former, was
added in 1777.

This came to an end in 1787; and the ten colleges were suppressed under
the Republic. A sort of Camp School on the plain of Sablons took their
place, when the war had broken out, and lasted about a year under the
name of the Ecole de Mars.

Under the Consulate in 1800, the Prytanée Français was founded,
consisting of four separate Colleges. The name was not long after
changed to the Prytanée Militaire; and after some time the number was
diminished, and La Flèche, which had in 1764 received the youngest
pupils of the old Royal Military School, became the seat of the sole
remaining establishment; which subsequently sunk to the proportions of a
mere junior preparatory school, and became, in fine, the present
establishment for military orphans, which still retains the title, and
is called the Prytanée Militaire de la Flèche.

A _special_ Military School, in the meantime, had been set up at
Fontainebleau in 1803, transferred in 1808 to St. Cyr, and thus taking
the place of the Prytanée Militaire and of its predecessor, the original
Ecole Royale Militaire, gradually assumed its present form.[15]

    [Footnote 15: Founded the Ecole Royale Militaire, 1751. Junior
    pupils transferred to La Flèche, 1764.

    Suppression of the Ecole Royale Militaire and establishment of ten
    Colleges, 1776.

    New Ecole Royale Militaire, for the best pupils of the Colleges,

    Suppression of the Colleges and of the Ecole Royale Militaire,

    Foundation of the Ecole de Mars, May 1794.

    Foundation of the Prytanée Français at Paris, Versailles, St.
    Germain, Fontainebleau, 1800.

    Foundation of the Ecole Spéciale Militaire at Fountainebleau,

    The four Schools of the Prytanée Français are converted into the
    Prytanée Militaire, 1806; and are transferred to La Flèche, 1808.

    The Ecole Spéciale Militaire is transferred to St. Cyr, also in

The course of study lasts two years; the usual number of cadets in time
of peace is five, or at the utmost six hundred; the admission is by
competitive examination, open to all youths, French by birth or by
naturalization, who on the first of January preceding their candidature
were not less than sixteen and not more than twenty years old. To this
examination are also admitted soldiers in the ranks between twenty and
twenty-five years of age, who, at the date of its commencement, have
been actually in service in their regiments for two years.

The general conditions and formalities are the same as those already
stated for the Polytechnic. It may be repeated that all the candidates,
in accordance with a recent enactment, must have taken the usual degree
which terminates the task at the _lycées_--the baccalaureate in

Those who succeed in the examination and are admitted, take an
engagement to serve seven years either in the cavalry or infantry, and
are thus under the obligation, if they are judged incompetent at the
close of their two years’ stay at the school to receive a commission, to
enter and serve as common soldiers. The two years of their stay at the
school counts as a part of their service. It is only in the special case
of loss of time caused by illness, that permission is given to remain a
third year.

The ordinary payment is 60_l._ (1,500 francs) per annum. All whose
inability to pay this amount is satisfactorily established, may claim,
as at the Polytechnic, an allowance of the whole or of half of the
expenses from the State, to which may be added an allowance for the
whole or for a portion of the outfit (from 24_l._ to 28_l._) These
_bourses_ or _demi-bourses_, with the _trousseau_, or _demi-trousseau_,
have during the last few years been granted unsparingly. One-third of
the 800 young men at the school in February 1856 were _boursiers_ or
_demi-boursiers_. Candidates admitted from the Orphan School of La
Flèche, where the sons of officers wounded or killed in service receive
a gratuitous education, are maintained in the same manner here.[16]

    [Footnote 16: About twenty-five are sent every year from La
    Flèche. The admissions from the army (_i.e._, of soldiers between
    twenty and twenty-five years old) do not amount to more than four
    or at the utmost five per cent. They are very frequently young men
    who have previously failed for St. Cyr, and who then enter the
    army as privates, and come in as such. They have to pass the same

It was the rule till lately that cadets appointed, on leaving St. Cyr,
to the cavalry should be placed for two years at the Cavalry School at
Saumur. This, however, has recently been changed; on entering St. Cyr
those who desire appointments in the cavalry declare their wishes, and
are put at once through a course of training in horsemanship. Those who
are found unfit are quickly withdrawn; the remainder, if their place on
the final examination allows of their appointment to the cavalry, are by
that time sufficiently well practiced to be able to join their regiments
at once.

Twenty-seven, or sometimes a greater number, are annually at the close
of their second year of study placed in competition with twenty-five
candidates from the second lieutenants belonging to the army,[17] if so
many are forthcoming, for admission to the Staff School at Paris. This
advantage is one object which serves as a stimulus to exertion, the
permission being given according to rank in the classification by order
of merit.

    [Footnote 17: Few usually present themselves; and these also, it
    is said, are very generally old _élèves_ of St. Cyr, who had not
    succeeded in obtaining admission to the Staff School before. They
    are not examined _with_ the pupils of St. Cyr, but are
    intercalated in the list according to their merit.]

The school consists of two divisions, the upper and the lower,
corresponding to the two years of the course. Each division is divided
again into four companies. In each of these eight companies there are
sub-officers chosen from the _élèves_ themselves, with the titles of
_Sergent_, _Sergent Fourrier_, and _Caporal_; those appointed to the
companies of the junior division are selected from the second year
cadets, and their superiority in standing appears to give these latter
some considerable authority, exercised occasionally well, occasionally
ill. The whole school, thus divided into eight companies, constitutes
one battalion.

The establishment for conducting the school consists of--

  A General as Commandant.

  A Second in Command (a Colonel of Infantry.)

  A Major, 4 Captains, 12 Lieutenants, and 5 Second Lieutenants of
Infantry; the Major holding the office of Commandant of the Battalion.

  A Major, 1 Captain, 34 Lieutenants, and 3 Second Lieutenants of
Cavalry to superintend the exercises, the riding, &c.

  A Director of Studies (at present a Lieutenant-Colonel of Engineers.)

  Two Assistant Directors.

  Six Examiners for Admission.

  One Professor of Artillery.

  One Assistant ditto.

  One Professor of Topography and Mathematics.

  One Professor of Military Administration, Military Art, and Military

  One Professor of Fortification.

  One Professor of Military Literature.

  Two Professors of History and Geography.

  One Professor of Descriptive Geometry.

  One Professor of Physics and Chemistry.

  Three Professors of Drawing,

  One Professor of German.

  Eleven Military and six Civilian Assistant Teachers (_Répétiteurs_.)

There is also a Quartermaster, a Treasurer, a Steward, a Secretary of
the Archives, who is also Librarian, an Almoner (a clergyman,) four or
five Surgeons, a Veterinary Surgeon, who gives lessons on the subject,
and twelve Fencing Masters.

The professors and teachers are almost entirely military men. Some
difficulty appears to be found by civilians in keeping sufficient order
in the large classes; and it has been found useful to have as
_répétiteurs_ persons who could also be employed in maintaining
discipline in the house. Among the professors at present there are
several officers of the engineers and of the artillery, and of the staff

There is a board or council of instruction, composed of the commandant,
the second in command, one of the field officers of the school staff,
the director of studies, one of the assistant directors, and four

So, again, the commandant, the second in command, one of the field
officers, two captains, and two lieutenants, the last four changing
every year, compose the board or council of discipline.

St. Cyr is a little village about three miles beyond the town of
Versailles, and but a short distance from the boundary of the park. The
buildings occupied by the school are those formerly used by Madame de
Maintenon, and the school which she superintended. Her garden has given
place for the parade and exercise grounds; the chapel still remains in
use; and her portrait is preserved in the apartments of the commandant.
The buildings form several courts or quadrangles; the Court of Rivoli,
occupied chiefly by the apartments and bureaux of the officers of the
establishment, and terminated by the chapel; the Courts of Austerlitz,
and Marengo, more particularly devoted to the young soldiers themselves;
and that of Wagram, which is incomplete, and opens into the parade
grounds. These, with the large stables, the new riding school, the
exercising ground for the cavalry, and the polygon for artillery
practice, extend to some little distance beyond the limit of the old
gardens into the open arable land which descends northwards from the
school, the small village of St. Cyr lying adjacent to it on the south.

The ground floor of the buildings forming the Courts of Marengo,
Austerlitz, and Wagram appeared to be occupied by the two refectories,
by the lecture-rooms or amphitheaters, each holding two hundred pupils,
and by the chambers in which the ordinary questionings, similar to those
already described in the account of the Polytechnic School, under the
name of _interrogations particulières_, are conducted.

On the first floor are the _salles d’étude_ and the _salle des
collections_ the museum or repertory of plans, instruments, models and
machines, and the library; on the second floor the ordinary dormitories;
and on the third (the attics,) supplementary dormitories to accommodate
the extra number of pupils who have been admitted since the commencement
of the war.

The commission, when visiting the school, was conducted on leaving the
apartments of the commandant to the nearest of the two refectories. It
was after one o’clock, and the long room was in the full possession of
the whole first or junior division. A crowd of active and
spirited-looking young soldiers, four hundred at least in number, were
ranged at two long rows of small tables, each large enough, perhaps, for
twelve; while in the narrow passage extending up and down the room,
between the two rows, stood the officers on duty for the maintenance of
order. On passing back to the corridor, the stream of the second year
cadets was issuing from their opposite refectory. In the adjoining
buttery, the loaf was produced, one kilogramme in weight, which
constitutes the daily allowance. It is divided into four parts, eaten at
breakfast, dinner, the afternoon lunch or _gouter_, and the supper. The
daily cost of each pupil’s food is estimated at 1f. 80c.

The lecture rooms and museums offer nothing for special remark. In the
library containing 12,000 books and a fine collection of maps, there
were a few of the young men, who are admitted during one hour every day.

The _salles d’étude_ on the first floor are, in contrast to those at the
Polytechnic, large rooms, containing, under the present circumstances of
the school, no less than two hundred young men. There are, in all, four
such rooms, furnished with rows of desks on each side and overlooked in
time of study by an officer posted in each to preserve order, and, so
far as possible, prevent any idleness.

From these another staircase conducts to the dormitories, containing one
hundred each, and named after the battles of the present war--Alma,
Inkerman, Balaclava, Bomarsund. They were much in the style of those in
ordinary barracks, occupied by rows of small iron beds, each with a
shelf over it, and a box at the side. The young men make their own beds,
clean their own boots, and sweep out the dormitories themselves. Their
clothing, some portions of which we here had the opportunity of
noticing, is that of the common soldier, the cloth being merely a little

Above these ordinary dormitories are the attics, now applied to the use
of the additional three hundred whom the school has latterly received.

The young men, who had been seen hurrying with their muskets to the
parade ground, were now visible from the upper windows, assembled, and
commencing their exercises. And when, after passing downwards and
visiting the stables, which contain three hundred and sixty horses,
attended to by two hundred cavalry soldiers, we found ourselves on the
exercising ground, the cavalry cadets were at drill, part mounted, the
others going through the lance exercise on foot. In the riding-school a
squad of infantry cadets were receiving their weekly riding lesson. The
cavalry cadets ride three hours a-day; those of the infantry about one
hour a week. The exercising ground communicates with the parade ground;
here the greater number of the young men were at infantry drill, under
arms. A small squad was at field-gun drill in an adjoining square.
Beyond this and the exercising ground is the practice ground, where
musket and artillery practice is carried on during the summer. Returning
to the parade ground we found the cadets united into a battalion; they
formed line and went through the manual exercise, and afterwards marched
past; they did their exercise remarkably well. Some had been only three
months at the school. The marching past was satisfactory; it was in
three ranks, in the usual French manner.

Young men intended for the cavalry are instructed in infantry and
artillery movements and drill; just as those intended for the infantry
are taught riding, and receive instruction in cavalry, as well as
artillery drill and movements.

It is during the second year of their stay they receive most instruction
in the arms of the service to which they are not destined, and this, it
is said, is a most important part of their instruction. “It is this,”
said the General Commandant, “that made it practicable, for example, in
the Crimea, to find among the old _élèves_ of St. Cyr, officers fit for
the artillery, the engineers, the staff; and for general officers, of
course, it is of the greatest advantage to have known from actual study
something of every branch.”

The ordinary school vacation last six or seven weeks in the year. The
young men are not allowed to quit the grounds except on Sundays. On that
day there is mass for the young men.

The routine of the day varies considerably with the season. In winter it
is much as follows:--At 5 A.M. the drum beats, the young men quit their
beds; in twelve minutes they are all dressed and out, and the
dormitories are cleared. The _rappel_ sounds on the _grand carré_; they
form in their companies, enter their _salles_, and prepare for the
lecture of the day until a quarter to 7. At 7 o’clock the officers on
duty for the week enter the dormitories, to which the pupils now return,
at a quarter to 8 the whole body passes muster in the dormitories, in
which they have apparently by this time made their beds and restored
cleanliness and order. Breakfast is taken at one time or other during
the interval between a quarter to 7 and 8 o’clock.

They march to their lecture rooms at 8, the lecture lasts till a quarter
past 9, when they are in like manner marched out, and are allowed a
quarter of an hour of amusement. They then enter the halls of study,
make up their notes on the lecture they have come from, and after an
hour and a half employed in this way, for another hour and a half are
set to drawing.

Dinner at 1 is followed by recreation till 2. Two hours from 2 to a
quarter past 4 are devoted to military services.

From 4 to 6 P.M. part are occupied in study of the drill-book
(_théorie_,) part in riding or fencing: a quarter of an hour’s
recreation follows, and from 6¼ to 8½ there are two hours of study in
the _salles_. At half-past 8 the day concludes with the supper.

The following table gives a view of the routine in summer:--

   4½ A.M. to 4¾  A.M. Dressing.
   4¾  “   to 7¼   “   Military exercises.
   7¼  “   to 8¼   “   Breakfast, cleaning, inspection.
   8¼  “   to 9½   “   Lecture.
   9½  “   to 9¾   “   Recreation.
   9¾  “   to 11¼  “   Study.
  11¼  “   to 1   P.M. Drawing.
   1  P.M. to 2    “   Dinner and recreation.
   2   “   to 4    “   Study of drill-book (_théorie_) or fencing.
   4   “   to 6    “   Study for some, riding for others.
   6   “   to 6¼   “   Recreation.
   6¼  “   to 8    “   Riding for some, study for others,
   8   “   to 8½   “   Supper.

The entrance examination is much less severe than that for the
Polytechnic; but a moderate amount of mathematical knowledge is
demanded, and is obtained. The candidates are numerous; and if it be
true that some young men of fortune shrink from a test, which, even in
the easiest times, exacts a knowledge of the elements of trigonometry,
and not unfrequently seek their commissions by entering the ranks, their
place is supplied by youths who have their fortunes to make, and who
have intelligence, industry, and opportunity enough to acquire in the
ordinary _lycées_, the needful amount of knowledge.

Under present circumstances it is, perhaps, more especially in the
preparatory studies that the intellectual training is given, and for the
examination of admission that theoretical attainments are demanded. The
state of the school in a time of war can not exactly be regarded as a
normal or usual one. The time of stay has been sometimes shortened from
two years to fifteen months; the excessive numbers render it difficult
to adjust the lectures and general instruction so as to meet the needs
of all; the lecture rooms and the studying rooms are all insufficient
for the emergency; and what is yet more than all, the stimulus for
exertion, which is given by the fear of being excluded upon the final
examination, and sent to serve in the ranks, is removed at a time when
almost every one may feel sure that a commission which must be filled up
will be vacant for him. Yet even in time of peace, if general report may
be trusted, it is more the drill, exercises, and discipline, than the
theory of military operations, that excite the interest and command the
attention of the young men. When they leave, they will take their places
as second lieutenants with the troops, and they naturally do not wish to
be put to shame by showing ignorance of the common things with which
common soldiers are familiar. Their chief incentive is the fear of being
found deficient when they join their regiments, and, with the exception
of those who desire to enter the staff corps, their great object is the
practical knowledge of the ordinary matters of military duty. “Physical
exercises,” said the Director of Studies, “predominate here as much as
intellectual studies do at the Polytechnic.”

But the competition for entrance sustains the general standard of
knowledge. Even when there is the greatest demand for admissible
candidates, the standard of admission has not, we are told, been much
reduced. No one comes in who does not know the first elements of
trigonometry. And the time allotted by the rules of the school to
lectures and indoor study is far from inconsiderable.


The examinations for admission are conducted almost precisely upon the
same system which is now used in those for the Polytechnic School.[18]
There is a preliminary or pass examination (_du premier degré_), and for
those who pass this a second or class examination (_du second degré_.)
For the former there are three examiners, two for mathematics, physics,
and chemistry, and a third for history, geography, and German. The
second examination, which follows a few days after, is conducted in like
manner by three examiners. A jury of admission decides. The examination
is for the most part oral; and the principal difference between it and
the examination for the Polytechnic is merely that the written papers
are worked some considerable time before the first oral examination
(_du premier degré_,) and are looked over with a view to assist the
decision as to admissibility to the second (_du second degré_.) Thus the
_compositions écrites_ are completed on the 14th and 15th of June; the
preliminary examination commences at Paris on the 10th of July; the
second examination on the 13th.

    [Footnote 18: The system was, in fact, first tried at St. Cyr, and
    adopted, on the representation of the Mixed Commission, at the
    Polytechnic. The previous method, by which different sets of
    examiners took different districts, had created distrust and

The subjects of examination are the following:--

  _Arithmetic_, including vulgar and decimal fractions, weights and
measures, square and cube root, ratios and proportions, interest and
discount, use of logarithmic tables and the sliding rule.

  _Algebra_, to quadratic equations with one unknown quantity, maxima
and minima, arithmetical and geometrical progressions, logarithms and
their application to questions of compound interest and annuities.

  _Geometry_, plane and solid, including the measurement of areas,
surfaces, and volumes; sections of the cone, cylinder, and sphere.

  _Plane Trigonometry:_ construction of trigonometrical tables and the
solution of triangles; application to problems required in surveying.

  _Geometrical representations_ of bodies by projections.

  _French_ compositions.

  _German_ exercises.

  _Drawing_, including elementary geometrical drawing and projections;
plan, section, and elevation of a building; geographical maps.

  _Physical Science_ (purely descriptive:) cosmography; physics,
including elementary knowledge of the equilibrium of fluids; weight,
gravity, atmospheric pressure, heat, electricity, magnetism, acoustics,
optics, refraction, microscope, telescope.

  _Chemistry_, elementary principles of; on matter, cohesion, affinity;
simple and compound bodies, acids, bases, salts, oxygen, combustion,
azote, atmospheric air, hydrogen, water; respecting equivalents and
their use, carbon, carbonic acid, production and decomposition of
ammonia, sulphur, sulphuric acid, phosphorus, chlorine; classification
of non-metallic bodies into four families.

  _History:_ History of France from the time of Charles VII. to that of
the Emperor Napoleon I. and the treaties of 1815.

  _Geography_, relating entirely to France and its colonies, both
physical and statistical.

  _German:_ the candidates must be able to read fluently both the
written and printed German character, and to reply in German to simple
questions addressed to them in the same language.

The general system of instruction at St. Cyr is similar to that of the
Polytechnic; the lectures are given by the professors, notes are taken
and completed afterwards, and progress is tested in occasional
_interrogations_ by the _répétiteurs_. One distinction is the different
size of the _salles d’étude_ (containing two hundred instead of eight or
ten;) but, above all, is the great and predominant attention paid to the
practical part of military teaching and training. It is evident at the
first sight that this is essentially a military school, and that
especial importance is attached both by teachers and pupils to the
drill, exercise, and manœuvers of the various arms of the service.

The course of study is completed in two years; that of the first year
consists of:--

          27 lectures in descriptive geometry.
          35     “       physical science.
          20     “       military literature.
          35     “       history.
          21     “       geography and military statistics.
          30     “       German.
  Total, 174

In addition to the above, there is a course of drawing between the time
when the students join the school early in November and the 15th of

  The course of _drawing_ consists in progressive studies of landscape
drawing with the pencil and brush, having special application to
military subjects, to the shading of some simple body or dress, and to
enable the students to apply the knowledge which has been communicated
to them on the subject of shadows and perspective. This course is
followed by the second or junior division during the first year’s

  The course of lectures in _descriptive geometry_ commences with
certain preliminary notions on the subject; refers to the representation
of lines on curved surfaces, cylindrical and conical, surfaces of
revolutions, regular surfaces, intersection of surfaces, shadows,
perspective, vanishing points, &c., construction of geographical maps,
and _plan côté_.

  The lectures in _physical science_ embrace nine lectures on the
general properties of bodies; heat, climate, electricity, magnetism,
galvanism, electro-magnetism, acoustics.

  There are twelve lectures in _chemistry_; on water, atmospheric air,
combustibles, gas, principal salts, saltpetre, metallurgy, organic

  There are fourteen lectures in _mechanics applied to machines_;
motion, rest, gravity, composition and resolution of forces, mechanical
labor, uniform motion, rectilinear and rotatory, projectiles in space,
mechanical powers, drawbridges, Archimedean principle, military bridges,
pumps, reservoirs, over and under-shot wheels, turbines, corn mills,
steam-engines, locomotives, transport of troops, materials, and
munitions on railways.

  The twenty lectures in _military literature_ refer to military history
and biography, memoirs of military historians, battles and sieges, the
art of war, military correspondence, proclamations, bulletins, orders of
the day, instructions, circulars, reports and military considerations,
special memoirs, reconnaissance and reports, military and periodical
collections, military justice.

  The thirty-five lectures in _history_ principally relate to France and
its wars, commencing with the Treaty of Westphalia and ending with the
Treaty of Vienna.

  The twenty-seven lectures in _geography_ and _military statistics_ are
subdivided into different parts; the first eight lectures are devoted to
Europe and France, including the physical geography and statistics of
the same; the second six lectures are devoted to the frontiers of
France; and the third part of thirteen lectures to foreign states and
Algeria, including Germany, Italy, Spain, Portugal, Poland, and Russia.

The studies for the first division during the second year of their
residence consist of--

          10 lectures in topography.
          27     “       fortification.
          15     “       artillery.
          10     “       military legislation.
          12     “       military administration.
          27     “       military art and history.
          20     “       German.
  Total, 121

One lesson weekly is given in drawing, in order to render the students
expert in landscape and military drawing with the pencil, pen, and

We must not omit to call attention to the fact that mathematics are not
taught in either yearly course at St. Cyr.

  The course in _topography_, of ten lectures, has reference to the
construction of maps, copies of drawings, theory, description, and use
of instruments for measuring angles and leveling, the execution for a
regular survey on the different systems of military drawing, drawing
from models of ground, on the construction of topographical drawing and
reconnaissance surveys, with accompanying memoirs.

  Twenty-seven lectures are devoted to _fortification_; the first
thirteen relate principally to field fortification, statement of the
general principles, definitions, intrenchments, lines, redoubts,
armament, defilement, execution of works on the ground, means necessary
for the defense, application of field fortification to the defenses of
_têtes de pont_ and inhabited places, attack and defense of
intrenchments, &c., castramentation; six lectures have reference to
permanent fortification, on ancient fortifications, Cormontaigne’s
system, exterior and detached works, considerations respecting the
accessories of defense to fortified places; eight lectures relate to the
attack and defense of places, preparations for attack and defense,
details of the construction of siege works from the opening of the
trenches to the taking of the place, exterior works, as auxiliaries,
sketches, and details of the different works in fortifications, plans,
and profile, &c.

  The students also execute certain works, such as the making of
fascines, gabions, saucissons, repair of revetments of batteries,
platform, setting the profiles, defilement, and construction of a
fieldwork, different kinds of sap, plan and establishment of a camp for
a battalion of infantry, &c.

  Under the head of _artillery_, fifteen lectures are given, commencing
with the resistance of fluids, movement of projectiles, solution of
problems with the balistic pendulum, deviation of projectiles, pointing
and firing guns; small arms, cannon, materials of artillery, powder,
munition, fireworks for military purposes; range of cannon, artillery
for the attack or defense of places or coasts, field artillery, military

  The students are practically taught artillery drill with field and
siege guns, practice with artillery, repair of siege batteries, bridges
of boats or rafts.

  The ten lectures allowed for the course of _military legislation_ have
for their object the explanation of the principles, practice, and
regulations relating to military law, and the connection with the civil
laws that affect military men.

  The twelve lectures on what is called _military administration_ relate
to the interior economy of a company, and to the various matters
appertaining to the soldier’s messing, mode of payment, necessaries,
equipment, lodging, &c.

  _Military art and history_ is divided into three parts. The first, of
five lectures, relates to the history of military institutions and
organization. The second, of fifteen lectures, refers to the composition
of armies and to considerations respecting the various arms, infantry,
cavalry, état-major, artillery and engineers, and the minor operations
of war. The third part, of seven lectures, gives the history of some of
the most celebrated campaigns in modern times. In the practical
exercises, the students make an attack or defense of a work or of a
system of fieldworks during their course of fortification, or of a
house, farm, village, in the immediate vicinity of the school, or make
the passage of a river.

  The students receive twenty lectures in _German_, and are required to
keep up a knowledge of German writing.


The examinations at the end of the first year take place under the
superintendence of the director and assistant director of studies. They
are conducted by the professor of each branch of study, assisted by a
_répétiteur_, each of whom assigns a credit to the student under
examination, and the mean, expressed as a whole number, represents the
result of the student’s examination in that particular branch of study.
The examination in military instruction for training (in drill and
exercises) is carried on by the officers attached to companies, under
the superintendence of the commandant of the battalion, and that
relating to practical artillery by the officer in charge of that duty.

The pupils’ position is determined, as at the Polytechnic, partly by the
marks gained at the examination, partly by those he has obtained during
his previous studies. In other words, the half of the credit obtained by
a student at this examination in each subject is added to the half of
the mean of all the credits assigned to him, in the same subject, for
the manner in which he has replied to the questions of the professor and
_répétiteur_ during the year; and the sum of these two items represents
his total credit at the end of the year. The scale of credit is from 0
to 20, as at the Polytechnic.

Every year, before the examinations commence, the commandant and second
in command, in concert with the director and assistant director, and in
concurrence with the superior officer commanding the battalion for
military instruction, are formed into a board to determine the amount of
the minimum credit which should be exacted from the students in every
branch of study. This minimum is not usually allowed to fall below eight
for the scientific, and ten for the military instruction.

Any student whose general mean credit is less than _eight_ for the
scientific, or _ten_ for the military instruction, or who has a less
credit than _four_ for any particular study in the general instruction,
or of _six_ for the military instruction, is retained at the school to
work during the vacation, and re-examined about eight days before the
re-commencement of the course, by a commission composed of the director
and assistant director of studies for the general instruction, and of
the second in command and the commandant of the battalion, and of one
captain for the military instruction. A statement of this second
examination is submitted to the minister of war, and those students who
pass it in a satisfactory manner are permitted by him to proceed into
the first division. Those who do not pass it are reported to the
minister of war as deserving of being excluded from the school, unless
there be any special grounds for excusing them, such as sickness, in
which case, when the fact is properly established before the council of
instruction, they are permitted to repeat the year’s studies.

Irregularity of conduct is also made a ground for exclusion from the
school. In order to estimate the credit to be attached to the conduct of
a student, all the punishments to which he can be subjected are
converted into a specific number of days of punishment drill. Thus,

For each day confined in the police chamber, 4 days’ punishment drill.

For each day confined in the prison, 8 days’ punishment drill.

The statement is made out under the presidency of the commandant of the
school, by the second in command, and the officer in command of the
battalion. The credits for conduct are expressed in whole numbers in
terms of the scale of 0 to 20, in which the 20 signifies that the
student has not been subjected to any punishment whatever, and the 0,
that the student’s punishments have amounted to 200 or more days of
punishment drill. The number 20 is diminished by deducting 1 for every
10 days of punishment drill.

The classification in the order of merit depends upon the total amount
of the sum of the numerical marks or credits obtained by each student in
every branch of study or instruction. The numerical credit in each
subject is found by multiplying the credit awarded in each subject by
the co-efficient of influence belonging to it.

The co-efficients, representing the influence allowed to each particular
kind of examination, in the various branches of study are as follows:--

Second Division, or First Year’s Course of Study.

  General Instruction.
    { Descriptive Geometry,                           6 }
    {   { Course,                                     6 }
    {   { Drawing and Sketches,                       2 }
    { Physical Science applied to the Military Arts,  6 }
    {   { Course,                                     6 }
    {   { Sketch and Memoir,                          2 }
    { History,                                        6 }
    { Geography and Statistical Memoirs,              5 }
    {   { Course,                                     5 }
    {   { Sketch and Memoir,                          2 }
    { Literature, Memoir on                           4 }
    { German,                                         4 }
    { Drawing,                                        3 } 40
  Special Instruction:--Drill, Practice, Manœuvers
    (Infantry and Cavalry,)                                7
  Conduct,                                                 3

First Division, or Second Year’s Course of Study

  General Instruction.
                                              Infantry.   Cavalry.
    { Topography
    {   { Course,                                   3 }        3 }
    {   { Maps, Memoirs, and Practical Exercises,   3 }        2 }
    { Fortification,
    {   { Course,                                   4 }        4 }
    {   { Drawings, Memoirs, and                      }          }
    {   {   Practical Exercises,                    3 }        2 }
    { Artillery and Balistic Pendulum,
    {   { Course,                                   4 }        4 }
    {   { Practical Exercises, School of Musketry   2 }        1 }
    { Military Legislation,                         2 }        2 }
    { Military Administration,
    {   { Course,                                   3 }        3 }
    {   { Sheets of Accounts,                       1 }        1 }
    { Military History and Art,
    {   { Course,                                   4 }        4 }
    {   { Memoirs and applications,                 1 }        1 }
    { German,                                       4 }        4 }
    { Drawing,                                      1 } 35     1 } 32
  Special instruction for
    { Infantry
    {   { Theory of Drill, Manœuvers--3 Schools,    4 }
    {   { Practical Instruction                     3 }
    {   { Regulations,                              2 }  9
    { Cavalry,
    {   { Riding,                                              3 }
    {   { Theoretical and Practical Instruction                7 }
    {   { Veterinary Art,                                      2 } 12
  Conduct                                                6          6
                                                        --         --
      Total,                                            50         50

To facilitate this classification in order of merit, three distinct
tables are prepared,--

  The first relating to the general instruction;
  The second relating to the military instruction; and
  The third relating to the conduct;

and they respectively contain, one column in which the names of the
students are arranged by companies in the order in which they have been
examined; followed by as many columns as there are subjects of
examination, for the insertion of their individual credit and the
co-efficient of influence, by which each credit is multiplied; and
lastly by a column containing the sum of the various products belonging
to, and placed opposite each student’s name.

These tables are respectively completed by the aid of the existing
documents, the first for the general instruction, by the director of
studies; the second for the military instruction, by the officer
commanding the battalion; the third for conduct, under the direction of
the commandant of the school, assisted by the second in command.

A jury formed within the school, composed of the general commandant,
president, the second in command, the director of studies, and the
officer commanding the battalion, is charged with the classification of
the students in the order of merit.

To effect it, after having verified and established the accuracy of the
above tables, the numbers appertaining to each student in the three
tables are extracted and inserted in another table, containing the name
of each student, and, in three separate columns, the numbers obtained by
each in general instruction, military instruction, and conduct, and the
sum of these credits in another column.

By the aid of this last table, the jury cause another to be compiled, in
which the students are arranged in the order of merit as established by
the numerical amount of their credits, the highest in the list having
the greatest number.

If there should be any two or more having the same number of total
credits, the priority is determined by giving it to the student who has
obtained a superiority of credits in military instruction, conduct,
general instruction, notes for the year; and if these prove
insufficient, they are finally classed in the same order as they were
admitted into the school.

A list for passing from the second to the first division is forwarded to
the minister at war, with a report in which the results for the year are
compared with the results of the preceding year; and the minister at
war, with these reports before him, decides who are ineligible from
incompetency, or by reason of their conduct, to pass to the other

The period when the final examinations before leaving the school are to
commence, is fixed by the president of the jury, specially appointed to
carry on this final examination, in concert with the general commandant
of the school.

The president of the jury directs and superintends the whole of the
arrangements for conducting the examination; and during each kind of
examination, a member of the corps, upon the science of which the
student is being questioned, assists the examiner, and, as regards the
military instruction, each examiner is aided by a captain belonging to
the battalion.

The examination is carried on in precisely the same manner as that
already described for the end of the first year’s course of study. And
the final classification is ascertained by adding to the _numerical_
credits obtained by each student during his second year’s course of
study, in the manner already fully explained, _one-tenth_ of the
numerical credits obtained at the examinations at the end of the first

The same regulations as to the minimum credit which a student must
obtain in order to pass from one division to the other, at the end of
the first year, which are stated in page 160, are equally applicable to
his passing from the school to become a second lieutenant in the army.

A list of the names of those students who are found qualified for the
rank of second lieutenant is sent to the minister at war, and a second
list is also sent, containing the names of those students that have,
when subjected to a second or revised examination, been pronounced by
the jury before whom they were re-examined as qualified.

Those whose names appear in the first list are permitted to choose
according to their position in the order of merit, the staff corps or
infantry, according to the number required for the first named service,
and to name the regiments of infantry in which they desire to serve.

Those intended for the cavalry are placed at the disposal of the officer
commanding the regiment which they wish to enter.

Those whose names appear in the second list are not permitted to choose
their corps, but are placed by the minister at war in such corps as may
have vacancies in it, or where he may think proper.

The students who are selected to enter the staff corps, after competing
successfully with the second lieutenants of the army, proceed as second
lieutenants to the staff school at Paris. Those who fail pass into the
army as privates, according to the terms of the engagement made on
entering the school.


This school was established in 1826, and is considered[19] the most
perfect and extensive institution of the kind in Europe,--perhaps the
only one really deserving the title, the others being more properly mere
schools of equitation.

    [Footnote 19: “Report of Observations in Europe during the Crimean
    War,” by Major Gen. McClellan.]

It is under the control of the Minister of War, and was established for
the purpose of perfecting the officers of the cavalry corps in all the
branches of knowledge necessary to their efficiency, and especially in
the principles of equitation,--and to diffuse through the corps a
uniform system of instruction, by training up a body of instructors and
classes of recruits intended for the cavalry service.

The instruction is entirely military, and is based upon the laws and
regulations in force with regard to the mounted troops. It includes;
1st. The regulations for interior service; 2nd. The cavalry tactics;
3rd. The regulations for garrison service; 4th. The regulations for
field service applied, as far as possible, on the ground, especially
with regard to reconnaissances; 5th. A military and didactic course of
equitation, comprising all the theoretical and practical knowledge
required for the proper and useful employment of the horse, his
breaking, application to the purposes of war, and various civil
exercises; 6th. A course of hippology, having for its object practical
instruction, by means of the model breeding-stud attached to the school,
in the principles which should serve as rules in crossing breeds and in
raising colts, to explain the phases of dentition, to point out the
conformation of the colt which indicates that he will become a good and
solid horse, the method to be pursued to bring the colt under subjection
without resistance, and, finally, to familiarize the officers and pupils
with all the knowledge indispensable to an officer charged with the
purchase and care of remount horses. This course includes also a
knowledge of horse-equipment, illustrated in the saddle factory
connected with the school; 7th. Vaulting, fencing, and swimming. The
non-commissioned officers are also instructed in the theory of
administration and accountability. The course of instruction continues
one year, commencing in the month of October. The pupils at the school

  1st. A division of lieutenants, (_lieutenants instructeurs_.)
  2nd.      “     of sub-lieutenants,
                     (_sous-lieutenants d’instruction_.)
  3rd.      “     of sub-officers,
                     (_sous-officiers élèves instructeurs_.)
  4th.      “     of non-commissioned officers, (_brigadiers élèves_.)
  5th.      “     of cavalry recruits, (_cavaliers élèves_.)

The lieutenants are chosen out of the regiments of cavalry and
artillery, as well as from the squadrons of the park-trains and military
equipages, from the lieutenants who voluntarily present themselves for
the appointment to the General Board of Inspectors. Their age must not
exceed thirty-six years.

The sub-lieutenants are appointed from the cavalry regiments, must be
graduates of the Special Military School, not above thirty-four years of
age, and have served at least one year with the regiment.

The sub-officers are selected from the cavalry corps--one from every two
regiments of cavalry and artillery, and every two squadrons of the
park-trains and military equipages.

The non-commissioned officers are chosen annually by the
inspectors-general--one from each regiment of cavalry:--from among those
that show a peculiar aptness for equitation and are distinguished by
good conduct, information, zeal, and intelligence; those who are
recommended for promotion in their corps are selected in preference.
Their age must not exceed twenty-five years, and they must have served
at least one year in the ranks.

These pupils, numbering about four hundred, are sent to the school by
order of the Minister of War. They continue connected with their corps,
from which they are regarded as detached while they remain at the
school. They receive additional pay. Those who after due trial are found
deficient in the necessary qualifications, are sent back to their

Upon the recommendation of the inspector-general of the school, the
officers who are serving as pupils, compete for promotion by choice with
the officers of the corps from which they are detached.

The cavalry lieutenant, who graduates first in his class, is presented
for the first vacancy as captain-instructor that occurs in the cavalry,
provided he has the seniority of rank required by law. The lieutenant
who graduates second obtains, under the same condition, the second
vacancy of captain-instructor, provided his division consisted of more
than thirty members. The sub-lieutenant graduating first, provided he is
not lower than the tenth in the general classification of the officers
of both grades, is presented for promotion to the first vacant
lieutenancy that occurs in his regiment.

The non-commissioned officers who pass a satisfactory final examination,
are immediately promoted to vacancies that have been preserved for them
in their regiments--those who have graduated among the first ten of the
class, being presented for promotion as sub-lieutenants, as soon as they
have completed their required term of service as non-commissioned
officers. Those who attend the school as non-commissioned officers,
frequently return as officers for instruction, and again in a higher
grade on the staff of the school.

Officers transferred from the infantry to the cavalry are generally sent
to this school for a short time at least. The captains-instructor of the
cavalry regiments, and the instructors of equitation in the artillery
regiments, are mostly selected from the graduates.

The school also receives by voluntary enlistment, such young men, not
above the age of twenty-one years, as desire to enter the cavalry
service. They are not admitted until they have been subjected to an
examination before a committee, by whom they are classified according to
their fitness. These volunteer enlistments for the cavalry school are
made at Saumur, at least a month before the commencement of the course,
on presentation of the certificate of classification and of approval by
the commandant of the school. The number is limited to fifty each year.

Such of these cavalry pupils as are distinguished for diligence and good
conduct and pass a satisfactory final examination are transferred to the
regiments of cavalry, for promotion to the rank of noncommissioned
officers by their respective colonels. Those who have not been found fit
for admission are sent back simply as privates.

A council of instruction is charged with the direction of the studies.
They propose useful changes, and direct the progress of the studies.
They are also charged with the examinations.

The recitations are by sections of about thirty each. In reciting upon
the general principles of tactics, equitation, hippology, &c., the
manner is as in our Military Academy; when reciting upon the movements
in tactics, all the commands and explanations of the instructor to the
troops are repeated “verbatim et literatim,” and in the tone and pitch
of voice used in the field. Perfect uniformity of tone and manner is
required. The object of thus reciting is to teach the pupils the proper
tone and pitch of voice, to accustom them to hear their own voices, and
to enable them to repeat the text literally at this pitch of voice,
without hesitation or mistake.

The course of hippology includes the structure of the horse, the
circulation of the blood, organs of respiration, &c., food, working
powers, actions, breeds, manner of taking care of him, ordinary ailments
and remedies, shoeing, lameness, saddling, sore backs, sanitary police,
&c., but does not comprise a complete veterinary course.

The practical exercises consist of:--the ordinary riding-hall drill,
including vaulting, the “kickers,” &c.; the carrière, or out-door riding
at speed, over hurdles, ditches, &c.; cutting at head; target-practice;
fencing; swimming; the usual military drills; skeleton squadron and
regimental drills; rides in the country; finally, in the summer,
frequent “carousels” or tilts are held.

The veterinary surgeons of the lowest grade are sent here upon their
first appointment to receive instruction in equitation, to profit by the
study of the model stud, and to learn the routine of their duties with
the regiments. They form a distinct class.

In the _Model Stud_, the number of animals varies. There are usually two
stallions and about twenty mares, (Arabs, English, Norman, &c.,) in
addition to those selected from time to time from among the
riding-animals. Attached to it is a botanical garden, more especially
for useful and noxious grasses and plants.

_School for Breaking Young Horses._--The best horses purchased at the
remount dépôts are selected for the officers, and sent to this place to
be trained. The number is fixed at 100 as a minimum. These, as soon as
their education is complete, are sold or given, according to the orders
of the Minister of War, to those officers who need a remount--in
preference, to officers of the general staff and staff corps, those of
the artillery, and mounted officers of infantry. These officers may also
select from among the other horses of the school, with the approval of
the commandant.

_School of Farriers._--This is attached to the cavalry school, and is
under the direction of the commandant. It is composed of private
soldiers who have served at least six months with their regiments, and
are blacksmiths or horse-shoers by trade. There are usually two men from
each mounted regiment. The course lasts two years; it comprises reading,
writing, arithmetic, equitation, the anatomy of the horse, thorough
instruction as to all diseases, injuries, and deformities of the foot,
something of the veterinary art in general, the selection of metals,
making shoes, nails, tools, &c., shoeing horses. The establishment has a
large shoeing shop and yard, a recitation-room, museum, and store-rooms.
In the recitation-room there are skeletons of horses, men, &c., as well
as some admirable specimens of natural preparations in comparative
anatomy, a complete collection of shoeing-tools, specimens of many kinds
of shoes, &c.--_Annuaire de l’Instruction_ 1861, _and_ “_Observations_.”




The staff is the center from which issue and to which are addressed all
orders and military correspondence.

The officers of the staff are divided into chiefs of the staff,
sub-chiefs, staff-officers, and aides-de-camp.

The colonels and lieutenant-colonels are employed as chiefs of the staff
in the different military districts of France, and in the divisions of
the army on active service. The ordinary posts of the majors and
captains is that of aides-de-camp to general officers.

When several armies are united together under a commander-in-chief, the
chief of the general staff takes temporarily the title of
_Major-Général_, the general officers employed under him that of

The duties of the chief of the staff are to transmit the orders of the
general; to execute those which he receives from him personally, for
field-works, pitching camps, reconnaissances, visits of posts, &c.; to
correspond with the commanding officers of the artillery and the
engineers, and with the commissariat, in order to keep the general
exactly informed of the state of the different branches of the service;
to be constantly in communication with the different corps, so as to be
perfectly master of everything relating to them; to prepare for the
commander-in-chief and for the minister of war, returns of the strength
and position of the different corps and detachments, reports on marches
and operations, and, in short, every necessary information.

The distribution of the other officers of different ranks, when it has
not been made by the minister of war, is regulated by the chief of the
general staff.

In every division of the army an officer of the staff is specially
charged with the office work; the others assist him when necessary, but
they are more usually employed in general staff duties, in
reconnaissances, drawing plans of ground, missions, the arrangement of
camps and cantonments, superintending the distribution of the rations,

The officers of the staff may further be charged with the direction of
field-works thrown up to cover camps and cantonments.

Staff officers of all ranks may be employed on posts and detachments. On
special missions they command all other officers of the same rank
employed with them. When a staff officer is charged with the direction
of an expedition or a reconnaissance, without having the command of the
troops, the officer in command concerts with him in all the dispositions
it may be necessary to make to ensure the success of the operation.

The staff of generals of artillery and of engineers is composed of
officers of their respective arms.

The war depot (_Dépôt de la Guerre_) was founded for the purpose of
collecting and preserving military historical papers, reconnaissances,
memoirs, and plans of battles; to preserve plans and MSS. maps useful
for military purposes, and to have them copied and published.

It is divided into two sections--one charged with trigonometrical
surveying, topography, plan drawing, and engraving; the other with
historical composition, military statistics, the care of the library,
the archives, plans, and maps. Each of these sections is under the
direction of a colonel of the staff corps, who has under his orders
several officers of his corps.

The war depot has taken a large share in the preparation of the map of
France. The first idea of undertaking this important work dates from
1808. After various delays and difficulties, the trigonometrical survey,
which had been for a time suspended, was recommenced in 1818. The work
was placed under the war depot, intrusted to the corps of geographical
engineers. Since this period the geographical engineers have been
incorporated in the staff corps, by the officers of which the work has
been continued. The primary triangulation was finished in 1845; the
secondary is now finished; the filling in the details will occupy
several years to come. The number of officers of the staff corps
employed on the survey has varied from twenty-six to ninety.


The officers of the French staff constitute a distinct and separate
corps, numbering thirty-five colonels, thirty-five lieutenant-colonels,
one hundred and ten majors, three hundred and thirty captains, and one
hundred lieutenants. None but officers of this corps can be employed on
the staff. When, by accident, there is not a sufficient number present,
regimental officers may be temporarily employed, but they return to
their regiments as soon as officers of the staff corps arrive to replace
them. The division of the staff into adjutant-general’s and
quartermaster-general’s department does not exist in the French service.

The only means of entering the staff corps is through the Staff School
of Application. Of the fifty student-officers which the School of
Application usually contains, twenty-five leave annually to enter the
staff corps, and are replaced by an equal number. Three of these come
from the Polytechnic, the remaining twenty-two are selected from thirty
pupils of the Military School of St. Cyr, who compete with thirty second
lieutenants of the army, if so many present themselves; but, in general,
the number of the latter does not exceed four or five.

The course of study in the Staff School of Application lasts two years.
The students have the rank of second lieutenant. On passing the final
examination they are promoted to the rank of lieutenant; they are then
sent to the infantry to do duty for _two years_, at the expiration of
which time they are attached for an equal period to the cavalry. They
may finally be sent for a year to the artillery or engineers.

This routine can not be interrupted except in time of war, and even then
the lieutenant can not be employed on staff duty until he has completed
his _two years_ with the infantry. However, officers who have a special
aptitude for the science of geodesy or topography, may even earlier be
employed on the map of France or other similar duty; and, further, two
of the lieutenants, immediately on quitting the Staff School of
Application, are sent to the war depot (_Dépôt de la Guerre_) to gain a
familiarity with trigonometrical operations.

The General Officers at their Inspections are required to report
specially to the Minister of War on the captains and lieutenants of the
staff corps doing duty with the regiments in their districts, both as to
their knowledge of drill and manœuvres, and their acquaintance with the
duties of the staff. They are to require these officers to execute a
military reconnaissance, never allowing more than forty-eight hours for
the field sketch and its accompanying report.

Officers of all arms of the rank of captain or under, are permitted to
exchange with officers of equal rank in the staff corps; but they must
previously satisfy the conditions of the final examinations of the Staff


The Staff School of Application is situated in Paris, in the Rue de
Grenelle, close to the Invalides. Of the ninety officers attending it,
sixty lodge in the building and thirty out of it, but all take their
meals in the town. Each has, in general, a room to himself. Servants are
provided in the proportion of one to about eight rooms. The officers are
forbidden to have private servants.

The staff of the school is composed as follows:--

  The Commandant, a General of Brigade.

  The Second in Command, Director of the Studies, a Colonel or
Lieutenant-Colonel of the Staff Corps.

  A Major of the Staff Corps, charged with the superintendence of the
interior economy and the drills and exercises.

  Three Captains of the same Corps, charged with the details of the
interior economy of the School, and to assist the Major in the
instruction of the Officers in their military duties. The Captains are
required to take the direction of a portion of the topographical works
on the ground.

  A Medical Officer.

Thirteen Military Professors, or Assistant Professors, viz.:--

  A Major or Captain, Professor of Applied Descriptive Geometry.

  A Major or Captain, Professor of Astronomy, Physical Geography, and

  A Major or Captain, Professor of Geodesy and Topography.

  A Major or Captain of Engineers, Professor of Fortification.

  A Major or Captain of Artillery, Professor of the instruction relative
to this arm.

  A Military Sub-Intendant, Professor of Military Legislation and

  A Major or Captain, Professor of Military Art.

  A Captain, Assistant Professor of Descriptive Geography; charged also
to assist the Professor of Fortification.

  A Captain, Assistant Professor of Topography; charged also to assist
the Professor of Geography.

  A Major or Captain of Cavalry, Professor of Equitation; he acts under
the immediate orders of the Major of the College.

  Two Lieutenants or Second Lieutenants of Cavalry, Assistant Professors
of Equitation.

  An Officer of Cavalry of the same rank, acting as Paymaster to the
Riding Detachment.

The Non-Military Professors are:--

  Two Professors of Drawing.

  Two Professors of German.

  A Professor of Fencing.

One hundred and forty-five horses are kept for the use of the
student-officers, and eighty-two men belonging to the cavalry to look
after them.

Both the studies and examinations at the Staff School hold an
intermediate place between those of the Polytechnic and St. Cyr, being
less abstract than the former, and higher and more difficult than the


The entrance to the Staff School of Application in France is, as is the
case in all the French military schools, by means of a competitive
examination, or, rather, by the results of three distinct examinations,
and by the selection of different sets of successful candidates. _Three_
are taken from the students leaving the Polytechnic, who have an
absolute right to the three first places in the Staff School, and
_twenty-two_ are selected from the thirty best students leaving St. Cyr,
and an equal number of sub-lieutenants of the line under twenty-five
years of age, if so many present themselves. The sub-lieutenants must
have one year of service in that rank, and they must make known their
request to be allowed to compete for admission to the Staff School to
the Inspector General, and, through him, to the Minister of War. It
should be added, that their number is generally extremely small.

The usual number of young officers admitted yearly to the school in time
of peace is twenty-five, but this number is sometimes considerably
exceeded, and we found no less than ninety present. The _three_
Polytechnic students select the Staff School after their final
examination, and the St. Cyr students make known their desire when the
whole are examined by a Board of Examiners, and the thirty best are then
selected as competitors for admission into the Staff School of

The sub-lieutenants also repair to St. Cyr, where they are examined
separately by the same examiners who have just conducted the examination
of the St. Cyr students, and in the same subjects.

Their marks or credits are then compared with those of the St. Cyr
pupils; and the relative position of the two sets of candidates is
ascertained, and the list of those to be admitted to the School of
Application determined accordingly.

These examinations take place before a Commission of Officers, composed

  A Lieutenant-General President, appointed by the Minister of War.

  The Director or Chief of the Dépôt de la Guerre.

  The Commandant of the School of Application.

  Four Colonels or Lieutenant-Colonels of the Staff, appointed by the
Minister of War.

  A Field Officer chosen from among the Officers employed at the Dépôt
de la Guerre, as permanent Secretary.

This Commission is also charged with drawing up and proposing
regulations for the approval of the Minister of War concerning the
interior organization and the course of study to be followed in the
school, and to make changes in the programmes for admission and for
leaving the school.

A very detailed account of the subjects of the entrance examination is
drawn out, and inserted in the _Journal Militaire_, and the _Moniteur_
every year. The following are the subjects:--

  (1.) Trigonometry and Topography.

  (2.) Regular Topography--the measuring of plane surfaces and leveling.

  (3.) Irregular Topography, Plane Trigonometry.

  (4.) Military Art and History, including--

    (_a._) History of Military Institutions at the chief periods.

    (_b._) Present composition of the French army.

    (_c._) Organization of an army in the field.

    (_d._) History of some of the most memorable campaigns, as those of
1796-97 in Italy, and of 1805 and 1809, in Germany.

  (5.) Artillery and Science of Projectiles.

  (6.) Field Fortification and Castremetation.

  (7.) Permanent Fortification.

  (8.) Military Legislation.

  (9.) Military Administration.

  (10.) Manœuvres.

  (11.) German Language.

  (12.) Drawing.

The marks assigned and the influence allowed to each of these subjects
are the same as those given in the final examination at St. Cyr. The
entrance examination places the students in order of merit.


All the details of the teaching are in the hands of a Council of
Instruction, similar to that of the Polytechnic, and consisting of the
General Commandant (President,) the Director of Studies, and three
Military Professors, appointed yearly by rotation. Other professors and
assistant professors, or officers of the staff of the school, may be
called in to assist the Council, but (except in deciding the list at an
examination) they have no votes.

This council does not interfere directly with the administration, the
common work of the school. It draws up, indeed, the list of lectures,
making any alterations in them, or in the books to be used which may
seem from time to time desirable. But the officer accountable for the
daily working of the school is the Director of Studies. His functions
appeared to us to bring him into more constant connection with the
pupils than was the case with the director of the Polytechnique. In all
the schools the General Commandant and the Director of Studies live in
the establishment; but at the _Ecole d’Application_ and at St. Cyr the
director “examines the methods of teaching, and proposes to the Council
of Instruction any modifications or improvements which may raise or
quicken the instruction. He inspects the work of the student-officers,
both in and out of the school. He keeps a register of the marks given by
the professors, and at the end of every three months brings the sum of
them before the General Commandant in a detailed report.” In fact, his
school functions are not modified, as at the Polytechnic, by a body of
able professors.

As already stated, there are fifteen professors, without reckoning those
of equitation, and thirteen of them are officers; but the system of
_Répétiteurs_, which we have seen so influential at the Polytechnic,
does not exist here.

The hours of work are, in summer, _i.e._ from May to November, from six
to five, and in winter from eight to five, with the exception of one
hour for breakfast and one hour for _étude libre_, which appears to mean
very little indeed. From seven to nine hours daily may be taken as the
amount, but (as is the case with most French schools) there is a
constant change, not only in the subjects taught but in part of the work
being _out_ and part _in_ doors, some really head work, much purely
manual. There does not appear to be the same intense application as at
the Polytechnic; indeed, the work for three months in the year is almost
entirely in the open air, consisting in making plans and military
sketches, either in the neighborhood of Paris or in the more distant
parts of the country; eight months are devoted to the in-door studies,
one month to the examinations.

The in-door studies are entirely conducted in the halls of study
(_Salles d’étude_), in each of which we found parties of twelve or
fifteen students seated. They are inspected constantly by the director
or some of the professors. None of the regular work may be done in
private. It seems everywhere a fixed belief in the French Military
Schools that very much would be done idly and ill if done in private.
This presents a striking contrast to the feeling on the subject in

The severer and preparatory studies of mathematics are supposed to have
been completed prior to entrance into the Polytechnic or St. Cyr. Some,
however, of the studies of applied science occupy considerable time at
the School of Application.

The following analysis will show the time assigned to each branch:--

  1. _Astronomy_ occupies 1½ hours weekly for the pupils of the first
year; afterwards it ceases entirely.

  2. To _Applied Descriptive Geometry_ a good deal of time is given, but
still only by the pupils of the first year. 12 hours a week are spent
upon it in the first half year, 10 in the second.

  3. _Military Topography_ occupies about 10½ hours in the first year, 6
in the second.

  4. A good deal of time is devoted to _Field Fortifications_. The
junior division, it is true, only begin it in their second half year of
study, and then only work at it for 1½ hours weekly. But the senior
division are occupied 4½ hours weekly in their first half year, and 7½
hours in their second.

  5. _The Study of Military Administration and Legislation_ is begun
immediately upon entrance. It occupies during both years 1½ hours

  6. _Lectures on Military Art and Tactics_ are also given for 1½ hours
weekly during both years, and after hearing these lectures the students
are occasionally required to write a military memoir on a campaign,
descriptions of reconnaissances, or of fields of battle, and to make
sketches of ground with accompanying reports. This course was noted by
General Foltz, the director of the school, as defective, on the ground
that it was too difficult to find a teacher for, or indeed to teach
military art; and he thought that lectures on military history, or such
works as Napoleon’s Memoirs, would be more useful to the pupils.

  7. _Drawing_ occupies throughout 4½ hours weekly, and great attention
is bestowed upon it. “We were shown a large number of works done by the
young officers of the school. To enumerate some of the most
important--there were specimens of objects, with shadows; perspective of
the exterior and interior of buildings, with shadows; perspective views
of country; machinery drawings, plan, section, and elevation; in
fortification, a plan of comparison of a portion of ground with proposed
field-works for defense; military bridges; reconnaissance, and memoir of
a route, with accompanying notes and sketches, done both on foot and on
horseback; plan of a portion of country made with a compass by parties
of ten, under the direction of a Captain (for this the trigonometrical
points and distances were furnished, and it was filled up by a minor
triangulation;) plan of a field of battle, made without points; and a
description of the battle.”

These drawings were mostly executed with great care, and we were told
that the course was fully as much as the student could accomplish in two
years. Some parts of it are done entirely in the _Salle d’étude_;
sketches are made on horseback in the neighborhood of Paris, always
under the direction of the professors, others again at great distances,
such as one at Biarritz last year, and the one on which the pupils are
to be engaged this year, is the line of operations of Wellington from
the Spanish frontier to Toulouse. The two last kinds of work are roughly
sketched, and finished at Paris. These summer occupations seem to stand
in place of vacations, of which there are none.

  (1.) To _Fencing_, three hours a week are given throughout.

  (2.) To the _Cavalry Drill_ two hours weekly in the first division. It
is replaced by _Infantry Drill_ in the second.

The studies which none but the senior division pursue are,--

  (1.) _Artillery_ studies, which occupy 4½ hours weekly.

  (2.) _Geography_, meaning chiefly the military geography of a country,
with a few lectures on statistics and political economy; these take 1½
hours weekly.

  (3.) _Geodesy_, or trigonometrical surveying, also for 1½ hours.

The only strictly literary occupation is the study of German for about
three hours per week during the whole time. We were told that a large
proportion of the pupils unite among themselves to learn English
privately, but no public course is given.


The students have two examinations to go through in each year; the first
commencing about the first of June, the last in November, and each of
the first year’s examinations is held before a jury consisting of--

  (1.) The General Commandant, or the Director of Studies; President.

  (2.) The Professor of the Course examined in.

  (3.) Two Officers appointed by the Council of Instruction.

The last examination in each year is, of course, the most important,
inasmuch as the passage from the Second or Junior to the First or Senior
Division, and in part from the Senior into the Staff Corps, is regulated
by the results of these examinations; and the value allowed to the last
examination in each year is just double of that assigned for the
examinations in June.

The examinations of the first year are confined to the subjects of study
followed during that year, viz.:--

Descriptive Geometry, Astronomy, Topography, Artillery, Fortification,
Military Art and Administration, German, Drawing, Register of Notes and

The professors and members of the jury are directed rigorously to
conform themselves to the following scale as regards the marks or
credits they award for the oral answers, graphical representations, &c.

   0 to  4 bad.
   5 to 10 passable.
  10 to 13 fair.
  14 to 18 good.
  19 to 20 very good.

The Co-efficients of influence of the various studies of the first year
are as follows:--

  Descriptive Geometry,
    { Theory,                       4 }
    { Geographical Representation,  3 }
    { Drawing of Machines,          1 }
    {   { Memoir,                   1 }
    {   { Drawing,                  1 }  9
    { Theory,                       4 }
    { Graphical Representation,     1 }  5
    { Theory,                       4 }
    { Graphical Representation,    *6 } 10
  Artillery,                             4
    { Theory,                       4 }
    { Graphical Representation,     2 }  8
    { Memoirs,                      2 }
  Military Art
    { Theory,                       4 }
    { Memoirs,                        }
    {   { On various questions,     1 }
    {   { On surveys,               2 }  7
  Military Administration,
    { Theory,                       4 }
    { Memoirs,                      1 }  5
  Manœuvres,                             2
  German,                                4
  Drawing,                               2
  Keeping of Memorandum Books,           1
  Conduct and Discipline,                1
  Riding and Knowledge of the Horse,     2
    { Riding,
    { Hippology,
       Total,                           60

  * Subdivision of the Co-efficients of the Graphical Representations.

    Survey with compass,                  1  }
    Rapid sketch,                         1½ }
    Itinery of the first survey,  }       1½ }
    Itinery of the second survey, }          }
    First Topographical Drawing,           ½ }
     { Second, with relief,                ¾ }
     { Third, on the scale of 1/20000      ¾ } 6

As soon as the examinations are concluded, the Council of Instruction,
prepares a provisory classified list of the students, made out in order
of merit from the credits or marks awarded by the Examining Jury in
connection with the above-mentioned co-efficients of influence, in a
similar manner to that already explained in the account of the
Polytechnic School, the student with the largest numerical credit being
placed at the head of the list.

This provisory list is submitted to the Consulting Committee of the
Staff Corps for transmission to the Minister of War.

In order to pass from the Second or Junior into the First or Senior
Division, every Student Officer must have obtained the following marks
or credits from the Jury, viz.:--

In Astronomy and Geometry, six out of twenty in each.

In all other branches of theoretical instruction, four out of twenty.

In the classification of the graphical representations in topography, a
mean of eight out of twenty, and in each of the other courses a mean of
six out of twenty; and as the general result of his various works and of
his examinations (the mean of the year being combined with the number
obtained before the jury in the proportion adopted by the Council of
Instruction,) he must have obtained a number of credits equal to
one-half of the maximum (1,200.)[20]

    [Footnote 20: There must be some error in the printed regulations
    on the subject.]

Every Student Officer who in his oral examination before the Jury has
failed in obtaining the minimum stated above is subjected to a fresh
proof before the Consulting Committee of the Staff Corps, and if this is
not favorable to him he ceases to belong to the school, and must return
to his regiment, unless such failure can be attributed to an illness of
forty-five days, in which case he may be permitted to double his first
year’s course of study.

If the second proof be favorable he is retained at the school, but
placed at the bottom of the classified lists prepared by the Council of

The co-efficients of influence for the second year are--

                                   Subdivision of the Co-efficients
                                   of the Graphical Representations, &c.

  Geography and Statistics,
     { Theory,                            4 }  5
     { Memoir,                            1 }
  Geodesy and Topography,
    { Theory                              4 }
    { Geographical Representation,        6 } 10
        { Survey with the Compass,                  1  }
        { Reconnaissance,                           1½ }
        { Itinerary of the first survey,  }            }
        { Itinerary of the reconnaissance }         1½ }
        { Drawing of a Fortress and its Environs,   1½ }
        { Reduction of the Drawings,                 ½ } 6

    { Theory,                            4  }
    { Graphical Representation,          3  }
    { Memoirs,                           1  }  8
        { First Drawing of a Military Bridge,       1  }
        {   Second ditto,                            ½ }
        { Breaching Battery                          ½ }
        { Drawing of Artillery Carriage,            1  } 3

    { Theory,                            4  }
    { Graphical Representation,          3  }
    { Memoir on a Fortified place,       2½ }
    { Memoir on a Project of Field
    {   Fortification,                   1½ } 11
         { Defilement,                              1 }
         { Project of Fortification,                2 }  3

  Military Administration,
    { Theory                             4  }  4

  Military Art
    { Theory                             4  }
    { Memoir on various questions comprised
    {   in drawing up a memoir,          2  }
    { Memoir on the survey with a Compass,
    {   or sketch reconnaissance         2  }  8

  Manœuvres,                                   3
  German,                                      4
  Drawing,                                     2
  Keeping of Note Books,                       1
  Conduct and Discipline,                      1

  Riding and Knowledge of the Horse,           3
      { Riding,                                     2  }
      { Veterinary Art,                             1  } 3
                      Total                   60

The examinations of the students of the Senior or First Division is made
in a similar manner to that already described for the Junior Division,
but after they are concluded, and prior to these students being admitted
into the Staff Corps, they are subjected to another examination before
the Consulting Committee of the Staff Corps, consisting of--

  3 Generals of Division on the Staff.
  3 Generals of Brigade.
  3 Colonels of the Staff.
  5 Lieutenant-Colonels, including the Secretary.

The professors belonging to the school may be called in to assist at
this examination, and when it is concluded the Consulting Committee
proceeds to the definitive classification of the Student Officers of the
First Division by causing the following documents to be placed before
them, viz.:--

The register of the notes of each Student Officer.

Tables of the value of their work; the classified list of passage to the
First Division, and the provisionary list for leaving, recently prepared
by the Council of Instruction. The numerical credits obtained in these
two classifications are added (each sum being halved) to the definitive
classification prepared by the committee. The total is divided by two,
in order not to exceed the regulated limit of 1,200 credits for the

Every Student Officer who, in this examination for leaving, has not
obtained the half of the maximum number of numerical credits is
considered to be inadmissible to the Staff Corps.

This classified list, prepared by the Consulting Committee of the Staff
Corps, fixes the position of the Student Officers in order of merit, and
according to this order of merit they enter the Staff Corps. The
committee reports to the Minister of War the names of the Student
Officers that are not eligible for the Staff Corps.

The first two or three places, we were told, are always remembered as
marks of distinction, but the honor does not descend lower, as in the
intense competition of the Polytechnic.

Students belonging to the First Division may also be permitted to double
the second year’s course of study on account of illness; but in no case
can an officer be permitted to remain more than three years at the



The _Collége_ or _Prytanée Militaire_ appears, in point of studies, to
differ from the schools that have just been described, chiefly in its
having only one department for the elder pupils, the scientific, with
merely occasional subsidiary lessons in grammar and literature.

The institution is a school for boys between the ages of ten and
eighteen; no one under ten or above twelve years old can be admitted:
and no one can commence a new course at the school after completing his
eighteenth year.

The prescribed instruction comprises the following courses:--

  Humanities (Latin, &c.)
  History and Geography.
  Physical Sciences.
  Natural History.
  Figure Drawing.
  Linear Drawing.

And the general object of the courses is to qualify the pupils to pass
the examination for the degree of Bachelor of Science.

The pupils also go through military and gymnastic exercises, and learn
to swim.

The school is under military discipline, is governed by a general
officer of the staff corps or a colonel in active service, as commandant
and director of studies, and by a lieutenant-colonel or major, with the
title and functions of second in command and sub-director. In addition
there are four officers, twenty-three professors and teachers, and
eighteen _répétiteurs_.

The yearly charge for paying pupils is 850 francs, and the cost of
outfit about 500 francs; but there are 400 free and 100 half-free places
(400 _bourses_ and 100 _demi-bourses_) granted by the state in favor of
the sons of officers, the order of preference being regulated as
follows, those who are orphans on both sides having the first claim, and
those who have lost their father, the next:--

  1. Those whose fathers have been killed, or have died of wounds
received in action.

  2. Those whose fathers have died in the service, or after retiring on
a pension.

  3. Sons of fathers who have been disabled in consequence of wounds
received in action.

Sons of non-commissioned officers or of private soldiers who have been
killed or have been disabled in action, who have been placed on the
retired list, or have been discharged after twenty years’ service, may
also be admitted, as a special mark of favor.

The candidates undergo an examination, not, however, for the purpose of
competition, but merely to show that they are qualified to enter the

The school is inspected annually by a general officer sent by the war
department, as also by an officer of the commissariat. There is no sort
of engagement or expectation that the pupils should enter the military
service. The nature of the studies holds out some inducement to them to
compete for admission at St. Cyr or the Polytechnic; and in the
examination for entrance at St. Cyr, it is stated that the sons of
military men have the privilege of being raised fifteen places in the
list of the order of merit. An officer’s or soldier’s son from La Flèche
would, in case of 300 candidates being admitted to St. Cyr, be able to
claim admission, if he came 315th on the list, to the exclusion of the
candidate who stood 300th.


The School of Musketry, formed by the Ministerial Order of 29th March,
1842, was only intended at first to supply instructors to the ten
battalions of Chasseurs who were armed with rifles. The results of its
establishment were, however, found so valuable, that the benefits of the
instruction it afforded were by degrees extended to the whole army.

In 1845, the Duc d’Aumale, who had taken a special interest in the
improvement of fire-arms and the better instruction of the soldier in
their use, was nominated Inspector-General of Schools of Musketry.
Besides the chief school at Vincennes, others were formed in the
principal garrisons; and eventually a regimental School of Musketry was
established in every regiment of infantry.

Some changes have been made in the system established under the Duke.
The School of Musketry at Vincennes has only been regularly organized on
its present footing since 1852. A portion of the fortress affords the
accommodation required for the theoretical instruction, while the
Polygon offers admirable facilities for practical instruction and target

The Staff of the School consists of,--

  A Commandant, a Lieut.-Colonel of Infantry.
  An Instructor in Musketry, a Major of Infantry.
  A Professor, a Captain of Artillery.
  An Assistant Professor, a Captain of Artillery.
  A Sub-Instructor in Musketry, a Captain of Infantry.

Each regiment sends an Officer (a Sub-Lieutenant or a Lieutenant) to
Vincennes, to go through the course of instruction. The course commences
on the 1st of March, and lasts four months. Two hours a day three times
a week are devoted to lectures on the construction and use of fire-arms,
and the theory of projectiles. Each officer is required to complete a
certain number of drawings of the separate parts of arms. At the
termination of the course, certificates are given, and, if favorable, go
towards the officer’s claim to be promoted “_au choix_.”

We were conducted over the rooms of the fortress set apart for the
school by the officer charged with the Theoretical Instruction (Captain
Févre, of the Artillery.) They consist of a large paved room, where the
officers perform their small-arm exercise in bad weather; of the
study-room, in which the drawings are executed; of a lecture-room or
amphitheater; of the library, chiefly supplied with technical works on
arms; and of a model-room, containing a very good collection of French
and foreign arms, and of portions of arms, to illustrate the lectures.
There are, besides, private rooms for the instructors, and a room for
the orderlies. On the ground floor a small forge has been fitted up for
the purpose of giving practical instruction in some of the details of
the manufacture of arms.

To produce accurate marksmen is not the only object of the School of
Musketry. Its staff may be considered a description of standing
committee, to whom inventions in arms and ammunition are submitted, to
have their qualities practically tested. On the day of our visits
experiments on the relative merits of three forms of balls were being
carried on, which we witnessed.

Quitting the fortress by a bridge over the ditch, in an angle of which
the Duc d’Enghien was shot, we entered on the Polygon or practice
ground. In a few minutes two detachments of troops, one from the
Chasseurs de Vincennes, the other from the 20th regiment of the line,
arrived and took up their ground in front of the practice butts. Of the
balls between which comparisons were to be made, one was proposed by M.
Minié, who was himself present, another by M. Nessler, the third was
named the ball “_de la garde_.” There were six targets in line in front
of the butt; the Chasseurs fired at three of them, and the 20th regiment
at the other three. A trench runs along parallel to the butts, and at a
few yards in front of them. The line of targets is in the space between
the trench and the butts. The trench gives cover to the range party, one
of whom is stationed opposite to each target, in a rude recess cut into
the side of the trench, to afford shelter in wet weather. Each time a
target is struck, the man opposite to it raises his banderol, which is
then seen by the firing party, and acknowledged.

The trench is continued to some distance beyond the butts, and is there
met by another trench at right angles to it; so that one may go up from
the firing party to the range party without any risk.

On the cessation of the firing, the officer in command of the range
party numbered the hits in each target. He marked separately the hits
where the balls had arrived sideways (shown by the form of the
perforation,) a very important consideration in comparative experiments
with oblong balls.

Prizes and honorable mentions are bestowed annually on the best shots.
The number of the regiment and the names of the men thus distinguished
are inserted in the official military journal.



This school, which is located at Paris, at the military hospital of
Val-de-Grâce, is under the control of the Minister of War. Its design is
to introduce the pupils in the medical service of the army to an actual
exercise of their skill, to complete their practical education, and make
them acquainted with the regulations, which govern the army in its
relation to the sanitary service.

Admission to the School of Application as resident physicians and
pharmaceutists, is gained by passing successfully a competitive
examination. These examinations are held at Paris, Strasburg, and
Montpelier, at uncertain periods, as the wants of the service may

For admission to the examination, the candidate for employment as
resident physician must have his name enrolled in a bureau of military
superintendence, and satisfy the following conditions:--1st. Be a native
of France; 2nd. Be not above thirty years of age at the time of the
examination; 3rd. Have received the degree of doctor of medicine from
one of the medical faculties of the Empire; 4th. Be free from any
infirmity that disables from military service; and 6th. Subscribe a
pledge of honor that he will devote at least five years to the military
sanitary service. The candidates are subjected to an examination in
pathology, medical therapeutics, anatomy, and practical surgery.
Candidates for the office of resident pharmaceutist must also be natives
of France, be not above thirty years of age, have a diploma of pharmacy
of the first class, be free from every disabling infirmity, pledge
themselves to at least five years service, and pass an examination upon
the materia medica, chemistry, and pharmacy.

During their continuance at the School, they receive a fixed annual
salary of 2,160 francs, and an allowance of 500 francs for the first
expense of uniform. After spending one year at the school and passing a
satisfactory final examination, they receive the brevet rank of medical
or pharmaceutical aid-major of the second class.

There is at Strasburg, in connection with the Medical School, a
Preparatory School, designed to prepare for the degree of doctor of
medicine the pupils belonging to the sanitary service of the army. It is
annually supplied with pupils, who, without having passed the usual
course of matriculation, are enabled to satisfy the conditions requisite
for admission to the first grade of a doctorate. Every pupil of the
preparatory school, has the right of admission to the Imperial Military
School of Application.--_Decrees of 13th of Nov., 1852, and 28th of
July, 1860; Acts of 18th of June, and 15th of October, 1859, and 4th of
August, 1860._


These schools, located at Brest, Toulon, and Rochefort, are under the
control of the Minister of the Marine; their design is to prepare
sanitary officers for service in the vessels of the imperial marine.

The posts of surgeon, or pharmaceutist, of the third, second and first
classes are assigned on examination, according to order of priority
determined by a medical jury. For admission as student in these schools,
after attaining to the first grade of the third class, it is necessary
to be at least sixteen years of age, and not above twenty three, to
produce a diploma as bachelor of sciences, to prove French nationality,
and to be exempt from every infirmity that can cause unfitness for the
marine service. Examinations for filling the vacancies in each school
commence on the 1st of April, and 1st of October, annually.

The instruction is continuous. The libraries, cabinets of natural
history, the botanical gardens, anatomical theaters, chemical
laboratories, cabinets of natural philosophy, are at the disposition of
the students. The candidates admitted, receive cards of membership. They
are required to pay the treasurer of the library a sum of 50 francs,
which is devoted to its maintenance.--_Ordinance of 17th July, 1835, and
15th May. 1842._


This school, located at the Road of Brest, on board the ship “_La
Borda_,” and under the control of the Minister of the Marine, is
designed for the instruction of youth destined for the corps of state
naval officers. Candidates are admitted to this school after a public
examination, which occurs annually. For admission to the examination,
they must prove; 1st. By the production of the records, that they are
French by birth or naturalization, and that on the 1st of January of the
year of the examination, they were at least fourteen years of age, and
had not passed the maximum of seventeen years; 2d. By the certificate of
a physician, that they have been vaccinated, or have had the small-pox,
and that they have no infirmity that disables them from the performance
of marine duty.

The matriculation of the candidate is effected between the 1st and 24th
of April, at the prefecture of the department in which the domicil of
the family is located. The examination is made at the principal office
for examination nearest to that domicil, or to the college where he has
been educated; the choice as regards the place of examination must be
made known at the time of matriculation.

There is required for admission into the school, a knowledge of
arithmetic, algebra, geometry, plane trigonometry, applied mathematics,
natural philosophy, chemistry, geography, the English language, and
drawing, in conformity with the course of study pursued at the lyceums.
The candidates must prepare a French composition, a translation from the
Latin, an exercise in English, a numerical calculation in plane
trigonometry, a geometrical drawing, and the off-hand sketch of a head.
These compositions are done at Paris, and the principal towns of the
departments simultaneously, on the 2nd and 3rd of July. The oral
examinations are commenced at Paris on the 2nd of July, and repeated at
the other towns in succession as previously announced. The oral
examinations are of two grades; the lowest serving to determine whether
the candidates are sufficiently well prepared for admission, the
higher--to which only those are subjected, who have successfully passed
the first--being the decisive one, and together with the compositions,
determining the final classification in accordance with the order of

The course of study continues two years, which are passed at the Board
of Brest on the ship “_La Borda_.” The expense of board is 700 francs,
and of the outfit, about 500 francs. A grant of the whole or half of the
amount of the expense, may be made to young men without fortune. The
insufficiency of the resources of a family for the maintenance of a
pupil in the school, must be authenticated by a resolution of the
municipal council, approved by the prefect. There may also be allowed to
each beneficiary, at his entrance into the school, the whole or the half
of his outfit. Application for this assistance must be made to the
Minister of the Marine at the matriculation of the candidate.

The pupils that have passed the examinations of the second year in a
satisfactory manner, are known as naval candidates of the second
class.--_Law of 5th June, 1850_--_Decree of 19th January, 1856_--_Acts
of Sept., 1852, and 1st January, 1861._


The practice of gymnastics is an essential part of the training both of
officers and men in the French army, and constitutes a portion of the
regular exercise in every military school. There are also several
schools specially devoted to this department of physical education, and
one styled the Imperial School of Military Gymnastics at the Redoute de
la Faisanderie, part of the fortifications near Vincennes, may be
regarded as the Normal School for training both officers and privates in
order to act as monitors or instructors in their respective regiments
and battalions. The following account of the instruction given, is
abridged from an article in the _New York Tribune_, under the heading,
“How the French and the English make their Soldiers.” The writer says
that Military Gymnastics, in the form and to the extent taught in this
school, is exclusively French, and is thought to have an important
bearing on the more frequent and deadly use of the bayonet in future

  About three hundred privates and officers compose the School of
Military Gymnastics near Vincennes, where three professors of the
science and art of gymnastics give a course of practical instruction for
about six months each year. The school is under the same regulations as
the School of Musketry--each colonel being responsible for the
instruction of his regiment, and the lieutenant-colonel directs the
application of the rules and regulations.


  The gymnastic exercises are divided into “elementary gymnastics,” and
“gymnastics applied,” that is, applied to special military purposes.
A general progression regulates all the exercises.

  The men are divided into three classes. The third class comprises all
the recruits. These are exclusively practiced in the first lessons of
elementary gymnastics during the first fortnight of their enlistment,
and before they proceed to regimental drill. The first class consists of
those who are proficient in the first four lessons of the general
progression; and the second class, of those who are preparing for the
first. The first class practices twice a week; the second, three times a
week; the third class twice a day, until the men have commenced their
regimental drill, and then once a week. Each practice lasts one hour and
a half. “Returns” are drawn up recording the zeal and progress of the
men, as in musketry instruction; and the captain instructor of
gymnastics has to send in, every month, to the lieutenant-colonel,
similar returns as to the general progress of the instruction, so that
the number of effectives of each company may be accurately known.

  None but the prescribed exercises are permitted by the instructor. He
must never allow the men to attempt any extraordinary or exaggerated
feats, that might cause accidents. His aim must be to develop the
strength, agility and dexterity of the soldier by a wisely regulated
exertion, and inspire him with that self-reliance which the various
occasions of his military life may demand. He must strive to rouse his
pluck and emulation by rendering the exercises as agreeable and as easy
as possible, taking all necessary precautions to prevent him from
injuring himself or becoming discouraged. He must never forget that the
perfect safety of the soldier under training, the pleasure of the
various exercises, and, above all, the soldier’s own desire to excel,
are the first and secret elements of success in gymnastics. Harsh
treatment must be carefully avoided, much more anything like turning his
efforts into ridicule when he fails, or punishing him for involuntary
awkwardness. In conclusion, he must not expect more than regularity,
precision, and relative perfection in these exercises, to which a
military form has been given merely to facilitate their study and their
application to the whole army.

  The men practice in their fatigue dress, in squads of ten or fifteen,
and are provided with belts.

  The first exercises are intended to make the body supple from head to
foot, turning the head from right to left, forward and backward, or
merely toward right and left, bending the body, raising the arms
vertically, with and without bending them; flinging out the right or
left arm, fists clenched, and describing a circle of which the arm is
the radius.

  No soldier marches so easily as the French. It is the result of his
method of learning to march. In the moderate and quick cadence the foot
comes flat to the ground, the point of the foot touching it first; in
the running cadence the movement is an alternate hopping on the points
of the feet. It is obvious that this mode of teaching to march must
enable the soldier to avoid the great cause of universal bad marching
and walking, namely, bringing the heel to the ground, thus shaking the
whole body, especially the spine, and consequently distressing the brain
and lungs. By the great elevation of the legs the soldier must habituate
himself to bringing the toes first to the ground, instinctively, to
avoid the shock, especially in the running cadence. During the practice
the soldier repeats the words “_one_--_two_,” as each foot comes to the
ground, in order to practice the lungs at the same time, and also to
give a rhythm to the performance.

  In order still more to direct locomotion to the fore-part of the foot,
so essential to good and easy marching, there is the following
practice:--1. Attention. 2. Flexion of the lower limbs. 3. Commence.
4. Cease. At the second command the soldier brings both feet together,
throwing the weight of the body forward. At the word _commence_, he
slowly lowers his body by bending his hams, so that the thighs touch the
calves of the leg, the arms falling beside the body, the weight of the
body being entirely thrown on the points of the feet. He then gradually
rises to the erect position.

  There is also what is called the “gymnastic chain.” Circles are traced
on the ground contiguously; the men are posted in these circles, in a
single rank, three paces apart. The instructor commands:--1. Squad will
advance. 2. Double. 3. March. 4. Halt. At the first word the soldier
throws the whole weight of his body on the right leg. At the word
_march_, he throws the left foot smartly forward, the leg slightly bent,
bringing the point of the foot to the ground, thirty-nine inches from
the right, and so in like manner with the right, always keeping the
weight of the body on the leg which feels the ground, allowing the arms
to take their natural motion for equilibrium. The first man (a monitor,
one of the best trained) runs successively through all the windings of
the chain of contiguous circles without stopping; the others follow,
preserving the distance. When the men meet each other at the
intersections of the circles, they shorten or lengthen the pace, so as
not to jostle each other, and so that two men shall not pass by the same

  To deliver a thrust or a blow with the bayonet, sword, or fist to the
best advantage, requires training of the subsidiary muscles, and such
scientific practice as places the body in the best position to aid and
intensify the effect. This is done by the “Pyrrhic Exercise.” The
command is:--1. Pyrrhic Exercise (right or left limb forward.) 2. Ready.
3. March. 4. Halt. At the word _ready_, the soldier faces to the left,
carries the right foot forward, the heel sixteen inches from the hollow
of the left foot, the right knee bent, the left leg stretched, the right
arm extended forward, the fist clenched, on a line with the shoulder,
the nails slightly upward, the left arm in a line with the left side and
but little bent, fist clenched, and about six inches from the thigh, the
nails toward the thigh, the upper part of the body inclined forward, the
head erect, the eyes looking to the front, the left shoulder lowered. At
the word march, the soldier straitens his body, bringing the right heel
near the hollow of the left foot without touching the ground, turns at
the same time his right forearm, so that describing a circle from below
upward, the fist lightly touches the right breast, then flinging the
fist smartly forward, the nails a little upward, and advancing the right
leg to about twenty-five inches, the foot striking the ground with
force, or an “attack,” as we call it in sword exercise, the upper part
of the body inclining forward, the left leg stretched, the foot flat,
the left arm turned outward and along the thigh as before. These
movements are continued until the words “company--halt” are given, when
the soldier faces to the right and comes to attention. The left arms are
practiced in like manner, and a rhythm is given to the performance by
the repetition of the numbers 1, 2, 3, by the soldier.

  A soldier must not be easily knocked off his legs; so there are six
positions for the practice devised to teach the soldier how to maintain
his equilibrium. He stands alternately on the right or left leg, bending
the other against the body with his locked fingers, or he stands on one
leg, the other bent behind, or he comes slowly to the kneeling position
and springs up smartly, flinging his arms suddenly above his head, the
nails turned inward, and then comes to attention, or he bends forward on
one foot, or backward in like manner, and to the right or left, all on
one foot.

  The elementary development of the muscles forms a most important part
of the training. By word of command the soldiers strike their breasts
with the right or left fist--strike out with the right and left as in
boxing--support cannon balls in the hand, one or both arms extended, and
hurl the balls to a distance. They fling an iron bar, held by the
middle; they support a heavy club in every possible position, at the
shoulder, behind the back, one with the left hand, another with the
right, at right-angles, or two together, one in each hand. They swing
the club horizontally and overhead, or vertically and behind, or round
and round the body.

  Preparatory to leaping, the proper muscles must be taught their
necessary contractions, and this is done to the words of
command--“Simultaneous flexion of the legs,” “Simultaneous flexion of
the thighs and legs,” whereat they hop on the right or the left leg
singly, and then on both together. They are practiced in advancing on
the position of kneeling on one leg alternately, obviously a very useful
mode of progression for a skirmisher in stealthily changing position
behind a low wall or a hedge.

  They are taught to walk systematically on the heels alone and on
tiptoe, and to fling a cannon ball with the foot by means of a strap
attached to it. As practice alone can habituate us to the proper
inclination of the body in ascending and descending, both these modes of
marching are carefully taught, attention being fixed to throwing the
weight of the body on the point of the feet in the former, and on the
heels in the latter.

  Their wrestling takes every shape and mode of contest. With extended
arms, the fingers interlocked, the left leg advanced, they push against
each other; or, holding each other by the hands or by the wrists, they
pull against each other; or, each man holding his left wrist with his
right hand, the thumb underneath, seizes with his left hand the wrist of
his antagonist, and then at the word “wrestle,” he pulls or pushes
uniformly or by jerks, to the right, to the left, forward, to the rear,
upward and downward, striving to displace his antagonist.

  Furnished with appropriate handles, with a short cord attached, they
pull against each other, each striving to drag his antagonist with one
hand, then with both hands; and then three wrestle together in like
manner, the central man pulling or resisting the outer two, or both of
these pulling against him in opposite directions.

  Then two wrestle in a sitting posture. They sit, closing the legs,
feet to feet, and sole to sole, with the aforesaid handle and cord
between their feet, and at the word of command pull away, striving to
raise each other. As soon as one is raised the contest ends, and the
victor holds the handle in his left hand. The instructor then makes all
those wrestle together successively who have won the handle, until only
two remain, and then ascertains the strength of these two by a
dynamometer, and makes a note of it.

  The last of the elementary exercises are those of traction, or drawing
against each other, holding on by a rope, either in pairs, or several
together pulling against a fixed point, which may be a dynamometer,
indicating the force of the combined pull resulting, or the men are
divided into two squads and pull against each other.

  As most of these exercises admit of a rhythm or cadenced sound emitted
by the men themselves, this vocal accompaniment is strongly recommended.
It certainly gives additional animation to the scene. Indeed the
cultivation of the voice is considered eminently essential in the course
of gymnastics. Singing exerts a salutary influence on the chest, and,
moreover, it is incontestable that it will be the means of powerfully
acting on the _morale_ of the French soldier, by teaching him songs of
patriotic and martial import. The singing-lesson at which I was present
was particularly interesting. The system is one recently invented,
wherein the ordinary notes are represented by arithmetical numbers--thus
occupying about one-third of the usual space. Pointing by means of two
canes to each representative number is all that is required by the
instructor. The pupils, about 300 men and officers, intoned the notes
with admirable precision. When the instructor opened out the canes they
made a crescendo--swelling to the loudest--and when he closed them
gradually it was a beautiful diminuendo, “in linked sweetness long drawn
out.” There was then sung a concerted piece in two parts, extemporized
by the highly-gifted Commandant, who figured it on the blackboard. It
was at once most accurately sung--first and second so admirably
concerted that the whole seemed as it were an organ of human
stops--alto, tenor, and bass most harmoniously blending.

  Such are the elementary gymnastics of the course.


  The exercises of applied gymnastics must be directed with extreme
prudence. Care must be taken by the instructor that the emulation of the
pupils should not degenerate into a spirit of rivalry, instigating them
to dangerous efforts.

  During cold weather they must abstain from executing leaps that
require violent efforts; at all times those who are not perfectly
disposed should not be required to leap at all. Carelessness and
inattention to the rules can alone cause those accidents apprehended in
these exercises.

  The dimensions of the obstacles to be leaped over must be gradually
increased; but no downward leap must ever exceed sixteen feet--five
meters. Such is the regulation; but really to leap down sixteen feet
seems no small matter, considering that the height of an ordinary
room--some ten or twelve feet--would make the nerves tingle if we had to
leap down that height; however, the French soldiers perform such leaps
with ease, and therefore we must conclude that all Anglo-Saxons here or
elsewhere can “go and do likewise.”

  The words of command are: 1. Attention. 2. Forward--leap--one, two,
three. At the second word, the man closes the points of the feet; at the
word one, he stoops on his lower extremities, slightly raising the heels
and stretching his arms to the rear, the fists clenched; he then rises
again, the arms hanging naturally down. At the word two, he repeats the
movement; at three, he recommences the same movement, stretches the hams
vigorously, throwing his arms forward, leaps the distance, or over the
obstacle, falls on the point of his feet, stooping down, and then comes
to attention.

  The same principle is observed in all leaping, whether to a height,
downward, or forward and downward--the only difference being in the
position of the arms. In leaping upward, the arms are flung overhead to
aid the ascent--the same in a downward leap; but if the leap be forward
and downward, the soldier begins with his arms in advance, and then
places them perpendicularly for the fall. The reverse takes place when
in leaping forward and upward.

  Thus they practice leaping in every possible direction--upward and
downward combined--upward, forward, and downward--to the right or to the
left--to the right and to the left and downward combined--the arms being
directed accordingly. They leap backward precisely in the same
directions, and according to the same rules. In leaping backward from
the top of a wall, the man first takes a glance at the descent, turns,
closes his feet--the heels projecting over the wall, stoops--the upper
part of the body being forward, places his hands outside his feet and
seizes the edge of the wall, the four fingers above, the thumb
underneath, and thus flings himself backward, his arms overhead. When
there is width as well as depth in the backward leap, the body and the
legs are flung off almost horizontally.

  The running leap is performed in a similar manner--the run being
quickened more and more up to the moment of springing forward. Some of
the leaps I saw performed were from fifteen to twenty feet. As a
complement to these leaping exercises, the ground may be prepared with
various objects to leap over, such as benches, tables, heaps of stones,

  The men are also progressively practiced in all these leaps, carrying
their arms and baggage. In such cases the downward leap must be
restricted to thirteen feet. The soldier holds his rifle balanced at the
trail with the right hand, the muzzle slightly raised, so as to prevent
it from touching the ground; he holds his sword (as the French soldier
has a sword) with his left hand. When the soldiers have become familiar
with leaping, the difficulty is increased by rendering movable first the
point of departure, and then the point of the fall, and, finally, both
these points are made movable. To leap from a body in oscillation, the
soldier leaps at the moment when the body is sinking. There is great
danger in leaping from an object in rapid motion. In case of necessity,
the soldier must face in the direction of the motion, and at the moment
of quitting it he must lay hold of it, shortening his arms, and so push
himself backward, lengthening his arms.

  It is a general principle that in leaping from a height of any extent,
the soldier should avail himself of anything at hand to diminish the
shock of the fall.

  The circumstances in which leaping must be resorted to are often
unforeseen, and require prompt decision; it is therefore important that
the men should be taught the following principles--useful to
everybody--to apply them spontaneously on all occasions:--

  _First._ To form a rapid judgment of the obstacle, and also of the
ground on either side. We scan the ground in advance of the obstacle, in
order to make a good choice of a footing for the leap; if the ground is
too smooth the foot may slip; on soft ground there can not be a good
footing for the leap. By scanning the ground beyond the obstacle, we
select our landing-place, and we foresee what difficulties we shall meet
with. A difference of level between the point of departure and the fall
modifies considerably the extent of the leap.

  _Second._ During the leap the breathing must be restrained, and the
air with which the lungs have been previously filled must be expired the
moment the man reaches the ground.

  _Third._ In leaps in width and height, fling out the clenched fists in
the direction the body is to take, so as to augment the impulse given by
the legs.

  To prove the utility of this principle, the men, in leaping, sometimes
hold in each hand a grenade of two-pounds weight, or a four-pound shot;
with this auxiliary the width of the leap is augmented.

  _Fourth._ In downward leaps, raise the arms vertically as soon as the
body begins to descend, in order that the body, reaching the ground on
the point of the feet, may sink vertically without losing its
equilibrium. If a man leaps into water, he places his arms at his side,
his hands on his hips, the feet close together, the points of the feet
lowered, the body stiff and rigid.

  _Fifth._ During the whole time of the leap keep the arms in the
parallel position they have at its commencement, in order to preserve
the equilibrium of the body.

  _Sixth._ In forward or wide leaps incline the body forward, in order
that the oblique action of the legs on the body may be more efficient.

  The recommendation to precipitate the last movements of the run
preceding the leap, has the important advantage of enabling the soldier
to incline his body as much as possible.

  _Seventh._ Fall on the point of the feet, the legs being close
together, bending all the articulations of the body from above downward,
in order that the shock be not transmitted to the head without being
lessened and attenuated by numerous decompositions of the force. The
articulations of the feet concur efficaciously with this result, and it
would be dangerous not to avail ourselves of them by falling on the
soles of the feet, especially the heels, as previously explained.

  _Eighth._ Avoid too rough a fall by giving to all the articulations a
general and supple “setting up,” so as to make a light bound on landing.

  _Ninth._ On landing avoid all useless motion, allow the muscles to
relax; their continued contraction and rigidity would interfere with the
body’s equilibrium.

  They also practice leaping with poles. These are of different
dimensions, beginning with the smallest--not longer than the rifle--and
finished with long ones from nine to twelve feet in length. He then
seizes the pole higher or lower, according to the distance of the leap.
Of course perfect success in this exercise depends greatly upon the
energy of the effort, and the long and rapid run by which it is
preceded. They also leap with two poles together from a height, the
poles being planted parallel and about two feet apart.

  Suspension-bars are made subservient to the training of the French
soldier. This exercise enables him to use his body as he pleases, in any
possible position, provided he can get hold of anything. Its beautiful
and splendid result is extraordinary strength of arms, legs, hands, and
fingers. Indeed, these suspensions of the body by the hands, the elbow,
the legs, by one hand, one leg, one finger, in every possible position,
show how the men are prepared for the thousand casualties of the

  They climb ropes after the manner of sailors, and horizontal beams are
raised at various heights from the ground, in which they learn to
preserve a perfect equilibrium--sitting, moving along them by the hands,
supporting the body, which is free to fall, and, finally, walking erect
upon them like a rope-dancer without his balance-pole! In these ticklish
positions they meet and pass each other--simulate a fall and recover;
the beams may be inclined or even set in motion, it matters not--they
hold on and do their work equally well--and drop to the ground without

  They are taught to pick their way over scattered stones or stakes
driven into the ground; and it has even been thought expedient to teach
them how to walk systematically on stilts.

  They are taught swimming--all its necessary movements before they go
into the water; and many, I was told, strike out at once, at the first
trial, thus proving the physiological or anatomical efficacy of the
well-considered mode of tuition. In the water they are practiced in
performing the feats required in actual warfare, carrying their arms and
accoutrements in a variety of ways, according to the supposed
circumstances of the campaign.

  Of course, if the men are taught to swim they must be sent regularly
into the water. This regulation, therefore, insures personal
cleanliness--the first rule of health, which is much needed in all
armies. The morality of most armies is generally above the average; it
should naturally be less--as nothing conduces more to long life than
exercise, regular hours, and a rational discipline. But cleanliness,
personal cleanliness is wanting, and we have to deplore the

  With a view to escalading, the French soldier is assiduously trained
in all the shifts of ladder-mounting--with ladders of wood and ladders
of rope--and he becomes as good as a sailor in pulling himself up a
rope, either looped, knotted, or smooth, from the ground to any
reasonable or unreasonable height. If a scaling-ladder be not at hand, a
tent-pole or any pole will do to enable him to get to the top of a wall
or the crest of a parapet. He is actually taught nine different modes of
performing this achievement so flattering to the ambition of the French

  The scaling of a represented turret was something beautiful to see.
“In the twinkling of an eye” or “done in no time,” can alone describe
the rapidity of the exploit.

  Every appliance may, however, be wanting on certain occasions in
war--it matters not--the French soldiers are taught how to mount a wall
without any instrument whatever--with their feet and the hands and the
fingers alone. Bullets and cannon balls leave holes and indentations in
the hardest walls--these are represented on the walls of the
Gymnasium--and thus they practice this last resort of the resolute and
determined besiegers. If there be no holes--no _points d’appui_ for the
ascent--what then? Why, then they build a _pyramid of men_--four men
stand as a base, two or four more perch themselves on the shoulders of
these, and then one mounts to the top on the shoulders of the latter by
way of apex!

  They have adopted all the fetes of the _trapèze_, as performed by
acrobats. These tend to strengthen the arms and promote that
self-reliance and confidence which are the prime elements of a good
soldier. Some of their swinging leaps with the _trapèze_ were
prodigious, from one end of the long gymnasium to the other, where they
alighted, and caught on the top of the wall, and descended to the
ground, with hands and fingers, by mimic bullet holes, as before

  Flying leaps on and over a wooden horse are practiced in every
possible direction, and the French cavalry are required to be able to
leap on their horses from the rear while galloping, and to leap over a
hedge or barrier together with the horses, but on foot, holding the
reins! It is impossible to believe that very many can do this; but that
is the aim, and the higher the aim the greater the effort, and something
worth having is sure to be done, even if we fail of the highest

  The most laborious of the practices is probably that of carrying, at
the top of their speed, all the implements of war, fascines, sand-bags,
gabions, projectiles, &c., whose weight is progressively increased from
twenty to fifty pounds. They must also practice carrying ladders, beams,
caissons, dragging gun-carriages, &c., and they are equally habituated
to carry rapidly and skillfully the wounded from the field of battle, by
placing men on litters, or any substitute at hand, in the gymnasium.

  Sword exercise, bayonet exercise, boxing and fencing are also taught,
but only the rudiments. In the regiments and battalions they have more
opportunities of perfecting themselves in these accomplishments.

  Such is a succinct account of the military gymnastics of the French.
The 300 various fetes and practices have only one object in view,
preparation for the possible and probable casualties of war, but they
have, meanwhile, the positive and immediate effect of giving the men the
utmost freedom of motion, _aplomb_, self-reliance, and that very useful
self-estimate in the soldier, namely, that he is superior to every other
in the world. It will take a vast deal to knock that conceit out of him.


The English Commissioners in their Report on “The best Mode of
Reorganizing the [English] System of Training Officers for the
Scientific Corps, together with an Account of Foreign and other Military
Education,” close with the following general remarks on French Military

The following summary may close our account of French Military

1. The French army combines a considerable proportion of officers
professionally educated, with others, who form the majority, whose
claims to promotion consist in their service, proved ability, and
conduct. One-third of the officers in the line, two-thirds of those in
the scientific corps, and the whole of the staff, receive a careful
professional education; the remainder are taken upon the recommendation
of their superior officers, from the ranks. But it was stated to us
expressly that such officers do not often rise above the rank of

2. There are no junior military schools in France, and no military
education commences earlier than sixteen. This is the very earliest age
at which pupils can be received at the Polytechnic or at St. Cyr, and
the _usual_ age is later; whilst in the case of the Special Corps,
strictly professional education does not begin till twenty or
twenty-one. The best preparation for the military schools is found to be
that _general_ (in France chiefly _mathematical_) education which is
supplied by the ordinary schools of the country, directed as these are
and stimulated by the open examinations for admission to St. Cyr and the

3. The professional education for commissions in the line is that
given at the school of St. Cyr. A fair amount of mathematics is required
at entrance, but the chief instruction given at the school is of a
professional character. Active competition, however, which is the
principle of all French military education, is kept up amongst young men
educating for the line by the competitive entrance to the school, by the
system of examinations pursued in it, and in particular, by the
twenty-five or thirty places in the Staff School which are practically
reserved for the best pupils on leaving.

4. In the Staff School itself the competitive system is acted upon;
there are strict examinations, and the pupils are ranged in the order of
merit on leaving the College.

5. The officers of artillery and engineers may be said to be in quite
a peculiar position in France, owing to the high education given at the
Polytechnic School. The consequence is, that the preparatory education
of French artillery and engineer officers is of the highest scientific
character. We have already spoken largely on this point, and need do no
more than allude to it.

6. We may remark, that preparatory military education in France is
mainly mathematical--at the Polytechnic almost wholly so. The literary
and classical elements, which enter so largely into all education in
England and Prussia, are in French military education very much thrown
aside. Lectures in military history and literature are said, however, to
succeed at St. Cyr.

7. The system of State foundations (_Bourses_) existing in the
Polytechnic and St. Cyr, and affording a curious parallel to the
military foundations in the Austrian schools, requires some notice.
Every pupil, in both the Polytechnic and St. Cyr, who can prove poverty,
is entitled to State support, either entire or partial. At the present
time, not less than one-third of the students in each of these schools
receive such maintenance. The system of civil _Bourses_ is of old
standing in France; most of these were destroyed at the Revolution. They
were renewed and greatly devoted to military purposes by Napoleon. The
extent to which they are given may seem excessive, but it must prove a
powerful incentive and assistance to talent.

8. It has been remarked that there is comparatively little practical
teaching in the School of Application for Artillery and Engineers at
Metz. But a very extensive practical training is in fact supplied to
these officers after they enter the service, remaining as they must do
with the troops until promoted to the rank of second captain, and
subsequently being employed in the arsenals, workshops, fortified
places, &c.

9. The French have no “senior departments” for military education. In
this respect their practice differs from that of England and Germany.


The following remarks on French Military Education are from the Report
of the English Military Education Commission submitted to Parliament,
and printed in 1870:

  1. The proportion of professionally educated officers in the line is
greater now than in 1856, when it was stated by the Commissioners in
their report to be one-third.

  2. The professional education for commissions in the line is given by
a two years’ course at St. Cyr, admission to the school being dependent
on competitive examination. Admission to the Artillery and Engineers is
obtained through the Polytechnic, where young men intended for
commissions in those arms receive a preparatory education of a highly
scientific character, in common with candidates for many other branches
of the public service. Admission to the school is obtained by
competition, and the choice of services is dependent on the results of
another competitive examination at the end of the two years’ course.
Commissions are then obtained in the respective corps, and the young
officers go for a further period of two years to the School of
Application at Metz, there to receive their strictly professional
instruction. The course of teaching at Metz is still mainly of a
theoretical character, and the main portion of the practical training of
the officers is deferred until they join their regiments. The Staff
Corps is recruited entirely from the Staff School; a very small number
of pupils from the Polytechnic have a claim to admission to the school,
but the great majority of the students are admitted by competitive
examination, open nominally to the sub-lieutenants of the army and to
the best students of St. Cyr, but in practice almost entirely confined
to the latter. The students join the school with commissions as
officers; at the end of the two years’ course they are definitely
appointed to the Staff Corps in the order in which they stand in a
competitive examination, but before being employed upon the staff they
are sent to do duty for five years with the various arms.

  3. The military schools in France are not, as in England and in
Prussia, placed under the control of a special department. They are all
under the immediate management of the Minister of War. There is,
however, for each branch of the service in the French army a consulting
committee (_comité consultatif_), or board of general officers, attached
to the War Department, for the purpose of giving advice to the Minister,
and in matters affecting the individual schools the Minister generally
consults the _comité consultatif_ of that branch of the service for
which the school is specially preparatory.

  4. Each school has its own _conseil d’instruction_, composed of
officers and professors of the establishment, which exercises a general
supervision over the course of instruction, and has the power of
suggesting alterations or improvements in it. The financial business of
the school is managed by another board (_conseil d’administration_); and
there is generally also a similar board (_conseil de discipline_), which
exercises more or less authority in questions of discipline. The effect
of this arrangement is to give the various officers and professors of
each school to some extent a voice in the general management of the

  5. The staff of officers and instructors employed appears, in most
cases, very large in proportion to the number of the students; 48 for
270 in the Polytechnic; 33 for 170 in the school at Metz; 62 for 600 in
St. Cyr, &c.

  Though there is in all the schools a military staff separate from the
staff of professors and instructors, and more especially charged with
the maintenance of discipline, the line of separation between the two
bodies is not, except at the Polytechnic, so distinctly drawn as in the
English military schools. The military professors exercise disciplinary
powers; while, on the other hand, the members of the strictly military
staff in almost all cases take some part in instruction. The latter
appear to be more utilized for this purpose than is the case either at
Sandhurst or Woolwich.

  6. Considerable care is exercised in the appointment of professors; at
the Polytechnic the candidates are selected by the _Conseil de
Perfectionnement_; at La Flèche they are recommended to the Minister of
War by the Minister of Public Instruction; at the Staff School and St.
Cyr the appointments are thrown open to competition.

  7. The discipline maintained at all the schools is of a very strict
nature; except for the youngest pupils at La Flèche it is entirely
military; the punishments are similar to those inflicted in the army,
and even include imprisonment. The maintenance of discipline is
considerably facilitated by the fact that the pupils at most of the
schools are actually subject to military law; and those of St. Cyr, if
dismissed from the school, are sent into the ranks as private soldiers.
There appears, however, in all the schools to be an absence of the moral
control over the young men which is exercised in the Prussian schools.
The Commandant of each school has very extensive powers in regard to
discipline, but in no case has he authority to dismiss a student from
the school without the sanction of the Minister of War.

  8. The principle carried out in France is that special military
education should not be begun until a comparatively late age, and should
be founded upon a groundwork of good general education in civil schools.
The only approach to a junior military school in France is that of La
Flèche, and this is mainly a charitable institution; the pupils, it is
true, learn drill, but beyond this no special military instruction is
given them. The course of study is the same as that at the _Lycées_ or
ordinary civil schools, and the pupils are under no obligation to enter
the military service. Nor can the Polytechnic be called an exclusively
military school; even those who enter the Artillery and Engineers from
it have their education in common with civilians at the very least until
the age of 18, and in the great majority of cases their strictly
professional instruction at Metz does not begin till 20 or 21. The very
earliest age at which a special military education commences in France
is 17, which is the age of admission to St. Cyr, and comparatively few
enter the school before 18 or 19. The knowledge required for admission
to St. Cyr is entirely such as is acquired at civil schools, and so much
importance is attached to a good general education that the degree of
either _bachelier ès sciences_ or _bachelier ès lettres_ is made a
necessary qualification for admission to the examination, while the
possession of both degrees gives considerable advantage to a candidate.
The principle of deferring the commencement of special instruction has
even received extension since 1856; the age of admission to St. Cyr,
which was then 16, has been now increased to 17, and the junior school
of La Flèche has been made even less military in its character than it
was at that time.

  9. When a professional education has once commenced, the principle
appears to be that it should be almost entirely confined to subjects
which have a practical bearing on military duties. Mathematics, as a
subject by themselves, do not form part of the ordinary course of
instruction at any of the special schools. The previous course at the
Polytechnic secures of course very high mathematical attainments in the
candidates for the Artillery and Engineers who enter Metz; but at Metz
itself the study of mathematics is no longer continued. In the same way
at the Staff School a knowledge of mathematics as far as trigonometry is
required for admission, and their practical applications to operations
of surveying enter into the school course; but no part of the time spent
at the school is devoted to mere theoretical instruction in pure
mathematics; yet the officers of the Staff Corps are intrusted with the
execution of those scientific surveys which in our service are in the
hands of the Engineers.

  St. Cyr offers to some extent an exception to the rule that the course
of study at the special schools should be of an exclusively professional
character, as the instruction given there during the first year is
partly of a general nature, embracing history and literature. This,
however, arises from the fact that the students from the _Lycées_
generally show a deficiency in the more literary subjects of a liberal
education, and a portion of the time at the school is therefore spent in
completing and improving their general acquirements. A knowledge of
arithmetic, algebra, and plane trigonometry is required as a
qualification for admission, but beyond a very brief revision of these
subjects, and a voluntary course for candidates for the Staff Corps,
mathematics are not taught at the school. It would seem indeed that,
except in the case of candidates for admission to the Artillery and
Engineers, mathematics do not hold so prominent a position in French
military education as is generally supposed in England to be the case.
For staff and regimental officers the main requisite demanded seems to
be a practical knowledge of trigonometry as required for surveying.

  10. Much time is devoted in all the French schools to drawing in its
various branches; some hours daily are invariably given up to the
subject; indeed the time spent upon purely geometrical drawing appears
almost to be excessive. The great importance attached to the drawing of
_machinery_ is a peculiar feature in all the schools. Landscape drawing
is one of the regular subjects taught to candidates both for the line
and the Staff Corps.

  The theoretical instruction given at every school is supplemented by
visits to numerous military establishments, manufacturing departments,
and fortresses. This is also a feature in the system of military
education in Prussia; in both countries it seems to be thought desirable
to afford young officers a practical insight into the working of the
various establishments connected with the army. In the case of officers
of the Artillery and Engineers it appears in France to be made a special
object to cultivate a mechanical genius, and to secure a thorough
acquaintance with manufacturing departments with which their
professional duties bring them into contact.

  Military law and administration (comprising financial and other
regulations connected with the army), and drill, riding, and fencing in
the way of practical exercises, form part of the education of officers
of all branches of the service; in drill, lectures explanatory of the
drill-book are invariably given in addition to the practical

  11. The system of instruction in all the French military schools is
more or less that of the Polytechnic. Lectures attended by large
numbers, enforced study of fixed subjects, the execution of all work
under close supervision of the instructors, and frequent periodical
examinations, are everywhere found. Active competition is the leading
feature of the system; the students are perpetually being “kept up to
the mark.” A fixed period of two years is in all cases assigned to the
course of study; the course can not be completed in a shorter time, and
the regulated period can not (unless under quite exceptional
circumstances) be exceeded.

  It seems also to be thought that, as a necessary consequence of the
strictly competitive system, the subjects upon which the competition
depends should be exactly the same for every student. No choice of
studies is allowed; those which enter into the examination are equally
obligatory for all. The only exception to this rule is at St. Cyr, where
in languages a choice between German and English is given.

  No pecuniary rewards are offered to the students at any of the
schools. The bestowal of the numerous _bourses_ which are granted to
those admitted to the Polytechnic and St. Cyr is regulated entirely by
the poverty of the candidates, without any regard to their ability.

  12. The education of officers in France is entirely concluded before
any regimental duty has been done. The French system is in this respect
the exact opposite of that pursued in Prussia, where no professional
instruction, as a rule, is given until a certain amount of service with
the troops has been performed. There are in France no establishments for
the instruction of officers of some years’ service, like the Staff
College in England, or the Artillery and Engineer School and the War
Academy in Prussia.

  13. The chief changes which have taken place in the military schools
of France since the publication of the Report of the Commissioners of
1856 may be summarized as follows:--

    (_a._) The modifications in the course of instruction at the
Polytechnic; the abridgement of the studies previously pursued; and the
slightly increased importance now attached to literary subjects.

    (_b._) At Metz, the introduction of an examination at the end of the
first years’ course of study.

    (_c._) At St. Cyr, the alteration of the age for admission to the
school from 16 to 17; the extension of the subjects of the entrance
examination; the modifications in the course of instruction, and the
postponement of the commencement of strictly military studies almost
entirely until the second year; the introduction of a stricter system of
discipline, combined with additional encouragements to good conduct and
industry; and the increased advantages offered with the view of
attracting to the school a higher class of professors and officers.

    (_d._) At La Flèche, the complete reorganization of the institution
with the object of more closely assimilating its general arrangements to
those of a purely civil school.

    (_e._) At the Staff School some modifications in the course of study
and in the mode of admission to the school have been made; but the most
important alterations are those adopted in July 1869, by which the
number of students admitted annually to the school is increased
considerably beyond the number of vacancies likely to occur in the Staff
Corps, and the novel principle is introduced that admission to the
school does not carry with it the certainty of permanent employment on
the staff.

  It may be added that there seems a tendency to diminish the importance
of mathematics as an element of preparatory military education, and to
attach slightly more weight to studies of a literary character. This is
more particularly seen at St. Cyr and at La Flèche, and to a less extent
at the Polytechnic. There is also a growing disposition to increase, in
the case of the cavalry and infantry, the proportion of officers who
have received a professional education.


  SC Sums charged to the Schools Estimate.
  MP Military pay charged to other Estimates.
  T  Total.
  CS Cost to the State.‡
  EP Each pupil.

  Name of School.           SC        MP          T          CS    EP
                         _Frs._    _Frs._      _Frs._     _Frs._   £.
  Polytechnic           719,673    85,515     805,188    568,188   78
  Artil’y and Eng’er
    school at Metz       99,500   416,350*    515,850    515,850   50
  St. Cyr             1,348,792    15,000   1,363,792    741,292   49
  Staff school           99,000   214,870*    313,870    313,870  168
  La Flèche             539,868    15,000     554,868    457,868   45
  Medical school        659,300       †       659,300       --     --
  Cavalry school
    at Saumur           227,000    18,500     245,500       --     --
    musketry schools     36,270       “        36,270       --     --
  Regimental schools    173,600       “       173,600       --     --
                      ----------  --------  ---------  ---------  ---
  Total               3,903,003   765,235   4,668,238  2,597,068  390

[* These sums include the pay of the officer students at these
establishments, amounting to 288,000 frs. at Metz, and 103,000 frs. at
the Staff School.]

[† The estimate for the Medical School appears to be exclusive of the
pay of all military medical officers employed at the school, but the
amount of this additional sum is not stated.]

[‡ For 1,520 pupils, who repaid 956,500 francs.]

  [Errata for Part I (France):
  _In the section on Mathematics, the form “assymplotes” is used
  several times alongside “asymptote(s)”. The spelling “assymptotic”
  occurs once at line break. Accents on French words are printed as
  shown; missing accents have not been supplied._

  [Footnote 4]
    _Footnote tag missing; position conjectural_
  the chief scientific creation of the first French Revolution
  patriotism and courage can not always supply
  returned to Paris in the reign of terror, “to see from his lodgings
    _quotation mark in original_
  are obliged to re-enter the army.
  chosen from former pupils of the school
    _“the” missing_
  and the life that is led in them.
  work heartily and zealously together
  Schools of Application for Artillery and Engineers
    _hyphen in “En-/gineers” invisible at line break_
  LESSONS--10-13. _Derivatives and Differentials ..._
  LESSONS 24-27. _Geometrical Applications continued ..._
    LESSONS 14-17.
  Geometrical demonstration of the formula.
  LESSON 3. _Integration of Differentials ..._
    LESSONS 3.
  LESSONS 1-3. _Revision and Completion..._
    _. missing_
  not enough in themselves to define objects completely._
    _final . missing or invisible_
  LESSONS 3-6. _Composition of the Velocities of a Point._
    _period . after “3-6” invisible_
  three movements of translation with respect to three axes
  of invariable form, but also in motion.
    _spelling unchanged_
  LESSONS 1-2. / Chemical sources of electricity.
    _period . after “1-2” missing or invisible_
  LESSON 3. 1. _Chemical Actions._
    LESSON 3.--1.
  Straight and curved rods.
  the general direction of the vibrating motion communicated.
  [Footnote 12]
  recently introduced at the school.
  Clerks and draughtsmen are provided as required.
    _header supplied from Table of Contents_
    _header supplied from Table of Contents_
  _Fifty-eighth Lecture._--(2.) ... artillery commands.
    _missing . after “commands”_
  which is indicated in the programme of the memoir.
    _final . missing_
  | 75 | 73 50 | 78 | 151 50 | 10
    _totals printed as shown: error for 11?_
  1st. The direction ... / 2d. The tracing ...
    _paragraph breaks added by transcriber for consistency_
  _Lecture_ 7.--Gauging of the volumes and valuation
  _Lecture_ 22.--Resistance to torsion.
  1st. Composition of the personnel and matériel of the Artillery
  At 5 A.M. the drum beats, the young men quit their beds;
  made without points; and a description of the battle.”
    _final ” missing_
  { Geographical Representation,  6 } 10
    _text unchanged: error for “Graphical”?_
  The prescribed instruction comprises the following courses:--
    _word AND supplied from Table of Contents_
  They leap backward precisely in the same directions
    in the some
  _First._ To form a rapid judgment of the obstacle,
  regular hours, and a rational discipline.
  but beyond a very brief revision of these subjects, and a voluntary
  course for candidates for the Staff Corps
    very beief ... condidates
  the execution of all work under close supervision of the instructors,

       *       *       *       *       *



       *       *       *       *       *


together with An Account of Foreign and other Military Education and An
Appendix. London: 1857. pp. 442 and 245, folio.

together with the Proceedings of the Committee, Minutes of Evidence,
Appendix and Index. Printed by Order of the House of Commons. London:
1855. pp. 230, folio.

HELLDORF’S _Dienst-Vorschriften der Königlich-Preussischen Armee_.
Berlin, 1856.

FRIEDLANDER’S _Kriegs-Schule_.

VON HOLLEBEN, _Paper on Military Education in Prussia_.

_Official Programme of the Principal Subjects of Instruction Taught in
the Artillery and Engineer School at Berlin_.

_Account of the War, or Staff School at Berlin_.

_Directions for the Supreme Board of Military Studies_. 1856.

_Directions for the Supreme Military Examinations Commission_. 1856.

BARNARD’S _National Education in Europe_. 1852.

BACHE’S _Report on Education in Europe_. 1838.


    [Footnote 1: Compiled from the “Report, and Accompanying Documents
    of the Royal Commission on Foreign Military Education,” 1857.]


According to the law of the 3rd of September, 1814, which is the basis
of the present military organization of Prussia, every Prussian above
twenty years of age, is bound to service in arms for the defense of his

The military force of the country is made up of three distinct bodies,
and the whole of the adult male population is distributed among them. It
consists of,--

I. The Standing Army.

II. The National Militia or _Landwehr_, divided into two portions, viz.,
the first _Landwehr_ and the second _Landwehr_.

III. The Last Reserve or _Landsturm_.

I. The standing army is composed of all young men between twenty and
twenty-five years of age. The period of service in time of war is for
five years, but in time of peace the young soldiers can obtain leave of
absence after three years’ service;--they belong for the remaining two
years to what is termed the “reserve,” receiving neither pay nor
clothing, and they are subject to be recalled if war should break out.

Encouragement, indeed, is given and advantages held out to induce men to
stay, and to take a new engagement for an additional term of six years;
but it is said that only a small number are thus obtained. The bulk of
the troops are men serving for this short time; and there are many, it
should be added, whose term of service is even yet shorter. For all
educated young men, all, that is, who pass a certain examination, are
allowed, on condition that they pay for their own equipment and receive
no pay, to shorten their service from three years to one. This privilege
appears to be very largely used. It should also be stated, that young
men of any class may volunteer to perform their service at any age after

The Prussian standing army amounts at the present time to about 126,000
men. It is divided into nine army-corps or corps d’Armée, one of which
is named the guard, and the others are numbered from I. to VIII. In each
there is a regiment of artillery and a division of engineers. A regiment
of artillery consists, in time of peace, of three divisions; each
division of one troop of horse artillery and four companies, of which,
one is Fortress artillery with two-horsed pieces. Each regiment has thus
three companies for the service of the fortress and twelve for field
service. The whole of the artillery is under the command of a general
inspector, and it is divided into four inspections. An engineer division
is composed of two companies. There are nine engineer divisions, one in
each army corps. The whole are commanded by a general inspector, and
they are divided into three inspections.

The promotion in the Prussian infantry and cavalry is regimental, and by
seniority, up to the rank of major; after that it is by selection; and
an officer who has been passed over two or three times may consider that
he has received an intimation to retire from the service. In the
artillery the promotion is by regiments; in the engineers it is general.

II. The first Landwehr, or Landwehr of the _first_ summons (_des ersten
aufgebots_,) consists principally of young men between twenty-five and
thirty-two years of age, who enter when they have completed their period
of service in the standing army. They are called out once every year for
service with the divisions of the standing army to which they are
attached, for a period varying from a fortnight to a month; and they may
be sent in time of war on foreign service.

Those who have passed through the first Landwehr, enter at the age of
thirty-two in the second Landwehr, or Landwehr of the _second_ summons
(_des zweiten aufgebots_.) They are called out only for a very brief
service once a year, and they can not at any time be ordered out of the
country, but continue to form a part of the _second_ Landwehr until they
are thirty nine years of age.

III. After the age of thirty-nine a Prussian subject belongs to the last
reserve or Landsturm, and can only be summoned to service in arms upon a
general raising, so to say, of the whole population, when the country is
actually invaded by the enemy.

With the standing army, the center of the system, all the other forces
are kept in close connection. For every regiment of the standing army
there is a corresponding regiment of Landwehr, and the two together form
one brigade. In the local distribution, every village and hamlet of the
Prussian dominions belongs to a certain regiment of Landwehr, serving
with a certain regiment of the army, and belonging accordingly to one of
the nine army corps.

Such is the military organization, which, from the important part played
in it by the _Landwehr_, is sometimes termed the Prussian _Landwehr_
system. The history of its formation is remarkable, and the
circumstances which led to its creation helped also to create the very
peculiar education of the army.

The Prussian _Landwehr_ or militia is not of modern origin; in its form
at least it is but a revival of the old feudal military organization, so
far as that consisted of raising the country _en masse_, instead of
keeping up a permanent, trained, and limited military force. _Landwehr_
or _Landsturm_[2] was the old German name for this feudal array, before
the system of standing armies was begun in Europe by Charles VII. of
France, with his Scotch regiments. It was possibly the failure of the
trained Prussian armies--long reputed the models of military
discipline--in the attack upon France in 1792, and still more signally
at Auerstadt and Jena, which partly led to the revival of the _Landwehr_
as the peculiar national force of Prussia. The means by which Stein, and
after his expulsion, Scharnhorst, called it into activity, was a master
stroke of policy under the existing difficulties of the country. The
following outline may be sufficient to explain its effects upon

    [Footnote 2: Thus _Landsturm_ is the word used for the rising _en
    masse_ of the Tyrol in 1809.]

The condition which Napoleon had exacted at Tilsit--a reduction of the
standing army from 200,000 to 40,000 men--would have lowered Prussia at
once to the rank of a second-rate power. It was adroitly evaded by the
plan of keeping only 40,000 men in arms at one and the same time,
disbanding these as soon as they were disciplined, and replacing them
constantly by fresh bodies. Thus the whole population of the country was
ready to rise in 1813, after the crisis of Napoleon’s retreat from
Russia. The plan was chiefly due to the genius of Scharnhorst, whose
early death deprived Prussia of her greatest scientific soldier. The
_Landwehr_ then proved itself a most efficient force, though its success
was promoted by the national enthusiasm, which must prevent our taking
such a period as a criterion of its permanent military working. Since
that time it has continued to be the national army of the country.

We were assured that this peculiarity of the Prussian army system, by
which almost every man in the country serves in his turn in the ranks,
has had a tendency to improve the education of the officers. It seems to
have been felt that the officers would not retain the respect of
intelligent privates unless they kept ahead of them in education. And
this impression appears to have been the cause of the royal edicts
passed in 1816, by which it was required that every Prussian officer
should pass two examinations before receiving his commission, one to
test his general education, and the other his professional knowledge.


    [Footnote 3: The chief authority for this paper is a very detailed
    account of the Staff School, (_Kriegs-Schule_,) by Friedländer,
    pp. 1-360.]

The Prussian system of military education stands in close connection
with the general education of the country, just as the Prussian military
organization is the peculiar creation of that country’s history. And the
greatest improvements in the army and in its scientific teaching have
been made at those remarkable periods when we should most naturally have
looked for them--the time of Frederick the Great and the Liberation war
of 1813-1814.

The leading principles of Prussian military education consist, _first_,
in requiring from every officer in the army proof of a fair _general_
education before his entrance, and of a fair _military_ education
afterwards. _Secondly_, they encourage a higher military education in a
senior school, which has almost exclusively the privilege of supplying
the staff.

In this requirement of a fair education, both general and military,
_universally_ from its officers, Prussia stands alone among the great
military nations of Europe, and this honorable distinction is in a great
measure the result of the diffused system of education throughout the
country, and of the plan adopted by Stein and Scharnhorst, to make the
officers the leaders of the army both in education and in military

The military schools of Germany may be said to have begun with the
Reformation wars. Some such were founded by Maurice of Saxony, the great
political and military genius of Germany in that century; the example
was soon imitated in Baden, Silesia, and Brunswick, and a curious sketch
of military education, by the hand of Duke Albert of Brandenburg, has
been lately published from the Berlin archives, in which theology and
mathematics hold the two most important places.

The first school of any real importance was founded in Colberg, by the
great elector, Frederick William, in 1653. This had considerable
success, and both his successors, King Frederick and Frederick William
I., improved it greatly, and finally transferred it to Berlin. It was
the time (about 1705, 1706,) of the great advance in military
engineering under Vauban and Coehorn, and a school for engineering was
founded, in which some of their pupils had a great share. The first
Prussian trigonometrical survey also dates as early as 1702; that of
England was not begun till 1784. It may indeed be said that the
scientific arms began to take a more favorable place in the Prussian
army about this time. They have held, and even still hold in some
respects, a less distinguished position in Germany than in France,
England, or Sardinia; and the first instance of an artilleryman being
made a general, was in the reign of Frederick William I.

On Frederick the Great’s accession he found several military schools in
existence. These had been chiefly founded by his eccentric father, who
had a passion for Cadet Houses and cadets, and their object is said to
have been to supply an education to the nobility, who at that time were
very ill-taught in Germany. After Frederick’s first wars, his own
attention was much occupied by the need of a better military education,
and he continued to work at the subject very zealously till his death.
His example on this point, as that of a great military authority, is
most instructive, since his object was at first only to educate cadets
_before_ their entrance to the army, but was afterwards extended to
completing the education of officers already on active service. His
views on the last point were carried out by Scharnhorst. They were the
germ of the present Prussian military education.

It is curious to observe that the Austrian Succession War and the Seven
Years’ War, the first great wars since Louis XIV., and which broke the
Thirty Years’ Peace of the eighteenth century, are periods at which
scientific military education made a great step in Europe. A Treatise of
Marshal Count Beausobre’s on the subject first showed the existing want;
it is entitled “_Utilité d’une Ecole et d’une Académie Militaire, avec
des Notes, ou l’on traite des Ecoles Militaires de l’Antiquité_”. It
attracted great attention on its appearance. Most of the military
academies properly so called, date from about this time. The earliest
warrant for Woolwich, dates in 1741. The Theresianum of Maria Theresa
was begun at Vienna about 1748. The first French school was the
celebrated engineer school of Mezières founded in 1749. This was soon
followed by the old military school of Paris in 1751, and by the school
for artillery at La Fère in 1756. Frederick’s own _Ritter Academie_
dates from 1764.

Frederick began this institution with his usual energy, immediately on
the close of the Seven Years’ War. “My fire is quenched,” he writes,
“and I am now only busied in improving the practice of my men. * * * *
The position of the common soldier may be left as it was before the war
began, but the position of the officers is a point to which I am
devoting my utmost care. In order in future to quicken their attention
whilst on service, and to form their judgment, I have ordered them to
receive instruction in the art of war, and they will be obliged to give
reasons for all they do. Such a plan, as you will see, my dear friend,
will not answer with every one; still out of the whole body we shall
certainly form some men and officers, who will not merely have their
patent as generals to show, (_die nicht blos patentirte Generale
vorstellen_,) but some capacity for the office as well.” He had, in
fact, seen with great admiration the improved military school recently
founded by Maria Theresa; and as it is best on such points to let this
great authority be heard for himself, we shall quote his own words:--

“In order to neglect nothing bearing on the state of the army, the
Empress founded near Vienna, (at Wiener Neustadt,) a college where young
nobles were instructed in the whole art of war. She drew to it
distinguished professors of geometry, fortification, geography, and
history, who formed there able pupils, and made it a complete nursery
for the army. By means of her care, the military service attained in
that country a degree of perfection which it had never reached under the
Emperors of the House of Austria; and a woman thus carried out designs
worthy of a great man.”

His letters show that he contemplated an improved school, and he says to
D’Alembert: “I send you the rules of my academy. As the plan is new,
I beg you to give me your honest opinion of it.” Accordingly, the
academy was founded. We will describe it in his own words:--

“An academy was founded at the same time, in which were placed those of
the cadets who showed most genius. The king himself drew up the rules
for its form, and gave it a plan of instruction, which stated the
objects of the studies of the pupils, and of the education they were to
receive. Professors were chosen from the ablest men who could be found
in Europe, and fifteen young gentlemen were educated under the eyes of
five instructors. Their whole education tended to form their judgment.
The academy was successful, and supplied able pupils, who received
appointments in the army.”[4]

    [Footnote 4: “Histoire de mon Temps.”--_Œuvres_, vi., p. 99.]

This school, which was opened in 1765, was Frederick’s only foundation
of the kind; he was occupied with it incessantly. The plan of its
studies was drawn up by his own hand, and we have many of his letters of
encouragement to its pupils or professors. Whether he is writing to
Voltaire, Condorcet, or “My Lord Marischal” Keith, he constantly shows
both his well-known attention to the economy of his new school, and a
paternal interest in his young cadets and their teachers.[5]

    [Footnote 5: He gives himself, in his forcible style, the reasons
    for his attention to early military schools. He had found his
    young nobility excessively averse to such education. “They shrink
    from the army,” he said, “because in this country it is a real
    training for the character. Nothing is passed over in a young
    officer; he is obliged to maintain a prudent, regular, and
    sensible conduct. . . . . . This is precisely what they dislike,
    and one still hears the absurd and insolent expression, ‘If my boy
    will not work, he will do none the worse for a soldier.’ Yes, he
    may do for a mere man-at-arms (_fantassin_,) but not for an
    officer fit to be advanced to the highest commands, the only end
    of a good soldier’s life, and which requires a really extensive
    knowledge.”--_Œuvres_, ix., 117, 120.]

Accordingly, both in professors and pupils, the new institution soon
gained an European character. Out of its twenty first directors, no less
than ten were distinguished foreigners; one of the best teachers at
Berlin was D’Antoni, a distinguished soldier from the Turin institution
and the artillery school at Alessandria--schools which were still the
representatives of the military science of the great Italian generals,
of the Duke of Parma, of Spinola, and Montecuculi.

This institution was still, as it would appear, upon the old principle
of juvenile army schools, nor does Frederick seem to have set on foot
any school for officers after entering the service. But he evidently
felt strongly the need of improving his staff officers, and of raising
the science of his artillery and engineers. Thus we find him referring
to the French engineer school at Meziéres; and he endeavored to raise
the intelligence and education of his officers. It may, however, be
suspected that the spirit of the “Potsdamer Côterie,” as it was called,
became gradually, and particularly after Frederick’s death, too literary
and speculative to suit the rough work of war; and it may, perhaps, be
thought that some defect of this kind is still traceable in the
excessive amount of teaching and the abstract nature of some of the
subjects taught in the staff school at Berlin.

Such seems to have been the opinion of Scharnhorst, the virtual author
of the present system of army education, and whom the Prussians still
regard as their first authority on that subject. “Instruction is given,”
he says, “at the military school in all literature, in philosophy, and
in many various sciences. Frederick seems to have wished to lay in it
the foundation of the education at once of an officer and of a learned
man. Few men, however, are able to excel at once in various branches of
human knowledge, and the surest means to do so in _one_ is not to
attempt it in _many_.”

We have referred to Frederick and his school rather to show the interest
he felt in military education, than because his institution was very
important. Military education was still very imperfect, and it
completely languished in Prussia till Scharnhorst established it on its
present footing.

Scharnhorst was himself an Hanoverian, but entered the Prussian service,
and had seen by experience the defects of their system in the campaigns
of 1792, 1793, and 1805. He had long devoted especial attention to
military education and to all the scientific part of his profession.
Along with Blucher and Gneisenau, he was considered one of the first
generals of the army, and, on the exhaustion of Prussia after Jena, he
was selected to remodel its whole system. He did not live to complete
his work, having been killed early in 1812; but his statue near the
bridge at Berlin, remarkable for its noble and thoughtful expression,
records the gratitude of Prussia to its greatest scientific soldier.

“The perfection of the French military organization,” says Mr. Alison,
“appeared to him in painful contrast beside the numerous defects of that
over which he presided. * * * * Boldly applying to the military
department the admirable principles by which Stein had secured the
affections of the burgher classes, he threw open to the whole of the
citizens the higher grades of the army, from which they had been
hitherto excluded. * * * * And every department of the public service
underwent his searching eye.”

The work began with the commission of 1807, of which both Stein and
Scharnhorst were members. And the regulation of 1808 laid down the
principle broadly, that the only claim to an officer’s commission must
be, “in time of peace, knowledge and education; in war, courage and

On these principles, during the next three years, Scharnhorst laid the
foundations of the present education. He abolished most of the existing
juvenile schools, with the exception only of the Cadet Houses, intended
almost solely for the sons of officers. He changed the previous war
school into a sort of school _d’Elite_, consisting of a senior and
junior department, in which the younger soldiers of all arms were to be
imbued with such knowledge as might give them a scientific interest in
their profession, and in which senior officers (also of all arms) were
to have a higher course of a similar nature, success in which was to
form a recommendation for employment on the staff. He began the plan of
the division schools, where all candidates for commissions, but not yet
officers, might conduct their military studies along with the practice
of their profession. Its idea was to make some military study
_necessary_, and successful study _honorable_, in the army. Finally, he
began the present system of careful examination on entering the army.

The following historical notice of the origin and successive changes of
the division schools is taken from a communication by Col. Von Holleben,
and a member of the General Inspection of Military Instruction to the
English Commission.

The cabinet order of the 6th of August, 1808, laid the foundation of the
present system of military education. It regulates the appointment of
Swordknot ensigns and the selection of officers, and declares that the
only title to an officer’s commission in time of peace shall be
professional knowledge and education, and in time of war distinguished
valor and ability.

The cabinet order of the 6th of August, 1808, could only come gradually
into operation; the system of military examinations had to be created,
and the educational institutions had to receive a new organization,
under the superintendence of a general officer. Four provincial boards
of examination were successively established, and on the 1st December,
1809, a body of instructions, still very vague and general, was issued
for their guidance.

A cabinet order of the 3rd of May, 1810, remodeled the military schools,
directing, in addition to the cadet schools at Berlin and Stolpe, the
formation of three military schools for Swordknot ensigns,
(_Portepée-Fähnriche_,) one at Berlin for the marches (_Die Marken_,)
and Pomerania, a second at Königsberg, for east and west Prussia, and a
third at Breslau, for Silesia; and the formation of a military school at
Berlin for officers. All these institutions were placed under the
general superintendence of Lieutenant-General Von Diericke, who had also
the special superintendence of the boards of examination. A board of
military studies was created and intrusted, under his control, with the
task of carrying the regulations into effect.

Before, however, the new institutions attained to any stability the war
years of 1813-14-15 intervened, and the operations of the board of
examinations ceased.

Soon after the conclusion of peace directions were given that the
examinations should recommence, with an equitable consideration of the
claims of the Landwehr officers, ensigns, and other young persons who
had grown up during the war.

At first there was only one board of examination at Berlin, with large
discretionary powers as to their mode of procedure. In April, 1816, a
cabinet order was issued to form boards of examination for the Swordknot
at every brigade, as the present divisions were then called, besides the
existing board at Berlin, for the examination for an officer’s

Contemporaneously with the nine boards of examination, the board of
military studies, by an order of January, 1816, directed the
establishment of schools for every brigade, and attempted to gradually
regulate the instruction they gave. The schools contained two classes,
the lower to prepare candidates for the Swordknot, the higher to prepare
candidates for the rank of officer. As, however, no standard of
attainment was required for admission into the schools, their
instruction had to commence with the first elements, and was charged
with more work than it could perform. The weaker scholars stayed two,
three, or more years in the lower class, and the education of the better
scholars was impeded.

During this and the following period the authority over the examination
boards (the _Præsidium_,) was distinct from that over the schools, (the
general inspection,) and it was not till later that both authorities
were vested in a single person. This division of powers, intended to
secure the independence and impartiality of the examinations, led to the
result that the two authorities were occasionally led, from a difference
of principles, to labor in different directions. Still, in the infancy
of military education, the rivalry it occasioned, was favorable to a
rapidity of development.

An order of the 16th of March, 1827, added French to the studies for the
ensigns’ examination, and fixed a higher standard of attainments in
military sciences for the officers’ examination.

Nearly at the same time, a cabinet order of the 27th of March, 1827,
directed that there should be only one class for Swordknot ensigns in
the division schools, and that after October, 1829, the candidate should
obtain a testimonial of fitness for the rank of Swordknot ensign
previous to admission as a student.

Accordingly young men had to be prepared for examination for the
Swordknot at their entrance into their corps, or might prepare
themselves by private studies and instruction during their service.

The task of the schools, still very comprehensive embracing all the
liberal sciences as well as the military, was accomplished during this
period in two courses of nine months, in a higher and a lower class.

A cabinet order of the 31st of January, 1837, introduced the entrance
examination, instead of the examination for the Swordknot, being
declared that every candidate for the commission of an officer, after
his reception into a corps, should prove in an examination his
possession of the knowledge requisite for a Swordknot ensigncy before
his actual appointment. At the same time a regulation of the ministry of
war, of the 17th of December 1836, remodeled and more precisely defined
both the entrance (Swordknot ensign) examination, and that for the
commission of an officer. This regulation, while it essentially modified
the instruction given at the division schools, furnished them at the
same time with a more certain clue for their guidance. The preparation
of youths for the Swordknot examination during their service in the
corps was discontinued. But the standard of the entrance examination was
still too low, requiring only a small portion of the branches of a
general liberal education, and that not in the shape in which they are
taught in our gymnasia. Hence the evil result, that young men, previous
to their entrance into a corps, had usually to prepare for the military
profession at private institutions instead of at the gymnasia, and
nevertheless brought with them a very defective amount of preparatory
training; on the other hand, the demands of the officers’ examination
were very multifarious. It still required the general scholastic
sciences by way of formal education, and the military sciences as a
special education for the military profession. Thus the task of the
division schools continued overwhelming, and an aim was set before them
which they could not attain.

A regulation of the 4th of February, 1844, reformed simultaneously the
whole system of military examination and education.

The views which guided these reforms, the improvements and advantages
which were hoped to be thereby obtained, were, in general, the

1. The military profession, like every other, requires a general school
education intended generally to cultivate the mind, distinct from the
subsequent special and professional education for which the former is
the necessary groundwork.

The former is tested in the examination for the Swordknot, the latter in
the officers’ examination.

2. The preparatory education required from the candidate for a Swordknot
is the function of the ordinary schools of the country. Nothing but what
they can impart is required, and from consideration of the youthful age
of the candidates (seventeen years,) the amount of preparatory training
required is not the attainment of the highest class of the gymnasium,
but only that required for admission into the Prima.

3. The required previous training not only gives the candidate a more
certain basis for his subsequent military education, but, as being the
groundwork of all professions, leaves him afterwards at liberty to
cultivate the special knowledge requisite for any profession that he may

4. The division schools are freed from a multifarious course of
instruction in the scholastic sciences, a task beyond their power: the
result of which was that the majority of scholars were very little
advanced in formal and general education, and but superficially grounded
in the elements of the professional sciences, while they spent years in
being drilled for an examination, instead of being educated for life.

5. If the division schools have an able staff of military teachers, they
can give a good professional education. The younger officers, even if
they never received the full training of the gymnasium, may still, by
their professional training, raise themselves above their subordinates,
(a class in Prussia often highly educated,) and are started with an
excellent preparation for their professional career.

6. By the amount of liberal education required in the examination for
the Swordknot, the friends of those destined for the military profession
are admonished to provide them an education equal to that received by
the members of other professions.

7. By the method pursued in the examinations the power is retained of
raising or lowering the standard according to circumstances. When the
supply of officers is deficient, the standard can be lowered; at other
times, as at present, it may be raised. Since the above-mentioned
regulations, the following essential alterations have been introduced:--

1. The examination for the Swordknot is again placed after admission
into the corps, but no one can be admitted to attend the division
schools without a testimonial of fitness for the rank of Swordknot

2. A testimonial of fitness for the university, _i.e._, to have passed
the abiturient examination, dispenses with the examination for the
Swordknot. In consequence of this rule fifty abiturients on an average
annually enter the army. These, as well as the selectaner of the cadet
corps, must be considered, in point of scientific education, an
excellent supply of officers. From the powerful impulse that military
instruction has received in the last fifty years, it may be expected
that the time is not distant when the candidate for an officer’s
commission, instead of passing the Swordknot examination, will have to
bring the finished training of the gymnasium; in other words, to have
passed the abiturient examination.

3. Instead of the seventeen division schools there are now by the
regulation of 1844, only nine, and a further reduction of their number
to four or three is contemplated, with an improvement of the staff of
teachers and a stricter supervision of the scholars.


The standing army composed in the manner and under the circumstances
already described, is supplied with officers who must have a good
general education, and have served in the ranks, or have obtained a
certain amount of professional instruction. The usual course is as

Young men obtain a nomination from the colonel of a regiment. This
nomination admits them merely to service in the regiment as privates,
with a recognition of their being candidates, _aspiranten_ or aspirants,
for the rank of officer. Before they obtain that rank, the following
conditions must be fulfilled. They must pass an examination in the
common subjects of a good general education, such as the sons of
well-born or wealthy civilians may be supposed to receive. They must
serve six or nine months with the troops; they must attend nine months
at a division school, or twelve months in the artillery and engineer
school, where they receive a course of special military instruction; and
they must pass an examination in professional subjects before a board
sitting at Berlin. They are then eligible for a vacancy. In order to
obtain a commission they require further the recommendation of the
officers of the regiment.

It is obvious to remark, that in obtaining a commission in the Prussian
service the candidate’s chance depends greatly on the recommendation of
the colonel and the after assent of the officers. The effect of this is
to maintain an exclusive character in the army. Above two-thirds of the
commissions are obtained by the course described above; the remainder
are granted to those who pass through the cadet schools.

Of these there are five altogether, four junior establishments, situated
in certain provincial towns, and one senior or upper school at Berlin,
to which the others are merely preparatory. They are all supported by
the state; mainly for the purpose of educating the children of
meritorious officers in want of assistance; but they are also open to
others. With the exception of the highest class of the upper school, the
_Selecta_ above mentioned, the instruction given is of a perfectly
general character, and there is no obligation even for those who have
received the most ample pecuniary assistance to enter the military
profession. The discipline, however, is military, the teachers are
mostly officers, the pupils are regularly drilled, and most of them
actually go into the army. This they do in ordinary cases without going
through the highest or select class in which professional instruction is
given; they merely pass the same preliminary examination as the
candidates nominated by the colonels of regiments; they enter the army
without their commissions, and have to obtain them in the same manner as
the other candidates, by serving six or nine months with the troops, and
by following their professional studies in the division or artillery and
engineer schools, and by passing the officers’ or second examination
before the examining board at Berlin. Those who do remain to go through
the highest or select class receive their professional instruction in it
instead of in the division or artillery and engineer schools, and they
are examined for their commissions by the board while still at the cadet

Thus, in the course usually followed, three requisites are exacted in
Prussia before a commission is given; first, a good general education;
secondly, some actual military service; and, thirdly, professional
knowledge gained by something like a year of military study. But the
military service is not required from the upper thirty students of the
_Selecta_ of the Cadet House.

It will be well to mention, at the commencement, the names of the two
examinations. The first, the preliminary examination, merely testing the
general education, admits to a particular grade among non-commissioned
officers; those holding it rank between sergeants and corporals, and in
consideration of their being candidates (_aspiranten_) for a commission
wear a different sword-knot, and hence have the name of Swordknot ensign
or _Portepée-fähnrich_. The first or preliminary examination is
accordingly called the _Portepée-fähnrich_ examination. The second, the
professional one, is the officers’ examination, for the commission of
second lieutenant.

These two examinations, for the grade of _Portepée-fähnrich_ and for the
officer’s commission, are either conducted or controlled by the Supreme
Military examinations Board, (_Ober-Militair-Examinations-Commission_)
in Berlin, a body partly composed of military officers, partly of
eminent civilians.

The various examining boards, the central and the local ones, which
conduct these two examinations, are quite independent of the military
schools, and were formerly presided over by a different head; but in
order that the system should be uniformly carried out, and as Colonel
von Holleben expresses it, that “_the examinations should exercise a
salutary influence on education, and that their standard should be
adjusted to the capacities of the schools_,” they have now been placed
under the same control as the military schools.

The whole department of military education is therefore now under the
control of a single high functionary, bearing the title of the general
inspector of the military schools, military education, and military
studies (_das Militair Erziehungs-und-Bildungswesen_,) who reports
direct to the king on all subjects relating to examination and
instruction. He submits his proposals on matters of administration to
the minister of war, who issues the necessary orders to the boards
charged with the financial control of the various schools.

The general inspector is assisted by a supreme council or board of
military studies, composed of field officers of the general staff and of
the special arms, the directors of the war school, of the supreme board
of military examinations, of the artillery and engineers school, the
commander of the cadet corps, some of the consultative assessors
(_Vortragenden Räthen_,) of the minister of worship, and of individuals
selected from the general body of learned men (professors.)

The principal military schools of Prussia may be divided into five

I. Those which give a good general education to the sons of meritorious
officers, but which are open to others, such as--

1. The Cadet Houses or Cadet Schools (_Cadetten-Häuser_,) which supply a
certain amount of instruction in military professional subjects.

II. Such as supply professional instruction to young men who are
candidates for the rank of officer in the Prussian army. These are--

2. The Division Schools (_Divisions-Schule_,) nine in number, one for
each army corps.

3. The artillery and engineers schools in Berlin.

III. Those which afford professional instruction to officers already in
the service, to qualify them for special duty, limited to--

4. The War School or Staff School (_Kriegs-Schule_,) in Berlin.

IV. Those intended to give special instruction for the training of
non-commissioned officers and men. Such as--

5. The School Division or Non-commissioned Officers School
(_Schulabtheilung_,) at Potsdam.

6. The Regimental Schools (_Regiments und Bataillons Schulen_.)

7. The Music and the Swimming Schools, and the Central Gymnastic School
in Berlin (_Central Turn-Anstalt_.)

8. The Veterinary School (_Thierarzeneischule_.)

V. Those intended to give gratuitous education to the children, boys and
girls, of non-commissioned officers and soldiers, whose parents are too
poor to provide for them. Such are,--

9. The Military Orphan Houses (_Militair-Waisenhäuser_,) at Annaburg,
Potsdam, and Pretzsch.

10. The schools for soldiers’ children.

In addition to these might be mentioned the Medical Institution,
particularly the Frederick-William’s Institution at Berlin, and the
Knight Academy (_Ritter-Academie_,) or Noble School, in Liegnitz.

The annual cost to the state of the military schools in 1856, appears to
be as follows:--

  S Salaries. Dollars.
  O Other Expenses. Dollars.
  T Total Dollars.
  N Number of Students.

                NAME.              |    S*   |     O*  |     T*  |  N
  Department of General Inspector, |   5,872 |     250 |   5,922 | ...
  Supreme Military Examinations    |   5,400 |     300 |   5,700 | ...
    Board,                         |         |         |
  Board of Military Studies,       |     848 |     ... |     848 | ...
  Board of examiners for           |         |         |
    Artillery Lieutenants,         |    ...  |      60 |      60 | ...
  Cadet House at Berlin,           |  12,944 |     ... |  12,944 | 420
    “     “      Potsdam,          |  15,805 |  24,285 |  40,090 | 200
    “     “      Culm,             |  15,738 |  18,436 |  34,174 | 160
    “     “      Wahlstatt,        |  16,253 |  22,706 |  38,959 | 200
    “     “      Bensberg,         |  15,935 |  24,853 |  40,788 | 200
  General War or Staff School,     |  18,552 |   3,013 |  21,565 | 120
  United Artillery and             |         |         |
    Engineers School,              |  15,025 |   1,910 |  16,935 | 240
  Veterinary School,               |   8,514 |   4,165 |  12,679 | ...
  Gymnastic School,                |   4,046 |     720 |   4,766 | ...
  Division Schools,                |  10,800 |   6,195 |  16,995 |  †
      “    Libraries,              |     400 |   1,200 |   1,600 | ...
  Miscellaneous,                   |     ... |     680 |     680 | ...
                    Totals,        | 146,132 | 108,777 | 254,909 |

  [* A Prussian dollar is equal to three shillings of English money,
  and 70 cents of United States currency.]

  [† Variable.]

Or about £38,236 annually, exclusive of the charge for buildings and
repairs, and the original outlay for their first establishment. The pay
of the student officers, and the pay and allowances of the military
professors and teachers, are, however, drawn from their corps, so that
the above-mentioned seems only to include the extra pay granted to the
professors, &c.

The expenses of the Non-commissioned Officers School, of the military
orphan houses, and of the schools for soldiers’ children, are not given
in the printed paper from which these details have been extracted.


Two examinations, one in general and the other in professional knowledge
are required of all candidates for a commission upon or soon after their
entrance into the army, unless they can bring a certificate of having
successfully completed the regular course of a gymnasium, in which case
they are excused from the first.

These two examinations, through which alone admission is obtained to the
rank of officer, are so important, and hold so prominent a position in
the Prussian military system, that we propose to preface our account of
the nature and extent of each of these examinations by a short tabular
statement of the circumstances under which the candidates for each arm
of the service respectively pass them.

  The following Candidates offer themselves,
      for the Preliminary, Ensign’s, or _Portepée-fähnrich_
          for the Second or Officer’s Examination (in all cases before
          the Supreme Board at Berlin.)

  Those presented by the Colonels of Regiments,
      Before, after, or during (usually before) six months’ service
      with the Troops, before the local Division Board;
          After nine months’ military instruction in the Division
  Those coming at the usual time from the Cadet House (from the class
  called _Prima_,)
      On quitting the Cadet House, before the Supreme Board at Berlin;
          After six months’ service with the troops, and nine months’
          military instruction in the Division School.
  Those who stay an extra year in the Special or Select class
  (_Selecta_) of the Cadet House,
      Before admission to the Special or Select class (_Selecta_,)
      before the Supreme Board at Berlin;
          On quitting the Cadet House, after one year’s instruction in
          the Select class _Selecta_.
  Those for the Artillery or Engineers, except when they came from
  the Special or Select class, (_Selecta_,)  of the Cadet House,
      After nine months’ service with the Troops, and three months’
      stay at the Artillery and Engineers School, before the Supreme
      Board at Berlin;
          After one year’s stay at the Artillery and Engineers School.

1. _The Preliminary or Ensign’s (Portepée-fähnrich) Examination._

According to a special law, any young man above seventeen and a half and
under twenty-three years of age, whether he be a private or a corporal,
if he has served six months in the army, and can obtain from the
officers of his company a certificate of good conduct, attention, and
knowledge of his profession, may claim to be examined for the grade of
ensign or (_Portepée-fähnrich_.) If he succeed in this examination, he
is recognized as a candidate, an _aspirant_ for a commission; but his
prospect of obtaining a commission is subject to a variety of subsequent

In practice, a young man who aspires to a commission applies to the
colonel of the regiment and usually obtains a nomination before he
actually joins; and, as the examination is entirely of a civil
character, he is usually glad to try and pass it at once. Having
recently come from school, he feels probably better prepared than he is
likely to be at any subsequent time: for on joining the corps, he will
have for some time to conform to the life of a private soldier, to sleep
and mess with the men, and to mount guard in his turn; and with the
drill and exercises, and the marching and manoeuvring with the troops,
he will have enough to occupy him to prevent his preparing for the
examination. The two qualifications for the ensign’s grade are, the test
of the examination and the six months’ service; but it appears to be
indifferent in what order they are taken, whether service comes first
and examination after, or _vice versâ_.

The examinations take place quarterly, at the beginning of every
January, April, July, and October. They are held in the great garrison
towns by local military boards, consisting of a president and five
examiners. Applications for permission to be examined must be made at
least a fortnight before, and must be accompanied by certificates
stating the candidate’s birth, parentage, &c.; certificates of diligence
and good conduct from the schoolmasters or other teachers who have
instructed him; and of bodily fitness from an army surgeon.

The local board of examiners is appointed by the general officer in
command of the army corps, the centers of examination corresponding in
present practice with the localities assigned to the division or
army-corps schools, nine in number, presently to be described.

The first part of the examination is on paper; a _vivâ voce_ examination

On paper the young men have to write three themes or compositions in
German, to translate two passages, one from Livy or Sallust, another
from Cæsar’s Commentaries, Cicero’s Epistles, or Quintus Curtius; to
translate sixteen or twenty lines from French into German, and two
passages, a longer and a shorter, from German into French. They have one
question in common arithmetic, one in equations, progressions, or
logarithms; one in geometry, one in trigonometry; they have one in
mathematical or physical geography, one in the general geography of
Europe and its colonies, and one in that of Germany and Prussia. There
is one question in Greek or Roman history; one in the earlier German
history; one in modern; and one in Prussian history. They have also to
show that they are acquainted with the common conventional signs used in
representing the surface of the earth in maps; and they have to copy a
small map of a group of hills.

The time allowed for each question is about three quarters of an hour or
an hour; for each German theme, it is as much as an hour and a half or
two hours.

The questions are of a comprehensive character; _e.g._ Give a history of
the campaign of 1813, or of the life of Alexander the Great; enumerate
the rivers flowing into the Mediterranean Sea, with the principal towns
situated upon each of them. The German themes are, first, a _curriculum
vitæ_, an account of the candidate’s life, which is, however, not
supposed to count in the result, and is merely for the examiner’s
information; second and third, two themes on some sentence or proverb,
for the first of which the examiner assists the candidate by _vivâ voce_
questions and corrections in drawing up the preliminary outline of
arrangement; for the second he is left entirely to himself.

There is a subsequent _vivâ voce_ examination in all the subjects,
drawing excepted. The candidates are taken in small classes, not
exceeding seven in number, and are examined together, but not in public.

The results of the examination are considered according to the system of
_predicates_ or epithets, sometimes also called _censures_. The
candidates’ answers are characterized as excellent (_vorzüglich_,) good
(_gut_,) satisfactory (_befriedigend_,) insufficient (_nicht
hinreichend_,) or unsatisfactory (_ungenügend_.) Numerical values are
attached to each of these epithets; “excellent” is marked with 9;
“unsatisfactory” counts as 1; and according to the amount of importance
attached to the different subjects the marks thus given are multiplied
by a higher or lower number, by 5 in one case, by 3 or by 1 in others.
German, Latin, and mathematics have all the highest estimate of 5, and
are each five times more important than drawing, which is marked by 1;
geography, history, and French, are each valued at 3. A young man who
gets the _predicate_ “excellent,” in German, will receive 45 marks, his
9 being multiplied by 5; whereas the same predicate for history would
obtain him only 15, and in drawing only 5 marks.

  German,            5 }
  Latin,             5 }
  Mathematics,       5 }
  History,           3 } Total, 25.
  Geography,         3 }
  French,            3 }
  Drawing,           1 }

A report is then drawn up, and according to the marks or predicates, the
candidates are pronounced as admissible with distinction, admissible
with honor, or simply admissible; or their re-examination after six
months, their re-examination after a year, or their absolute rejection,
is recommended.

This report, with the candidates’ certificates, is forwarded to the
supreme military examinations board at Berlin, and, if approved by them,
is submitted in their quarterly report to the king; and the result, when
sanctioned by him, is communicated to the respective corps.

The candidates are all informed not only of the practical result, but
also of the particulars of their examinations; they are told in what
subjects they have failed, and in what they have succeeded. The
candidates can not, under any circumstances, try more than three times.

The young men who pass, are thus, so far as their qualification in point
of knowledge is concerned, pronounced admissible to the ensign’s grade.
They have of course to complete their six months’ service with the
troops. Yet even when this is completed, a vacancy in the list of
ensigns must be waited for, and months may pass before the aspirant
receives the distinctive badge, the special Sword-knot, which marks his
superiority to the corporals, and shows that he has gained the first
step that leads to a commission.

The examination that has now been described is obviously one for which
preparation may be made in the common public schools, and under the
usual civilian teachers. A young man of seventeen need not have been
positively destined to the military profession, nor have gone through
special preparation for any length of time beforehand. The boards of
local military examiners are content to take them as they are offered,
inquiry only being made as to their birth and connections, and their
previous behavior at school or under tuition.

In fact, those who have passed successfully through the full course of a
school which prepares for the universities (a gymnasium,) are excused
the ensign’s examination. The certificate they have received on going
away from school, upon the _abiturient’s_ or leaving examination, as it
is called, is considered quite sufficient; except in the case of
candidates for the artillery or engineers, who are expected to show
greater proficiency in mathematics; and certainly a boy in the head
class of a gymnasium ought to be able to pass the preliminary
examination with perfect ease and with credit. The amount of knowledge
required and the particular subjects selected are not those of the
first, and are scarcely those of the second class of a gymnasium; and
the assertion was even made that a boy from the upper third class might
very well hope to pass for an ensigncy. Possibly a little extra tuition
from the preparatory establishments, which are said to have sprung up
with the special function of “fabricating Fähnrichs” might in this
instance be required.

The official programme is here given, and may be compared with the
studies prescribed in the upper classes of the Cadet House at Berlin,
(_see_ the account of that school.)

  1. In their own language, good legible handwriting, a correct style,
free from orthographical or grammatical mistakes, facility of expression
in writing and speaking; some evidence of a knowledge of German

  2. In Latin, facility in understanding the Latin prose writers
ordinarily read in the second class of a Prussian gymnasium. A written
exercise in translation from Latin into German; grammatical analysis of
some passages.

  3. In French, facility in reading and in translating from German into
French, and French into German, grammatical analysis of French
sentences, and a knowledge of syntax.

  4. Mathematics:--

    (_a._) Arithmetic and Algebra;--familiarity with the ordinary rules
for the extraction of the square root of whole numbers and of fractions;
Proportion and its applications including questions in Partnership and
Compound Proportion; the theory of powers and roots, with integral and
fractional, positive and negative exponents. Equations of the two first
degrees, with one or more unknown quantities; Logarithms, Logarithmic
Equations, Arithmetical and Geometrical Progression, and practice in the
application of the various theories.

    (_b._) The complete elements of Plane Geometry, measuration of
rectilineal figures and of the circle, transformation and division of
figures; the first elements of the application of Algebra to Geometry.

    (_c._) Plane Trigonometry, Trigonometrical functions and their
Logarithms. Use of trigonometrical tables. Calculation of particular
cases of triangles, regular polygons, and segments of circles.

  In consideration of the especial importance of this discipline for
officers of the artillery and engineers, a higher predicate (_i.e._ a
greater number of marks) will be required in the exercises of candidates
for these two services; the knowledge expected in their case will be,
though not more extensive, more thorough and deep.

  5. Geography:--The general principles of Mathematical and Physical
Geography, knowledge of our planetary system, of the motions of the
Earth, and of the phenomena immediately dependent upon them. Readiness
in drawing from memory the outlines of the more important countries,
with their principal mountains, rivers, and cities. General outlines of
Political Geography, in the case of the mere states out of Europe; a
detailed account of the elements of European statistics, more
particularly in the case of Germany and Prussia.

  6. History:--A knowledge of the more remarkable events in the history
of great nations, of the general connection, causes, and consequences of
these events; a knowledge of the remarkable men of all such nations down
to the present time. Special knowledge of the history of Greece, Rome,
Germany, Prussia, with particular reference in this last case to its
external growth, inner development, and to the principal events of the
most important wars since the middle of the eighteenth century.

  7. Readiness in general drawing, and in constructing mathematical
figures; some skill in drawing plans of positions and mountains, in the
way of preparation for military plan drawing.

  8. The candidate may, in addition, be examined in other subjects, in
which his certificates show that he has been instructed; for example, in
Natural Philosophy, so far as included in his previous course of

It must be remembered that either before or after this examination some
months must be spent in actual service with the troops by all but the
pupils belonging to the _Selecta_ of the cadet school; and that nine
months of study at the division and artillery and engineer schools
intervenes before the officers examination takes place.

2. _The Second or Officer’s Examination._

The second or final examination for a commission, which generally ensues
when the work of the division school is over, is held in Berlin only,
and is conducted immediately by the central commission, to which
reference has so often been made--the supreme Military Examinations
Board, the _Ober-Militair-Examinations Commission_. This board or
commission, a list of the existing members of which is given in page
179, consists, for the purpose now in consideration, of a president and
five examiners, selected from the larger number to examine candidates
for commissions.

The examinations are held continually; two opportunities are afforded
every year to the candidates sent from each of the various army corps.
The requisite papers must be forwarded to the commission eight days at
least beforehand, and the candidates must appear in Berlin, and take up
their quarters in the buildings placed at the disposal of the board on
the Friday preceding the day fixed for the examination. The examination
usually begins on the following Monday, and lasts through the week. The
expenses of the journey are allowed, except, perhaps, when the candidate
comes up a second time.

The certificates to be presented are the following:--

1. The certificate of birth, age, parentage, &c. (This is called the

2. The _Curriculum Vitæ_, (an account of the circumstances of the
candidates’s past life, his education, employment, &c., &c.)

3. The certificate that he has already passed through a previous
examination (the _Tentamen_,) held by the authorities of the division

4. A certificate of conduct during his stay at the division school.

5. A military drawing (_Croquis_,) with an attestation given by his
instructor that it is the candidate’s own doing.

This examination, like the preliminary one, is partly on paper and
partly oral. General directions are given that the examiners in both
cases shall look mainly to the question whether the candidate has
sufficient positive knowledge of his subjects, and capacity to explain
and express himself, that mere lapses of memory shall not be regarded,
and that natural endowments shall be principally looked to.

In the written examination, the candidate has four questions given him
in what is called the knowledge or theory of arms (_Waffenlehre_,)
including under that term all kinds of ammunition; three in tactics; one
question in the rules and regulations which touch the duty of a
subaltern officer; two questions in permanent and two in field
fortification; one exercise in surveying, to test his acquaintance with
the common instruments, and one to try his knowledge of the principles
of plan drawing (_Terrain-Darstellung_;) while his general skill in
military drawing is proved by his either copying a plan placed before
him, or drawing one from a relief model of a mountainous district (_nach

There is a _vivâ voce_ examination in all the subjects.

The commission meets once every month to consider the examinations held
since their last meeting. The result is announced under the form of the
_predicates_ or epithets already more than once referred to. Honorable
mention is accorded to an _excellent_ examination, and mention to a
_good_ one. If there has been an unsatisfactory result in one of the
subjects, the candidate may compensate for it by superiority in other
subjects, but can only in this case be qualified as _satisfactory
(befriedigend,)_ and an adequate knowledge of “arms” and tactics is
regarded as indispensable in candidates for the infantry or cavalry, and
in “arms” and fortification in those for the artillery and engineers. No
superior work in other subjects is allowed to make up for a deficiency
in these.

If a candidate’s work is marked as _insufficient (nicht hinreichend,)_
he is sent back for another half-year, and if he has done
_unsatisfactorily_, for a complete year of additional study, with leave
to appear for re-examination after that interval. In a case of
re-examination, the two last _predicates_ (_nicht hinreichend_ and
_ungenügend_) entail final rejection.

The report of the board is submitted to the king; the results are
communicated to the various corps. The announcements sent to the
candidates state the predicates assigned to the various portions of
their work. Those who have passed, receive certificates of being
qualified for the second lieutenant’s commission:--

This rank, however, is not immediately granted. A vacancy may be long in
occurring, and must be waited for. Promotion is given according to their
seniority on the list of ensigns in the regiment. Another condition must
also be satisfied. When a vacancy occurs, the senior ensign’s name can
not be submitted to the king for his appointment without a document
stating on the part of the officers of the regiment that he has the
requisite knowledge of the duties of the service, and that they consider
him worthy of admission amongst them (_würdig in seine Mitte zu
treten_.) If the majority is opposed to his admission, the name of the
next ensign in order of seniority is, without further discussion,
brought forward; if a minority or merely some individual officers take
exception, they state the grounds of their opinion, which are then
submitted for consideration.[6]

    [Footnote 6: This certificate, according to a statement received
    in conversation, is in the first instance from the officers of the
    company, to the effect that the ensign in question is well
    conducted and likely to be a desirable addition to their number;
    then from the major of the battalion, and from the colonel of the

Special merit in the examination may be, at the king’s pleasure, held a
sufficient reason for promotion before all candidates examined at the
same time.

The following is the programme of the studies, proficiency in which is
expected of candidates at the second or officer’s examination:--


  A. _Of Gunpowder_.

  1. General views on gunpowder and its application.

  2. Ingredients of gunpowder; its qualities and use.

  3. Fabrication of the same; principles on which the manufacturing
process is based.

  4. Statement of the various kinds of gunpowder in use, and their
distinctive qualities.

  5. Of the ignition, combustion, and power of gunpowder.

  6. Qualities of good powder; examination of the same:

    _a._ According to their external characteristics.

    _b._ According to force developed.

      _a._ By the mortar eprouvette.

      _b._ By the smaller eprouvette.

      _y._ Or, in default of such instruments, by practical experiment.

  7. Manner of preserving gunpowder; characteristics and treatment of
damaged gunpowder.

  8. Precautions to be taken in working with gunpowder, and transporting
the same.

  9. The most ignitible materials for percussion caps, and the like.

  B. _Of Artillery_.

  1. Classification of guns, according to species, calibre, and the kind
of warfare for which they are intended. (Field, siege, and standing

  2. General qualities to be required of a properly constructed piece of

  3. Construction of the piece; description of the same according to the
various kinds of guns, specifying the use of the different parts.
(An exact statement in figures is only called for in reference to the
length, weight, and diameter of the piece.)

    _a._ Materials; qualities required of them; enumeration of the
materials generally employed.

    _b._ Interior construction of the piece; length of bore, chamber,
windage, and touchhole; their influence on the range.

    _c._ External construction of the piece; appliances for pointing and
managing it, and connecting it with the gun-carriage.

    4. Construction of the gun-carriages; enumeration of the different
kinds of the same, according to the description of gun, its destination,
and materials.

    _a._ Specification of the principal component parts of the

    _b._ Distinctive characteristics of the construction of the various
denominations of carriages.

    _c._ General principles for determining the proper construction of
the same.

    _d._ General notions relative to the proportion of the weight of the
carriage to the piece.

  5. Construction of the limbers.

    _a._ Enumeration of the different kinds of limbers.

    _b._ Principal component parts and distinctive characteristics of
the construction of the various kinds of limbers.

    _c._ General notions relative to the weight of the limber in
proportion to the piece and the gun-carriage.

  6. Statement of the various descriptions of wagons used by the field
artillery, and their destination.

  7. Ammunition; enumeration and description of the objects belonging to
it. (Exact statements in figures are only required for the diameter and
weight of the principal kinds of projectiles.)

    _a._ Projectiles; statement of the species of projectiles used for
the different kinds of guns, and their construction.

      α. Bound shot, cannon ball, grape.

      β. Shells; their various species.

      γ. Light balls.

      δ. Stones.

    _b._ Charges; general description of them,

      α. In field-pieces.

      β. In heavy artillery.

    _c._ Primings; enumeration and description of the various kinds of

    _d._ Other military fireworks; statement of the principal species,
and their general construction.

    _e._ Transport of ammunition by limbers and carts; packing of the

  8. Moving and working the guns:

    _a._ General notions on the working of field-pieces.

    _b._ Different kinds of operations with field-pieces; unlimbering
and limbering up.

    _c._ Position of field-pieces in firing, with regard to effect,
cover, and celerity of movement.

    _d._ Principal manipulations in working the same.

      α. Loading.

      β. Pointing.

      γ. Discharging; the process according to the different kinds of

    _e._ Ascertaining the efficiency of a gun previous to using it.

    _f._ Momentary unserviceability of guns.

    _g._ Expedients for repairing a disabled carriage.

  9. Artillery practice.

    _a._ Exposition of the theory of firing (as far as it can be
elucidated by a knowledge of the elements of mathematics;) general
notions concerning the curve of round and hollow shot, and the influence
of the force of powder, of gravity, and of the air’s resistance upon
their velocity; the curve after the first graze; trajectory of grape

    _b._ Classification and denomination of the various methods of
firing or throwing projectiles.

    _c._ Range; conditions on which it depends; its practical limits.

    _d._ Effect of projectiles.

      α. Probable accuracy of practice; circumstances on which it

      β. Force of the blow; circumstances on which it depends.

    _e._ Recoil, jumping, or bouncing; explanation of such occurrences.

    _f._ Application of the various descriptions of guns, projectiles,
and methods of firing, according to the nature of the mark, the
distance, the position of the adversary, and the ground.

  C. _Of Small Arms._

  1. Classification and denomination of small arms.

  2. General principles applied to the construction of the musket, the
infantry and wall-piece rifle, the carbine, the cavalry rifle, the
pistol, and the engineer musket (if the candidate is in the engineers.)

  3. Description of their construction and arrangement in particular;
enumeration of the separate parts (an exact statement of dimensions only
required for the principal ones;) object and effect of the same.

  4. Estimate of the practical utility of the various kinds of fire-arms
as employed by one infantry and cavalry (no technical or theoretical
investigation, but only practical remarks.)

  5. Ammunition, as the ball, cartridge, and patch:

    _a._ Its preparation.

      α. In the usual manner.

      β. In cases of need, in default of the usual implements.

    _b._ Preserving, packing, and transporting it, both in carriages and
by the soldier himself.

  6. Management of small-arms:

    _a._ Theory of firing (in its general scientific bearings, _vide_
artillery) as applied to small-arms: repeated elucidation of the curve,
line of metal, axis produced, and the relative position of these three
lines in the different ranges.

    _b._ Practical rules for loading, presenting, taking aim, and
discharging, at different elevations of the adversary, and at different

  7. Cleaning and preserving the arms.

  D. _Of Side-Arms._

  1. Classification and denomination of the same:

    _a._ Cavalry side-arms.

    _b._ Lances.

  2. Statement of the general principles on which their construction is

  3. Examination of the state of side-arms on receiving them (within the
limits mentioned above in C. 4.)

  4. Effect and management of the same.


  A. _Army Organization._

  1. General sketch of the organization of the Prussian army.

  2. Characteristics of the different kinds of troops (arms;) their
peculiarities (their weapons are included under the former head,) their
equipment and destination.

  B. _Elementary Tactics._

  1. Account of the regulations concerning the distribution and
formation of a battalion of infantry, a regiment of cavalry, and a
battery, in line or column.

  2. Formation of the different columns from the line, forming square,
deploying and forming line, movement in advance, to the rear and to the
flank, changing front and direction in line and column.

  3. Formation of _tirailleurs_ and skirmishers; posting, covering,
moving, reinforcing, reducing, and relieving the same.

  4. General rules on the conduct of the separate arms in action.

    _a._ Engagement of infantry under fire and hand to order, in attack
and defense.

    _b._ Charge of cavalry, attack _à la débandade_, wheeling off of the
fourth subdivisions (platoons,) skirmishing.

    _c._ Employment and conduct of artillery in action.

  5. General principles relative to the combined action of the different

  6. Tactical advantages of ground; level, hilly, open, close,
uninclosed, and broken ground.

  7. Attack and defense of localities, such as heights, woods,
farm-buildings, villages, and defiles; false attacks, demonstrations.

  C. _Field Service._

  1. Of Marches. General rules, method, and object; precautions, van and
rear guards, covering parties.

  2. Escort of transports of powder, provisions, and prisoners of war,
in one’s own and in an enemy’s country.

  3. Surprises, ambuscades, and reconnaissances.

  4. Service in cantonments, camp, and bivouac, outposts, picquets,
advanced picquets, reserve picquets (movable and stationary,) patrols.

  5. Taking up quarters in ordinary marches and cantonments.


  A. _Field Works._

  1. Object of breast-work and ditch profiles in plains. Plan of
field-works; open works, salient angle, its dimensions.

  2. Dead angle and dead ground. Removal of dead ground; flanking; line
of defense; dimensions of re-entering angle.

  3. Inclosed works; dimensions and space inclosed; works with salient
angles only, and with both salient and re-entering angles.

  4. Erection of works to be defended by artillery; firing _en
barbette_, and through embrasures; platforms; magazines.

  5. Communication with interior of inclosed works.

  6. Artificial obstacles for strengthening field-works; requisites for
their selection and application; method of construction; advanced
ditches (demi and entire;) trous-de-loup; abattis; palisades and
fraises; barriers; chevaux-de-frise; pickets; caltrops; harrows; sluices
and inundations; fougasses; blockhouses; caponiers; double, single, and
demi-caponiers _à revers_.

  7. Strength of garrison of field-works.

  8. Defilading, horizontal and vertical, of open and inclosed works;
traverses and bonnettes.

  9. Construction of small open and inclosed field-works; marking out;
tracing; profiling; number and employment of workmen; excavating the
ditch; formation and revetment of the slopes with sods, fascines,
wicker-work, gabions, sand-bags, wood, or stones; selection,
preparation, and application of the reveting materials. (Of the
execution of the revetment only so much as may show whether the examinee
will be capable of undertaking the direction of such works in an
efficient manner.)

  10. Fortification of heights and defiles.

  11. Object, general arrangement, and advantageous situation of a

  12. Arrangements for the defense of woods, hedges, houses, churches,
and churchyards.

  13. Attack and defense of a redoubt; surprise; attack by open force.

  14. Repairing and destroying roads, fords, and bridges, wooden and
stone; construction of foot bridges, carriage bridges, bridges across

  B. _Permanent Fortifications._

  1. Construction of a bastioned front in a plain, with ravelin,
tenaille, and covered way, in plan and profile, after the first system
of Vauban, with the improvements of Cormontaigne; name and destination
of every single part, angle, and line.

  2. Brief description of a regular attack upon a bastioned fortress;
sketch of the preparations for attack; lines of circumvallation and

  Description of parallels, approaches, demi-parallels, and the duties
of the infantry in them; saps, trench cavaliers; carrying the covered
way, crowning the glacis, passage of the ditch, escalade of the rampart.
These operations to be detailed according to their object, position, and
arrangement, but without special reference to their technical execution.

  General notions relative to the batteries of a besieging army, their
position, object, calibre of guns, and practice.

  3. Outlines of the system of defense of a fortress relative to the
employment of infantry and cavalry in garrison, and of the standing
artillery in arming the fortress and placing it in a state of defense
against a regular attack or an attack by open force in all its stages.

  Especial knowledge of the duties of infantry and cavalry in garrison,
in guarding, occupying, and defending the works, and in sallies,

  4. Historical sketch of an actual siege (on which the examinee has
attended a lecture,) and the principles of the attack and defense of
fortresses in general.

  5. Account of the situation, form, arrangement, and object of some of
the means employed for increasing the permanent strength of fortresses,
exclusive of the more technical points.

    _a._ The rampart of the body of the place. Angle of the bastions and
its effect; length of flanks and faces; auxiliary flanks; empty and
solid bastions attached and detached fausse-brayes.

    The escarp, earthen wall, revetment, demi-revetment, simple
crenneled wall, arched crenneled wall, revetment _en décharge_;
perpendicular and parallel casemates.

    _b._ The main ditch, dry, wet, and dry or inundated at pleasure;
sluices, coffer-dams, reservoirs.

    _c._ Outworks. Ravelin, tenaille, counterguards, cover-faces,
envelopes, tenaillons, lunettes.

    _d._ Advanced works. Simple and double tenaille; horn-work before a
bastion or redoubt; crown-work; double crown-work; advanced ditch, with
advanced covered way.

    _e._ Detached works, open or inclosed at the gorge.

    _f._ Interior works. Cuts inside the bastions; réduits; citadels.

  6. Historical notions of the characteristics of some of the principal
systems of fortification, _e.g._ the old and modern Italian, the old
Dutch, Vauban’s second and third manner, the ideas of Coehorn, Rimpler,
the French school, and that of Montalembert, compared with Vauban’s
first system, but without statement of proportions; in addition to this,
the characteristics of the latest Prussian fortifications, always with
the omission of details more especially technical.

  7. Modified methods of attack; surprise, assault, bombardment,
blockade; explanation and statement of circumstances in which attacks of
this kind are practicable.


  1. Knowledge of the instruments generally employed in military
surveying, and their use.

    _a._ Instruments for measuring and marking out straight lines;

       Signals, bandrols, or _jalons_, common staves, picket posts,
rods, measuring chains, measuring cord, the step.

    _b._ Instruments used for protracting the lines measured, viz.--

       The step measure, calliper compasses, beam compasses, dividing
and reducing compasses.

    _c._ Instruments for measuring and marking out horizontal angles:

      The square, the plane table, caloptric compasses, the reflector,
the sea-compass, the prismatic compass, the astrolabe:

    _d._ Instruments for measuring vertical angles:

      Lehmann’s dioptric rule, Schmalkalder’s holometer, the quadrant.

    _e._ Leveling instruments:

      The ordinary mason’s level, the spirit level, the water level,
the spirit level _à lunette_, the plumb rule, Lehmann’s dioptric rule
in connection with the plane table, placed horizontally, the surveyor’s
rule, Schmalkalder’s holometer.

  2. Operations in surveying with the plane table, astrolabe, reflector,
and compass.

  3. Topographical survey of a locality (theoretically and practically,)
reconnoitring, geometrical triangulation, detailed survey.

  4. Hasty or rough sketch of certain objects, and entire (but limited)
sections of country.

  5. Drawing plans.

    _a._ Notion of the elements of topography; rising and sloping
ground, running and standing waters, division of ground in a military
point of view, and characteristics of the same; open, inclosed,
elevated, hilly, mountainous, broken ground.

    _b._ Theory of plan drawing.

      α. The first elements of the science of projection, and the
construction of instruments for measuring slopes.

      β. Fundamental rules for plan drawing in general, and for drawing
mountains in particular. Statement of the various angles of depression
of inclined planes through mountainous regions.

      γ. Of the horizontals, and the laws dependent upon them, relative
to mountainous districts.

      δ. On the laws of defiles.

      ε. On ascertaining the difference of elevation, and drawing

      ζ. View of the accessories of plan drawing; the choice of colors
and of type, and the order in which the operations necessary for
preparing a plan are performed.

    _c._ Practical plan drawing from copies and models.


  A. _Exercises in Military Composition._

  1. Drawing up reports on incidents connected with the service, and
with the duties of a subaltern officer, directed to the military
authorities and superior officers of every rank.

  2. Instructions to subordinates.

  3. Applications and memorials.

  B. _Acquaintance with the General Regulations of the Service._

  1. The laws on disciplinary and military punishments.

  2. The proceedings in courts-martial, drum-head courts-martial, and
courts of honor.

The preparation for this second, severer, and professional test that has
just been described, is usually obtained in the division schools, of
which an account will shortly follow, and to which any young man once
accepted as a candidate, who has served his six months with the troops,
and has passed his preliminary or ensign examination, may be admitted,
even though a vacancy has not yet occurred, and he has not yet received
his definitive promotion to the ensign’s grade.


_The Cadet Schools or Cadet Houses._

The actual military education of Prussia commences with the cadet
houses, the schools intended for pupils before entering the army. They
are divided into two classes, the junior and the senior. They can not
indeed be called exclusively military schools, since the education which
most of their pupils receive is one which fits them for civil
professions, and is not specially military; and there is no obligation
even on those who have received the largest amount of pecuniary
assistance to enter the military profession when they leave the cadet
house. The highest class, however, of the Upper Cadet School of Berlin,
called the _Selecta_, receives strictly military teaching for a year,
and the schools may fairly come under this denomination, as being mainly
intended to educate the sons of officers who are in want of assistance,
and as possessing a military discipline, uniform, and spirit.

These are five in number, four preparatory schools, and one a finishing
institution; the four first in the provinces, at Culm, Potsdam,
Wahlstatt, and Bensberg, the last in the capital itself. At the four
junior schools, boys may be admitted at 10 or 11, and may remain till
15; at the upper school the ordinary stay is from 15 or 16 to 18 or 19.

The whole constitute together a single body, called the cadet corps.
Boys may enter the school at Berlin on passing an examination, without
previously attending one of the lower schools; but those who are sent up
by the authorities from Culm, Potsdam, Wahlstatt, and Bensberg, are
received without examination, being already members of the corps.
A single officer exercises the command of the whole; and a single
commission, of which the general inspector is chairman, regulates all
matters relating to the admission of candidates into the body.

The whole number at present is between 1,100 and 1,200, of whom 420 are
in the Upper School at Berlin, 205 in the Preparatory School at Potsdam,
and 200 at each of the other houses.

The cadets are of two kinds, the King’s cadets and the Pensioners or
paying pupils; the former are 720 in number, the latter about 420. The
pensioners pay 200 dollars (30_l._) a year for board and instruction
together; the King’s cadets are aided in various degrees accordingly to
the following scale:--

  240 pay 30 dollars (4_l._ 10_s._) each.
  240 pay 60 dollars (9_l._) each.
  240 pay 100 dollars (15_l._) each.

Foreigners are admissible at a yearly payment of 300 dollars (45_l._,)
and a few extra day scholars (_Hospitanten_,) when the classes are not
too full, are received for 20 dollars a year (3_l._)

The King’s cadetships are granted, according to the pecuniary
circumstances of the applicants, to the children of officers of the
standing army, or of the Landwehr, who have distinguished themselves or
have been invalided in actual service in the field; to the children of
non-commissioned officers who have in like manner distinguished
themselves and received severe wounds in the service; and to those of
any citizens who have performed any special service to the state. The
sons of meritorious officers who have died in indigence or have retired
upon pensions, the sons of indigent officers in general in the standing
army, and the sons of meritorious non-commissioned officers of
twenty-five years’ standing, are also in like manner eligible.

In very special cases of poverty, the supplementary payment is dispensed
with altogether.

Pensioners are admitted from all classes and professions according to
priority of application, and to their qualifications as shown by their
examination. A great number of these are said to be the sons of
officers, of those, namely, who are not in need of pecuniary assistance.
And the number of the pensioners generally appears to be steadily on the
increase. In the regulations printed in 1850, the places open for this
class of cadets are stated to be only 216; at present, as has been seen,
provision is made for something like double that number.

The four junior schools at Culm, Potsdam, Wahlstatt, and Bensberg, are
all divided for purposes of instruction upon the same uniform plan into
four classes, numbered up from six to three--_Sexta_ at the bottom;
_Quinta_; _Quarta_; and _Tertia_ at the top. The upper school at Berlin
succeeds with three classes, the second, the first, and the special or
select--_Secunda_, _Prima_, and _Selecta_. Each of these classes,
however, may contain any number of co-ordinate subdivisions, all taught
the same subjects, and presumed to contain pupils of the same capacity.
No teacher, it is considered, can satisfactorily undertake to give a
lesson to more than thirty at a time; and the Secunda at Berlin was thus
parted out in the year ending March, 1856, into eight little sets of
rather less than thirty, the Prima into six, and the Selecta into two.

_Junior Cadet House._

The junior cadet house at Potsdam occupies four or five buildings a
little way out of the town. The class-rooms are on the usual Prussian
plan, not arranged for lectures to large, but for lessons with small
numbers. One distinguishing feature is the character of the arrangements
of the rooms up-stairs, in which the boys pass their time out of school
hours. They are very comfortable chambers, perhaps rather small for the
numbers at present placed in them; they are ranged along a corridor; ten
pupils are placed in each, and between every two rooms is the apartment
of one of the resident tutors (_Erzieher_ or _Gouverneur_,) who sees
that all goes on right in these two rooms under his charge. Here the
boys sit and work, and during the hours when they are expected to be
preparing their lessons, are carefully looked after by their tutors.

These little apartments occupy one whole floor of the building. The
floor above is that of the dormitories, containing each, perhaps, as
many as sixty. The number at present in the school was stated to be two
hundred and five, and the accommodation properly intended for only one
hundred and sixty.

Colonel von Rosenberg, the commandant of the school, stated that eleven
was the usual age at which the pupils came. This he appeared to think
was rather too early, and he was inclined to attribute to this cause
certain points in the character of young men who have been educated in
the cadet corps. Eighty of his two hundred and five pupils were
pensioners, or paying pupils; many of these also were the sons of
officers. The teachers and tutors are partly civilians and partly
military men, about an equal number of each. The four classes, Tertia,
Quarta, Quinta, and Sexta, are subdivided into nine, so that the average
number at a lesson would not be more than twenty-three.

_Senior Cadet House._

The upper or central cadet school is in the older part of Berlin, in the
_Neue Friedrichs Strasse_, where on the pediment surmounting the gateway
the inscription, MARTIS ET MINERVÆ ALUMNIS M.DCC. LXXVI, records the
erection by Frederick the Great, ten years before his death, of the
large and stately quadrangle which formed the original house. Here the
pupils are quartered, and in the great court within, they go through
their exercises. There are several houses on both sides of the street
attached to the service of the institution, and buildings are in course
of erection to accommodate additional numbers.

A large separate building contains the present class-rooms. In the first
of these which we visited, thirty cadets were engaged in military
drawing; in another, twenty-four of the second class, the Secunda, were
busy at their Latin lesson.

The room was fitted up on what appears to be the usual plan, with a
series of parallel desks on the same level, ranged along the outer wall,
and a sufficient space between them and the inner wall for the teacher
to pass freely up and down. His desk was at one end in front of the
boys. The lesson was in Quintus Curtius. The teacher (a civilian) made
them construe each a sentence, and asked questions in parsing, &c., &c.,
much in the English manner. There was no taking places. This in German
schools appears to be confined to quite the lower classes. There is a
separate lecture-room here again for lessons on Natural Philosophy and
Chemistry, with a small gallery of models, instruments, &c., attached to

A large hall is used on state occasions, and serves the purpose also of
an examination-room; it is called the hall of the Field Marshals, and is
adorned with portraits of the sovereigns of Prussia from the Great
Elector downwards, and of the field marshals both of the time of
Frederick the Great and of more recent date, among whom is the Duke of
Wellington. Here also is kept Napoleon’s sword taken at “La Belle
Alliance,” and presented by Marshal Blucher.

Passing to the first floor of the great quadrangular building, we found
ourselves in one of the sitting-rooms of the cadets. Seven boys had a
couple of rooms, consisting of a common sitting-room, and a common
bed-room. Five is the number for which this amount of accommodation was
intended, and to five the number will be reduced when the new buildings
are completed. In a second and larger pair of rooms we found twelve

Here also is the library, containing 10,000 volumes, and comfortable
apartments occupied by the various superintending officers.

The boys, their morning lessons completed, had been going through their
military exercises under the superintendence of their officers; but they
were now collected in their studying-rooms, and were seen forming at the
doors, each small party under the command of its senior, ready to march
into the large and handsome dinner-hall.

Into this the whole body of young men presently moved by companies,
proceeding to station themselves in front of the tables. The tables are
ranged in parallel lines on each side of the central passage, and
accommodate each of them ten, four sitting at each side, and a senior at
each end. The order was given by the officer on duty for “prayer” (_Nun
beten wir_,) and a short silent grace was followed by the immediate
occupation of the seats, and the commencement of the meal. The
arrangements in general appeared to be excellent.

The number in the school during the past year had been 420. The four
companies into which the whole body of the pupils is divided, each
contain a certain proportion from each of the three classes; the senior
in each company being invested with the charge of the juniors; those who
are in the Selecta taking rank as under officers. In every room (_Stube_
or _Wohnzimmer_) there is one _Selectaner_, who is responsible. The
ordinary ages are 15, 16 in the Secunda; 16, 17 in the Prima, and as far
as 19 in the Selecta. No one is, as a rule, allowed to pass more than
one year in a class; if in that time he can not qualify himself for
advancement, he is dismissed. The rule does not, however, appear to be
strictly enforced. The general preservation of discipline appears to be
a good deal intrusted, as in English public schools, to these senior
pupils of the age of eighteen or nineteen. There are Resident Tutors
(_Erziehers_ or _Gouverneurs_) as at Potsdam, who see a good deal of the
pupils, especially in the evenings, when they go into the sitting-rooms,
sit with them, help them in their work, play at chess with them, &c.,
&c. But they do not sleep close at hand between the sets of rooms, as at
Potsdam, but at some little distance off.

The official arrangements for the control of the discipline consist
principally in the system of what are called _Censur_ Classes. This is a
peculiar system which requires some explanation. There are five _Censur_
Classes quite independent of the ordinary classes of the school. A boy
on entering the Cadet School is always placed in the third of these
classes; if he behaves ill, he falls to Class IV. and is under
restrictions. Class V. is reserved for serious cases of misconduct, and
any one who incurs the penalty of descending to it, is subject to
continual superintendence, and is confined to the walls. Class II. gives
considerable, and Class I. still more ample privileges. The members of
this class (usually only quite the elder boys) are allowed great freedom
in the way of going out into the town.

In each of the studying-rooms (the _Wohnzimmer_) the list of the
occupants’ names hangs up on the door inside. One for example was
noticed containing twelve names. To each was attached his rank in the
_Censur_ Classes, as well as his position in the ordinary classes. At
the head stood one _Selectaner_, who in this instance was in charge of
the room; then followed the _Primaners_; and the list was completed by
nine of the _Secunda_. As at the time of our visit (just after the
Easter holidays and the yearly examination) the whole Selecta of the
year had just quitted, the room was in the charge of the senior
_Primaner_. The authority exercised by these senior boys appears to be
very considerable.

The competition for admission to the Selecta, and for the after
selection for immediate promotion, was spoken of as very considerable.

The number who came to the Berlin Cadet House without previously going
to one of the junior establishments was said to be only a small

The boys both here and at Potsdam were of course all found dressed in a
military uniform.

The studies pursued in the Cadet Corps agree nearly with those of the
common public schools, but of these there are three different kinds:--

1. The ordinary first-class school, the _gymnasium_ of the Prussian
States, is, strictly speaking, a school which prepares for the

2. The second-class schools have the name of _Real_ or _Practical
Schools_; they deal with the actual application to business and work,
not with the theory of mathematics or of language, and they may be said
to resemble in some degree the schools occasionally attached in English
towns to Mechanics’ Institutes, or in the United States, to the Public
English High School or the Higher Department of a Union School. Young
men who have passed successfully through a gymnasium may be admitted to
the army without passing the preliminary or _Portepée-fähnrich_
examination. Those who complete their time at a _Real_ School have not
hitherto been allowed the same privilege.

3. There is a third and intermediate class called a _Real_ or _Practical
Gymnasium_, and to this, according to the statements of the official
books, the courses of the Cadet Schools have hitherto corresponded. It
appears, however, that there is only one specimen of the _Real
Gymnasium_ now in existence, the Coëln School in the old town of Berlin.
The system here is said to be more practical than the _Gymnasium_, and
less professional or mechanical than the _Real School_.

It is intended during the present year to assimilate the course of
instruction at the Cadet Schools more nearly to that followed at the
_Gymnasium_ or University School; the studies of the senior Cadet School
at Berlin will be raised to a higher standard, but Greek and Hebrew,
which are taught in all gymnasiums, will not be introduced.

The two systems have corresponded as follows :--

  Class in the Cadet Corps.   Age.   Corresponding Class in the
                                     _Real_ Gymnasium.
    6th, or _Sexta_,           12      5th, or _Quinta_.
    5th, or _Quinta_,          13      4th, _Quarta_.
    4th, _Quarta_,             14      Under 3d, _Unter-Tertia_.
    3d, _Tertia_,              15      Upper 3d, _Ober-Tertia_.
    2d, _Secunda_ (at Berlin,) 16      Lower Second, _Unter-Secunda_.
    1st, _Prima_,              17      Upper Second, _Ober-Secunda_.

The Selecta, the Military Class, corresponds with the classes of the
Division Schools, and with the first year’s course of the Artillery and
Engineers’ School.

The plan pursued, both as regards, first, the subjects taught, and
second, the amount of time, is as follows:--

The instruction consists throughout, from _Sexta_ up to _Prima_, of
lessons in Latin, German, French, Arithmetic, History, Geography.
Natural History begins in the _Quinta_, at 12 or 13 years old, with
Botany and Zoölogy; Mineralogy follows, at 14 or 15; Natural Philosophy
at 15 or 16. The first elements of drawing, with the use of rulers,
compasses, &c., begins also in _Quinta_, at 12 or 13. Practice in
regular plan-drawing is gradually and increasingly given in every year.
The first elements of geometry are taught in the _Quarta_, and Euclid I.
47. _Pythagoras_, has to be mastered at 14 years old. Theoretical
Arithmetic, in combination with Algebra, is commenced apparently in the

The subjects taught in the _Secunda_, _Prima_, and _Selecta_, that is,
the course of the Upper School at Berlin, has hitherto been as

  _In the Secunda:_

  Quintus Curtius, Cicero’s Orations, and Ovid’s Metamorphoses; in
Mathematics, the completion of Plane and commencement of Solid Geometry;
Quadratic Equations; the Physical, Statistical, and Ethnographical
Geography of Europe; Ancient History, and History of the Middle Ages,
down to the Thirty Years’ War; a first course of Natural Philosophy;
French and German Composition continued; Theory and Practice of Military

  _In the Prima:_

  Livy and Virgil; in Algebra, Progressions, Logarithms, Exponential
Equations; Trigonometry, Mathematical and pure Physical Geography in
general; Modern History; second course of Natural Philosophy, Heat,
Electricity, Magnetism, Sound, Light; French, Exercise in Speaking, &c.;
History of German Literature; Composition, extempore Exercises; Military
Drawing continued.

  _In the Selecta:_

  Arms and Munitions, and Artillery; Fortification, Tactics, Military
Literature Practical Exercises, Military Drawing and Surveying;
exercises in French and German; Mental Philosophy; Chemistry; and the
Differential and Integral Calculus for those who propose to enter the
Artillery or the Engineers.

The Secunda have weekly--

            6 hours of Latin.
            3  “    of German.
            4  “    of French.
            5  “    of Mathematics.
            2  “    of History.
            2  “    of Geography.
            2  “    of Natural Philosophy.
            2  “    of Lessons in Drawing.
            2  “    of Religious Instruction.
            2  “    of French Conversation.
  Total,   30 hours weekly.

The Prima--

  The same amount in Latin, German, French, Mathematics, Natural
Philosophy, French, Conversation, and Drawing; in History 3, and in
General Geography 2, and Mathematical Geography 1; of Religious
Instruction 1. 33 hours weekly.

The _Selecta_ have--

          4  hours of Tactics.
          2    “   of Military Literature.
          1    “   of Military Law and Regulations.
          5    “   of Artillery.
          5    “   of Fortification.
          2    “   of Plan Drawing.
          2    “   of Mental Philosophy, or English.
          2    “   of Chemistry.
          2    “   of Mathematics.
          2    “   of French.
          2    “   of German.
  Total, 29 hours weekly.

The lessons appear to be going on from 8 to 11 or 12 in the morning, and
from 2 to 4 or 5 in the evening. The pupils have two hours’ drill twice
a week. They get up at half-past 5, have breakfast, and an hour’s
preparation before lessons begin. There are similar hours of study in
the evening from 6 to 8; and some of the pupils also take private
lessons from the teachers.[7] During these special hours of study
(_Arbeitstunde_,) the chambers are visited by the officers and tutors,
assistance is given and diligence enforced. From 8 to half-past 9 they
study as they please; the tutors are a good deal with them in the rooms;
at 10 all are in bed. Wednesday and Saturday are half holidays; on
Sunday they attend morning service in the garrison church, and after
that is over, are allowed to be more or less absent in the town, to be
with their parents, relations, and friends.

    [Footnote 7: Not from the Tutors, but from the non-resident
    Professors and Teachers.]

For the 420 cadets of the Institution at Berlin, there appear to be
about twenty professors and teachers not residing in the school, the
majority of whom are civilians; and in addition to these, twenty tutors
and superintendents resident in the buildings. Of these, sixteen are
military officers, half of whom are permanently attached to the corps,
and half on duty from various regiments, and four are civilians. The
cadets being divided into four companies, each containing so many of the
Selecta, so many of the Prima, and so many of the Secunda, to each of
these companies are attached one captain, one first-lieutenant, and two
second-lieutenants, all of whom, however, take some part in the
instruction; and one civilian (_Civil-Erzieher_) is added with the
especial duty of looking after and assisting the studies of the cadets
of the company.

The holidays are one month in summer (in July and August,) ten days or a
fortnight at Christmas, eight days at Easter, and four at Whitsuntide.

The rules for the entrance of cadets into the army are as
follows:--Those who complete their year in the Prima are considered
to be sufficiently prepared for ordinary admission. They are sent
in to an examination before the Supreme Examinations Board (the
_Ober-Militair-Examinations-Commission_) before examiners entirely
independent of and unconnected with the instruction of the cadets; and
the majority, if they pass, are admitted simply as _Portepée-fähnriche_,
on the same conditions as the young men already spoken of who enter upon
the recommendation merely of the commanding officer of a regiment and
the approval of the commanding officer of an army corps. Like these,
they serve in the regiment, they attend the Division Schools, and in due
time offer themselves for examination for a commission.

Out of this number, however, the sixty who do best are retained, and
reserved to receive in the special military class of the Cadet School
the instruction which the others are to seek in the Division Schools.
These remain another year in the Cadet House, and undergo at its close,
before leaving the Cadet House, their officers’ examination before the
Supreme Board. The thirty best are once more selected, and receive
immediate promotion. Their patents are signed and they join their
regiments at once as second-lieutenants. The other thirty, if they have
satisfied the examiners, receive a certificate of qualification, and
enter with the rank of _Portepée-fähnrich_, and with, the prospect of
receiving commissions without further examination, as soon as vacancies
occur. Any one who fails to pass his examination must enter, if at all,
simply with the rank of _Portepée-fähnrich_, and has to qualify himself
in the Division Schools for attempting a second time the examination for
the officer’s patent.

Such is the system as recently modified. Till quite lately only thirty
were promoted from the Prima to the Selecta, and these thirty, unless
they failed wholly, obtained immediate commissions at the end of the
year. It has been found desirable to introduce the stimulus of
competition, to offer a definite reward in the way of superior
advantages to the best students, and to make it obviously worth a young
man’s while to exert himself, and to be thoroughly diligent during this
final year in the Selecta at the Cadet School.

Young men who, after passing the examination in the Prima, desire to
enter the artillery and engineers, follow the usual course leading to
the Artillery and Engineers’ School. They enter an artillery regiment,
or a division of the engineers; they serve for nine months, they enter
the special school, they are eligible after the first quarter to the
grade of _Portepée-fähnrich_, and at the close of their first year are
examined for their lieutenant’s commission. Those who remain in the
Selecta have the great advantage of passing from the Cadet School
immediately into the Artillery and Engineers’ School as lieutenants, and
commence their course there accordingly at the beginning of the second
of the three years. As, however, the school-year closes at the end of
April, in the Cadet Houses, and begins in the Artillery and Engineers’
School on the 1st of October, these select cadets also pass five months
with their regiment in actual service before recommencing their studies.

The average number who pass in this manner into the Artillery and
Engineers’ School is stated by the authorities of the Cadet House to be
three annually from the Selecta, and six or eight from the Prima.

It can hardly have escaped observation, that the studies pursued as a
qualification for entering the army are, with the exception of the
Selecta, almost entirely non-professional, even here in this part of the
general system, which is in other respects most military in its
character; and the tendency seems to be to carry out to a still greater
extent the theory of continuing to as late an age as possible a good
general education. There is evidently a general desire in Prussia, to
take the officers of the standing army exclusively from the
well-educated or the higher classes.

In the arrangements for the lessons, the very temperate or even timid
use of the stimulus of competition deserves to be noticed. It appears,
however, to have been lately employed with advantage in the highest
class. At the same time, the provision made for giving really good
instruction, and for placing all the boys in close relation with their
teachers, can not but excite admiration. The small numbers of which the
classes consist, and the care which seems to be taken in providing good
teachers, both deserve attention.

The domestic arrangements, without being remarkable for the scrupulous
cleanliness or the magnitude of the new institutions in Austria,
certainly in some respects are more in accordance with English feelings.
The greater privacy afforded by the use of rooms where few live
together, is certainly more analogous to what has been found most
desirable for English boys in large English schools, though most likely
the contrary system is not less well-adapted to the national character
in France and in Austria.

_2. The Division Schools._

There are nine Division Schools for the whole army, one for each army
corps, and they are placed at the following towns:--

Potsdam, Königsberg, Stettin, Frankfort on the Oder, Erfurt, Glogan,
Neisse, Münster, and Trèves.

Here the young aspirant finds himself with nine or ten companions and a
body of teachers amounting to about half that number, appointed by the
commanding officer of the army corps, and differing considerably in
different districts in their talents and ideas of education. They are
often, though not always, selected from officers who have been at the
Staff School, and afterwards at the Topographical Bureau. Their
additional pay for teaching is uncertain; it depends upon the surplus
remaining after the expenses of the household, and the money paid in
purchasing books, instruments, &c., is deducted from the yearly
allowance made to the school by the government. At best it is not high.
It is calculated by the number of lectures, and at the most amounts to
something more than 4_l._ 10_s._ (30 thalers) for the lectures on a
single subject, given, it must be remembered, during the course of
little more than six months in the year. The highest pay given in the
Potsdam School to any one professor amounted to something more than 15
_l._ (100 thalers) yearly for lectures on three subjects, averaging ten
or twelve lectures weekly for about six months. This must be estimated
by a Prussian, not an English standard, being nearly equivalent to
five-twelfths of the annual pay of a second lieutenant in that service.
Still the sum is very low; and this, with some other obvious
deficiencies, injures the working of the schools.

The young candidate for a commission begins a course of Tactics,
Fortification, theory of Drawing and Surveying, Military Literature,
Artillery, &c., Military Essays, and Drawing of Plans, which must be
finished at the school in nine months, although it may be continued
longer in private if the candidate is not prepared to pass his
examination. As long as it lasts, twenty-three hours a week are devoted
to study, besides the time occupied by questions, which the teachers are
required to set from time to time, in order to keep up the pupil’s
previous knowledge of French and Mathematics. The course is divided into
the purely theoretical and practical divisions, the first of six and a
half months, the latter of two and a half. We have already given a very
full account of the studies in p. 188.

The arrangement of studies is systematic, and the number of hours
devoted each week to lectures on the various subjects of study and to
gymnastic riding and fencing, is as follows:

  Fortification,                          4
  Artillery, &c.,                         3
  Tactics,                                4
  Military Surveying (theoretically,)     4
  Military Literature,                    2
  Instruction on Military Duties,         1
  Plan Drawing,                           5
  Gymnastics,                             2
  Riding,                                 2
  Fencing,                                2
    Total,                               29

The subjoined plan gives the exact employment of time for each day
during the week :--


  Hours. |  Monday.           |  Tuesday.      |  Wednesday.       |
   8- 9} |                    | Military       |                   | *
   9-10} | Fortification.     |   Literature.  | Tactics.          |
         |                    |                |                   |
  10-11  | Instruction on     |}               | Plan drawing.     |
         |   Military duties. |}               |                   |
         |                    |}Artillery, &c. |                   |
  11-12  |}Plan drawing.      |}               |                   |
  12- 1  |}                   |                |                   |
  12½-2½ |                    | Gymnastics.    |                   |
         |  Thursday          |  Friday.       |  Saturday.        |
   8- 9 }|                    |                |                   |
   9-10} | Fortification.     | Artillery      | Tactics.          |
         |                    |                |                   |
  10-11} | Military           |  Plan Drawing. | Military          |
  11-12} |   Surveying        |                |   Surveying       |
         |   (theoretically.) |                |   (theoretically.)|
         |                    |                |                   |
  12½-2½ | Riding.            | Fencing.       |                   |

  [* Dinner time, 3 o’clock. Time for studying, from 6 till 8 o’clock,
  or from 7 till 9 o’clock every evening.]

The lecturer has to draw up what is called the thread of the lecture
(_leitfaden_,) a sort of programme containing its leading heads,
intended to assist the memory of the pupils in giving a full account of
it afterwards; and the contents of the different lectures on Tactics,
Arms and Munitions, Fortifications, &c., are written out very minutely
by the students. Ten pages of close print are devoted to these
programmes in Helldorf; and the translation already given (pp. 188-194)
will show that the list of military subjects adverted to is

At the end of the nine months spent at the Division School, the
“_Officier Aspiranten_” go to Berlin for the examination for their
commission. If they can not pass this, they return to study by
themselves for their second trial. Unless by special permission from the
King, they can not try more than twice.

The examination is conducted by the Supreme Commission for Examinations
at Berlin, and has been already described.

The Division Schools were founded at the end of the great War. Their
germ appears in Scharnhorst’s general order in 1810, which, among other
things, instituted three War Schools for the candidate for commissions
(_Portepée-fähnriche_.) These three War Schools seem to have been
changed into the Division Schools in 1813 and 1816. At first, indeed,
they were much more numerous than at present, as their name implies,
there being two Divisions to each Army-Corps. There are now, as we have
mentioned, nine; and Corps School or Army-Corps School would be the more
correct designation.

Their importance as the institutions for special military instruction to
all “_Officier-Aspiranten_” of the army led us to inquire carefully with
regard to their efficiency, and in particular from two distinguished
officers, on whose judgment and scientific experience great reliance
might be placed. One of these, it may be added, possessed constant means
of knowing all the details respecting them.

I. Formerly, it appears, it was not possible to limit these schools to
their true object, purely military instruction. This was the special
object of their creation; but owing to the defective _general_ education
which candidates often brought with them into the army, the Division
Schools were too much used as a means of meeting this deficiency.

II. The opinions we obtained were certainly not favorable with regard to
the present efficiency of these schools. It seemed to be agreed, that
from various reasons, the military education given was susceptible of
much improvement; that some of the Division Schools were really
defective in teaching, whilst none could be pointed to as strikingly
good. But it was also admitted that these blemishes arose from
remediable defects in the working of the schools; that their principle
was in itself sound, and capable of being carried out more perfectly,
and excellently adapted to the object of giving some military
instruction to all desirous of becoming officers of the infantry and

III. The causes assigned for the present defects in the efficiency of
the Division Schools were chiefly the following:--

(_a._) That they were far too numerous.

Educated and scientific as Prussia may be called, it is not found
practicable to supply _nine_ army schools with exactly the sort of men
fitted for the work of education. The pay, it must be added, is
insufficient to attract many, and thus (as we were informed,) although
many officers of intelligence are sometimes not unwilling to leave the
life of drill for the life of education for a year or two, few do so
with the serious purpose of doing it _well_. Neither the position nor
the emoluments tempt them to make it a profession. Officers in command
of the district have made the appointments, and often have
“good-naturedly,” as it was said, appointed unfit persons, known as
studious men.

(_b._) The small number of pupils in each school was also spoken of as a
very great disadvantage, as doing away with all emulation amongst

(_c._) The independence which each school has enjoyed, and the want of
any central body to watch its working and regulate its system, is also
said to have had bad results. The teaching has been far from
uniform,--in one school energetic, in another lax; in one school the
most important subjects taught, in another, a little of everything; in a
third, some special crotchet of a teacher. This has acted badly on the
examinations, since it was thought hard to reject an “_aspirant_” who
had done parts of his work well, and had been evidently ill taught or
superficially instructed in others.

The remedies suggested were,--

(1.) Considerably to diminish the number of these schools. This, we were
told, was about to be done by reducing them from _nine_ to _three_. Such
a course would obviously tend to remedy two of the evils complained of.
It would give a larger choice of teachers, and afford more liberal means
of remunerating them, and a larger attendance and competition of pupils.

(2.) To place the schools under the more direct regulation and
management of the Central Educational Department at Berlin. This step
would improve their teaching by subjecting it to constant inspection and
reports. It would insure uniformity in the system of instruction and
subjects of study; and, when combined with the presence of able
teachers, it would enable the Board of Examiners at Berlin to pursue a
more strict and unvarying course in rejecting ill-qualified candidates.
By these means the teaching in the school would probably become more
definite and higher.

One other point was mentioned to us as doubtful. It was thought that the
time for attending the Division School came too soon after a young man’s
entrance into the army, when he had but recently obtained his liberty,
and was likely to be much more unwilling to be sent to school again than
might have been the case a year or two later. General von Willisen, who
urged this objection to us, was consequently for deferring the
attendance at the Division Schools several years in an officer’s life.

We should add, however, that as in Prussia a young _Officier-aspirant_
is still partly a private soldier, we were told that many were glad to
exchange the severity of regimental discipline for the Division School.

_3. The United Artillery and Engineers’ School at Berlin._

Young men desirous of obtaining commissions in the Artillery or
Engineers follow the course which has already been described. They join
either with a nomination from a colonel of artillery or engineers, or as
scholars from the Cadet House. They submit themselves for examination
for the grade of Ensign (_Portepée-fähnrich_); they serve their time
with the troops, they go through a course of professional study, and are
examined in it for their officer’s commission by the Board at Berlin. If
they come from the highest class, the _Selecta_ of the Cadet House, they
have the privilege of joining the corps with the rank of officer.

In these respects the system is the same for them as for the
_Aspiranten_ in the other arms of the service.

The distinctions are, that first, in the preliminary or Ensign’s
Examination, a somewhat greater acquaintance with mathematics is
required from them; secondly, that they prepare for the Officer’s
Examination, and follow their professional studies, not in the Division
Schools, but in a separate Special Arm School at Berlin. Moreover, nine
months’ service with the troops, instead of six, is required before they
can enter the Special Arm School. They enter it also with the rank only
of corporal, and are not eligible to the grade of Swordknot Ensign until
they have passed three months at least in the school.

Their Officer’s Examination before the Supreme Board at Berlin takes
place after nine months more, at the end of the first year at the
school, and after passing they are eligible to the rank of officer.

When a vacancy occurs their claim to an actual commission is considered,
and the usual formalities are fulfilled. Their names are submitted for
approval to the officers of the corps, and with that approbation laid
before the King; and they thus in due time obtain their rank as
Sub-Lieutenants respectively of Artillery or of Engineers.

This rank, however, is provisional, and their position is that of
supernumeraries. Their education as officers may be complete, but their
education as officers of Artillery or of Engineers has scarcely in fact
commenced. They have before them a third examination, that of the
Special Arm, their _Vocation-trial_ or _Berufs-prüfung_. Or, more
correctly speaking, they have not one but two to pass, for the third
examination is divided into two stages, one to be passed at the end of
each of the two years which yet remain of the course. It is only when
these are completed, after a three years’ stay, that the young man is
finally allowed to join his corps as a second-lieutenant.

Failure in the officers’ examination at the close of the first year is
attended with the penalty of returning to the corps and resuming service
in the ranks with the troops. Whether or not the rejected student may be
permitted to return after an interval to join again the classes of the
first year, or after passing, upon a second trial, the officers’
examination, to enter the classes of the second year, will depend upon
the extent of his failure.

Failure in the examination at the close of the second year is similarly
visited with the punishment of return to the corps. As they have already
passed the officers’ examination, they may endeavor to effect a transfer
to a regiment of the line; or, under certain circumstances, they may be
permitted to study privately in preparation for the third year’s course,
and may offer themselves for a second trial.

If a student fails in his last examination at the close of the third
year, he may be allowed, in like manner, under favorable circumstances,
to re-enter the third year’s classes, and try to qualify himself by an
additional year of study, losing, of course, his seniority. Otherwise,
he joins the corps as a supernumerary, with the pay of an infantry
officer, and waits till he can obtain a commission in the line.

Candidates for commissions in the engineers enter the corps, it should
be observed, originally as volunteers, finding their own clothing, and
receiving no pay; but as soon as they enter the school they are
regularly paid by the state, and receive their pay in the usual course
of the service from the division to which they belong.

The studies of the three years are arranged in accordance with the
system that has just been described. Those of the first year are common
to the two arms, and correspond, in a general way, with what is taught
in the Division Schools or in the highest class of the Cadet House.
Those of the second year are devoted to the special arm subjects. In
Mathematics, Artillery, and Fortification, the lectures are common to
the artillery and engineers; in drawing they are divided.

In the third year a considerable separation takes place. Mathematics are
still taught, and there is a special class of the most advanced students
in the Differential and Integral Calculus, the Higher Geometry, and in
Analytical Mechanics and Hydraulics; this, however, is purposely
restricted to about one-third of the class, by raising the requirements,
if necessary.

The course is divided in each year into the theoretical and the
practical part. The year commences in October with the former, and the
studies for the nine months succeeding are for the most part theoretical
only. In June the examinations take place. July, August, and a part of
September are given up to practical exercises. Something like the last
three weeks of September are allowed for a vacation.

The general control of the school is in the hands of the General
Inspectors of the two services, the artillery and the engineers. These
two are the _Curators_ of the school and form the _Curatorium_. They
make their reports to the General Inspector of Military Education, of
whom mention has already been made. The immediate management is
intrusted to a director, who is a field officer of artillery or
engineers, of the rank of commandant of a regiment, and he has a
captain, appointed by the _Curatorium_ as his assistant.

There is a Board of Studies, of which the Director is chairman,
consisting of the Senior Professor of Mathematics, of the Instructors of
Artillery and Engineering in the third Cœtus, and of an equal number of
officers of the two services named by the Curators.

Four officers, three from the artillery and one from the engineers,
acting under the captain, are charged with the care of discipline and
order; these are the _Direction_ Officers.

There are twelve military and eleven civilian professors and teachers.
Among the military professors and teachers may be included any of the
direction officers.

The examinations of the first year are conducted by the usual Board, the
Supreme Military Examinations Board; but for those of the second and of
the third year, there is a separate board, chosen from the two services
by the Curators, and otherwise unconnected with the School.

The numbers in the school vary from 216 to 240. In time of peace about
five are yearly admitted for each regiment of artillery, and two or
three for each division of engineers. The great majority have entered
the army from the usual places of civil education, a few from the Prima
of the Cadet House, on the same terms as the others, and a small number,
who are usually among the best pupils in the school, from the Selecta,
who come as officers, and after a short service with the troops, enter
the second year’s classes, provided there is room, preference being
always allowed to the students already belonging to the school, who have
succeeded in passing the examination of the first year.

The Artillery and Engineers’ School buildings stand in Berlin itself, in
the principal street, _Unter den Linden_, No. 74, near the Brandenburg
Gate. They bear the following inscription: _Artillerie und Ingenieur
Schule. Stiftung Friedrich Wilhelms_ III. M.DCCC.XXII.

On the occasion of our visit to the school, we were allowed by the
kindness of the authorities to be present at some of the lectures. The
students of the second year were attending the course on the History of
the Art of War, and the immediate subject was an account of and
criticism on the battle of Blenheim. The young men, about forty-five in
number, were ranged in desks facing the Professor, but not in the manner
of an amphitheater. The lecture was interesting, animated, and generally
instructive; it was perfectly professorial in character, and the young
men took notes. A class of the students of the first year, thirty-five
in number, were engaged in topographical drawing. The artillery division
of the third year students were in another room, listening to and busily
taking notes upon a lecture (also professorial) on the construction of
gun-carriages: the number was about forty-five.

Only the students of the first year are lodged in the building; and
owing to the unusually large number lately admitted, an adjoining house
has been taken to afford additional room. The accommodation in general
is rather limited. Two stories in the upper part of the building are
occupied by the somewhat scantily furnished chambers; there appeared in
some cases to be two young men in one room, in other cases four, or as
many as six or seven to a bedroom and sitting-room. The students who
lodge in the building dine together in a mess-room; and there is a
billiard-room, with coffee-rooms adjoining it, for the general use,
looking out from the ground floor front into the Unter den Linden. There
is a library, a small laboratory attached to the lecture-room employed
for the subjects of Chemistry and Natural Philosophy, and a small
collection of apparatus required for illustration on the latter subject.

On quitting the school, the engineer students, as soon as they obtain
their commissions, are employed for three years with a Division of
Engineers; then for three years in a fortress to superintend buildings;
and then again with a Division of Engineers. They are then eligible to
promotion as first-lieutenants.

The artillery students, in like manner, join and serve with their

Promotion in the artillery is by regiments, in the engineers it is
general throughout the whole corps.

We should not omit to call attention to the fact, that the only instance
which has come to our knowledge of the promotion of _officers in their
own arm of the service_, being made contingent on their passing an
examination, is to be found in the Prussian Artillery and Engineers.
First-Lieutenants belonging to those corps must pass an examination
before they can be promoted to the rank of captain. This regulation does
not exist for any other part of the Prussian service, and it is
considered a great grievance by the officers of those corps, as it may
be exacted at the age of forty, from the most highly educated officers
of the Prussian army.

The pay of subaltern of engineers is somewhat higher than that of the
artillery, infantry, and cavalry. Above the rank of subaltern, the pay
of the artillery, cavalry, and engineers, is on an equality, but
superior to that of the infantry. The engineers have, moreover, a
prospect of employment of a civil nature when they return from active
service; to lucrative positions of this kind they are not unfrequently

It should be mentioned before quitting the subject, that all the
officers of the artillery and engineers are bound, in consideration of
three years’ maintenance in the school, to serve a period of six years,
before they can exercise the usual privilege allowed to Prussian
officers of withdrawing from the service.

[_A particular account of the Course of Instruction in this School will
be given in a separate article under the title of the Institution._]


The War School (_Kriegs-Schule_) in Berlin has undergone many changes
since its foundation in the time of Frederick the Great. It is now the
Staff School of Prussia, _i.e._, the only, or almost the only, means of
obtaining a staff appointment is by passing through it, and the
education given is particularly intended to form staff officers. Its
plan and methods of teaching differ, indeed, from the very commencement
from the French Staff School, and bear much more resemblance to the
senior department at Sandhurst, with the exception that the senior
department is not at present a necessary means towards a staff

Thus the _Kriegs-Schule_ does not take young men of twenty-one or
twenty-two and educate them (like the French Staff School) for the staff
and the staff alone. Its pupils are men of twenty-five or twenty-six,
officers of three years’ standing, or five years’ service since their
first entering the army. At this comparatively ripe age they become
candidates for entrance to the Staff School, and, if admitted, they
spend there three years of laborious study, with no very brilliant
prospects to crown it, as only a very small number obtain what may be
called the lowest prize, admission to the Topographical Department; and
out of these only two or three yearly of the most distinguished pupils
gain the Staff. The rest return to their regiments, and are employed as
adjutants or as teachers in the Division Schools.

The process of entrance is as follows:--An officer of three years’
standing desires to go to the Staff School. Any one may send in his name
as a candidate for the entrance examination to the minister of war,
having obtained a certificate from his superior officer that he
understands his regular duty, has no debts, and is capable, both as
regards his abilities and bodily strength, of making a good staff
officer. Little difficulty is made about admission to become a
candidate, nor is there any regulation to limit the number from any one
corps or regiment, so that there may be often found in the Staff School
more in proportion from the infantry than the cavalry, and _vice versâ_.
Some regiments, we heard, hardly ever send officers to the school.
Practically, indeed, the regulation requiring three years of active
service bears hard upon the artillery and engineers in comparison with
the other services; for, as the officers of these two corps only enter
their own school after they have been near a year in the service, and
spend three years there, they must have been in the army nearly seven
years before they can enter the Staff School.

The candidate for the Staff School is examined in the capital of the
province in which his corps is stationed. The examination is early in
April, and it is held at the provincial town instead of Berlin, in order
to diminish expense. But the questions are sent from the board of
examiners in Berlin, and the same are given in the different provincial
towns at one and the same time. The examination is much on the same
subjects, and requires about the same actual knowledge as that which was
passed at least three years before for a lieutenancy, but owing to the
difference of age, the questions are put and are expected to be answered
in a much more scientific form than on the first occasion. Thus, we were
told, such an essay as “Give an account of the wars of Francis I. and
Charles V.,” would at the _Kriegs-Schule_ Examination rather be stated
thus: “What was the influence of these wars on the policy and religion
of Europe?”

The examination is entirely upon paper; it occupies from ten to twelve
days of about five hours daily, the superintending staff officer in the
province presiding over it. But his business is limited to reading out
the questions sent to him, and taking care that no books are brought in,
or any improper means used. The answers to the questions have to go
through a double ordeal, the military ones being first examined by some
of the staff of the general commanding in the province, and afterwards
by the commission of examiners at Berlin. The final decision rests with
the chief of the Prussian staff, who recommends the successful officers
to the minister of war.

There is an average of sixty or seventy candidates yearly. Only forty of
these can be taken. If some additional case seems meritorious, the
officer may obtain a promise of appointment, but his entrance is
deferred. It is not uncommon to try more than once.

The entrance examination passed, the school opens on the 1st of October,
to continue its lectures, with a fortnight’s break at Christmas and at
Easter, till the first of June. It has its 120 pupils, divided into
their three classes, one for each year, working (with only little of
practical work) under professors, military for the lectures of a
military, and civil for those of a non-military character. No
difficulty, we understood, is found here, as we had heard to be the case
at St. Cyr, in enforcing the fullest attention to the lectures of the
civilian professors; each is respected according to his knowledge of the
subject, and it would be thought as absurd for a military professor to
undertake a non-professional subject, as _vice versâ_.

The method of working is that so commonly followed in the Prussian
universities of listening to numerous lectures, and taking copious notes
upon them. Nearly five hours daily, from eight in the morning till one,
are often continuously occupied in this manner; for although only twenty
hours of attendance are absolutely exacted weekly (an amount which to
our own students would seem more than ample) ten more are said to be
necessary to enable an officer to do any justice to the various subjects
of which he is expected to show some knowledge at his examinations.

These lectures are usually read aloud; there is no questioning and
answering. The student, after five morning hours, must spend at least
five or six more in copying them out, or in writing an essay on the
subject of some of the lectures. Of these one is given about every three
weeks, but only on military subjects. They are carefully corrected and
sent back to the student with the notes of his teacher, and their merit
influences the final estimate of his whole work.

Besides this daily work, the examinations are at once a stimulus and a
means of testing proficiency. These occur every three months, but the
yearly ones are the most important. They are entirely upon paper. In the
quarterly ones the papers are only given for two hours at a time daily,
and take the place of two common lectures; in the other examinations
they are daily for four or five hours. They are entirely essays upon the
numerous subjects lectured on in the school, History of War, Philosophy,
Tactics, &c.

Perhaps there is no better way of giving an idea of the mode of studying
than by a statement of some of the subjects of these essays. They have
been supplied to us by the kindness of Lieutenant Berger, of the 28th
Infantry, from whom we have received much valuable information on the

    _General Essays._

  On Tactics:--I. A Prussian Division, added to which is,--

    1 Regiment of Infantry,
    1 twelve pounder Battery,
    1 Cavalry Regiment,

  is in retreat from Goldberg to Jauer (in Silesia.) The enemy is
following. A position is to be taken up to stop his advance, whatever
his numbers may be.

  A map of the position being given:--

    (_a._) Describe the position.
    (_b._) Draw up the troops.
    (_c._) Write an explanatory criticism.

  (To be worked at home in two days.)

  Three Corps d’Armée march against Berlin from different points. The
army in Berlin is ordered to meet them. (To be done in five hours.)

  Permanent Fortification. For what purpose are the fortifications in
the main ditch intended, and how are they to be constructed? (Five

  Military Geography. The Saxon land between the Elbe and Saale, and its
influence upon the operations of war in North and South Germany. (Five

  Criticism on the organization of the French Battalion. (At home in one

  _Examination Essays, Staff School.--Military History, Tactics and

  1. In what respects did the earlier form of military art,
strategetically and tactically, favor defensive wars _generally_, and in
particular assist Frederick II. in the Seven Years’ War? (Two hours.)

  2. The duties of the Staff in time of peace. (Two hours.)

  3. Position of Landwehr Officers on and off duty. (Two hours.)

  4. What is the value of the Cavalry formation _en échelon_, with
particular reference to the Austrian mode? (Two hours.)

  5. Is only one sort of Infantry necessary, or is Light Infantry
essential? (Two hours.)

  6. How may the mobilizing of an Army be best expedited? (Five hours.)

  7. Describe the different sorts of field works particularly used in
war. (Two hours.)

  8. How is the Artillery of a Corps d’Armée to be used in the different
emergencies of battle? (Five hours.)

  _Literary and Scientific._

  1. The Geological characteristics of the country between the
Carpathian Mountains and the Vistula on one side, and the Yaldai
Mountains and the Dnieper on the other. (Two hours.)

  2. By what political conjunctures was the power and influence of
England peculiarly advanced in the 18th century? (Five hours.)

  3. On the magnetic effects of the electric stream. (Two hours.)

  4. Characteristics of Greek literature, and its chief authors in the
time of the Peloponnesian War. (Two hours.)

The knowledge required is seen in the account of the Staff School,
(p. 395) and in the list of the Lectures given above. Besides military
subjects, it includes a very full course of Ancient and Modern History,
an addition to the History of War (which last alone occupies seven hours
weekly for the last year,) a good deal of Logic and Philosophy of Art
and Literature, and of Political Economy. Some of these lectures have
probably been introduced from the school, having a double object, that
of giving a diplomatic as well as a military education. This was the
original idea of Frederick the Great, who, in all his plans of military
teaching, laid a great stress on the general literature which he himself
valued so highly. This diffusive study is a strong contrast to the
principle of “little, but well,” and to the constant practical exercises
in the laboratories insisted on by the early teachers of the Polytechnic
School in France.

The following is the plan of the lectures for the three years. Twenty
lectures a week are the minimum:--

_Course of First Year._


  Tactics,                       4 hours.
  Artillery,                     3   “
  Field Fortification,           2   “
  Military and Political
    Administration and Economy,  2   “
  Mathematics, Pure and Mixed,   6   “
                                17 hours.

  For Choice.

  Universal History,             4 hours.
  Universal Geography,           3   “
  Physical Geography,            4   “
                                10 hours.
  Total, 27 hours.

  [_Numbers printed as shown._]

  _Course of Second Year_

    Tactics,                        4 hours.
    Permanent Fortification,        2   “
    Special Geography and Geology,  4   “
                                   10 hours.

  For Choice.
    Universal History,              4 hours.
    Mathematics,                    6   “
    Logic,                          4   “
    Physics,                        4   “
    Lectures on Horses,             2   “
                                   20 hours.
                            Total, 30 hours.

  _Course of Third Year._

    History of War,                 7 hours.
    Staff Duty,                     3  “
    Art of Sieges,                  2  “
    Military Jurisprudence,         1  “
                                   13 hours.

  For Choice.
    General History of Literature,  4 hours.
    Mathematics,                    6  “
    Higher Geodesy,                 3  “
    Chemistry,                      4  “
                                   17 hours.
                            Total, 30 hours.[8]

    [Footnote 8: Lectures each week in the War School, Prussia.

    1Y First Year.
    2Y Second Year.
    3Y Third Year.

    WAR SCHOOL.                    | 1Y | 2Y | 3Y
    Mathematics, Pure,             |  3 |  3 |  3
       “        Mixed,             |  3 |  3 |  3
    H. Geodesy,                    | .. | .. |  3
    Physical Geography,            |  2 | .. | ..
    General      “                 |  4 | .. | ..
    Special      “                 | .. |  4 | ..
    Universal History,             |  4 |  4 | ..
    General History of Literature, | .. | .. |  4
    Logic,                         | .. |  4 | ..
    Physics,                       | .. |  4 | ..
    Chemistry,                     | .. | .. |  4
    Veterinary Art,                | .. |  2 | ..
    Tactics,                       |  4 |  4 | ..
    Artillery,                     |  3 | .. | ..
    Fortification, Field,          |  2 | .. | ..
           “        Permanent,     | .. |  2 | ..
           “        Sieges,        | .. | .. |  2
    Military Administration,       |  2 | .. | ..
    History of War,                | .. | .. |  7
    Staff Duty,                    | .. | .. |  3
    Military Law,                  | .. | .. |  1
    French,                        |  6 |  6 |  6
    Russian,                       |  4 |  4 |  4
                Total,             | 37 | 40 | 40

    It would be impossible to enter on a detailed criticism either of
    these lectures or of the essays mentioned in the note above which
    evidently imply great study. We invite a comparison with the
    French plan, which we have given elsewhere, but the difference of
    age must be taken into account. The mathematical course at this
    school is,--

    1st year. Plane and Spherical Trigonometry, Quadratic Equations,
    involving several unknown quantities, the Binomial Theorem, and
    the Elements of Analytical and Solid Geometry.

    2d year. Analytical Geometry and the Differential and Integral

    3d year. Mechanics, Statics, Dynamics, Projectiles, and slight

    Only the first year is obligatory.]

It will be seen that the above course is entirely theoretical; no
practical work (as in France) relieves the sedentary labor of ten hours
daily for more than eight months of the year. But as soon as the first
year’s course is ended, all the officers who are supposed to know
drawing before coming to the school, are sent into the country for three
weeks to practice military drawing and surveying; and those of the third
year go through (also for the same period) a similar course of staff
duty. These last are sent under the direction of the officer who is
Professor of Staff Duty at the School; each student officer gets his
separate orders, and they meet and are told off every morning for their
day’s work, reconnoitering fortresses, surveying the frontiers between
Austria and Prussia, &c., &c. During the remaining three summer months
the students are sent in successive classes to those arms of the service
which are not their own, and after the usual military exercises are
completed they must bring back with them a certificate of proficiency
from the commanding officer. This amount of time was spoken of as being
too little.

If we are surprised at not finding a greater amount of practical work
included amongst the labors of the school, we must remember that it is
chiefly postponed to a later period of the officer’s career, when the
probability of his being required to use it on the staff is greater.
This is when he has gained his place in the Topographical Department,
and is working there upon trial to test his fitness for the actual
staff. He is then employed during winter in working on the Theory of
War, and during summer in military surveying and drawing.

Such is the method and extent of the officer’s work at the Staff School;
a few more words are needed on the character of his examinations, which
here as everywhere else must greatly influence the character of the

There are no less than nine examinations during the three years, one for
every three months, but the final one at the end of each year is the
more important, as a sort of summing up of the year’s work. In marking
for this the merit of the essays done at home is taken into account. The
result in each branch of work and on every examination is entered by the
several professors in a book kept at the directory, and the pupils have
a right to inspect the report of their own work. The net result of his
own three years’ work is also sent to the officer after leaving the
school through the authorities of his regiment. The certificate of this
contains the criticism on each branch of his work in detail.

The subjects given for essays will show the nature of the chief
examinations (_i.e._ those at the end of each year;) four or five hours
is the time generally allowed to a difficult subject, the examination
stretching over a number of days, in proportion to the subjects taken
up. The pupil may bring in his notes of lectures, on which extraordinary
care is bestowed, and which must contain everything that can be said on
the subject. Much value is said to be attached to the rapidity with
which an essay is worked, as showing a quality valuable in an officer.
There is, as we have observed, no _vivâ voce_ of any kind in this
School. Some competition exists in the Staff School, (and it is almost
the only Prussian school where we find it,) for the knowledge that only
eight or ten out of the forty pupils can obtain the Topographical
Department, and only two out of these eight or ten, the staff, acts as a
competitive stimulus. We must add, however, that although a minute
account of the _positive_ merits of the pupils is drawn up and sent to
them at the end of their career, they have no means of ascertaining
their _relative_ positions; and this may always leave room for doubt,
whether the places in the Typographical Department and on the Staff are
strictly given by merit, or whether patronage does not here step in.
Another ambiguity may be remarked in the fact that the relative
importance of the subjects of study is not known. It may of course be
surmised, that a knowledge of the Peloponnesian War is not marked so
highly as that of the Seven Years’ War; but any indefiniteness as to
what is or what is not important, will generally lead to an attempt to
know something _of all_ the subjects mentioned, and it would undoubtedly
be better to affix its definite value to every subject. It would prevent
what seem to us valid objections to the present system of the Staff
School, the attempt to crowd in too many subjects, instead of mastering
thoroughly a few.

The final examination having been completed in June, the student goes
through the three weeks of staff duty we have described, and finishes
his last three summer months in that branch of the army in which he has
not yet served. He then returns to his regiment, where he receives the
certificate of his three years’ work. But no list is published of the
order of merit in which the officers stand. If the certificate is
satisfactory, he forwards it to the Chief of the Prussian Staff, with a
request to be employed in the Topographical Department of the Staff. If
this is granted, he receives an order to join it in about two years,
_i.e._ about nine or ten years after first entering the service.

About eight officers are yearly sent to the Topographical Department,
and serve there for two or three years, surveying and drawing in summer,
working at military science in the winter. The correction of the
Topographical Map of Prussia is in their hands. Finally, two out of
these are selected for the Staff; the remainder return to their
regiments, to become adjutants or to teach in the Division Schools.

The most immediate advantage of being in the staff corps is promotion to
a captaincy at any age, which, considering the extreme slowness of
promotion in Prussia, may be termed an early one. This is generally
gained within two or three years after joining the corps, _i.e._ at
thirty-three or thirty-four. In other corps hardly any one has a chance
of becoming captain till after forty.

We may add, that the number of officers in the Topographical Department
is about forty, on the staff itself sixty-four. No one belonging to the
staff is below the rank of captain, or above that of colonel. Every
general of division has one officer of the staff attached to him, and
two adjutants, the first nominated by the chief of the staff, the two
last by the king, and these two belong rather to the officer than to the
general. They are not removable with him. The adjutants are not officers
of the staff, though they are often chosen from amongst those who have
been at the Staff School. They are nominated by the king upon reports
sent into him by the generals of division, and the appointment is not
considered a great prize, as it implies neither extra pay, promotion,
nor permanency; the adjutants are promoted in the usual course, and
then, upon promotion, return to their regiments. The adjutants of
battalions and regiments are appointed, like our own, by the officers
commanding. The name of aide-de-camp does not exist in the Prussian
service, but that of adjutant is used in its place.



There are three Military Orphan-Houses in Prussia for the children of
soldiers, two for boys, one at Potsdam, and the other at Annaburg, and
one for girls at Pretzch. Although intended for orphans, they receive
children whose parents are too poor to provide for them. They receive a
good elementary education and are brought up for trades, and can make
their selection between a civil and a military career. The English
Commissioners report that they found 800 pupils in the Orphan-House at
Potsdam, of whom 200 were under the charge of female teachers; 520 were
in the senior department, including thirty-six in the music class, who
will go into the Regimental Bands, and about twenty who formed a
separate military class, who would probably enter the Artillery School.

The School at Annaburg, and the subsidiary Girls’ School at Pretzsch,
are both Protestant in character; no religious teaching is supplied for
Roman Catholics. Roman Catholic boys are all sent to Potsdam, and Roman
Catholic girls are provided for in ordinary schools, and in private
families, and payment made on their behalf out of the funds of the

Dr. Bache in his “_Report on Education in Europe_,” gives the following
account of these institutions.

_Military Orphan-House at Potsdam._

  This institution was founded in 1724, by Frederick William the First
of Prussia. The reputation of Franke’s Foundations induced this monarch
to rival the benevolence of the clergyman, and to establish on a scale
proportioned to his greater means, a house for the education of the
orphans of his soldiers. While, however, the recipients of Franke’s
bounty are free to choose their career in after life, and only so far
bound to the institution, as a sense of gratitude may prompt, the youth
who passes through the Military Orphan-house of Potsdam, must enter the
military service for twelve years. Three of these, indeed, are the term
of service of every citizen, and I believe the three years in the
non-commissioned officers’ school are now counted as part of the twelve,
and thus the actual number of extra years of service is reduced to six.
The institution began with one hundred and seventy-nine children, both
girls and boys being received; this arrangement continued until a few
years since, when the girls’ school was removed from Potsdam, and the
establishment at present is for male pupils only. There are between
three and four hundred in the elementary or boys’ department. In the
early history of the orphan-house two attempts are recorded to introduce
manual labor, as a profitable speculation; neither of which appears,
however, to have succeeded. The first of these, the manufacture of
Brabant lace, was introduced in 1743, and after various modifications of
the mode of applying the labor of the children, it was finally abandoned
in 1795. In 1744, the culture of silk was introduced extensively
throughout the kingdom, and especially enjoined at the orphan-houses;
but this attempt was not more successful in the end than the other, and
the culture is not kept up in this institution.

  The present spacious buildings were chiefly constructed under the
reign of the founder and of Frederick the Great. Additions have,
however, been made from time to time since, and the whole plan is hardly
yet completed. The institution may be considered as divided into three
departments or schools; an elementary school, (called the Boys’ House,
_das Knabenhaus_,) a trade school, and a music school. The buildings for
the elementary school are erected about a spacious court, which serves
as an exercising and play-ground. On the ground floor are the refectory,
in which all the youth from the different schools composing the
institution, meet three times a day, and the study and play-rooms,
lavatory, &c. The study-rooms form a long range, and when the doors of
communication are opened, one teacher can superintend the whole of the
classes. The school-rooms are on the first and second floors, and are
calculated for divisions of forty boys each. There are six dormitories,
furnished with wooden or iron bedsteads, the latter having been more
recently introduced and found to answer well. The bedding consists of a
straw bed beneath, and a mattress of hair above. Each dormitory is
superintended by a teacher, who sleeps at one end of it. There are also
dwelling-rooms for the teachers, officers, &c., and in the court a very
large wash-house, with a drying-room above it.

  The buildings occupied by the trade and music schools are separated by
a street from the others, and with the dwellings of the officers, a room
for gymnastic exercises, and musical practice, and the workshops, form a
second immense series of structures. The infirmary is near to them, and
is under a separate direction; subordinate, however, to the general
executive body. It is divided into rooms assigned to patients suffering
from different complaints. A schoolmaster gives instruction to the
convalescent. The arrangements in the dormitories of the trades’ school,
are similar to those used in the army, and the Superintendence and
discipline are strictly military.

  The part of the building occupied by the music school, contains
separate rooms for practicing by individuals, class-rooms, and
dormitories. There are rooms in the main pile for the meetings of
teachers, for a small library, &c.

  The executive board of this school depends partly on the ministry of
war, and partly on that of public instruction; the former, however, is
the controlling authority. Under this board is the military
superintendent, or director, to whom the chaplain, the secretaries, the
economist, the military superintendent of the day, the teachers,
commandants of companies, the inspectors of the trades’ and music
school, and other officers, are directly responsible. The clergyman is
the superintendent of the elementary school, and has a general charge of
all the intellectual and religious instruction.

  The orphan children of soldiers are received for maintenance, at any
age, by the authorities of the establishment, but if under six years,
are boarded with their friends or others until six, and then admitted
into the house at Potsdam; they remain there until fourteen or fifteen
years of age, and, if of sound constitution, are transferred to the
trade, or to the music school, where they remain four years, and whence
they pass, if their conduct has been good, to the school for
non-commissioned officers. I have never seen a body of young men all so
well physically developed as the pupils of the trade school, a result
produced by constant attention to their education on this point.
Children who are not healthy, or who have failed in the elementary
school, are apprenticed at fourteen, and the institution ceases to have
the charge of them.

  In the _Elementary School_, the usual branches taught in the common
schools of Prussia are pursued, including reading, writing, arithmetic,
the German language, geography, drawing, religious instruction, and a
little natural history. The boys are divided into four classes,
according to their proficiency, and all the classes below the first are
subdivided into two sections, each being under the charge of a teacher,
and having a separate recitation room. These sections contain about
forty pupils each. A monitor of order from among the pupils, has charge
of a section on entering and leaving the school-room, and render such
service as the master requires during the lesson; he is assisted by one
of the class in the distribution of the books, slates, and other
implements of instruction. The teachers keep each a roll, upon which the
character of the recitation and conduct of the pupils is entered, and
which is examined weekly by the chaplain, and submitted to the board of
teachers at their meetings. No youth, who is below a certain grade upon
this roll, is permitted to enter the trades’ school. There are about
five hours of instruction on four days of the week, and about
twenty-three in the whole week. The holidays are, a week at Easter, four
days at Michaelmas, a fortnight in the latter half of July, and from the
twenty-third of December, to the second of January. For those who have
no friends to go to, the Christmas festivities are kept up in the
school, as in the private families of the country.

  The board of teachers meet once every fortnight, and the director, or
his substitute, or the chaplain, presides. At their meetings, all
matters relating to instruction and discipline are discussed.

  The form of the discipline of the school is military, but a spirit of
mildness tempers it, suiting it to the age of the pupils. The boys, in
general, are divided into four companies, each of which has a
commandant, (a non-commissioned officer of the highest grade,) who has
charge of the instruction in military exercises, and ranks with the
teachers of the school. These companies form a battalion, and are
drilled without arms, and inspected by the director, or an officer
appointed by him. In turn the commandants of companies, acting as
officers of the day, have general charge of the military and police
duties. Two of the teachers, also, in turn, act as inspectors of the
day, and have the general superintendence of the pupils in study and
recreation hours, in the duties of personal police, at meals, and in the
dormitories, relieving each other at different parts of the day. They
are co-ordinate in authority with the officer of the day, and he is
expected to relieve and aid them in the maintenance of order. These
officers report immediately to the director.

  The four companies are subdivided into sections of eleven, over each
of which one of the boys is placed, with the title of overseer, or
corporal, and he is responsible for the good order of his section, and
may be assisted in his duties by one chosen from it. From among these
corporals one is selected for the general control and superintendence of
the others, and marches the company to the lavatory, to meals, to the
dormitory, &c., being responsible for them whenever they are collected
as a company. The boys composing a section are placed at meals upon the
same side of the table with the corporal who has charge of them. The
younger pupils do not join these companies at once, but are kept
together in a division which is under female superintendence, has a
separate overseer, and is under different regulations as to rising,
going to bed, and other particulars of discipline and police from the
elder pupils.

  All the duties of domestic and personal police, and some of those of
domestic economy, are performed by the boys enrolled in the four
companies. They clean their own shoes, brush their own clothes, attend
to the police of the different parts of the building, serve the meals,
and make their beds. That the various duties may be attended to in an
orderly way, there are, besides those already spoken of, special
overseers appointed among the pupils, who have general charge of them
while engaged in certain duties, and of particular localities. Thus
there is an overseer of the room where the clothes and shoes are kept,
who has charge of the exchange of the Sunday for week day dress, and
vice versa; an overseer of the room where the shoes are brushed and
blacked; an overseer of the lavatory; four superintendents of
cleanliness, who direct the pupils while washing and combing their hair;
one of hair cutting; two of serving the table, who have charge of a
detail of thirty pupils, who serve and clear the tables and clean the
knives and forks; one, of the manual labor classes; one, of the sick in
the hospital; one, of those who are unwell, and must report to the
physician; one, of the lights; one, to prevent the passing of bounds;
one the pupils who sing the liturgy in the church; one to conduct the
pupils, whose shoes require repairs, to the shoemaker; besides, those
for the classes and the younger boys, already mentioned, and a few
others. I make this enumeration in order to show the minuteness of the
arrangements for police and discipline, and the extent to which they are
conducted by the pupils themselves. The selections for appointments are
made by the teachers and officers, and submitted to the chaplain and
director for their approbation. A part of the pupils employed as
superintendents receive small pecuniary allowances, and all enjoy many

  Some of the pupils, who are found to have a taste for music, receive
special lessons, and are employed, when sufficiently proficient, to give
the signals for the different duties of the day. Eight pupils are thus
selected to be taught the bugle and fife, and twelve the drum.

  In regard to conduct, the pupils are divided into four grades,
according to the reports of the teachers and officers, a revision of the
classification taking place every quarter, and the director having, in
the meantime, the power to displace a pupil in a case of emergency. The
first class grade is composed of pupils distinguished for unvarying good
conduct, and on holidays its members are allowed to leave the
orphan-house alone to make small purchases at discretion, and are
neither subject to corporal punishment nor to the stoppage of their
meals. The second class is composed also of meritorious pupils, but of a
lower grade of conduct than the first; they are permitted to leave the
school sometimes, but not so often as the others, and are generally
under supervision. From these two grades only, the superintendents or
overseers are taken. Pupils of the third grade stand between those who
are decidedly good or bad, and are treated accordingly. They are the
last who are permitted to pass from the elementary to the trades’
school, on completing their course in the former. Those of the fourth,
or lowest grade, are kept constantly under supervision, have no
allowances, no leaves of absence, are separated, when possible, from the
rest of the pupils, and are even punished by an inferior diet.

  The health of the pupils is promoted by frequent bodily exercise, and,
when the weather permits, in the open air. Thus they have regular
gymnastic exercises four times a week, are drilled by companies four
times, and by battalion twice a week, take frequent walks, and in
summer, bathe every day. The regular manual labor in this department of
the school is confined to knitting and tailoring. The gymnastic
exercises are conducted by two teachers, each taking charge of one of
the companies, of which two attend the lesson at the same time, and
assisted by pupils selected from among the most proficient in the
exercises. There are two swimming lessons given to each company, in
summer, every week. In the ordinary division of the day, in summer,
between two and three hours are allowed for manual labor, the same for
recreation, two hours for exercise, and nearly eight for sleep.

  Their clothing is a neat uniform jacket of blue cloth, of a military
fashion, gray or white pantaloons for the winter, and a brown linen
jacket and white linen pantaloons for the summer, and their officers are
distinguished by badges similar to those worn in service. The diet is
generous, and, besides the three meals, bread is served as a luncheon in
the morning and afternoon intervals.

  An opportunity is given to those who are to pass into the trades’
school, to ascertain the trade which they may wish to follow, by a trial
during the last year of the elementary course.

  The order of the day, with merely slight variations during four days
of the week, in summer, is as follows:--The pupils rise at a quarter
before five o’clock, and proceed by companies to the lavatory, two
companies occupying it at once and alternating, the other two being,
meanwhile, engaged in cleaning their shoes. Wash and comb their hair. At
half past five the boys detailed to serve the meals proceed to the
refectory under their two superintendents. At a quarter before six the
bugle sounds, and the companies assemble, by sections, in the
court-yard. Morning prayers and breakfast. Those who are slightly sick
report to the physician. At a quarter before seven, the boys assemble
according to classes, and at seven are marched to the school-rooms. At a
quarter before nine a luncheon of bread is served out to them. School
closes at eleven, and the pupils are free for three-quarters of an hour.
Dinner at about a quarter before twelve. The pupils brush their clothes,
and are inspected by the officer of the day. From a quarter past one to
half-past two, review the morning lessons in school. From a quarter to
three until five, are occupied with manual labor in the work-rooms. Part
of the pupils receive instruction in music, and the first and second
classes in drawing; a stated number take a swimming lesson; the
drummers, fifers, and buglers also have a lesson. A luncheon of bread is
distributed. One of the companies is at drill, one at gymnastics, and
the other pupils bathing or walking until seven. Evening prayers in the
refectory, and supper. Wash, and have recreation until nine, when they
retire. The younger pupils retire at half-past eight.

  In winter, the different occupations of the day are each one hour
later than in summer, until half-past two, when the hour of review of
the lessons is omitted, and the exercises, as far as appropriate to the
season, follow in the same order as in summer, until half-past five, at
which hour the pupils go to the school-room, and remain until a quarter
before seven.

  On Wednesday and Saturday, an hour is devoted to religious
instruction, the other lessons being omitted, except the physical
exercises on Wednesday. Stated days and periods of the day are assigned
for the exchange of the weekday clothes for those of Sunday, for taking
clothes or shoes requiring repairs to the tailor or shoemaker of the
establishment, for hair-cutting and combing, for washing the neck and
shoulders, the feet, and for other minute matters.

  The object of the _Trade School_, is, in part, to economize the funds
of the institution, by making within its walls articles of clothing
required for the pupils, but more to secure the acquisition, not only of
general mechanical dexterity, but of a trade, which may serve to
increase their emoluments when they enter the military service. There
are, at present, one hundred and four pupils.

  In order to pass into the trades’ school from the elementary division,
the pupil must have reached at least the second class, have been above
the fourth grade in conduct, be between fourteen and fifteen years of
age, and of a bodily constitution fitting him for the military service.
The course lasts three years. The school has a special inspector, or
superintendent, who is responsible to the director of the whole
institution, or, in fact, to his substitute.

  The different trades now taught here are those of blacksmiths,
saddlers, tailors, shoemakers, and lithographers. The last named has but
seven pupils admissible to its school, and the next to the last
forty-four. These numbers depend upon the demand for the occupation
subsequent to leaving the establishment, the space required for the
operations of the trade, the difficulty of teaching, &c. As each pupil
is in general permitted, on advising with the inspector, to choose his
employment, it sometimes happens that boys are sent into the town to
learn a trade not taught in the school. Changes of occupation are very
rare, but are sometimes permitted. The blacksmiths are principally
engaged in the repairs of arms, the saddlers make the caps and
accoutrements, &c., used in the house, the tailors all the uniforms, the
shoemakers supply not only this orphan-house, but that of the girls with
shoes, and the lithographers are occupied in copying forms for the
school or war department, manuals, &c. They work about seven hours a
day, under a master-workman from the town.

  An hour of each day is spent in gymnastic or military exercises in the
open air in summer, and in winter in the large room before spoken of.
The military exercises, besides the ordinary ones, comprise some which
are peculiar to the Prussian service. The usual exercises of gymnastics
are introduced, omitting any which seem to have a tendency towards the
tricks of the mountebank. For instruction in these exercises, the whole
school is divided into two parts, and each again into squads, so that
the teacher need have but twelve to fourteen under his charge.
Non-commissioned officers are the under teachers, and in turn are
superintended by higher teachers, and by an inspector.

  There can be no doubt that to these well regulated and perseveringly
continued exercises it is, in great part, due that the physical
development of these youths is, on the average, so perfect. Judicious
recreation, a proper diet and clothing, great cleanliness, a proper
number of hours of work, of instruction and sleep, no doubt, are
necessary, each and all in their degree, but great influence must be
besides allowed to the gymnastic exercises.

  The pupils have two hours of instruction during the day, intended to
keep up their knowledge of the branches taught in the elementary school,
rather than to teach new ones. Military drawing is, however, added.

  When not in the shops, nor in school, nor at exercise, they are
superintended by non-commissioned officers. The discipline in this
school is military in spirit, as well as in details.

  Those pupils who have manifested a decided musical talent in the lower
school, are here instructed thoroughly in the theory and practice of
music. The object is to supply musicians to the regimental bands. These
pupils have a separate superintendence from those of the other schools,
and different hours of exercise and duty. They keep up the knowledge
acquired in the elementary school, as is done in the trades’ school.

_Military Orphan-House at Annaburg._

The following plan of instruction was prepared by Dr. Harnisch, one of
the most distinguished teachers of Prussia, formerly Principal of the
Teachers Seminary at Weissenfels.

In order to rise to the place of a non-commissioned officer, the pupil
must have gone through the lowest classes of the Upper School, where
there are the following studies:--

  Religious instruction, arithmetic, singing, the German language,
calligraphy, geography and history, algebra, geometry, trigonometry, and

The courses in the different branches are arranged as follows:--

  FIRST. _Religious Instruction._


  Class VII. Bible stories, psalms and hymns, appropriate to the season.
Four hours per week.

  Class VI. Histories from the Old and New Testament, portions of the
history of the Christian church, catechism. Four hours per week.

  Class V. Reading and explanation of the Bible, and of its arrangement.
The gospel and historical works are selected, and the history is
connected with the geography of the Holy Land. Catechism. Five hours.

  Class IV. Doctrines of the Lutheran church, taught by Luther’s
catechism. Five hours.


  Class III. Moral instruction, duties to God and man. Three hours.

  Class II. Reading the Bible with comments, the pupils making
abstracts. Three hours.

  Class I. (Two years.) The first year a repetition of Luther’s
catechism. The second, a history of the Christian dispensation. Three

  Every class commits verses from the Bible to memory.

  SECOND. _Arithmetic._ Mental and written arithmetic are taught
together, that the readiness afforded by the one, and the accuracy of
the other, may both be cultivated.


  Class VII. The four ground rules, with three places of figures
mentally. Application to questions in weights and measures. Three hours.

  Class VI. The same rules extended. Three hours.

  Class V. Fractions, with applications to weights and measures. Three

  Class IV. Proportions. Three hours.


  Class III. The applications of proportions to questions of weight,
strength, value, time, and general quantity. Two hours.

  Class II. Exercises in practical algebra. Two hours.

  Class I. Review of the course. First year, practical operations.
Second, theory of arithmetrical processes. Two hours.

  THIRD. _Vocal Music._


  Classes VII & VI. Practice of songs, adapted to youth of a cheerful,
serious, military, or religious cast, with one part. Two hours.

  Classes V & IV. Choral and other songs, with the different parts.
Elements of music. Two hours.


  Classes III, II, & I. More difficult choral pieces. Theoretical
instruction continued. One hour. There is, besides, instruction given to
a select choir, intended to conduct the vocal exercises of the church.

  FOURTH. _Reading._ In the lower classes, a readiness in reading, and
in the higher, the style of reading, is attended to especially. Pieces
learned previously, by heart, are recited.


  Class VII. A good pronunciation, and some facility in reading. Six

  Class VI. Readiness in reading, and repeating the substance of what
has been read. Familiar illustrations. Five hours.

  Class V. Reading some work in reference to knowledge useful in common
life. Four hours.

  Class IV. Reading, with attention to emphasis. Four hours.


  Class III. Reading the Bible and sacred melodies, with the view to
correct reading in this kind of composition. Two hours.

  Class II. Reading various selected works, in and out of the class.

  Class I. Reading continued, and recitations from works previously

  FIFTH. _Orthography and Writing._ These may be taught together in the
same way as mental and written arithmetic; the teacher is, however, at
liberty to follow his own method.


  Class VII. Copying on slates from the blackboard. Four hours.

  Class VI. Copying on paper, from the board, and from books. Four

  Class V. Writing from copy-slips, from books, or from dictation.
(Practice in spelling and writing.) Four hours.

  Class IV. Similar exercises continued. Four hours.


  Class III. Copying useful papers, such as registers, accounts,
contracts, &c. Two hours.

  Class II. Calligraphy, with Roman as well as German letters; practice
in orthography; reading of letters and documents in various
handwritings. Two hours.

  Class I. Copying papers relating to the management of the institution,
as a practical introduction to business. One hour.

  SIXTH. _Useful knowledge taught by induction._


  Class VII. The pupils give their ideas, verbally, of surrounding
objects of the most simple kind, of the commonest productions of nature
and art. Conversations relating to them. Drawing the most simple
mathematical figures on the slate. Three hours.

  Class VI. Descriptions of animals and plants, the former in the
winter, the latter in the summer term. Written remarks on these, serving
to afford exercise in the formation of phrases and in orthography. Four

  Class V. The most essential parts of physics and natural history, the
pupils taking notes of the lessons. Four hours.

  Class IV. Compositions on various subjects. Letters relating to civil
and military affairs. Four hours.


  Class III. History of Prussia, and drawing of maps. Four hours.

  Class II General geography, particularly that of Europe. Passing from
physical to political geography. Civil geography in connection with the
former. Five hours.

  Class I. Universal history. One year is devoted to ancient and one to
modern history. Selections are made of the more important parts of
history. Five hours.

  The remaining studies only belong to the higher school.

  SEVENTH. _German grammar and style._


  Class III. Logical and grammatical instruction of the German language

  Class II. Idiom of the language. Compositions on military subjects,
with especial reference to correctness of grammar.

  Class I. Acquaintance with the best writers. Exercises of composition
on subjects taken from history.

  EIGHTH. _Geometry._


  Class III. Teaching the names and properties of mathematical figures
by induction, in connection with drawing.

  Class II. Equations, with application to problems of common life.

  Class I. Elements of trigonometry.

  NINTH. _Drawing._


  Class III. Drawings from common objects, varying the positions, &c.

  Class II. Copying flowers, or drawings of implements.

  Class I. Architectural drawing with instruments, drawings of
furniture, &c.

Dr. Bache makes the following remarks on the above plan:

  I have allowed myself to present this extended programme, because it
conveys, in as brief a compass as possible, excellent ideas of the
succession of courses in an elementary school, and in a technical or
trade school, for such the higher school must be considered. It should
be remembered that the main purpose is the preparation of youth for the
military service, and hence that the wants of the service are especially
consulted. Another fact must be remembered, namely, that this is a
Lutheran school, and therefore the religious instruction is adapted to
the particular views of that church. The course of morals of the third
class, I must say, however, seems to me out of its place, for although
our duties to God and our neighbor are of course best learned from his
Word, yet their inculcation by precept and example can not commence too

  In the arithmetical course, the union of mental and written arithmetic
is absolutely essential. The gradation appears to me good, and the
application to questions of common life gives a zest to such studies,
attainable in no other way. The theory of arithmetical processes,
however, should accompany or follow more nearly their practical
acquisition. Indeed, if they are taught as they ought to be, by
induction, the theory goes with the practice.

  If the youth at Annaburg take the same pleasure in the exercises of
song, from the elements to the completion of the musical course, as
those of the school[9] actually superintended by the author of this
project, the success will be complete.

    [Footnote 9: Seminary for Teachers at Weissenfels.]

  The connection of orthography and writing, especially if combined with
early reading, is natural.

  The exercises of induction, which in the lower classes are well drawn
out, deviate from the appropriate track in the fourth class, and in the
geographical and historical courses do not return to it. The system in
both these branches is rather synthetical than inductive. There is a
great temptation to break away from this method, into that of giving
positive instruction, from the apparently greater rapidity of progress
of the pupil; some teachers have abandoned it altogether, as too slow,
though ultimately to their cost, as appeared to me in cases where I had
an opportunity of comparing the results.

  The writing is preceded by an introductory course of drawing, which
might with excellent effect be so extended as to branch out into
complete courses of drawing and writing.

  As this plan results from an extended experience, the number of hours
of instruction, per week, necessary to secure the results, is an
important datum, and as such I have retained it, whenever it was
inserted in the original programme.


A military school of a somewhat peculiar character for training up young
men for the duties of non-commissioned or _under_ officers exist at
Potsdam, and is known as the School Division.

The rules of the Prussian Military system, which require only three
years absolute service in the standing army in time of peace, evidently
entail a great practical difficulty in this respect. The soldiers, as a
rule, prefer to quit the service at the end of their three years’ time,
and require great inducements to persuade them to remain. As one
inducement, the state has declared that twelve years’ service gives a
non-commissioned officer a formal claim to civil employment; as, for
example, on the railways or in the custom-houses. Their pay also as
non-commissioned officers goes on increasing according to the length of
their service; and it was stated to be the usual practice not to advance
soldiers to be non-commissioned officers until they had signed an
undertaking to serve for a longer period than could be exacted of them

A further means of supplying the want has been sought, and appears to
have been found in the School Division. The circumstances of its origin
have placed this establishment in immediate connection with the Corps of
Guards, to which, in a military sense, they belong, at whose
head-quarters, the town of Potsdam, their buildings are situated, and
whose garrison duty in the town they occasionally undertake.

At its first commencement the pupils chiefly came in drafts from the
Military Orphan-Houses. But the applications from the country in general
have been so numerous that this practice has been, it is said,
abandoned, and a higher class of admissions has been attempted. The
Commander of the Battalion of _Landwehr_ for the Circle (_Kreis_)
receives all applications in that Circle; he sees that the candidate is
examined on the spot, in reading, writing, and cyphering; and forwards
the name, height, age, and other particulars (the _Nationale_) to the
authorities. The decision is said to be mostly made by the candidate’s
height, and his medical certificate, and to be rather a difficult
matter. Only one-third of the applications are successful. A new boy had
just presented himself with his father at the time of our visit; both
son and father were well dressed, and apparently belonged to the middle
rather than the lower classes. There seems every reason to be satisfied
with the amount of acceptance with the country which the school had
begun to receive.

The age of admission is from seventeen to twenty, and the youth on
entering the school takes a military engagement to give two years of
service in the standing army for each year of his maintenance at the
school, in addition of course to those three years of military service
to which every Prussian is bound, but with the privilege of counting as
military service the period spent at the school.

The usual school course is one of three years, and his engagement is
thus for a term of nine years; that is, deducting three spent at the
school, six years’ time with the troops.

The School Division is 496 strong; there are four companies of 124 men.
The whole body is commanded by a captain, or major, who has an adjutant.
To each company are attached four officers and fourteen non-commissioned
officers; the latter teach in the two first years, the former in the
third. The school course begins on the 1st of October; the afternoons of
three days in each week are employed in ordinary school instruction, but
the remainder of their time in winter and their whole time in summer is
devoted to military training. The school instruction is not carried
beyond reading, writing, and arithmetic up to the rule of three;
geography, drawing skeleton maps, and copying, and learning the
significance of military representations of ground. Some very
respectable specimens of their skill in copying maps were produced; it
appeared to be a favorite exercise.

About 150 are admitted yearly, an extra number being taken to supply
possible vacancies; about 130 yearly are drafted into the army, six
usually as _under_ officers at once, forty at least with certificates of
being qualified to receive the grade in a short time; and the whole
number who go out have generally obtained their appointment before
twelve months are completed. The highest number that may go out at once
as under (or non-commissioned) officers is twelve; three for each
company. Many, however, have latterly, it is said, become so within six
weeks after their leaving.

Where the young men are strong and full-grown, they are allowed to join
the army at the end of two years; their whole service (two years for
each at the school) being therefore reduced to six years.

Young men, on the other hand, who show no disposition or likelihood to
turn out good _under_ officers, are sent off to complete the usual time
as privates.

The proportion of non-commissioned officers in the standing army who are
taken from the School Division was not easy to ascertain. It differs
extremely in different regiments. In one, it was stated that out of the
ordinary complement of 180, fifty came from hence. On the other hand, it
was asserted that the general proportion was not more than one in forty.
A certain number have obtained commissions; but no prospect of such
promotion appears to be held out, and any tendency to carry forward the
studies with a view to it is discouraged and checked.

The buildings, in the outskirts of Potsdam, are large, new, and
handsome, forming three sides of a spacious court or imperfect
quadrangle. The dining-rooms are used also as exercise-rooms, and it was
made a point to let us see a portion of the pupils go through their
gymnastics and exercises; and more particularly their sword and bayonet
exercise. Twenty or thirty young men, very healthy and strong-looking,
went through the latter exercise in two lines; after which came a single
combat with the bayonet, all under the direction of an officer.

The sleeping-rooms are fairly large, and well ventilated, on the same
floor. Twelve slept in each. During the day the wooden bedsteads are
placed one above another. It was said that iron bedsteads are being
generally introduced. Each young soldier is provided with a small
cupboard above his bed. The non-commissioned officers had horsehair, the
young men themselves straw paillasses. There was a stove in the room,
but it was said not to be used.

The school-rooms are on the upper floor. The skeleton maps already
referred to were here produced; one, of the two hemispheres, others
illustrating Prussian history, showing the original size of the Prussian
territory, its extent and condition under Frederick the Great, the whole
course of its gradual extention, &c., very fairly drawn, and creditable
to the young men.

The time devoted to the training which is given in the School Division
appears long. What is now done in three years might as well be done in
half that time. The object, however, is secured of retaining the service
of the men during a lengthened period in the standing army.


The Regimental Schools are chiefly intended to train up non-commissioned
officers. This is more particularly the case in the artillery, which
does not obtain its _under_ officers from the School Division at


The Noble-School at Liegnitz is merely an endowed school, founded by the
Emperor Joseph I. while Silesia was yet an Austrian dependency, and
specially intended for young men of good birth in that country. There
are some military foundations in the school for the sons of officers of
good birth; and the two military men who take part in the instruction
are paid by the state, on the same footing as officers employed in the
State Military Schools.

   *   *   *

[Of one of the Institutions above described (The Artillery and
Engineers’ School at Berlin) we shall give a fuller account, and in the
meantime we close this comprehensive survey of military instruction in
Prussia with the following reflections of the English Commissioners.]


1. Attention has often been drawn to the peculiar feature of Prussian
Military Education, the double examination for the rank of officer. The
principle adopted seems to be the exaction of a proof from _all_
officers that they have received a good, general, and professional
education, rather than the selection of a smaller number for higher
training in a military school. The decree of 1808 first laid down the
rule for the whole army, “that the only title to an officer’s commission
shall be, in a time of peace, education and professional knowledge,--in
time of war, distinguished valor and ability.”

2. The spirit of emulation is not so much called out in Prussia as it is
in France. Early distinctions are acknowledged and appealed to, but
somewhat sparingly. The following words express the view taken on this

“A testimonial of fitness for the University,” says Colonel von
Holleben, (_i.e._, to have passed the Abiturient examination) “dispenses
with the examination for the ensigncy. In consequence of this rule fifty
_Abiturients_ on an average annually enter the army. These, as well as
the _Selectaner_ of the Cadet Corps, must be considered in point of
scientific education, an excellent supply of officers.”

3. It will be seen that in the above words there is no reference to