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Title: Perpetual Motion
Author: Verance, Percy
Language: English
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Perpetual Motion


  Comprising a History of the Efforts to Attain Self-Motive
  Mechanism with a Classified, _ILLUSTRATED_ Collection and
  Explanation of the Devices Whereby it Has Been Sought and Why
  They Failed, and Comprising Also a Revision and Re-Arrangement of
  the Information Afforded by "Search for Self-Motive Power During
  The 17th, 18th and 19th Centuries," London, 1861, and "A History
  of the Search for Self-Motive Power from the 13th to The 19th
  Century," London, 1870, by Henry Dircks, C. E., LL. D., Etc.


[Illustration]


    BY

    PERCY VERANCE



    Copyright 1916
    By
    20th Century Enlightenment Specialty Co.



CONTENTS


For Summarized Table of Contents, see page 358 _et seq._

                                                                    Page
    Introduction                                                       3

    Preface                                                         7-10

    Introductory Essay                                             11-21


    CHAPTER I.

    Devices by Means of Wheels and Weights                         22-67


    CHAPTER II.

    Devices by Means of Rolling Weights and Inclined Planes        68-75


    CHAPTER III.

    Hydraulic and Hydro-Mechanical Devices                        76-117


    CHAPTER IV.

    Pneumatic Siphon and Hydro-Pneumatic Devices                 118-162


    CHAPTER V.

    Magnetic Devices                                             163-174


    CHAPTER VI.

    Devices Utilizing Capillary Attraction and Physical
        Affinity                                                 175-194


    CHAPTER VII.

    Liquid Air as a Means of Perpetual Motion                    195-196


    CHAPTER VIII.

    Radium and Radio-Active Substances Considered as a
        Conceived Source of Perpetual Motion                     197-199


    CHAPTER IX.

    Perpetual Motion Devices Attempting Its Attainment by a
        Misconception of the Relation of Momentum and Energy     200-211


    CHAPTER X.

    The Alleged Inventions of Edward Sommerset, Sixth Earl and
      Second Marquis of Worcester, and of Jean Ernest
      Eli-Bessler (Councillor) Orffyreus                         212-255


    CHAPTER XI.

    Conservation of Energy. A Discussion of the Relation of the
      Doctrine of Conservation of Energy, and the Possibility
      of Perpetual Motion                                        256-269


    CHAPTER XII.

    Will Perpetual Motion Ever Be Accomplished? A Discussion by
      the Author, with a Review of the Opinions of Eminent
      Scientists on the Subject                                  270-357



PREFACE.


The author has no apology to offer for the production of this book. He
has spent his life in environments that have brought him into constant
contact with mechanics, artisans and laborers as well as professional
men, engineers, chemists and technical experts of various types. He
knows a great many men--young men, for the most part--are constantly
working on the old, old problem of Perpetual Motion; that much money,
and much time are being spent in search of a solution for that problem
which all scientific and technical men tell us is impossible of
solution.

It is believed by the author that a classification and presentation of
selected groups of the devices produced in the past by which it was by
the inventor believed, self-motive power had been attained, will save
much work in fields already thoroughly exploited.

So far as the author knows no book on the subject has appeared since
1870. The various encyclopedias published contain articles on the
subject, but they are necessarily brief, and not satisfying to young
men who have become interested in the subject.

In 1861, Henry Dircks, a civil engineer, of London, published a
work entitled "Perpetuum Mobile; or, Search for Self-Motive Power,
During the Seventeenth, Eighteenth and Nineteenth Centuries." The book
contains 599 pages, and was followed in 1870, by a second series by the
same author entitled "Perpetuum Mobile, or a History of the Search for
Self-Motive Power from the Thirteenth, to the Nineteenth Century." In
these two books there is amassed a wonderful amount of material showing
on the part of the author diligence, great patience and wide and
thorough search.

The author of these works was not enamoured of his subject, and his
books clearly show that he was not writing them because of any interest
he had in the subject of Perpetual Motion. On the contrary, they appear
to have been written because of a deep detestation entertained by the
author for the subject of Perpetual Motion, and a contemptuous pity for
any one seriously interested in the subject. Mr. Dircks's works may
be said to be the works of a scold. His sentiments were deep, and his
impulses strong, which accounts for the vast amount of labor he did in
the preparation of his books. Those books are now out of print, and it
is believed by the author of this book that they may well remain so.
They contain much material that no one would be justified in wading
through. The most complicated mechanisms devised by enthusiastic
dreamers are shown in the same detail with which the inventors
described them in presenting them to the public, or to the patent
offices. Little is to be gained by this.

So complicated are many of the devices that only technically trained
engineers could read them understandingly, and few technically trained
engineers are now greatly interested in self-motive power devices. We
believe that every useful or interesting purpose is served if enough
devices are collected, classified and presented to show the various
principles relied upon by the inventors; with an explanation of why
they failed--i. e., wherein the principles relied upon are wrong, and
while possibly not out of harmony with any mechanical principles then
known, are entirely out of harmony with principles since discovered and
now well known.

In the preparation of this volume a vast amount of the information
furnished by the two works of Mr. Dircks has been rearranged,
reclassified, and used.

Everyone who has to any extent, by environment, associated with the
mass of people who are not technically educated, knows that the
persons who are still interested in the subject of Perpetual Motion,
and who still seek its attainment, are not technically trained
engineers or mathematicians, but for the greater part untrained people
of naturally strong mechanical sense, and of natural mechanical and
mathematical adaptation.

This book is written for the perusal of that large class of people. It
is not designed as an argument either for or against the possibility of
the attainment of Perpetual Motion.

The author is content to classify and present--clearly, it is
hoped--the leading endeavors that have been known in that field of
effort, and to explain their failure.

It is believed by the author that the perusal of the present volume by
anyone whose mind has been attracted by the subject of Perpetual Motion
will result in an enlightenment, and, it is also believed, will have
a tendency to direct his mind from a struggle with theories long ago
exploded, and may result in directing his efforts to things practical,
and not without hope of attainment.

This work is offered only to minds mechanically or mathematically
inclined. It is not even hoped that it will interest people who prefer
fiction to fact, nor people who read simply for idle entertainment.



INTRODUCTORY ESSAY


Perpetual Motion as used in this book is to be taken in its
conventional, and not in its strict literal sense. The strict literal
analysis of the two words implies unceasing motion. Of this we have
many illustrations--the tides, the waves of the ocean, the course of
the earth around the sun, and in the movements of all heavenly and
astronomical bodies. In fact, it is difficult to conceive in a strictly
scientific sense of any substance having an entire absence of motion.

Perpetual Motion as used in this book means what it is usually
understood to mean--Self-Motive Power--a machine that furnishes the
power to keep its parts going as a machine. In this sense Perpetual
Motion has always engaged the minds of many, many people--and what is
more natural? As soon as a boy begins to take an interest in moving
parts of machinery, vehicles, locomotives, and what not, he perceives
that the application of power results in the motion of bodies, and
again that bodies in motion are productive of power. A wheel moved by
muscular, or other mechanical power, is made by machinery to elevate
water, and elevated water can be made in descending to run machinery.
The windlass, or other wheel, turned by applied force, lifts buckets
from wells--raises stone, and elevates heavy bodies, if desired. Heavy
bodies descending can be, and are used through means of machinery to
make machinery run.

A great many similar illustrations could be given. What, then, is more
natural than that a boy with an active mind who is at all mechanically
turned, as most boys are, begins to wonder why, if wheels lift stones,
and if stones descending make wheels run, cannot a machine be made that
will lift stones, or other weights, and in turn be run by the descent
of the lifted stones, or other weights? Why, if the turning of wheels
lift water, and if descending water makes wheels go, should not an
adaptation be made by which the same machine will elevate water, and be
run by the descent of the elevated water?

That it cannot be done is now the consensus of opinion of all
technically trained mechanics, but, that it can not be done, and why it
can not be done, is sure not to occur to the boy, nor to the man who
has only a strong natural mechanical sense to guide him, and has not
the advantage of technical training.

Again, it is well known that many, many men have spent considerable
sums of money and given hours and hours, and days, and months, and
years of close and careful thought, and experiment to the production
of a machine that will accomplish Perpetual Motion, and that many have
announced to the world that they had succeeded in its accomplishment,
but that all their devices so far have turned out failures.

It is to no purpose to tell the Perpetual Motion worker that he is
seeking to attain the impossible; that the attainment of self-motive
power has been demonstrated to be an impossibility. He will answer,
or, at least, he will reason to himself that many things once
pronounced impossibilities and claimed to be so demonstrated, have
since been attained. The Perpetual Motion worker is usually a person
of active intelligence, and being enamoured of mechanical projects
is likely to read extensively along mechanical lines, and knows as
every well-informed person knows, that there are many instances in
the history of the discovery and development of the most important
mechanical inventions and scientific discoveries where the persistent
efforts of so-called enthusiastic dreamers and cranks finally triumphed
over the settled and conventional "impossibilities" of dignified
scientists.

When, less than a century ago, it was proposed to propel a ship across
the Atlantic ocean by steampower, Ignatius Lardner, a scientific
teacher, lecturer and interpreter of real note and merit wrote a
book "demonstrating" the physical impossibility of a vessel carrying
enough fuel to propel itself through that distance of water. The book
was actually printed, but was scarcely off the press until the first
steamship had successfully crossed the Atlantic with steampower, and
steamed triumphantly into port.

After communication by electric telegraph was well established and
had been in successful commercial use for decades, it was proposed to
converse by long distance over a wire. The idea was hooted and declared
impossible, and it did seem so, and yet today, there is scarcely a farm
house in the nation but what has an instrument by which the occupants
can talk over wires not only to their near-by neighbors, but to remote
cities.

Prof. Samuel P. Langley, less than two decades ago undertook in a
thoroughly scientific manner to accomplish what is called "heavier than
air flight." His scientific ideas on the subject were entirely correct,
but he did not have the advantage of engine refinement as it is known
today, by which high energy development can be attained with an engine
or motor of small weight. Nevertheless, Prof. Langley succeeded
in flying a considerable distance, and in fact, made a number of
successful demonstrations of the _physical possibility_ of heavier than
air flight. Prof. Simon Newcomb, who is to be ranked as the greatest
astronomer, mathematician and scientist the United States has ever
produced, and with the possible exception of Benjamin Franklin, the
most original thinker along scientific lines, wrote an article which
was published generally in scientific journals, in which he warned
Prof. Langley of the folly of his attempts, not claiming, however, the
scientific impossibility of heavier than air flight, but claiming that
it could never be of any real practical value; that the instability of
the air, etc., limited flight by man to a daredevil show performance.
A child then born would now be scarcely grown, and yet, aeroplanes are
in use in every civilized country in the world for observation and
military purposes, and even for carrying mail to places not otherwise
easily accessible.

Thousands of flights are undertaken every day with the confident
expectation of a successful trip and return. How many, many boys
and mechanics, prior to the achievement of human flight, have been
attracted by the problem, only to have their ambitions and dreams
discouraged and suppressed by being told that the scientific world
knows that human flight is impossible--"God made man to walk on the
ground, and the birds to fly, and if Nature had intended that we should
fly we would have been equipped with wings," and probably to be dubbed
"Darius Green," as a reminder of the inglorious fate of the pseudo hero
of that name in Trowbridge's clever and immortal poem about Darius
Green and his Flying Machine.

The announcement of the discovery of rays by means of which views may
be made and photographs taken through substances supposedly opaque to
all light rays was scouted as a ridiculously visionary dream; but the
discoverers were not dismayed by scout and ridicule, but persisted in
their dreams and enthusiasm. There is not a village of any considerable
size in the civilized world but has its X-Ray Machine by which foreign
substances in the flesh may be viewed and photographed and located with
exactitude, fractures examined and all surgical operations aided to the
benefit and health and recovery of the sick and wounded. Mankind is the
recipient of the benefits resulting from the fact that enthusiastic
cranks were not deterred by ridicule and supposed demonstrations of
their folly.

The above are only a few of the many like instances recorded in
scientific progress. While not accurately true, and while less true
during the last two decades than formerly, it is, nevertheless, a
general truth that scientific progress has been made in spite of, and
in the face of discouragement and ridicule from the multitudes who were
destined to be benefited by the discoveries made by the persistent
so-called cranks.

These facts are all well known to the Perpetual Motion enthusiast. It
is, therefore, of no avail to tell him that the scientific world has
pronounced his aspirations and attempts but dreams, and that Perpetual
Motion workers are by the scientific world denominated cranks.

If it be admitted that Perpetual Motion is, as scientific men tell
us, a chimerical dream, it is still to be very greatly doubted if the
world at large is to be benefited by dissuading minds from working
on the problem. There is no doubt that many persons who have become
more intensely interested in mechanics by thinking and working on the
problem of Perpetual Motion, have thereby been lead to study more
and more generally into mechanical subjects, and became not merely
tyros, but useful men in various mechanical pursuits. Many doubtless
have followed mechanical subjects to which they were introduced by
labors toward Perpetual Motion, to the making of useful and valuable
inventions and discoveries.

Notwithstanding the fact that a countless number of devices for the
attainment of Perpetual Motion have been proclaimed and exhibited, it
is to be supposed that those actually proclaimed and brought to light
constitute but an infinitesimally small proportion of those actually
made. It is to be supposed that the Perpetual Motion worker has some
sense, and that the great majority of them before proclaiming his
apparatus would want to know himself that it was not a failure, and
would not, when ushered before the public, bring upon him humiliation
and jeers. It is to be believed that in nearly every instance the
produced device was tested before being proclaimed and ushered into the
light of day. It goes without saying that all that were so tested were
failures, and were never heard of except by the inventor and a very few
intimate friends or co-laborers. Those that have been heralded to the
world represent only that small proportion where over-confidence in the
operation, or a disregard for the truth, or some other unexplainable
something caused the inventor and his friends to make the announcement
and disclosure of the device before the test.

It is almost impossible to conceive of a person of any intelligence
exposing himself to the ridicule resulting from the failure of a
pompously heralded device, when a simple test would have saved the
exposure, and yet the civilized world has been filled with Perpetual
Motion devices proclaimed and heralded with trumpet blast, which, when
tested, "didn't work."

It is not, however, the purview, or purpose of this book, to incite
people to work on the problem of Perpetual Motion, neither is it its
purview or purpose to dissuade them from it.

In the works of Mr. Dircks, mentioned in the preface of this work, the
devices for Perpetual Motion are classified somewhat with reference to
the time each was produced. In some instances with reference to whether
or not patents were applied for and obtained, or as to the source of
information concerning them.

A careful examination of the devices presented in Mr. Dirck's two
works, and of those, information concerning which has been obtained
elsewhere, leads the author to believe that nothing is to be gained by
an attempted classification along those lines.

In countless instances Perpetual Motion seekers of different races and
living in separate countries, and, indeed, on different continents,
centuries apart, have sought the attainment of Perpetual Motion by
practically the same devices, and inventor after inventor has brought
forth alleged inventions depending upon precisely the same underlying
mechanical principle.

The author has attempted to classify the various devices presented in
this book according to the underlying mechanical principles upon which
the inventor chiefly relied for the success of his invention. Even this
classification is extremely difficult and not well distinguished. Many
of them, indeed most of them, depend for their success upon more than
one mechanical principle, and the classifications thereby inevitably
intermingle and overlap what otherwise would be their distinguishing
boundaries. Still it is believed by the author that it is the best
that could be adopted, and that no better or clearer classification is
possible than the one here presented.

The various devices are classified by the author under the following
heads:

Devices by Means of Wheels and Weights.

Devices by Means of Rolling Weights and Inclined Planes.

Hydraulic and Hydro-Mechanical Devices.

Pneumatic Siphon and Hydro-Pneumatic Devices.

Magnetic Devices.

Devices Utilizing Capillary Attraction and Physical Affinity.

Liquid Air as a Means of Perpetual Motion.

Radium and Radio-Active Substances Considered as a Conceived Source of
Perpetual Motion.

Perpetual Motion Devices Attempting Its Attainment by a Misconception
of the Relation of Momentum and Energy.

to which is added--

  "A Discussion of the Alleged Inventions of the very eminent
    Edward Sommerset, Sixth Earl and Second Marquis of Worcester,
    and Jean Ernest Eli-Bessler Orffyreus.

Also--

  "A Discussion by the Author of the 'Doctrine of Conservation
    of Energy, and Its Relation to the Possibility of Perpetual
    Motion.'"

And--

  "A Discussion by the Author of 'Will Perpetual Motion Ever Be
    Accomplished?'"



CHAPTER I

DEVICES BY MEANS OF WHEELS AND WEIGHTS


Wilars de Honecort

While attempts at Perpetual Motion are as old as the human race,
not many of the more ancient devices have been preserved, either by
engraving or by explanation.

Among the very earliest of these attempts of which we have detailed
information is the device of Wilars de Honecort. He was an architect,
and lived in the thirteenth century. The information is preserved in "A
Sketch Book" by him which was deposited and remains in the Ecole des
Chartes at Paris. About the middle of the nineteenth century comments
were published in France on this ancient device. Some of these were
translated into English. The following account is an extract from a
translation made by Professor Willis, of Cambridge.

"_Many a time have skilful workmen tried to contrive a wheel that shall
turn of itself: here is a way to make such a one, by means of an uneven
number of mallets, or by quicksilver._"

Wilars de Honecort presents to us a device for a perpetual motion;
it is not clear whether he intends to claim the contrivance of it, or
whether he had met with it in the course of his travels. It differs
very little from a well-known contrivance for this purpose which has
been so often published, and its fallacy so fully explained in popular
books, that it is unnecessary to dwell at length upon the mechanical
principles which it involves. It is extremely curious in this place,
because it shows the great antiquity of the problem, the solution of
which has wasted the time, the brains, and the means of many an unhappy
artisan or philosopher.

In the drawing we have now before us, the two upright posts, which are
framed together and skilfully braced so as to ensure their steadiness,
support between them a long horizontal axle, to the center of which
is fixed a wheel with four spokes. The absence of perspective in this
drawing makes the wheel appear as if it were parallel to the frame,
instead of being, as it is, at right angles to it.

[Illustration]

Seven mallets, or arms, each loaded with a heavy weight at the end, are
jointed at equal distances to the circumference of the wheel, so that
those which happen to have their joints below the diameter of the wheel
will hang freely down, but if the wheel be turned round by hand or
otherwise, the weights of those which are on the ascending side will,
in succession, rest on its circumference, and will, in that position,
be carried over the highest part of the wheel and downwards on the
descending side, until the arms that bear them are brought into a
vertical position and a little beyond it, and then the weight will fall
suddenly over and rest on the opposite position on the circumference
of the wheel, until its further descent enables it to dangle freely
as before. The effect of this mechanism upon the position of the
weights is not truly represented, for the upper mallet has fallen over
too soon. In the modern form of this contrivance a pin, or stop, is
introduced, by which the mallet, when it falls over, is compelled to
rest so that its arm shall point to the center of the wheel, and thus
the descending weight be held at a greater distance from the center
than when ascending. It is extremely probable that this difference is a
mere error of the artist, for the drawing has the appearance of having
been made from a model of the wheel at rest; a condition in which, of
course, it would always be found, unless moved by some external force.
The inventor seems to have thought that the action above described
would always place four weights on the descending side, and leave but
three on the ascending side, each weight as it rises to the top being
intended to leap suddenly over to the descending side, in the manner
just explained; or perhaps, as M. Lassus suggests, the contriver
imagined that the blows given to the wheel in succession by the falling
mallets would help it forward. It is surprising that although the
slightest model would show the failure of devices of this class to
persons incapable of mathematical reasoning, yet such machines have
been seriously proposed in books, and are continually recontrived by
ingenious workmen. The allusion to quicksilver in the manuscript shows
that Wilars was acquainted with the well-known contrivance described
in the books already referred to, in which portions of that metal
inclosed in channels are used instead of the falling weights.


A Repetition of Wilars de Honecort's Plan

This device was brought forth in 1831 in England, and illustrates what
we say in the Introductory Essay to the effect of inventors working on
the same plan in different parts of the earth and centuries apart.

[Illustration]

We are unable to give the inventor's name. He was a correspondent to
Mechanics' Magazine, and the description furnished by the inventor as
published in Mechanics' Magazine, is as follows:

Description.--A A A is a ring of thin wood; B B B, several spokes,
movable round the fixed points C C C, and only allowed to move one way
by the construction of the openings D D D; E E E, heavy weights fixed
to the ends of the spokes.

From the position in which the wheel is at present, it is evident
that the weights on the right-hand side (1 and 2) acting at a greater
distance from the center than those (4 and 5) on the other side, will
cause that side to descend until the spoke 1 reaches the position 3,
when it will exert no moving influence, but by which time the weight 8
will have fallen into the position 1, when a similar effect will take
place, and so on with the rest.


Leonardo da Vinci

It is with a mingled feeling of sorrow and exaltation that we note the
Perpetual Motion labors of the great Leonardo da Vinci. Of all of the
men who ever gave the subject more than a passing notice he is the most
famous.

Leonardo da Vinci was an Italian, born in 1452, and died in 1519. He
was the illegitimate son of Florentine, lawyer. His mother has been
variously described as a peasant, and as of gentle birth. Little about
her is known. The father belonged to a family of lawyers, and never
repudiated the son, but took him, educated him, and cared for him. It
is well for the world that he did, for Leonardo da Vinci has perhaps
contributed more to art and learning in the world than any other single
individual that ever lived. He was a painter, a sculptor, an architect,
a musician, a mechanician, engineer and natural philosopher. Each
subject in art or science that he touched he not only mastered, but
improved and embellished. He painted the original of the well-known
picture of the Christ and His twelve Apostles, known as the "Last
Supper," or the "Last Supper of Our Lord." This, and Mona Lisa, are
perhaps the paintings by which he is known to the greatest number of
people, and are considered by many connoisseurs the highest perfection
in art ever attained by mortal man.

But, as painter and sculptor, he is to be regarded as among the
greatest, if not the very greatest that ever lived. In art he ranks
beside, if not ahead of Michelangelo and Raffael, and yet they are
known only as artists, while he was preeminent in both art and science.
The work he did in natural science was entirely original and emanated
from an inherent initiative and originality, and as a scientist, he is
entitled to rank below only Newton, Gallileo and Copernicus, and very
few others. In all the history of the world he is the only man of whom
it can be said that he attained the apex of eminence in both art and
science.

The information concerning Leonardo da Vinci's devices for obtaining
Perpetual Motion is extremely meager. There does not seem to be extant
any detailed explanation of just how he expected his different designs
to work.

All that is known concerning his efforts is sufficiently illustrated by
the following cuts and language from Dircks:

  Fig. 1 may be taken as a scheme belonging to the fifteenth
  century. It seems to be placed at the head as a simple or
  elementary design for future improvement. It is a chambered drum
  wheel, containing balls or weights, which, being always farthest
  from the center on one side, as compared to the other, are
  expected to keep the wheel constantly rotating.

  Fig. 2. Failing in this scheme, the inventor next offers one with
  weighted levers, which are to fall outwards on one side, but to
  fall inwards on the opposite side, the weight at the same time
  sliding up the lever when vertical at the bottom, so as to be
  nearer the center throughout on the ascending side. But how
  the weight is to be made to ascend _at the bottom_ remains to be
  shown.

  [Illustration]

  Fig. 3. The difficulty of elevating the weight would appear to
  have suggested its immersion in a trough of water, as here shown.
  The weights seem to be attached to some contrivance to float them
  _upwards_; but we are perplexed, and so no doubt was da Vinci,
  how to sink them, or being sunk, how to render them again buoyant
  by any self-motive process.

  Fig. 4. It would appear as though the difficulties observable in
  Fig. 3 were attempted to be met here, in a plan which evidently
  combines several views of the case, yet without removing the main
  difficulty; for although the weight at the end of the long arm
  may be quite capable of sinking in the liquid, we still inquire,
  How is it ever to be raised again?

  Fig. 5 seems to be an incomplete sketch, and a mere variation
  on the preceding designs, with the addition either of machinery
  below to be worked by it, or to give it motion. Possibly it was
  proposed to have a magnet at the bottom of the vessel.

  Fig. 6 appears to be two designs in one sketch. On one side we
  have long single levers, with a single weight at their ends, and
  a weight between each at the periphery; on the other end, double
  or forked levers and double weights. Its mixed character renders
  it probable that it was merely some preliminary sketch.

  The great value of the present exhibition of these early
  contrivances of misdirected mechanical ingenuity consists in the
  convincing evidence which they afford, that all young inventors
  who occupy themselves in the search for self-motive machines,
  do little more than reproduce the blunders of a past age.
  After a lapse of five centuries modern inventors often become
  patentees of contrivances which are only more complicated than
  the assumed-to-be overweight wheel of Wilars de Honecort, or the
  six similar ones of Leonardo da Vinci. But such has hitherto
  been the ignorance of mechanics on this subject, that Fig. 1 of
  the annexed diagrams has frequently been adduced by writers on
  the subject, as the veritable wheel invented by the Marquis of
  Worcester, in the seventeenth century!


A. Capra's Device

In 1678, A Capra, of Italy, revived the ancient, but still favorite
scheme that dates back to the 13th century. (See page 22 ante.) He
illustrates his idea with the following figure and the following
comment:

On the wheel A (of the facsimile engraving opposite), which
must be hung well equipoised between two uprights, are appended
counter-weights, eighteen in number, all precisely at the same
distance from each other, and all exactly of the same weight. The
counter-weights are provided with a small ring by which they are hung.

[Illustration]

Whilst the counter-weights B are farther from the center C of the
wheel, they weigh more than the counter-weights I, because these
are low and nearer to the center C of the wheel, so that the
counter-weights B descend and the weight I drops; and whilst the
weight B is alternately descending and the weight I ascending, the
wheel will revolve continually. But it must be understood that it is
necessary to make the wheel perfectly true in equilibrium, so that
it do not weigh more on one side than on the other on account of the
counter-weights.


The Device of Dixon Vallance. England, 1825

This inventor was certain he had overtaken and captured the
ever-illusive Perpetual Motion. He gives a description of his happiness
and his machine in the following effusively joyous language:

  The annexed drawing shows how I have at length taken this
  enticing jilt (perpetual motion), though after a long and weary
  chase--

    Through pleasant and delightful fields,
    Through barren tracts and lonely wilds;
    'Mongst quagmires, mosses, muirs and marshes,
    Where deil or spunkie never scarce is!
    By chance I happened on her den,
    And took her when she didna ken.

  [Illustration]

  W W W W represents a wheel with twelve hollow spokes, in each
  of which there is a rolling weight or ball. C C C C is a chain
  passing over two pulleys P P. There is an opening round the
  wheel from the nave to the circumference, so as to allow the
  chain to pass freely and to meet the weights. The weights are
  met by the chain as the wheel revolves, and are raised from
  the circumference till they are at last brought close to the
  nave, where they remain till, by the revolution of the wheel,
  they are allowed to roll out to the circumference. By this
  arrangement the weights are, on one side of the wheel, always at
  the circumference, so that that side is more powerful than the
  other, which causes the wheel continually to revolve. F F F F
  is the frame of the machine; M M M M the mortices for joining
  the two sides of the frame by cross rails. The arrows point out
  the direction in which the wheel turns.--I am, yours, &c., Dixon
  Vallance. Liberton, Lanarkshire, Nov. 10, 1825.


Furman's Device

Strange as it may seem, the patent office of the U. S. government as
late as 1884 and 1886, received and filed, seriously considered and
granted Letters Patent on Perpetual Motion Devices as appears from the
description of Furman's Device following, and from Schirrmeister's
"Mechanical Movement," and Enbom & Anderson's "Improvement in Pumps,"
appearing on pages 38 and 76 respectively, supra.

These were not denominated Perpetual Motion Devices by the inventors,
but the specifications show them to be simply that and nothing more.

July 15, 1884, George H. Furman, of Rochester, Ohio, U. S. A., was
granted U. S. Patent No. 301979, on

    "A New and Improved Motor."

The essentials are sufficiently shown by the following excerpt from
the specifications and the following figure. We have omitted Figure 2,
mentioned in the specifications:

  UNITED STATES PATENT OFFICE.

  George H. Furman, of Rochester, Ohio.

  MOTOR.

    Specification forming part of Letters Patent
    No. 301979, dated July 15, 1884.
    Application filed March 6, 1884. (No model.)

  The action of the motor is as follows: A suitable quantity of the
  small weights _d_ being placed in the outer drum, F, through the
  door _f_, the machine being at rest, they will accumulate at the
  lower part of the drum F in the pockets _c´ c´_. Now, to run the
  machine a person will apply his hands to the rim H and revolve
  the outer drum, F, in the direction of the arrow shown in Fig.
  1. This movement of the outer drum will cause the weights _d_ to
  be carried in the pockets _c´ c´_ to the upper side of the drum,
  at which point they will roll from the pockets _c´ c´_ into the
  pockets _b b_ of the inner drum, G, where their weight will cause
  the drum G and shaft E to revolve. _As the pockets_ b _of the
  inner drum pass below the shaft E they empty the weights into the
  troughs_ c´ _of the outer wheel, F, to be again carried above the
  shaft and dropped into the pockets_ b, _so that the inner wheel,
  G, and shaft E will be revolved continuously._

  [Illustration]

Schirrmeisters Mechanical Movement

July 6, 1886, Charles Schirrmeister, of Brooklyn, Kings County, State
of New York, U. S. A., obtained Letters Patent No. 345077, on a new and
useful

"Mechanical Movement."

The essentials of the patented device appear from the following
excerpts from the specifications, and the following figures
accompanying the specifications. (Figs. 2, 3 and 4 we do not show.)

  [Illustration]

  The object of my invention is to furnish a cheap and simple
  _means for imparting mechanical power_; and I accomplish this by
  means of a series of radial arms placed at right angles to and
  projecting from the axis of motion where power is first applied,
  and so arranged that each arm is in a different vertical plane,
  said arms being weighted at each end with a ball of metal. Some
  of these arms are also made hollow and inclose sliding or rolling
  weights, which move back and forth as the axis revolves, and the
  motion is still further re-enforced by a series of springs which
  are attached to the axis by a lever and eccentric.

  [Illustration]

  Taking the simplest form of my device, I illustrate the same by
  the accompanying drawings, in which--

  Figure 1 is a side elevation of the entire apparatus. Fig. 2 is a
  sectional view showing the hollow arm with a rolling weight. Fig.
  3 is an end view showing the operation of a re-enforcing spiral
  spring. Fig. 4 is a detailed view showing still further the
  method of re-enforcing motion by springs. Fig. 5 is a view of the
  driving-pulley with its hollow arms.

  Similar letters refer to similar parts in the several views.

  A is the axis to which the power first imparting motion is
  applied.

  N are the bearings supporting the same.

  B is the driving-pulley attached to said axis, and from which
  motion is imparted by means of the driving belt _b_ to any point
  desired.

  C are the hollow arms of the driving-pulley B.

  D are the solid arms radiating from the axis A.

  E are the hollow arms radiating from the axis A.

  F are the solid balls or weights secured to the ends of the arms
  D and E.

  _a_ are the sliding or rolling weights, which are inclosed within
  the hollow arms C and E.

  _c_ are the slots cut into the hollow arms E, to relieve the
  air-pressure formed by the backward and forward motion of the
  weights _a_.

  G are springs so arranged as to expend their force upon the axis
  A by means of the connecting rods H, both attached to the springs
  and one attached to the axis A by means of the eccentric I and
  the other to the wheel J at one end of the axis.

  K is a balanced lever, upon which the springs G may rest, said
  lever being supported at each end upon the springs L.

  M is a crank attached to one end of the axis A, and serves to
  show the place and manner in which the power may be applied.

  The manner of constructing and operating my invention is as
  follows: The entire apparatus is made of steel or iron, and
  the shaft, bearings, arms, springs and connecting-rods are of
  ordinary form. The main or driving pulley is cast with four
  hollow arms, in which round weights are inclosed, which move
  back and forth within the arms when the wheel is set in motion.
  The solid arms, as well as the hollow arms, which are used
  in addition to those forming a part of the driving-pulley,
  are arranged by means of set-screws a suitable distance apart
  upon the axis and in different perpendicular planes, so as to
  give steadiness in motion. A thread is cut upon each end of
  these arms, and the fixed weights are then screwed on. When
  the shaft or axis revolves, the weights which move toward the
  ends of the arms above the center accelerate the motion, and
  the momentum of the machine aids in overcoming the resistance
  caused by the weights, which are below the center. At the same
  time the revolution of the eccentric and crank-pin upon the
  axis depresses the connecting-rods, which in turn depress the
  springs, which, being released as soon as the eccentric and
  crank-pin have reached their lowest point, contribute a lifting
  power to overcome the resistance above mentioned. As shown in the
  drawings, these springs joined to the connecting-rods may be
  supported and assisted by other springs.

  The power is applied by hand, operating upon a crank at the end
  of the axis, or may be imparted by steam, hot air, electricity,
  or in any other known method, and is conducted to any desired
  point by means of the belt _b_.

  Having fully described my invention, what I claim as new, and
  desire to secure by Letters Patent, is:

  1. The combination, in apparatus for increasing mechanical
  power, of an axis, as A, supported upon bearings N, with a
  driving-pulley, as B, having hollow arms, as C, with movable
  weights, as _a_, and radial arms, both solid and hollow, the
  latter having movable weights, together with fixed weights
  attached to the end of each arm, all substantially as and for the
  purpose described.


Ferguson's Device

James Ferguson was an eminent Scotch mechanician and astronomer. He
was born in 1710, and died in 1776. He was reared in very humble
circumstances, and is known as the Peasant Boy Philosopher. A most
interesting story of his life was written by Henry Mayhew, and
published in England in 1857, entitled "The Story of the Peasant Boy
Philosopher."

He prepared astronomical tables of great value and lectured on
astronomical and mechanical subjects. His lectures were edited by a no
less eminent man than Sir David Brewster.

[Illustration]

While Perpetual Motion seemed to have received considerable time and
attention from him, and while his writings show that he examined
a great many mechanical devices, he seems all the time to have
entertained serious doubt of the possibility of a machine having
self-motive power. However, in 1770, he devised a machine for the
purpose of producing Perpetual Motion. It does not appear that he
ever offered the machine to the public, or sought publicity for it.
A description of it is to be found in his Common Place Book in the
University Library, Edinburg. The description there furnished is as
follows:

  The axle at A is placed horizontally, and the spokes B, C, D,
  etc., turn in a vertical position. They are jointed at _s_, _t_,
  _u_, etc., as a common sector is, and to each of them is fixed a
  frame as R, S, T, etc., in which the weights 7, 8, 9, 1, 2, etc.,
  have liberty to move. When any spoke as D is in a horizontal
  position, the weight I in it falls down and pulls the part _b_
  of the then vertical spoke B straight out, by means of a cord
  going over the pulleys K and k to the weight I. The spoke C _c_
  was pulled straight out before, when it was vertical, by means
  of the weight 2, belonging to the spoke E _e_ which is in the
  horizontal position D _d_; and so of all the others on the right
  hand. But when these spokes come about to the left hand, their
  weights 4, 5, 6 fall back, and cease pulling the parts _f_, _g_,
  _h_, _i_; so that the spokes then bend at their joints X, _y, z_,
  and the balls at their ends come nearer the center A, all on the
  left side. Now, as the balls or weights at the right hand side
  are farther from the center A than they are on the left, it might
  be supposed that this machine would turn round perpetually. I
  have shown it to many who have declared it would; and yet for all
  that, whoever makes it, will find it to be only a mere balance. I
  leave them to find out the reason.


B. Belidor's Device

This device was incubated in the brain of an American. His name is
unknown. We have denominated it "B. Belidor's Device," not because B.
Belidor was the inventor, but because the account of the invention was
furnished by him. This device seems to the author to have possessed
originality, though, of course, it failed to work for reasons clearly
apparent.

[Illustration]

An account of it was given in the Journal of Franklin's Institute,
Philadelphia, in 1828. The article contributed by B. Belidor is as
follows:

  Even the pursuit after perpetual motion, hopeless as it is, may
  not be considered entirely vain, in occasionally leading to
  useful modifications of machinery. As an instance of this, I
  here submit to you a plan suggested by an ingenious friend of
  mine, several years ago, as in the diagrams annexed, Fig. 1, a
  perpendicular, and Fig. 2 a horizontal view.

  A A, two vertical wheels, placed diagonally, and revolving on the
  axes X X. The levers B B and C C are hinged at the peripheries
  of the wheels. By rotation the arms B B are projected from the
  center of motion, while the arms C C are drawn in.

  It is plain that a series of arms as shown in Fig. 2, will
  produce an eccentric motion, causing the weights at their ends
  apparently to preponderate on the side B.--BELIDOR.


Desagulier's Proposition on the Balance

This so-called problem is of doubtful classification. The author of
the problem did not claim that the discovery of the problem discloses
any means for attaining Perpetual Motion, and, yet, it is apparent
that if the author of the problem was correct in his solution of it,
Perpetual Motion was thereby already within his grasp. The difficulty
about it all is that while the problem is quite interesting, the
author's solution shows that he was not familiar with even fundamental
mechanics. The name of the author was J. T. Desagulier, LL.D., F. R. S.
He was a minister of the gospel, but evidently gave considerable
attention to mechanical questions. He is mentioned in chapter X of this
work.

Rev. Desagulier presented two problems of the balance. One he calls "A
Proposition on the Balance, not taken notice of by Mechanical Writers,
explained and confirmed by an Experiment." The article under this
heading is as follows:

  [Illustration]

  In the last papers I published in "Philosophical Transaction"
  against this perpetual motion, described in No. 177, I intreated
  the author to permit me to say nothing as to what alterations he
  might make in his engine, resolving to leave it to others to show
  him that upon that principle all he can do signifies nothing. But
  I find since, in the "Nouvelles de la Republique" for December
  last, that he still persists to urge some new contrivances,
  which being added, he conceives his engine must succeed. To this
  I answer, that I undertook only to shew that his first device
  would faile, which yet I should scarce have done if I had thought
  a dispute of this nature could have lasted so long. To come,
  therefore, to the point where he saith that this engine may well
  succeed without alteration, because he hath tryed with liquors
  put into bellows immersed in water; I again say that I grant
  him the truth of the experiments, but deny the consequences he
  would draw from them. I have already given the reasons of my
  dissent, which this gentleman is not pleased to understand. But
  to end all controversies, he may please to consult Mr. Perrault,
  De la Hire, or any other at Paris well known to be skilled in
  hydraulicks, and I doubt not but he will find them of the same
  opinion with Mr. Boyle, Mr. Hook, and other knowing persons here,
  who all agree that our author is in this matter under a mistake.


  A Proposition on the Balance, not taken notice of by Mechanical
    Writers, explained and confirmed by an Experiment.

A B is a balance, on which is supposed to hang at one end, B, the scale
E, with a man in it, who is counterpoised by the weight W hanging at A,
the other end of the balance. I say, that if such a man, with a cane
or any rigid straight body, pushes upwards against the beam anywhere
between the points C and B (provided he does not push directly against
B), he will thereby make himself heavier, or overpoise the weight W,
though the stop G G hinders the scale E from being thrust outwards from
C towards G G. I say likewise, that if the scale and man should hang
from D, the man, by pushing upwards against B, or anywhere between
B and D (provided he does not push directly against D), will make
himself lighter, or be overpoised by the weight W, which before did
only counterpoise the weight of his body and the scale.

If the common center of gravity of the scale E, and the man supposed
to stand in it, be at _k_, and the man, by thrusting against any part
of the beam, cause the scale to move outwards so as to carry the said
common center of gravity to _k_ _x_, then, instead of B E, L _l_ will
become the line of direction of the compound weight, whose action
will be increased in the ratio of L C to B C. This is what has been
explained by several writers of mechanics; but no one, that I know of,
has considered the case when the scale is kept from flying out, as here
by the post G G, which keeps it in its place, as if the strings of the
scale were become inflexible. Now, to explain this case, let us suppose
the length B D of half of the brachium B C to be equal to 3 feet, the
line B E to 4 feet, the line E D of 5 feet to be the direction in which
the man pushes, D F and F E to be respectively equal and parallel to
B E and B D, and the whole or absolute force with which the man pushes
equal to (or able to rise) 10 stone. Let the oblique force E D (= 10
stone) be resolved into the two E F and E B (or its equal F D) whose
directions are at right angles to each other, and whose respective
quantities (or intensities) are as 6 and 8, because E F and B E are in
that proportion to each other and to E D. Now, since E F is parallel
to B D C A, the beam, it does no way affect the beam to move it
upwards; and therefore there is only the force represented by F D,
or 8 stone, to push the beam upwards at D. For the same reason, and
because action and reaction are equal, the scale will be pushed down
at E with the force of 8 stone also. Now, since the force at E pulls
the beam perpendicularly downwards from the point B, distant from C
the whole length of the brachium B C, its action downwards will not be
diminished, but may be expressed by 8 × BC; whereas the action upwards
against D will be half lost, by reason of the diminished distance
from the center, and is only to be expressed by 8 × B C/2; and when
the action upwards to raise the beam is subtracted from the action
downwards to depress it, there will still remain 4 stone to push down
the scale; because 8 × B C - 8 × B C/2 = 4BC. Consequently, a weight
of 4 stone must be added at the end A to restore the æquilibrium.
Therefore a man, &c., pushing upwards under the beam between B and D,
becomes heavier. Q. E. D.

On the contrary, if the scale should hang at F, from the point D, only
3 feet from the center of motion C, and a post G G hinders the scale
from being pushed inwards towards C, then, if a man in this scale F
pushes obliquely against B with the oblique force above mentioned, the
whole force, for the reasons before given (in resolving the oblique
force into two others acting in lines perpendicular to each other)
will be reduced to 8 stone, which pushes the beam directly upwards at
B, while the same force of 8 stone draws it directly down at D towards
F. But as C D is only equal to half of C B, the force at D, compared
with that at B, loses half its action, and therefore can only take off
the force of 4 stone from the push upwards at B; and consequently the
weight W at A will preponderate, unless an additional weight of 4 stone
be hanged at B. Therefore, a man, &c., pushing upwards under the beam
between B and D, becomes lighter.

The other problem presented by Rev. Desagulier is denominated by him
"An Experiment explaining a Mechanical Paradox, that two bodies of
equal weight suspended on a certain sort of balance do not lose their
equilibrium by being removed, one farther from, the other nearer to,
the center."

The article concerning this problem is as follows:

  If the two weights P W hangs at the ends of the balance A B,
  whose center of motion is C, those weights will act against each
  other (because their directions are contrary) with forces made
  up of the quantity of matter in each multiplied by its velocity;
  that is, by the velocity which the motion of the balance turning
  about C will give to the body suspended. Now, the velocity of
  a heavy body is its perpendicular ascent or descent, as will
  appear by moving the balance into the position _a b_, which
  shews the velocity of P to be the perpendicular line _e a_, and
  the velocity of B will be the perpendicular line _b g_; for if
  the weights P and W are equal, and also the lines _e a_ and
  _b g_, their momenta, made up of _e a_ multiplied into W, and
  _b g_ multiplied into P, will be equal, as will appear by their
  destroying one another in making an equilibrium. But if the body
  W was removed to M, and suspended at the point D, then, its
  velocity being only _f d_, it would be overbalanced by the body
  P, because _f d_ multiplied into M would produce a less momentum
  than P multiplied into _b g_.

  [Illustration]

  As the arcs A _a_, B _b_, and D _d_, described by the ends of
  the balance or points of suspension, are proportionable to their
  sines _e a_, _g b_, and _d f_, as also the radii or distances
  C A, C B, and C D; in the case of this common sort of balance,
  the arcs described by the weights, or their points of suspension,
  or the distances from the center, may be taken for velocities of
  the weights hanging at A, B, or D, and, therefore, the acting
  force of the weights will be reciprocally as their distances from
  the center.

  Scholium.--The distances from the center are taken here for the
  velocities of the bodies, only because they are proportionable to
  the lines _e a_, _b g_, and _f d_, which are the true velocities;
  for there are a great many cases wherein the velocities are
  neither proportionable to the distances from the center of
  motion of a machine, nor to the arcs described by the weights or
  their points of suspension. Therefore, it is not a general rule
  that weights act in proportion to their distances from the center
  of motion; but a corollary of the general rule that weights act
  in proportion to their velocities, which is only true in some
  cases. Therefore, we must not take this case as a principle,
  which most workmen do, and all those people who make attempts
  to find the perpetual motion, as I have more amply shewn in the
  Phil. Trans., No. 369.

  But to make this evident even in the balance, we need only take
  notice of the following experiment:--A C B E K D is a balance in
  the form of a parallelogram passing through a slit in the upright
  piece N O standing on the pedestal M, so as to be moveable upon
  the center pins C and K. To the upright pieces A D and B E of
  this balance are fixed at right angles the horizontal pieces
  F G and H I. That the equal weights P W must keep each other
  in æquilibrio, is evident; but it does not at first appear so
  plainly, that if W be removed to V, being suspended at 6, yet it
  shall still keep P in æquilibrio, though the experiment shews it.
  Nay, if W be successively moved to any of the points 1, 2, 3, E,
  4, 5, or 6, the æquilibrium will be continued; or if, W hanging
  at any of those points, P be successively moved to D, or any of
  the points of suspension on the cross-piece F G, P will at any of
  those places make an æquilibrium with W. Now, when the weights
  are at P and V, if the least weight that is capable to overcome
  the friction at the points of suspension C and K be added to V,
  as u, the weight V will overpower, and that as much at V as if it
  was at W.

  From what we have said above, the reason of this experiment will
  be very plain.

  As the lines A C and K D, C B and K E, always continue of the
  same length in any position of the machine, the pieces A D
  and B E will always continue parallel to one another, and
  perpendicular to the horizon. However, the whole machine turns
  upon the points C and K, as appears by bringing the balance to
  any other position, as _a b e d_; and therefore, as the weights
  applied to any part of the pieces F G and H I can only bring
  down the pieces A D and B E perpendicularly, in the same manner
  as if they were applied to the hooks D and E, or to X and Y, the
  centers of gravity of A D and B E, the force of the weights (if
  their quantity of matter is equal) will be equal, because their
  velocities will be their perpendicular ascent or descent, which
  will always be as the equal lines 4 _l_ and 4 L, whatever part
  of the pieces F G and H I the weights are applied to. But if to
  the weight at V be added the little weight _u_, those two weights
  will overpower, because in this case the momentum is made up of
  the sum of V and _u_ multiplied by the common velocity 4 L.

  Hence follows, that it is not the distance C 6 multiplied into
  the weight V which makes its momentum, but its perpendicular
  velocity L 4 multiplied into its mass. Q. E. D.

  This is still further evident by taking out the pin at K; for
  then the weight P will overbalance the other weight at V, because
  then their perpendicular ascent and descent will not be equal.

The Rev. Dr. Desagulier was evidently a man of scientific turn and
capacity. It is unusual to find ministers deeply interested in
scientific matters, and yet, he seems to have been. The net result of
his experiments can be succinctly stated as follows:

In the first problem there is _no change in the distance of the center
of gravity from the support_, and, therefore, there could be no
disturbance of the equilibrium.

In the second problem there _is a change in the distance in the center
of gravity from the support_, and there must have been a disturbance of
the equilibrium.


John Haywood's Device

In 1790, John Haywood, of Long Acre, Middlesex, draftsman and mechanic,
obtained British patent on:

  "A machine for working mills and engines without the aid of fire,
  water, or wind, or in aid of all or any of those or any other
  powers."

  The specification describes the device as follows:

  [Illustration]

  "The machine acts on a rotative principle, or, in other words,
  has a revolving circular or circulating motion round an axis,
  center, or centers. It may be made or constructed of any
  materials or matter whatsoever, so it be of sufficient strength
  to sustain the power of action when applied to any mill, engine,
  or machine to which action or motion can or may be communicated
  by a wheel. The size or dimensions of this machine are by no
  means confined, but may be varied or altered as circumstances may
  require.

  "References to the drawings of the machine hereunto
  annexed:--Fig. 1 is the section of the machine. A, A, B, a
  cranked or double center, fixed to the stand or frame D by the
  bolts E. C, C, the wheel which turns or revolves round that part
  of the cranked center mark A. F, levers which turn or revolve
  round the cranked center B. G, G, rollers or weights which
  revolve in the circular guides or grooves by means of the leavers
  F. H, H, circular grooves or guides which are affixed to the
  inner sides of the wheel. N. B.--the distance from A to B is the
  radius in all cases to determine the space between the center
  of the guide or groove H and the center of the roller or weight
  G. The distance of the two concentric circles which form the
  guides or grooves H must be equal to the diameter of the roller
  or weight G. I, I, springs which stop the rollers or weights G
  from returning when at the horizontal diameter of the wheel. K,
  weights, which may be increased or diminished at pleasure. L,
  ledges which connect the sides of the wheel together. N. B.--By
  fixing cogs or teeth on the rim of the wheel, so as to connect it
  with any mill, machine, or engine to which motion can be given by
  a wheel, the power of this machine may be communicated."


Explanation of the Failure of the Preceding Wheels and Weights Devices

It must not be presumed that the preceding devices shown in this
chapter constitute any considerable part of the Wheels and Weights
Devices that have been constructed through the hope of attaining
Perpetual Motion. Of all the means whereby Perpetual Motion has been
sought wheels and weights have been by far the most prolific. There is
scarcely a village or a rural community in the civilized world that
cannot point out its Perpetual Motion worker, and he generally starts
with wheels and weights, though often, after long labor and final
failure with wheels and weights, he still exploits other attractive
fields of hopeless endeavor. Of the devices of that kind, accounts of
which have appeared in scientific journals, or application for patents
upon which have been made, and, indeed, patents often granted, it would
be possible to write a book of thousands of pages, but to do so would
be to no purpose.

It is believed by the author that the preceding devices are sufficient
to illustrate, and show the controlling features of all the various
mechanical contrivances for the utilization of wheels and weights as
a means of Self-Motive Power. Countless others could be shown of more
or less complicated mechanism, but an examination would disclose the
fact that each gets back to some combination of parts well illustrated
in the preceding. Also, in endeavoring to express why all wheels and
weights devices have failed to work, each essential point of weakness
is disclosed in the preceding. Now, why have they failed to work, and
wherein are they inherently wrong and unscientific?

A cursory examination of the preceding devices shows that each depends
ultimately on the supposition:

1. That a descending weight elevates an equal weight through a distance
equal to the descent, and at the same time overcomes the frictional
resistance of mechanism, both ascent and descent being measured on
perpendicular lines, or

2. That weights affixed to an axis and caused to have a longer leverage
on the descending side than on the ascending side, and consequently the
downward pull on the long lever side is supposed to be greater than the
downward pull or resistance on the short lever side of the axis.

If the fallacy of these supposed principles is explained and fully
understood, it disposes, and disposes effectually, of the possibility
of obtaining Perpetual Motion by means of wheels, weights and the force
of gravity.

It should be remembered that a wheel is a lever, or rather it is a
continuous series of levers--nothing more--nothing less.

[Illustration]

We first refer to the figure shown in A. Capra's device, page 33
ante. The left side of this wheel is, of course, supposed to be the
descending side on which the weights are farthest from the center
of the wheel. It is apparent that only five weights are having any
leverage advantage whatever, while a much greater number are being made
to ascend. The advantage which a few of the weights have by virtue of
the leverage pulling downward is always exactly counterbalanced by an
_increased number_ of weights being drawn upward. It should be borne in
mind that the direction of the force of gravity is toward the center
of the earth, and not in the direction of the motion of the wheel,
except at the extreme left side of the wheel.

Again, consider the figure appearing on page 63. It is manifest that
the weights on the right hand are further out, and have a leverage
advantage of the weights on the left hand side, but it is also manifest
that there is, and always must be, a greater _number_ of weights on the
left hand side. The _greater leverage_ of the weights on one side is
exactly balanced by the greater number of weights on the other side.

For a further illustration, take the figure shown on sheet 65, ante.
The weight "1" has a distinct advantage over weight "5." Weight "2"
has a distinct advantage over weight "6." But here we have only three
weights: 1, 2 and 8, tending to pull the wheel from left to right,
whereas there are five weights, 3, 4, 5, 6 and 7, tending to prevent
its going to the right.

In other words, if weights 1, 2 and 8 were removed, it is clear that
the wheel would turn back to the left by reason of the action of the
weights 3, 4, 5, 6 and 7. Here again the _leverage advantage_ which
weights have descending is counterbalanced by the _increased number of
weights_ on the opposite side acted on by the force of gravity, tending
to prevent the descent of those having the greater leverage.

[Illustration]

All the simpler devices failed, of course, to work. The more
complicated devices are simply efforts to overcome the elementary
principles that prevented the simpler devices from working. Among
these that of Dixon Vallance (see page 34, ante), is best adapted
to illustrate the folly and the fallacy of these various devices to
overcome elementary principles.

We here refer to the figure appearing on page 35, ante, shown in
connection with Dixon Vallance's Device. The obvious purpose was to
keep all the weights close to the hub, except those depended upon to
produce continuous motion by their greater leverage.

To the untrained and untechnical person it would perhaps not be
manifest at first just why the Vallance machine failed to work. Here is
its failure: Weight "c" must be raised toward the hub of the wheel. To
raise that weight requires the application of force. That force must be
supplied. The belt "cc" would work more freely if it were not elevating
a weight, and the force required from "w" to turn the wheel so as to
elevate the weight at "c" is counterbalanced by the resistance the
weight "c" offers to being raised, and consequently to the motion of
the belt and in turn to the progress of the wheel.

It should always be remembered that, omitting friction, the energy
exerted by a descending body is the _perpendicular distance_ of its
descent multiplied by its weight. For, notwithstanding what its course
may be from an elevated point to a lower point the energy accumulated
in the descent is still the product of the perpendicular distance and
the mass, or weight.

In all of these devices it is apparent that every weight is brought
back by some force from the lowest point it reaches to the same
elevation from which it started to descend. It is axiomatic, therefore,
that the perpendicular ascent is equal to the perpendicular descent.
The ascending weight and the descending weight are, of course, the
same. Therefore, the product of the weight and the perpendicular
distance of _ascent_ is exactly equal to the product of the weight
and the perpendicular distance of _descent_. Hence, there is an exact
balancing of energies, and no motion results. Any motion imparted by
wind, water or steam will, if the moving force be withdrawn, soon be
overcome by unavoidable friction, and a state of rest follows. There
can be no doubt that any attempt to attain Self-Motive Power by means
of wheels, weights, levers, and the force of gravity must result in
failure. The thing itself is physically impossible.

In addition to what is above stated, read carefully Chapter XI, on
Conservation of Energy; also read Chapter XIV, entitled "The Seeming
Probability of Effecting a Continual Motion by Solid Weights in a
Hollow Wheel or Sphere" at page 290 of this book.



CHAPTER II

DEVICES BY MEANS OF ROLLING WEIGHTS AND INCLINED PLANES


Device by Mercury in Inclined Glass Tube and Heavy Ball on Inclined
Plane

Neither the inventor's name nor his nativity can we give. An account of
the invention was furnished by a correspondent to Mechanics' Magazine
in 1829. The account is as follows:

  To the curious who delight in mechanical intricacies, to whom
  ingenuity of contrivance is the goal for which they run, nothing
  seems to afford and require such endless resources as that
  most puzzling thing--perpetual motion. The unfortunate name
  "perpetual motion," if changed for "mechanical experiment," would
  eventually, perhaps, remove the real cause of censuring it, by
  the different idea of the object aimed at.

  I now beg leave to offer some account of a combination of
  movements, which, from its originality, and seeming to possess
  every requisite for retaining it in action, may possibly be
  acceptable.

  [Illustration]

  This diagram shows a side view. On the stand A are raised two
  supports B, each having a center hole at _a_, to receive the
  axle of the balanced apparatus, consisting of C, a glass tube
  containing a portion of mercury G; and D, a grooved scaleboard,
  in which a ball, E, can roll backwards and forwards. F F are two
  jointed levers, which are to serve, when struck by the ball, to
  reverse the position of the compound balance: the whole centred
  at _a_, the tube at _b_, and the grooved board at _c_. In its
  present position, the mercury (it is supposed), having flowed to
  the end C, will depress D, and cause the ball E to roll to D, and
  depress the end G F D; and so on continually.


Series of Inclined Planes

This scheme is of English origin, and was promulgated in 1864. The
name of the inventor is unknown, but he described his invention in a
communication to a scientific publication in the following language:

  The accompanying diagram represents a series of inclined
  semi-tubes connected together in the form of a rectangle.

  [Illustration]

  The ball A, is placed at the top of an incline in such a
  position that it shall descend to B, at which point it will have
  sufficient velocity or gravity to carry it up the ascent to C;
  and so supposing the inclines and ascents to be endless, the
  repetition of the movement must be also endless. I think it is
  not unreasonable to suppose that a perpetual movement of the
  ball will take place, from the fact that the velocity imparted
  to it by its _first_ descent is sufficient to carry it from A to
  C, _those two points being at the same level_. I think the only
  thing to guard against is the ball rushing over the point C,
  and thus accelerating the velocity at each descent. The incline
  on road upon which the ball runs can be made either circular,
  square, octagonal, or, in fact, almost of any form.


Device by Oscillating Trough and Cannon Balls

(Name of inventor unknown)

An adaptation from a "Perpetual Pump" substituting cannon-balls for
water.

An account of this invention was published in London in 1825, in the
language of the inventor, who says:

  The description of the perpetual pump has suggested to me
  whether the long-sought "perpetual motion" may not be found by a
  simple mechanical alteration of that machine, and substituting
  a cannon-ball as a _primum mobile_, in lieu of the water, not
  always obtainable. I would recommend that in the bottom of
  the trough be inserted at each end two dropping-boards, of a
  triangular form, moving on an axis at one corner, one of which
  falling below the level of the trough at the elevated end, the
  other shall be raised by the stop affixed to the standard-post,
  which, throwing the ball again back to the former end, shall
  depress that, until the same process is repeated in perpetual
  activity.

  DESCRIPTION.--Fig. 1. A, the trough, swinging on an axis at B. C,
  the cannon-ball, raised by one of the dropping-boards, D, whilst
  the other falls through the opening at E, into the trough. F, the
  support or stop, raising the dropping-board D. The center of the
  trough ought to be pierced, leaving the sides as a support to the
  ball, which ought not to be wider than the ball may travel freely
  through.

  [Illustration]

  Fig. 2. D D, the dropping-boards, which pass through the center
  so as to leave a sufficiency of the trough as a resting place for
  the ball to give a momentum, and depress the trough, previously
  to its being again raised by the dropping-board.

We meekly venture to call the attention of this inventor, if he is
still living, and to any others who may be working along the same
line, that to our certain knowledge water is more generally obtainable
than cannon-balls. We, therefore, suggest the use of water instead of
cannon-balls.


Unpublished Incline Plane and Weights Devices Noted by the Author

Except the preceding three devices the author does not remember ever
to have seen reported in any book, patent, application for patent,
or report, the account of a device for obtaining self-motive power
by means of weights and inclined planes, and yet, it is believed by
the author from the use that has been made of inclined planes and
rolling weights in demonstrating mechanical principles by many natural
philosophers, and also from devices that have from time to time been
brought to the attention of the author during thirty years last past,
that the inclined plane with rolling weights has been a fertile field
of folly among Perpetual Motion seekers.

On a number of occasions the author has been asked to view and inspect
mechanical devices of that kind, which it was claimed by the confident
inventor and his friends "would surely work when just one little thing
could be overcome." The phraseology was sometimes varied a little from
the preceding quotation, but the substance was always there.

In one instance the device attracted the enthusiastic attention
and elicited breathless interest from a doctor and surgeon of much
more than ordinary skill and intelligence in his profession, and
was hopefully regarded by a number of other persons who had had
schooling advantages and were supposed to be versed in the rudiments of
mechanics, and, it would seem to the author, ought at first sight to
have perceived the fallacy and hopelessness of the inventor's dreams.

All of these claimed inventions relying on the inclined plane with
rolling weights were so nearly alike in the principle involved that all
may be illustrated by the following explanation:

[Illustration]

The above figure shows a vertical section of a device that illustrates
the controlling principle in all of these devices. It is manifest that
the balls between A and C are hanging equally between A D and C D, the
points of suspension A and C being in a horizontal line. It is also
manifest that there will be a greater number of balls on the sloping
incline A B than on the sloping incline B C. The Perpetual Motion
seeker has always argued to himself that the _four_ balls between A and
B should pull stronger to the left at B than the _two_ balls between
B and C can pull. Sometimes this device has been varied whereby the
balls would roll freely down the incline from B to A and then roll back
toward C down another incline where they would be supposed to strike a
lever and impel a ball from C to B, which ball would then roll down the
incline B A, and so on indefinitely.

The error of all this lies in the fact that the four balls between B
and A will not elevate the two balls between B and C for the reason
that they are on a less inclined slope. As we would ordinarily state
it, B C is a "steeper" incline. One ball between B and C by force of
gravity pulls stronger toward C than one ball on B A will pull toward
A. It is manifest, therefore, that an equilibrium requires a greater
number of balls on B A than B C.

B A is longer and accommodates a greater number of balls than can be
accommodated on B C. The number of balls that can be accommodated
on the respective sides is always found to be such that the small
number of balls between B C pull in the aggregate toward C the same as
the greater number of balls between B and A pull toward A, and thus
equilibrium is established.

It is manifest, therefore, that with the pull from B toward C equal to
the pull from B toward A, the mechanism finds its balance and motion
ceases. This is true of all similar devices.



CHAPTER III

HYDRAULIC AND HYDRO-MECHANICAL DEVICES


Enbom & Anderson's Pump

"June 13, 1882 U. S. Patent, No. 259514 was granted to Andro Enbom and
John A. Anderson, of Augusta, Kansas, U. S. A., on

"Improvements in Pumps."

It seems probable that the inventors did not suspect, and that the
patent office examiners did not discover that the device had in
the claimed "Improvement" the essentials of self-motive power. An
examination of the specifications clearly shows, however, that the
claim of the inventors that "the water lifted by the pump is caused in
its passage over the wheel A² to give power to the same and thus lessen
the labor required," presupposes the principle of self-motive power.
The following figure taken from the specifications and the following
excerpt from the specifications illustrate the intended operation:

The operation is substantially as follows: By the application of power
to the crank a revolution is given to the main shaft A, and by means
of this the pump-handle is properly actuated through the intermediate
mechanism described. The water lifted by the pump is discharged
through the spout _e´_ to the buckets of the wheel _a_², and by these
is delivered to the trough F. By means of the construction described
the water lifted by the pump is caused, in its passage over the wheel
_a_², to give power to the same, and thus lessen the labor required to
produce a given result.

[Illustration]

We suggest to the inventors that if instead of elevating the water to
the place of discharge E´ they discharge it at the level of the trough
"F" they will lessen the distance of elevation and will save many times
the energy that can be realized by the descent of the water from the
level of E´ to the level of "F."


Device of "Ed. Vocis Rationis"

In 1831 Mechanics' Magazine printed an article contributed by a
correspondent who signed himself "Ed. Vocis Rationis." He claimed to
have invented a very powerful Perpetual Motion Machine.

His enthusiasm is as interesting as his device is absurd. We give the
article as published in full:

  [Illustration]

  I propose to endeavor to show how my plan of perpetual motion
  could be applied to practical and useful purposes. With a
  view to this, I give the prefixed sketch, with the following
  description of its construction and use: Let A represent the
  side-wall or gable-end of a house, from 40 to 50 feet in
  elevation; B, a cistern, filled with water, having an orifice
  near its bottom, and another open at the top, for the ready
  escape of waste water, as before; C, a reservoir, so far filled
  with water as not to come in contact with the bottom of the
  water-wheel D, which, being an undershot wheel, may, of course,
  be of such radius as is suitable for the power required to raise
  the water. Let E be another cistern, filled with water, equal
  to and provided with orifices as in cistern B, both orifices
  together discharging water faster than it escapes from the
  lower orifice of the cistern B; F, two (or more, as the case
  may require) pumps, or expressing-fountains, supported against
  the walls by ties _d d_, and having their cylinders inserted in
  the reservoir C, and their lower suckers fixed at a little less
  than 32 feet above the surface of the fluid in the reservoir
  C. These expressing-fountains discharging their water into
  the cistern E a trifle faster than it escapes from its lower
  orifice, at an elevation of at least 33 or 34 feet above the
  surface of the water in the reservoir C, will afford space for
  water-wheels, supported against the wall by the upright K, say
  three water-wheels, G H I, of at least eight feet in diameter
  each, or two only of greater diameter. The upper wheel G being an
  undershot one, if not of greater radius than four feet, which it
  might be, may have its axle fixed at an altitude of at least 30
  feet, and allowing the space of a foot between each water-wheel
  for the troughs a and b, which collect and convey the water from
  wheel to wheel, will give a space of 22 feet, occupied by the
  three water-wheels, leaving 10 feet for the descent of the water
  by the trough _c_ to the cistern B (which may be four or five
  feet in depth), and thence to the reservoir C, which may be three
  or four feet in depth; also the cistern E may be four or five
  feet in depth, and all of other corresponding dimensions _ad
  libitum_. To produce the motion, remove the plugs or stoppers
  from the lower orifices of the cisterns E and B; the water
  rushing from the latter turns the great water-wheel D, which
  works the expressing-fountains into the upper cistern E; from the
  orifices of which, the water escaping turns the undershot wheel
  G (which may be of larger diameter, if required); whence being
  collected by the spout _a_, it shoots over and turns the wheel H;
  being collected by the spout _b_, it turns the overshot wheel I;
  whence being collected by the spout _c_, it is conveyed into the
  cistern B, from thence to the water wheel D, and, finally, into
  the reservoir C, from which it is raised again by the fountains
  into the upper cistern E; and so on as long as you please, or
  as long as the whole keeps in repair and in good order. The
  apparatus may, with facility, be stopped for convenience at any
  time without fear of derangement, because the fountains carrying
  water faster than it escapes from the lower orifices, the
  cisterns will be always full; and it may be again set in motion
  with equal facility. With the above proviso, it cannot stop till
  the prevailing natural causes which gave it motion--viz., the
  pressure of the atmosphere and the descent of water, which in
  their nature and tendency are of themselves perpetual--shall be
  diverted. Thus you may have the power, free and disposable, of
  three water-wheels in perpetual motion, to be applied to such
  useful purposes of machinery within the building as its inmates
  may require. A supply of water-mills might be thus provided in
  any situation--in the center of the metropolis or other large
  towns--in places subject to a deficiency of rivulets suitable for
  mills on the common system. Neither would there be any necessity
  for resorting to rivers, or raising immense buildings upon their
  banks; wherever there was a convenient house, it might be readily
  appropriated with little further expense than machinery.

      Yours, etc.,
      ED. "VOCIS RATIONIS."

    Jan. 10, 1831.


Böckler's Plates

In 1662 George Andrew Böckler published a work on mechanics. The work
is replete with fine drawings. Not a great deal of space is devoted
to Perpetual Motion devices, but the following three plates which are
numbered 150, 151 and 152 in his work are shown as Perpetual Motion
devices.

These devices do not appear to have been the inventions of Böckler
himself, but are devices noticed by him. They are not explained with
any considerable detail.

[Illustration]

Figure 150 is "A Water Screw," and it is stated that the inventor
intends it for a Perpetual Motion device, and it is further stated that
he has scarcely worked out his purpose. The author states that the
excellence consists in the proportion and distribution of the wheel,
balls and weights, and says further that he does not describe it in
detail, and that it is his intention to publish at a future time a
separate treatise on Perpetual Motion in which this and other similar
machines will be considered.

He gives the first as Fig. 150, "A Water Screw," the purpose of which
is not quite so obvious as to be understood at the first view of the
figure; for the inventor intimates that he intends it for a perpetuum
mobile. He has, however, scarcely worked out his purpose, as we may,
nevertheless, say without any prejudice to the inventor. Nor will
we here describe how the excellence of this work consists in the
proportion and distribution of the wheel, and the balls or weights,
because it is our intention to publish, at a future time, a separate
treatise on the perpetuum mobile, in which we shall consider this and
several similar machines.

Figure 151 is "A Water Screw," having a grindstone for cutlery. The
author remarks concerning this machine as follows:

  [Illustration]

  This machine also is intended for a perpetuum mobile. The
  inventor discharges water from the reservoir A, by the canal B,
  on the water-wheel C, which turns the open screw-cylinder D, by
  means of the toothed wheel E, the cog-wheel F, the spoked wheel
  G, together with the cylinder H, and the spoked wheel I, whilst
  this spoked wheel I, catching the small cog-wheel L, together
  with the cylinder M, and the handle R, turns the small spoked
  wheel of the screw-cylinder H, and the screw-cylinder itself,
  and thus draws up again the water discharged from the reservoir
  A through the spiral screw Q. In order to render this machine
  useful, a couple of grindstones are placed on the cylinder D.
  Concerning this machine, it is particularly to be considered,
  whether a sufficient amount of water can be raised again, as has
  been frequently remarked before about similar works.

Figure 152 is said to represent "A Double Water Screw, with Double
Pump," and the author observes:

  This machine is, on the whole, similar to the preceding ones.
  The water is discharged from the round or square reservoir A,
  by B, on the water-wheel C. A continual supply of water for the
  water-wheel is provided as follows: The crown wheel H is fixed
  on the upright cylinder M, and is turned by the revolutions of
  the cylinder, whilst it turns at the same time the upper wheel L,
  which, acting on the spokes of the double screw K, K, draws up
  sufficient water by I, I, and then, as stated, discharges it by
  B, on the wheel C.

  The machine may be rendered useful by furnishing the cylinder D
  with the double crank E, to drive the two pistons of the tubes
  F, F, which lift the water through the pipes G, G, into the
  reservoir N, whence it may be carried off for service.

  [Illustration]


John Linley's Hydraulic Device. 1831

An account of this was published in 1831 in Mechanics' Magazine, and is
as follows:

  32. Perpetual Water-wheels and Pumps (vol. 14, 1831).--A
  correspondent gives a description of a plan which he says he
  believes to be entirely original, and not without considerable
  claims to plausibility, thus:

  [Illustration]

  Let _a b c d_ represent a wooden cistern, or trough, half filled
  with water; E F G, three overshot water-wheels, supported by the
  upright piece; K is another cistern, or trough, filled with water
  up to the dotted lines; P is a syphon to convey water from the
  lower to the upper cistern K; R is a beam supported from the
  cistern; S T U are moveable cranks attached to the horizontal
  shafts through the center of the water-wheels--each crank has a
  connecting-rod to the beam R; V W are two curved spouts to convey
  water from one wheel to another. It may be well here to premise
  that each water-wheel has a pump and beam, as only one is seen in
  the section.

  Now, in order to put the machine in motion, it is only necessary
  to draw a portion of water from the syphon over the wheel E,
  which immediately revolves, consequently the pump L M draws water
  from the lower to the upper cistern K. Now, the water passing
  over the wheel E is collected by means of the curved spout V,
  and is conveyed upon the middle wheel F, which also gives motion
  to another pump, and draws in like manner. Again, the water
  passing over the middle wheel, is collected as before by another
  curved spout W; consequently, the lower wheel is put in action,
  accompanied with another pump. Hence it is obvious that three
  water-wheels and three pumps are worked by one stream of water
  from the syphon. What more is required to perpetuate its motion?

      John Linley.

    Wicker Sheffield, May 28, 1830.


Device of Author of the "Voice of Reason"

In 1831 a contributor who signed himself Author of the "Voice of
Reason," furnished to the scientific journals of England an account
of what he claimed was a Perpetual Motion Device invented by him. It
should be said to his credit that he claimed no surplus power for his
device--only that it would run itself. He, in fact, stated that his
machine could not perform more than the simple operation of pumping its
own water.

The principle upon which he relied is sufficiently shown by the
following figure, and the following excerpt from the contributed
article:

  Observing that persons no less distinguished than Bishop Wilkins,
  the Marquis of Worcester, etc., have amused themselves with
  such things as perpetual motion, it may be some apology for a
  humble individual residing as I do in a very retired part of
  the country--scarcely within reach of much society--to confess
  that by way of a little rational amusement and relief to the
  mind, I have at times, amid a variety of other investigations
  and inventions, amused myself amongst the rest, with this of
  perpetual motion. The result I will, with your permission, lay
  before your readers. That I trespass upon your pages, you are
  indebted to your correspondent, Mr. Linley, whose invention
  I thought might partially lead to an anticipation of one of
  my own, a model of which I constructed a short time ago. The
  system which first came to my mind, as likely to lead to the
  accomplishment of perpetual motion, was that of the syphon;
  experimenting with which, opened discoveries that might prove
  useful in hydrostatics. Amongst these was a mode of equalizing
  the horizontal surface of the water in two separate vessels of
  different altitudes. The following sketch will afford an idea of
  my invention.

  [Illustration]

  Let A be a vessel, having two orifices, one at the bottom of it,
  _a_, and the other open at the top for waste water _b_, filled to
  the brim. B, a reservoir, so far filled with water as not to come
  in contact with the bottom of the great wheel C, whose axle turns
  in the wood _c_, attached to the side of the reservoir; _d_, a
  crank fixed to the axle of the great water-wheel, which turning
  moves up and down the rod _e_, attached to the beam E, which
  works the pump D, having its cylinder inserted in the reservoir
  B; _f_, an upright attached to the upper vessel A, to form a
  support for the beam E; the whole, together with the cylinder
  of the pump, being supported and tied together by the woodwork
  _g g g_.

  To produce the motion, draw the plug from the orifice _a_,
  from which the water gushing out with considerable force will
  immediately turn the water-wheel, which communicating motion, by
  the crank _d_ and rod _e_, to the beam E, will cause the pump D
  to be worked, the water from the spout passing into the upper
  vessel A. Now, the cylinder of the pump, if one only be used,
  must be of suitable dimensions, or the velocity of its movement
  so increased by means of a multiplying-wheel as to enable it to
  discharge water into the upper vessel A faster than the same
  escapes through the lower orifice _a_; consequently, the vessel
  A will soon overflow from the capacious opening at _b_, to which
  a trough is attached, which collecting the waste water, causes
  it to descend also upon the circumference of the water-wheel;
  thus contributing to its movement, and at the same time tending
  to preserve an uniform supply of water in the reservoir for the
  continued action of the pump. Hence you have a perpetual motion,
  so long as the whole keeps in repair and in good order, which is
  all that can be expected of any perpetual motion, constructed as
  it must be of perishable materials.

  But of what use are all the perpetual motion machines, if they
  can perform no other work than that of keeping themselves in
  motion? For it is evident, in the case of my machine, that if I
  wish to increase the power of the wheel, fixed as it is in size,
  radius, etc., I must increase the jet of water, and consequently
  the pumps must be made of corresponding dimensions, or exert a
  corresponding increase of force or velocity to replace the water;
  so that it is evident, neither Mr. Linley's machine nor mine,
  in their present fixed state, can perform more than the simple
  operation of pumping their own water.

  And this is the case with all the perpetual motion machines I
  have ever observed--they can exert no useful or disposable power
  beyond that of keeping up an equilibrium, or getting beyond the
  point of equilibrium.

        Yours, etc.,
      AUTHOR OF THE "VOICE OF REASON."


An Italian Device

In 1825 there was published in London in Mechanics' Magazine the
account of a very ancient invention by an Italian. He had written an
account of his invention in Latin. It had been translated and furnished
to Mechanics' Magazine by a correspondent of that Magazine. The
communication so furnished as published is as follows:

  The underwritten is translated from an ancient Latin book * * *
  (entitled "De Simia Naturæ," Autore Roberto Fludd), which treats
  of every science known at the time it was published, and largely
  of the science of mechanics. What followed I have extracted
  merely to show that the discovery of the perpetual motion was as
  nearly attained then, perhaps, as it is now.--I am, &c., P.

  _Of another useful invention for raising water easily, by
    the which a certain Italian ventured to boast that he had
    discovered the Perpetual Motion._

  DESCRIPTION OF THE INSTRUMENT.--A is an exhauster, or pump.

  [Illustration]

  B, a little wheel placed at the bottom of the exhauster, about
  which pestils, or circular flaps of prepared leather, revolve
  lightly, so that they rise easily: they are connected by crooked
  iron.

  C C C, pestils, or circular leathers, by means of which the water
  is raised in the pump.

  D, a wheel, by which the said circular leathers are raised up.

  E, a pinion, moving the wheels D and B.

  F is a wheel, continued from the wheel G, whose teeth the pinion
  E propels circularly.

  H, a pinion moving the wheel G.

  USE OF THE INSTRUMENT.--This instrument is classed with those
  of the first sort, on which account it is absolutely necessary
  for a multitude of purposes, because it bears upward a large
  quantity of water with the least labor; for the number of wheels
  is not variable; but the length of the receiver A is about the
  proportion of 35 feet, and its breadth one foot and one-third.
  The concavities of it should be made exactly round, that they
  may not lose any water by contracting in their ascension; the
  concavity of the pump, therefore, should be perfectly round. The
  great water-wheel should be 24 feet diameter, and the wheel G 20
  feet.

  The Italian, deceived by his own thoughts, conceived that as
  much water would be raised by this pump as would keep the wheel
  perpetually in motion; because he said that more force was
  required at the extremity of this machine than at the centre;
  but because he calculated the proportions of power wrong, he was
  deceived in practice.


P. Valentine Stansel's Device. Prior to 1657

(Exact date not known):

  [Illustration]

  A, B, C is a large cistern of water, above which is another
  cistern D, E, which is supplied from the lower cistern by the
  pump X, operated by the water-wheel M, N, the crank L of which is
  attached by a rod K to the horizontal beam H, I, K, which swings
  at H, from the side of the upper cistern, as shown at F, G, H.
  The force-pump X, on the depression of the plunger O, causes
  the water to rise up the vertical pipe P, Q, R, S, and thence
  discharge itself into the cistern D, from which a small portion
  is allowed to escape through the short pipe T, V, whence it falls
  on the water-wheel, and so on continuously.


Vogel's Device

In 1847, A. F. Vogel, of Leipzig, invented what he called

"Hydrostatic General Mobile."

It was described at the time in a pamphlet, and its operation
is sufficiently illustrated by the following annexed figure and
explanation:

  [Illustration]

  A water-wheel, A, B, C, D, raising the water by means of which it
  is to be operated. This is effected, he supposes, by the wheel
  acting at A, by the pressure of one of six pins D, on a vertical
  rod, attached to a horizontal beam, working on a centre, and its
  opposite end being secured to the pump-rod of the barrel M, N.
  The projector has an idea that by means of flaps, which close the
  cells of the wheel as they pass under rollers at B, while at C
  there is a similar contrivance to open the flaps and let out the
  water, and therefore by its retention on the descending side it
  will become more effective in turning the wheel.


A Water Wheel-Driven Pump

This device is claimed by the writer to be an adaptation of Rangely's
Patent Roller Pump. A description by the writer, whose name is not
given, was published in Mechanics' Magazine, 1823, in the following
language:

  I think it possible to produce a self-moving power by such a
  machine as that, a drawing of which is now prefixed. From its
  very simple construction, a very brief description is necessary.
  A represents a pump immersed in a reservoir B; the pump is worked
  by the rotary motion of the water-wheel C, which is four feet
  in diameter. On the shaft of the water-wheel is the drum-wheel
  D, working by a small cord the wheel E, on the axis of the pump
  discharging the water by the pipe F into a reservoir G over the
  water-wheel. In this reservoir is a cock to regulate the quantity
  of water to be discharged on the wheel. The wheel on the shaft of
  the water-wheel being nine inches diameter, and the wheel on the
  axis of the pump three in diameter, the latter will consequently
  make three revolutions for one of the water-wheel. As the pump
  is not required to turn with great velocity, the speed might be
  regulated by the quantity of water thrown on the water-wheel, the
  latter being four feet in diameter, and the wheel on its shaft
  nine inches; consequently the radius or arm of the wheel has near
  4½ powers to counteract the friction of the axis of the pump and
  water-wheel, and of a fine cord passed over the wheels D and E.
  If necessary, the friction of the machine might be still farther
  reduced by the axes of the pump and water-wheel being made to run
  in gudgeons with friction rollers.

  [Illustration]

  The pipe H is intended to convey the surplus water from the
  reservoir over the wheel to the reservoir below.

  The pump might easily be turned by a cog-wheel; but this is
  unnecessary, as the cord passing over the drum-wheels will do
  equally well, and is, besides, a more simple method.


"A Journeyman Mechanic's" Device

The gentleman, whose real name is unknown, but who styled himself "A
Journeyman Mechanic," made an invention, an account of which appeared
in "Mechanics' Magazine," in 1831. It was an attempted adaptation of
the wellknown principles of Barker's Mill.

The inventor undoubtedly thought he had successfully solved the long
sought problem of Self-Motive Power, and he benevolently and graciously
offered to contribute his valuable invention to the world, having "no
wish to profit by monopoly."

We cannot but contrast the plenary benevolence of his heart with the
mechanical paucity of his head. He describes his invention with the
following language and figure:

The inventor offers the accompanying sketch, with description of an
Hydraulic Mover, for communicating power to machinery, and recently
invented by him:--

  A is a hollow cylinder or pipe, forming the upright shaft of a
  mill on Barker's well-known and effective centrifugal principle.

  B B, the lateral pipes from ditto; _a a_, the jets of water,
  whose centrifugal force gives the motion.

  C, beam to support the machinery, built at each end into the wall
  D D.

  E E, two cog-wheels to communicate the motion to

  P, the rod of a pump (on Shalder's principle), which derives
  its supply from the well into which the water from the pipes is
  conducted, which it raises to

  [Illustration]

  H, a cistern into which one end of a syphon, I I, is introduced,
  the other end of which is soldered with an air-tight joint into
  the top of pipe A, to which it thus supplies the water which is
  continually running from the pipes B B, producing a constant
  motion which may be given by carrying the horizontal rod F
  through the wall D, to machinery for any purpose. And, if the
  statement in the pamphlet on Hydrostatics, by the Society for
  the Diffusion of Useful Knowledge, as to the effect of Barker's
  Centrifugal Mill, be correct, the power gained must be very great.

  The advantages of the invention are obvious. The whole of the
  machinery for a large factory may be contained underground,
  which, indeed, will be the most desirable situation for it,
  and valuable room will thus be saved; the expense of erection
  will not be great; and the saving in coals, &c., necessary for
  a steam-engine of the like powers, will be immense. I might,
  perhaps, have secured much benefit to myself by taking out
  a patent for the discovery, but I have no wish to profit by
  monopoly. All I desire is, that it may be recollected that the
  machine was invented by one who is

      A JOURNEYMAN MECHANIC.


James Black's Device

In 1858, James Black, Machine Maker, of Edinburgh, Scotland, applied
for a British patent on

"An improved mode or means of obtaining, applying, and transmitting
motive power."

The expected operation is sufficiently illustrated by the following
figure and excerpt from the specifications:

  A face plate or disc is fixed on an axis, and has formed in it
  a number of wipers, eccentrics, or curved paths, which receive
  (in the space taken out) a pulley or roller, free to revolve
  on its own axis, and attached to an adjustable lever in equal
  balance with the desired lift or pressure. On rotary motion being
  communicated to the plate (by a band or otherwise), the pulley or
  roller moves round the eccentrics or paths, imparting a rocking
  motion to the lever (similar to the action of a beam), wherefrom
  motion may be transmitted or applied, as desired, or converted by
  suitable appliances into any description of motion.

  [Illustration]

  In connection herewith, a pump may be set in a tank of water,
  and a tank added above; on the same shaft with the face plate
  is a water-wheel driven by the water from above; when it passes
  the centre, the water falls into the lower tank and is pumped up
  again; whatever weight of water is in each stroke is equalized by
  a balance weight on the lever; the number of eccentrics and size
  of water-wheel may be increased to correspond with the quantity
  of water required to secure a desired power.

  One means of imparting rotary motion from my arrangement is by
  attaching at the end of the lever a crank and connecting rod of
  same radius as the lift of the lever, carried over the centre by
  a fly wheel.

  The invention is applicable to the actuating of pumps, mincing
  machines, and other machinery, instruments, and apparatus, and to
  parts thereof; to propelling on land and water, and to various
  motive purposes.

  Fig. 1 is an elevation, showing an arrangement for obtaining
  power according to my invention. X is the general framework
  of the apparatus; A, a disc or plate, mounted on a shaft E,
  and formed with curved paths B; the same shaft E also carries
  a water-wheel W, provided with vanes or blades _w w_, as is
  usual; C is a roller, working in the paths B, and connected to
  a lever D, attached to rods _d d_ of pumps G G. G¹ is a balance
  weight at the further end of the lever, which is supported in
  the bearing _f_; H H are tanks fixed below the water-wheel, and
  I is a tank set above it; _i i_ are supply pipes, for conveying
  the water from tanks H H to the tank I; _j j_, escape water
  pipes. The water falling from the tank I on the wheel W, drives
  that wheel in the usual manner; and when it passes the centre,
  the water falls into the lower tanks H, from which it is pumped
  up again into the upper tank I by the pumps G, actuated by the
  levers E, driven by the rollers C, in the pathways B of the face
  plate A, as the latter is caused to revolve by the revolution of
  the water-wheel W on the same shaft with it, thus producing a
  continuous motive power.


Archimedean Screw and Liquid

This device was made public by a communication from a correspondent to
"Mechanics' Magazine" in England, in 1823. The device is described as
follows:

  [Illustration]

  A is the screw turning on its two pivots G G; B is a cistern to
  be filled above the level of the lower aperture of the screw
  with mercury (which I conceive to be preferable to water on many
  accounts, and principally because it does not adhere or evaporate
  like water); C is a reservoir, which, when the screw is turned
  round, receives the mercury which falls from the top; D is a
  pipe, which by the force of gravity conveys the mercury from
  the reservoir C on to (what, for want of a better term, may be
  called) the float-board E, fixed at right angles to the centre
  of the screw, and furnished at its circumference with ridges
  or floats to intercept the mercury, the moment and weight of
  which will cause the float-board and screw to revolve, until,
  by the proper inclination of the floats, the mercury falls into
  the receiver F, from whence it again falls by its spout into the
  cistern G, where the constant revolution of the screw takes it up
  again as before.

  To overcome this (the power of the fluid in the screw to turn
  it backwards), I thought of placing a metallic ball, or some
  mercury, on the ledge above the floats (as at H in the drawing),
  of just so much weight, and no more, as would exactly neutralize
  this backward endeavor; whether or no this would increase the
  difficulty of raising the mercury in the screw I cannot say,
  having never tried the experiment.


John Sims's Problem. 1830

John Sims, a Welshman, furnished the following suggested device to
"Mechanics' Magazine" in 1830:

  Let us suppose an apparatus to be constructed of the description
  represented in the annexed engraving: _a_ is a water cistern,
  whence water is to be raised by the pump _b_, to supply the
  cistern; _c d_ is a small pipe with a stop-cock at _e_, which
  lets the water from cistern _c_ into a strong water-tight bellows
  _f_. The bellows have no valve, but a cock _g_ to let out the
  water into cistern _a_; _h_ is a weight, and _i_ a rack on the
  top of the bellows which works in the cogs on the axle of the
  large cog-wheel _j_; _j_ turns the little cog-wheel _k_, that
  gives motion to the arm _l_, and works the pump-handle _m_; _n_
  is an upright rod on the end of the lever _o_, which rod has a
  turn at _p_ and _q_ for the top of the bellows to press against
  in ascending and descending. The water being let into the bellows
  from the pipe _d_, will cause the top of the bellows, with the
  weight and rack, to ascend till the former reaches and presses
  _p_, which will move the lever _o_ and the arm or rod _r_; by
  which means the stop-cock _e_ of the pipe will be shut, and the
  cock _g_ opened, and the water let in from the bellows into the
  cistern _a_. The top of the bellows will now descend till it
  comes down and presses the turn _q_, which will again shut the
  cock _g_ and open _e_, on which the water will again flow from
  the pipe into the bellows, and cause the top with the rack to
  ascend.

  [Illustration]

  Now it is generally known that the power of an hydrostatic
  bellows is thus calculated:--

  As the area of the orifice or section of the pipe,

  To the area of the bellows:

  The weight of water in the pipe is,

  To the weight the bellows will sustain on the top-board.

  We will suppose, therefore, the pipe _d_ to be 10 feet high, with
  a bore equal to 1 square inch, which would give 120 cubic inches,
  and about 4¼ lbs. of water. Let us suppose, also, the boards
  of the bellows to be 20 inches square, which gives 400 square
  inches. When the water is let from the pipe into the bellows,
  there will be a pressure of 4¼ lbs. on every square inch, which
  on the whole will amount to 1,700 lbs. Now take half of this
  force and place it on the top of the bellows; there will then be
  a working power of 850 lbs. up and down, and allowing the bellows
  to raise one foot, it will contain about 20 gallons of water.
  Now the question is, will not the machinery, with a moving power
  of 2 feet and 850 lbs., raise 20 gallons of water 10 feet, which
  would, of course, cause the motion to be perpetual?--JOHN SIMS.

    Pwllheli, North Wales, Dec. 11, 1829.

The foregoing device brought from another correspondent the following:

  Had Mr. Sims gained the power exerted by the descending weight
  on his bellows, he would have been fortunate indeed; but it
  unfortunately happens that its returning power (or an equivalent)
  was expended in raising it.

  With respect to his question, whether a circulation of water
  would be kept up by the arrangement, I answer, no; as the
  velocities will be in the inverse ratios to the forces, and the
  descending column of 120 inches must expend itself forty times
  to raise the ascending one to the height of twelve inches, as
  proposed:--

  10 ft. or 120 in. × 40 = 4,800, lifting force or power.

  400 in. × 12 = 4,800, opposing force, resistance, or weight.

  Here is an equilibrium, and nothing gained to overcome friction
  or the weight of the atmosphere on the piston of the pump. Were
  it possible to annihilate both friction and atmospheric weight,
  even then, unless the power exceed the weight, the power would
  not be a moving one.


A Perpetual Pump, by an Unknown Inventor

In Volume I of "Mechanics' Magazine," 1823, appears an account by a
correspondent of a Perpetual Motion device which is illustrated by the
figure, and the quotations following:

  _a b c d_ is the section of the reservoir, &c., showing the
  wheel, the pump, &c. A B is an overshot water-wheel; C D the
  working beam; E the pump; F a pipe from the top of the pump,
  through which the water was to fall upon the wheel; C G an arm,
  communicating, by means of a crank attached to an horizontal
  shaft through the centre of the wheel, motion to the lever or
  working beam, and so raising water from the reservoir by means of
  the pump; H I the water. It was supposed that the water which had
  fallen upon the wheel into the reservoir would be raised by means
  of the pump, fall through the horizontal pipe, and so produce a
  continued rotary motion.

  [Illustration]

The persistence of Perpetual Motion workers is amusingly illustrated
by the inventions of William Willcocks Sleigh and Burrowes Willcocks
Arthur Sleigh. Their devices were so extremely complicated and not
susceptible of being understood, and hence are mentioned rather than
shown in this work.

In 1845, William Willcocks Sleigh, a doctor of medicine and surgery,
of Chiswick, Middlesex, England, applied for and obtained British
Patent on what he called

"A Hydro-mechanic apparatus for producing motive power."

He took out other patents on hydro-mechanical devices in 1853, 1856,
and 1860. Then in 1864, his son, Burrowes Willcocks Arthur Sleigh took
out two patents on similar devices, and then in 1866, still another
patent.

The specifications for each of the above mentioned patents are lengthy
and detailed. The inventors evidently had the greatest confidence in
their efforts, though surely they never put them to actual test. They
seemed to have been mechanically stupid, and incapable of correct
mechanical thinking, but their efforts were so tireless and so earnest
that we submit that the Sleigh family had done its full, fair share in
the efforts to accomplish Self-Motive power.

Equally amusing are the efforts of James Smith of Seaforth, Liverpool,
and Sidney Arthur Chease, Liverpool, gentlemen: These two co-laborers
applied for British patents on four different Hydro-mechanical
devices--one in 1858, two in 1863, and one in 1865. On three they
obtained patents, and on the other one provincial protection. One of
them seems to have been a capitalist, and the other one a machinist.
Their models were complicated beyond understanding, and apparently
they were laboring in the dark without intelligent plan. They seemed to
have thought that when a complicated mess of machinery parts and fluid
were assembled Perpetual Motion must somehow result.

Nothing could be gained by setting forth their inventions fully, but
their labors were so great, and their efforts so intense that we feel
like preserving their names from oblivion, and hence we give them
mention here.


Why Hydraulic and Hydro-Mechanical Devices for Obtaining Perpetual
Motion Failed to Work

Next to wheels and weights, the use of liquids in a hydraulic,
hydrostatic, or hydro-mechanical manner have been sought to be utilized
by Perpetual Motion seekers as a means of obtaining energy from the
machine not supplied to the machine. The foregoing are only a few of
the many devices of that kind, but they are the most simple of those
that have been brought to light, and consequently better illustrate
the manner in which it has been sought to utilize the interesting
properties of liquid pressure and mobility in the solution of the
problem.

An examination of the preceding devices discloses that in each case the
inventor sought by the energy of the descent of a liquid to elevate
through the same distance of ascent the same or a greater quantity of
the same liquid, or in some cases to obtain from the pressure of a
liquid a greater force than is required to expand a bag, bellows or
vessel, submerged the same distance below the level.

The impossibility of all of these schemes is apparent from the same
reasoning that is applied to illustrate and show the impossibility of
obtaining Perpetual Motion by the use of wheels, weights, levers and
the force of gravity.

In each case the basic idea and error was in supposing that by some
possibility the descent of a liquid through a given distance could be
made to deliver more energy than would be required to elevate the same
quantity of liquid the same distance. As a matter of fact, the descent
of a liquid, the same as any other weight, through a given distance
represents exactly the amount of energy necessary to elevate the same
weight of liquid through the same distance measured vertically. Some
loss by friction of the liquid in the containing tubes is inevitable as
well as from friction in the working parts of the mechanism. Therefore,
as this loss continues, some outside energy must be supplied. If all
friction could be eliminated (which is an impossibility) and if the
liquid were started in motion, the motion would be constant, but no
energy could be taken from it for running other machinery without
reducing the motion.

There have been many arguments on this subject. We select one which was
elicited by the publication in "Mechanics' Magazine" of an account of
the device of the author of the "Voice of Reason." This argument was
published in "Mechanics' Magazine" in 1831, and is as follows:

  I am induced to make an attempt to demonstrate the utter
  impossibility, under any circumstances, of making a water-wheel
  that will supply itself instead of having any surplus power.

  The accompanying drawing represents part of an overshot wheel
  in section, the buckets only part filled, by which the whole of
  the water expended continues to act through a greater portion of
  the circumference than it otherwise would do. The area of the
  vertical section of the complement of water to each bucket is
  made 40 inches; and taking the breadth of the wheel at, say 28
  2/3 inches, gives 40 lbs. as the weight of water in each bucket;
  therefore, as there are 12 buckets containing 40 lbs. each, No.
  13 30 lbs., and No. 14 only 20 lbs., altogether making a total of
  530 lbs. acting on the wheel at the same time;--to show clearly
  all the effect that can be expected from this, I have divided the
  horizontal radius into a scale of 40 equals parts (there being
  40 lbs. in each bucket); and from the gravitating centre of the
  fluid contained in each is drawn a perpendicular to the scale,
  where the effective force, or weight in each bucket, may be read
  off as on the arm of a common steelyard. The weights will be
  found as follows, viz:--

    No.   Lbs.
    1     21½
    2     26¼
    3     30½
    4     33¾
    5     36¾
    6     38¾
    7     39¾
    8     40
    9     39½
    10    38
    11    35¾
    12    32½
    13    21
    14    12

  It is therefore quite evident that, although we have 530 lbs.
  acting on one side of the wheel, a column of water weighing
  446 lbs. reacting at the same distance from the centre, on the
  opposite side, will exactly balance the whole 530 lbs. contained
  in the buckets; so that about a sixth of the expenditure rests on
  the axis without producing any useful effect, and the wheel so
  loaded must remain in a state of rest. Now, in spite of friction
  and the _vis inertia_ of matter, if we suppose the wheel at
  work, it can raise only 446 lbs. at the expense of 530 lbs.; but
  even if it could raise the whole 530 lbs., we should then be but
  little nearer the mark, for we must remember that the gravitating
  centre of our power falls through a space of only 8 ft. 11 in.,
  while the water must be raised at least 11 ft. before it could be
  laid on and delivered clear of the wheel.

  [Illustration]

  As a further means of coming at the end I had in view at the
  commencement of this letter, I will conclude with a simple rule
  for calculating the quantity of water a wheel of this kind will
  raise:--Multiply the number of pounds expended in a minute by
  the height or diameter of the wheel in feet, divide the product
  by the height (also in feet) of the reservoir to be filled, and
  two-thirds of the quotient will be the answer required. Example,
  for the wheel above described, making six revolutions per
  minute:--

          42 buckets on wheel.
           6 revolutions per minute.
         ---
         252 buckets filled per minute.
          40 the weight of water in each bucket.
       -----
       10080 lbs. expended per minute.
          10 feet height of wheel.
      ------
  11) 100800 momentum, dividing by 11 feet as the height of reservoir.
      ------
     3) 9163.636 divided by 3.
        --------
        3054.545 multiplying by 2.
               2
        --------
        6109.09  answer in lbs.

  So that for every 1008 gallons expended on the wheel, we only
  gain sufficient power to supply 611 nearly.

        See also Chap. XV, Bishop Wilkin's Work, appearing at page
        297 et seq. supra.



CHAPTER IV

PNEUMATIC, SIPHON AND HYDRO-PNEUMATIC DEVICES


The Hydrostatical Paradox

Next to the wheel with levers and weights, we believe this simple
Hydrostatical Paradox has more frequently occurred to mechanical and
scientific tyros as a means whereby it was hoped to attain Perpetual
Motion. There is no record that we know of of the name of anyone who
has ever attempted it, and, yet, the instances are doubtless myriads.

The author believes he has heard dozens of young persons mention it as
a means of obtaining a continuous flow of water.

In 1828, Niel Arnott, M. D., published the third edition of his
"Elements of Physics, or Natural Philosophy." At page 141 under
the subject of "Mechanics" he comments generally on the subject of
Perpetual Motion, and says:

  What an infinity of vain schemes--some of them displaying great
  ingenuity--for perpetual motions, and new mechanical engines
  of power, etc., would have been checked at once, had the great
  truth been generally understood, that no form or combination of
  machinery ever did or ever can increase, in the slightest degree,
  the quantity of power applied. Ignorance of this is the hinge on
  which most of the dreams of mechanical projectors have turned. No
  year passes, even now, in which many patents are not taken out
  for such supposed discoveries; and the deluded individuals, after
  selling perhaps even their household goods to obtain the means
  of securing the supposed advantages, often sink in despair, when
  their attempts, instead of bringing riches and happiness to their
  families, end in disappointment and utter ruin. The frequency and
  eagerness and obstinacy with which even talented individuals,
  owing to their imperfect knowledge of this part of natural
  philosophy, have engaged in such undertakings, is a remarkable
  phenomenon in human nature.

At page 270 in treating on "Hydrostatics," he says:

  [Illustration]

  A projector thought that the vessel of his contrivance,
  represented here, was to solve the renowned problem of the
  perpetual motion. It was goblet-shaped, lessening gradually
  towards the bottom until it became a tube, bent upwards at _c_,
  and pointing with an open extremity into the goblet again. He
  reasoned thus: A pint of water in the goblet _a_ must more than
  counterbalance an ounce which the tube _b_ will contain, and must
  therefore be constantly pushing the ounce forward into the vessel
  again at _a_, and keeping up a stream or circulation, which will
  cease only when the water dries up. He was confounded when a
  trial showed him the same level in _a_ and in _b_.


Pickering's Device

In 1858, Peter Pickering, Landed Proprietor of Danzig, Prussia, applied
for a British patent on

"An Atmospheric Engine."

It may be described as follows:

  [Illustration]

  1, 2, 3, 4, 5, are cylinders 18 feet long or high and 3 feet
  diameter, so that the surface of each piston has 1,296 square
  inches acting with an atmospheric pressure of 15 lbs. to the
  square inch, causes a pressure of 19,440 lbs. to each cylinder
  (saying nothing of friction, which will be accounted for later);
  6, 7, 8, 9, 10, pistons of each cylinder, as they must be placed
  when the engine begins to work; 6, 7, 8, 9, causing a vacuum
  under each piston (as they have for the first time been brought
  into their present situation by main force), afterwards, when the
  engine is permitted to start, they will regulate themselves; No.
  10 lies flat on the bottom of the cylinder; 11, 12, 13, 14, 15,
  piston rods acting on shaft No. 16; 17, wheel to communicate the
  engine's power to the machinery of the engine itself; 18, wheel
  to communicate the engine's power to the wheel or propelling
  screw of a ship, manufactory, locomotive, etc.


Stuckey's Device

In 1842, William Henry Stuckey, Esquire, of St. Petersburgh, applied
for a British patent on

"A Pneumatic Engine for Producing Motive Power."

His specifications describe his alleged invention as follows:

  [Illustration]

  Fig. 1 is a front view of my said pneumatic engine, partly in
  section. A¹ and B¹ two horizontal cylinders, united at their
  inner extremities a, a, which rotate on gudgeons that have
  their bearings C, C, in the upright standards D, D; A² and B²
  two pistons which work to and fro in these cylinders; E¹ and E³
  two hollow arms or tubes which radiate from the cylinder A¹,
  and E², E⁴, two similar arms or tubes which radiate in opposite
  directions from the cylinder B¹, each cylinder having an open
  communication with the arms or tubes attached to it. F¹, F²,
  F³, and F⁴, four other cylinders, affixed to a circular ring
  R, R, open at top to the atmosphere, and open at bottom to the
  radial tubes E¹, E², E³, E⁴, connected with them at their outer
  extremities. G¹, G², G³, G⁴, pistons working in the cylinders F¹,
  F², F³, and F⁴, and H¹, H², H³, and H⁴, caps screwed on to the
  flanges of the cylinders. The different parts described form a
  wheel, which, on being set in motion, rotates on the gudgeons in
  the bearing C, C. The motion is produced as follows:--I adjust
  the wheel so that the tubes E¹ and E³ shall be in a vertical
  position; and pour into the tube E¹, through the cylinder F¹,
  withdrawing the piston G¹, as much mercury or other suitable
  fluid body (previously determined by calculation) as will fill
  the tube from the point of its connection with the inner cylinder
  A¹ up to the bottom (_a_, _a_,) of the outer cylinder F¹. The
  mercury thus introduced flows into the cylinder A¹ at the back of
  the piston A², and presses that piston forward to the extremity
  of its range, the piston G¹ being then restored to its place in
  the cylinder F¹, and pressed close down on the mercury in the
  tube E¹. I next turn the wheel till the tubes E² and E⁴ are in a
  vertical position, by which turning the mercury therein is forced
  into the tube E³, flowing down which it drives the piston G³ of
  the cylinder F³ forward to the extremity of its range, leaving a
  vacuum in the cylinder A¹ at O, equal to the difference between
  the heights from which the mercury descends in the tubes E¹ and
  E³. I then fill the tube E² and cylinder B² with mercury, to the
  same extent and in the same way as I previously filled the tube
  E¹ and cylinder A¹, after which I turn the wheel till the tubes
  E¹ and E³ are once more in a vertical position, whereby I produce
  a vacuum in each pair of tubes, and their intermediate cylinder,
  to the degree of the difference before explained. To the four
  tubes there are attached four cocks K¹, K², K³, K⁴, which, after
  the vacua have been obtained, are closed; and to the four rods
  of the pistons of the outer cylinders F¹, F², F³, F⁴, there are
  attached four hanging or balance weights L¹, L², L³, L⁴, in such
  manner that they shall co-operate with the atmospheric pressure
  on the said vacua in giving rotation to the wheel. M¹, M², M³,
  M⁴, are jointed levers, by which these weights are connected at
  one end with the pistons G¹, G², G³, G⁴; and N¹, N², are cords
  or bands, by which they are suspended at the other end from
  standards P, P, projecting from the ring R, and bearing pulleys,
  over which the cords or bands pass, each cord or band serving to
  suspend the two weights which are opposite to each other, for
  which purpose it is passed internally across the wheel and over
  the exterior of one of the cylinders A¹ or B¹. The cords or bands
  are attached to the weights at the lower ends thereof, and pass
  over small pulleys close to the points of connection, so that
  the cords or bands, when pulled, may act the more effectually on
  the weights. It will be readily understood that when any two of
  the tubes are in a vertical position, and the mercury or other
  suitable fluid has descended to the bottom of the lower tube,
  its pressure on the piston of the outer cylinder G¹, or G², or
  G³, or G⁴, will cause the weight connected with that piston to
  turn inwards towards the centre of the wheel, by which movement
  a strain is exerted on the connecting cord or band N¹ or N²,
  which throws up the opposite weight at top, and causes it to
  force down the piston of the top cylinder, or the surface of the
  mercury in the upper tube, whereby any excess of pressure at
  the bottom of the lower tube is transferred to the top piston,
  where it acts in aid of the atmospheric pressure on the vacua
  obtained in manner aforesaid. The four cocks K, have regulating
  rods connected to them in the way common in steam and other
  engines, so that as each tube comes into a vertical position
  the cock attached to it is opened, and as it passes from that
  position towards the horizontal, is shut, so that the mercury
  always retains its proper position in the tubes or cylinders, and
  is acted on by the pressure of the atmosphere at those points
  only where such pressure can be of service. The power of this
  wheel will be, of course, in proportion to the vacua produced in
  manner aforesaid, and to the altitude of the columns of mercury
  employed. The inner cylinders might be dispensed with, and the
  tubes be made to communicate directly with each other, but I
  prefer, for most purposes, the arrangement which I have before
  described, with the two intermediate cylinders A¹, B¹; where the
  inner cylinders are dispensed with, I make use of eccentrics
  instead of the joined levers before described, to enable the
  weights to turn to the extent of about half a circle. The number
  of tubes also need not be limited to four, but increased to any
  convenient extent.


Prof. George Sinclair's Device

This device was invented by George Sinclair, who was a professor of
philosophy at Glasgow University. He died in 1696. In 1669 he published
a work on Pneumatics, and in that work claimed to have discovered
Perpetual Motion. Explanations of his device consumed eighteen pages of
a Latin work on Pneumatics. It very absurdly depended for its operation
upon the delivery of water from the short leg of a siphon, instead of
the long leg. The figure illustrates the contemplated operation.

[Illustration]


Jacob Brazill's Device

In 1839 Jacob Brazill, of Deptford, Kent, Governor of Trinity Ground,
applied for a British patent on

"Improvements in Obtaining Motive Power."

In his application he describes his alleged invention as follows:

  My invention consists in a certain arrangement or combination
  of mechanism wherein the atmospheric air is employed as the
  impelling agent, being brought to bear in such a manner as by
  exerting a constant urging pressure, to produce a continuous
  rotary motion, and applies to all the purposes where a prime
  mover is required.

  [Illustration]

  Fig. 1 is an end view of the apparatus _a_, _a_, are the
  bearings, top and bottom, for the vertical shaft _b_, which
  bearings are to be so constructed as to produce the least
  possible amount of friction. _c_ is a large drum furnished with
  radial plates or fans, some of the plates being so arranged as to
  slope down towards the bottom plate, thus forming, as it were,
  a series of boxes decreasing in their transverse dimensions as
  they approach the boss. This drum is to be put in motion by means
  of a current of air directed through the pipes _d_ and _e_,
  from the two pairs of double bellows _f_ and _g_. _h_ is a worm
  fixed on the vertical shaft by means of a tightening screw, or
  in any other convenient way, taking into the worm wheel _i_ on
  the horizontal crankshaft _j_, supported in bearings _k_, _k_.
  The cranks _l_, _l_, work the bellows by connecting rods _m_,
  _m_; _n_ is a spur wheel taking into a pinion _o_, on the axle of
  which is a winch handle _p_, for starting the apparatus.

  What I claim as my peculiar right is, the impulsion of a current
  of air against the fans of a drum (as that at _c_) through
  pipes, as at _d_ and _e_, for the purposes of a motive power,
  together with a certain arrangement of mechanism, by means of
  which the action first induced shall be kept up.


Läserson's Device

In 1860 Marc Antoine F. Mennons, of Paris, applied on behalf of Louis
Diodor Läserson of Moscow, Russia, for, and obtained, a British patent
on

"Certain Improvements in the Production of Motive Power, and in the
Apparatus Connected Therewith."

He described the essentials of his device as follows:

  [Illustration]

  The invention consists in the application of the ascensional
  force of air or gases developed under water to the generation
  of motive power, and in the combination of apparatus, by means
  of which the power thus produced is accumulated, transmitted
  and applied. The principal element of this combination is a
  wheel or disc (shown in plan and section, Figs. 1, 2), the
  dimensions of which are proportioned to the power required. On
  the circumference of this wheel are fixed at equal distances
  a given number (say sixteen) of flexible air reservoirs _a_,
  communicating with an equal number of tubular passages _b_,
  which open in the nave _c_. In the length of the fixed shaft
  _d_, on which this wheel is mounted, are formed two cylindrical
  cells E by which the air is admitted to and discharged from
  the flexible reservoirs _a_ by the tubular passages _b_, with
  which they correspond. The hydro-atmospheric wheel thus mounted
  and immersed to the required depth in a suitable reservoir as
  in _f_, is placed in communication by its hollow shaft with an
  air-compressing apparatus of any convenient form, which in its
  turn is connected with the shaft of an ordinary hydraulic wheel.
  The latter being set in motion acts on the forcing apparatus, by
  which a jet of compressed air is thrown into the hollow shaft
  of the hydro-atmospheric wheel by the entry cell corresponding
  with the orifices of the fourth quadrant or lowest immersed
  section of the latter. The air injected following the tubular
  passages within its range enters and inflates the corresponding
  flexible reservoirs, which thus acquiring an ascensional
  force proportioned to their displacing capacity and degree of
  immersion, carry forward the wheel in their movement towards
  the surface. On reaching the water line the tubular passage
  come into communication by the nave orifices with the discharge
  cell of the fixed shaft, and give egress to the air compressed
  in the flexible reservoirs, which collapse simultaneously with
  the inflation of the succeeding series by which they have in
  the meantime been replaced in the fourth quadrant. The latter
  following the ascensional movement of their predecessors give
  place to a third series, and collapse in the same way on passing
  the surface, so that each air reservoir on re-entering the water
  in the continued revolution of the wheel presents comparatively
  little resistance until it arrives at the turning point, when
  the communication with the entry cell of the axle being again
  established the movements above described are reproduced. The
  force thus developed by the hydro-atmospheric wheel, which
  represents about three times that of the prime motor, may be at
  this stage applied to the required transmissions of movement.
  When natural watercourses are not to be had within a reasonable
  distance of the locality in which the force is to be applied, it
  becomes necessary to replace them by an artificial fall.


Von Rathen and Ellis's Device

In 1866 Anthony Bernhard Baron Von Rathen and George Henry Ellis, both
of London, applied for and obtained British patent on

"A New or Improved Mode of Constructing a Motive-power Wheel Whereby to
Obtain Permanent Motion by the Application of Compressed Air or any
other Elastic Fluid."

In the specifications for patent the essentials of their invention are
described as follows:

  This invention may be considered supplementary to an invention
  of the Baron Von Rathen of an elementary motive-power engine,
  for which a patent has been granted to him, No. 818, and dated
  March 23, 1865, and consisting in a newly-discovered plan for the
  construction of a motive-power wheel or engine, on the principle
  that the motor, consisting of compressed air or other elastic
  fluid, is maintained in permanent activity and without removal
  or renewal, and the useful resistance of the air in the chambers
  is on the surface of a fixed cylinder, the motion is regular and
  direct, the wheel rotating on its fixed central axis.

  The nature of our present invention consists principally in our
  providing, instead of that a motive-power wheel having its axis
  upon fixed bearings in an eccentric position and turning in an
  oscillating cylinder. The motor being brought through a hollow
  shaft, or any convenient channel, is introduced into one or more
  closed chambers formed upon the longest arm of the power wheel
  for the purpose of driving it round; by this means, according to
  the uniform pressure of the elastic fluid upon all surfaces, we
  obtain not only a continuous but an additional degree of driving
  power from the leverage given by the position of the wheel. There
  is, as shown in Fig. 1 of the accompanying drawing, a fixed arm
  or driving rod fixed upon the cylinder by which to impart motion
  to a crank, piston, or other apparatus. We propose to obtain
  the motor by pumps worked by or in connection with the power
  wheel, and having other suitable and necessary appliances for
  regulating, storing, transmitting, and manipulating the force
  supplied to or communicated by the power wheel, as have been
  described, to be applied with the plan for working the elementary
  motive-power engine hereinbefore referred to.

  Fig. 1 is a vertical section of the power wheel revolving inside
  and moving the oscillating cylinder.

  A¹ and A² are air-tight chambers, the former being the driving
  chamber and the latter intended to check or counterbalance its
  wedging or binding effect upon the cylinder, owing to the extra
  leverage obtained and the pressure upon the surface of the rod
  B, the wheel will revolve in that direction by the action of the
  elastic force which finds its useful resistance on the internal
  surface of the cylinder C. D¹, D², D³, D⁴, are packings to render
  the two chambers air-tight and to afford bearings for the four
  arms of the wheel upon the cylinder; E, E, are two tubes for
  conducting the motor into the chambers, and F is the axle, upon
  which the wheel is firmly fixed and driven round with it.

  [Illustration]

  Fig. 2 is a side elevation of the power wheel. F is the hollow
  shaft or axle through which the motor passes from the pumps or
  reservoir in connection therewith, and upon which the wheel
  rotates; G is the rod or arm fixed at one end to the cylinder C,
  and attached at the other end by a joint or coupling H to the rod
  I, acting within a cylinder to give motion to the piston K; L is
  one of the side covers of the power wheel, and N the support or
  framework for the wheel.


Richard Varley's Device

In 1797 Richard Varley, of Damside, Lancashire, England, a merchant,
applied for and obtained a British patent on

"A New Perpetual Moving Power."

His device is explained by the following excerpt from his application:

  "My invention consists of a method of applying the weight of the
  atmosphere upon a wheel in any other fluid, and by that means
  destroying its spring or reaction, the manner of doing which I
  describe as follows, agreeable to the drawing (Fig. 6) annexed:

  [Illustration]

  "A is a circular vessel, made of copper or any other substance,
  capable of containing water, and covered with a top part so as
  to be perfectly air-tight. B is a wheel placed in the inside of
  the vessel, with its axle perpendicular, the uppermost part of
  which comes through the top of the vessel, and is made to work
  air-tight; the lower end runs in a step within the vessel, and
  no part of the wheel is to touch the vessel but its axis. C is a
  cylinder placed firmly upon the wheel. D is the piston, suspended
  by a chain to a strong spring fixed on the wheel. This spring
  is to be made of such strength as that when the whole weight
  of the atmosphere is upon the piston the air will only move it
  about one inch down. E is the tube leading from the axle, which
  is hollow from the top to the level of the wheel, so as to admit
  the external air by this tube to the piston D, which piston is a
  circular vessel, made air-tight, and exactly fits the cylinder.
  There is a joint in the tube E at F, which is made air-tight by
  leathers, so that when the piston descends the tube may give way
  to it. G is a small tube leading from the bottom of the cylinder
  to the center of the axle, and from thence brought out at the
  end of it, and by which the air is extracted from the cylinder
  by means of an air pump and a vacuum formed in it. On the top
  part or any other convenient place of the vessel, are fixed two
  cylinders or tubes of a proportional size to the cylinders on
  the wheel, one of which is a condensing cylinder, by means of a
  screw and piston, and by which the water in the vessel may be
  compressed; the other has its piston suspended at the bottom,
  and the top part of the cylinder being filled with air as the
  other piston is screwed down this rises, and condenses the air in
  the cylinder, the spring of which keeps the water in the vessel
  pressed to all parts alike; and when the air is extracted from
  the cylinder C and the piston D is forced down by the external
  atmosphere into the cylinder, this pressure is continued, and the
  condensed air expands in proportion and prevents any tendency
  to a vacuum being formed, which would cause a cohesion of all
  the parts. By this means the external air is suspended upon the
  wheel by the chain, the same as a weight, and the spring of the
  atmosphere being taken from the cylinder there is nothing to
  oppose this weight, there being no spring in water; and this
  power may be increased in proportion to the size and number of
  cylinders on the wheel and its diameter."


Siphon and Funnel Device

This was the work of an Englishman whose name is unknown. An account of
it appeared in "Mechanics' Magazine," 1828, in the following language:

  _a_ is a circular glass vessel 1 foot 6 inches diameter; _b b_ a
  tube fixed thereunto; _c c_ are funnels containing valves; _d_,
  a float of hollow copper, or any light substance; _e_, an open
  mouth; _f_, an open vessel filled with mercury as high as the
  dotted line.

  It is well known that several experiments were made by M.
  Venturi, Sir Isaac Newton, etc., demonstrating that a vessel
  shaped thus--

  [Illustration]

  will emit water with a much greater rapidity than a vessel shaped
  thus--

  [Illustration]

  say, with more than a third as much speed. I propose, then, to
  have the mouth of the vessel _a_ of the former shape, being the
  natural form of flowing water. The vessel _a_, and tube _b_,
  must be completely filled with mercury, by means of the funnels
  _c c_, which will also contain mercury. In order to set the fluid
  in motion, the valve in the large vessel _c_ is to be raised;
  the mercury (which was hitherto held up by a greater weight of
  atmosphere) will instantly run out of the mouth _e_, and must
  be suffered to do so till the mercury in _c_ is level with the
  dotted line; by this time the mercury in _a_ will have obtained
  a momentum which will be more than equivalent to the pressure of
  the atmosphere: consequently, the mercury will run out of the
  large vessel _a_, till it falls as low as the dotted line; the
  float _d_, resting on the mercury, of course, falls with it,
  opens the valve, and admits a proportionable quantity of mercury
  through the tube _b_, driven by the pressure of the atmosphere
  (the height from the mercury in _f_, to the top of the tube
  _b_, being only 26 inches, which is 2 inches less than what the
  atmosphere will at all times raise mercury in a vacuum).

  [Illustration]

  By this means will there not be a continual circulation of
  mercury?


Orchard's Vacuum Engine

In 1826 there was published in "Mechanics' Magazine," London, a
communication from a Mr. Orchard, concerning an invention he considered
himself as having made. The account is published in his own words, and
is as follows:

  A is an iron reservoir nearly filled with mercury; B, a tube
  twenty-four inches long, having its lower end inserted in that
  reservoir; and C and D, two cocks for the convenience of filling
  the tube B. From this another tube M proceeds at right angles, to
  the vessel G. In this latter tube is the cock F, to admit of, or
  shut off, a communication between the tube and the vessel G. This
  communication being closed, the tube B is carefully filled with
  mercury; after which the cock D is closed and the cap E screwed
  on.

  [Illustration]

  The vessel G is to be filled with mercury through the cock H,
  the pipe I being open to allow of the escape of air. When this
  vessel has been filled, the cock H should be closed and its cap
  screwed on; and the pipe I be also closed by a valve, which is
  to be pressed tight by the cap on the head of the pipe. I is a
  vent-pipe, open at the top. The space represented by the double
  lines is a panel of thick plate glass having two horizontal lines
  described on its surface, whereby the attendant may observe the
  quantity of mercury within the vessel.

  The cock F being closed, a quantity of mercury must be allowed
  to run out of the vessel G, equal to the space 1, 2, 3, 4,
  which space will become a vacuum. If, therefore, the cock L be
  then opened, to allow of the discharge of a certain quantity of
  mercury on the wheel, and the cocks C and L also opened, the
  mercury will continually rise from the reservoir A into the
  vessel G, and thence be discharged on the wheel, whence it will
  again fall into the vessel A, to keep up the supply. The cock F
  must be so adjusted as to admit into the vessel G a quantity of
  mercury equal to that which is discharged by the cock L. This can
  be ascertained and regulated by means of the panel of glass above
  described.

  The specific gravity of mercury being 7½ ounces, it is evident
  that but a small quantity of it is required to turn the wheel,
  which has no friction but that of the axis on which it turns.


Robert Copland's Device

In 1819 Robert Copland applied for a British patent on

"A New or Improved Method or Methods of Gaining Power by New or
Improved Combinations of Apparatus, Applicable to Various Purposes."

His specifications describe in great detail his invention in the
following language:

  [Illustration]

  Figure 1 is a view of a machine by which I purpose to derive a
  disposable force or power from the action, weight or pressure
  of the atmosphere, through the medium of the column of water
  or other heavy liquid descending on one side of the enclosed
  vertical wheel, and from thence through the centrifugal wheel,
  being returned into the same reservoir from which the pressure
  of the atmosphere raises it to be again delivered on the top of
  the vertical wheel to supply the discharge on the descending
  side, arising from the centrifugal force communicated to it by
  the rotary velocity of the centrifugal wheel, and the pressure of
  the descending column overbalancing the reaction or resistance of
  the atmosphere at the discharging apertures of the centrifugal
  wheel. Thus a small quantity of water or other liquid (according
  to the size of the machine required) being continually returned
  onto the top of the vertical wheel by the pressure or action of
  the atmosphere, and acting by its unbalanced gravity or impetus
  in its descent, will produce a disposable force or power of
  any required magnitude, by increasing the size or number of
  the machines, provided the height the fluid is required to be
  raised is not quite so high as the column which the atmosphere,
  when lightest, will raise of that fluid, and allowing for the
  requisite velocity on the vertical wheel. In Fig. 1, A is the
  feeding pipe through which the fluid is raised by the pressure
  or action of the atmosphere on the fluid in the lowest reservoir
  in which the lower end of the pipe is immersed, closed by a
  cock, sliding plate, valve or shutter, to allow the machine
  to be filled at the commencement, and which may be under the
  surface of the fluid, also to keep it air-tight. The other end
  is inserted air-tight into the top reservoir, or by a curve, as
  shown by the dotted line _a_, joined to pipe C, and delivering
  upon the vertical wheel, without any top reservoir. In this case,
  if water is used, the highest part of the bend or curve inside
  should not exceed thirty feet above the level of the water in
  lowest reservoir. B is the top reservoir, the lowest internal
  part of which should never exceed twenty-nine or thirty feet
  above the water in lowest reservoir, but it will admit the top
  of the reservoir, if wished, to be rather higher than when the
  curved tube _a_ only is used. It must be quite air-tight, and
  supported as convenient. C is a pipe, joined air-tight to top
  reservoir, or forming part of A, _a_, C. C is a movable flap
  of strong leather, or other substance, which may be joined to
  the lowest part of C, where the water is delivered so high on
  the wheel and where floats with hinges are used on the wheel to
  prevent its going down on the ascending side; but not necessary
  when water is delivered lower on the wheel. D, D, D, D, is the
  fixed and immovable waterway, and the fixed case or cover (of
  the vertical wheel), of which it is a part, joining also the
  stuffing boxes, through which the axle of the vertical wheel
  moves air-tight, thus entirely enclosing and surrounding every
  part of the wheel but the projections of the axle, and allowing
  the float boards and wheel just to turn freely in it without
  touching in any part except the axle in turning in the packing
  of the stuffing boxes; the float boards are fastened on to the
  iron rim or sole of the vertical wheel by very strong hinges or
  movable joints just within the fixed waterway D. E is a pipe or
  pipes joined air-tight to the fixed cover or case enclosing the
  vertical wheel where the water is to be taken off it, having
  their lower ends inserted air-tight also into the bottom of
  the fixed and immovable top of the centrifugal wheel in such
  a direction that they may deliver the water into the moveable
  waterway of the centrifugal wheel as near as possible in the
  same direction as the water circulates in the wheel. F, F, is
  the centrifugal wheel, of any diameter convenient, according to
  the size of the machine, placed horizontally above the fluid
  in the lowest reservoir, so as to move on its axis as near as
  possible to the surface of the fluid without touching it, having
  an immovable cover or top, leaving a hollow waterway round the
  rim, into which the fluid is discharged from E in the direction
  of the wheels' motion. G, G, are the discharging apertures of the
  centrifugal wheel. H, H, is the surface of the fluid in I, I,
  the lowest reservoir, containing a sufficient quantity of water
  when the machine is put to work, to allow the bottom of feeding
  pipe A to be immersed in it at least two feet below the surface,
  or a greater depth may be given to that part of the reservoir
  under the mouth of pipe A, forming a sort of well in which A may
  be inserted any required depth, better to exclude any particles
  of air or bubbles mixed with the water nearer its surface from
  ascending in pipe A. This reservoir should be large enough to
  contain the whole of the water used before the machine is filled.
  K, K, are the ends of the axle of vertical wheel outside of the
  stuffing boxes of the fixed case, and are the only parts of the
  vertical wheel seen, and turning air-tight through the packing
  or stuffing boxes, or in any other manner the external air is
  entirely excluded from the vertical wheel when at work; _e_ is
  an air-tight cock to discharge the air out of the machine when
  filling. L is an aperture into top reservoir, or into highest
  part of pipe A, _a_ when no top reservoir, closed air-tight by
  a screw cap; by this the whole machine is filled in every part
  with the fluid used before it can be set to work, the bottom of
  pipe A and apertures G (as well as cock to bottom of pipe E
  when required) being previously closed. P is part of the axle on
  which the centrifugal wheel revolves. Before the machine can be
  put to work everything being previously arranged as directed, the
  apertures at G and bottom of A (and at E if required also), must
  be closed by sliding plates, valves, cocks, or other methods, as
  most convenient, and every part of the machine must be filled
  with the water or fluid used by the aperture L, or any other
  convenient method by which the highest parts may be filled, the
  air allowed to discharge by opening E and O, the latter to be
  shut as soon as the centrifugal wheel is filled, and the cock at
  E closed where required, when the water is above it a little, _e_
  continuing open so as to allow the air to be entirely discharged
  from every part, which being done, and the machine entirely
  filled with water, this cock and aperture L must be carefully
  closed; having then fixed upon the most convenient method for
  giving the required assistance to set the machine to work, by
  giving the centrifugal wheel motion, and assisting it till
  arrived at the velocity fixed, it must be put in motion and the
  apertures G opened; after it has got a little into motion, and as
  soon as the velocity of the wheel has given a centrifugal force
  to the water sufficient to overbalance the slight difference in
  the height of the feeding and descending columns, the pipe A must
  be opened; a discharge from the apertures G will now take place,
  which is supplied from top reservoir B over the loaded side of
  vertical wheel, where, by its gravity and impetus acting on
  the float boards, it causes the wheel to turn till it descends,
  so as to be discharged through E, on the rim or waterway W, of
  the centrifugal wheel, which it strikes with the velocity of
  its descent in nearly the direction of the wheel's motion, and
  is discharged through apertures G into the water contained at
  commencement in lower reservoir I, from whence this discharge
  is again supplied by the pressure of the atmosphere, returning
  it through pipe A into top reservoir, or through _a_, C, and
  the part intended of the vertical wheel. As the velocity of the
  centrifugal wheel is accelerated, the velocity of the descending
  column over the vertical wheel will also be accelerated, and,
  consequently, the vertical wheels, when having arrived at their
  respective fixed velocities, the assisting force being no longer
  necessary, may be withdrawn, and the centrifugal wheel may now
  receive what assistance is required to support its velocity from
  the vertical wheel through the connecting shafts and wheelwork,
  or in any other manner.


Eaton's Perpetual Siphon. London. 1850

The account of this is taken from Dircks's great work, mentioned in the
preface, and is as follows:

  This is a plan proposed by Mr. Eaton in 1850, and consists in
  providing two water cisterns A, B; the short leg of a siphon C
  enters the upper cistern, and terminates in three escape pipes,
  capable of being rotated by the pulley _a_, connected by a
  band with the pulley _b_, affixed to the vertical shaft _c_,
  rotated by the inverted Barker's mill D, constructed on the short
  leg of the inverted siphon E, supplied from the bottom of the
  upper water cistern. By this means it was expected to keep up a
  continual flow down the pipes C and up E, as shown by the arrows.

  [Illustration]


Legge's Hydro-Pneumatic Power Device. 1850

This is an English production, and the inventor claims that it is the
result of fourteen years' study. We take the description from Dircks.
It is as follows:

  It is a dome-shaped vessel; its upper part A filled with air,
  and the lower half with water, as at B. This vessel contains two
  apparatus for returning the water which is worked through C D,
  apparently like pump barrels. The air is to be at from 250 to 500
  pounds pressure on the square inch. When once started it will (it
  is stated) go on as long as it is oiled. The inventor estimates a
  one thirty-second share at one thousand pounds value.

  [Illustration]


Waterblowing Machine

In 1827 "Mechanics' Magazine," London, published an account of an
invention which was furnished to it by some correspondent. The
invention, it seems from the communication, had previously been
described in an appendix by Dr. Brewster to a volume of Ferguson's
lectures, and it also seems that the description furnished "Mechanics'
Magazine" was copied from such appendix. The following is the article
as it appeared in "Mechanics' Magazine":

  I am encouraged to send you the following attempt at perpetual
  motion, because I think it is upon a principle that has not yet
  been examined in your pages.

  In Dr. Brewster's appendix to Ferguson's lectures, the following
  description is given of what is called a "Water Blowing Machine":
  "Let A B (see Fig.) be a cistern of water, with the bottom of
  which is connected the bended leaden pipe B C H. The lower
  extremity H, of the pipe is inserted into the top of a cask or
  vessel, D E, called the condensing vessel, having the pedestal P
  fitted to its bottom, which is perforated with two openings, M N.
  When the water which comes from the cistern A is falling through
  the part, C H of the pipe, it is supplied by the openings or
  tubes, _m_ _n_ _o_ _p_, with a quantity of air which it carries
  along with it. This mixture of air and water, issuing from the
  aperture H, and impinging upon the surface of the stone pedestal
  P, is driven back and dispersed in various directions. The air
  being thus separated from the water, ascends into the upper part
  of the vessel, and rushes through the opening F, whence it is
  conveyed to the fire, while the water falls to the lower part
  of the vessel, and runs out by the openings M N." The author
  then goes on to describe the construction of the pipe B C H,
  in the curve of which some nicety is required, and to explain
  some atmospherical phenomena upon the principle of this machine,
  adding that "Franciscus Tertius de Lanis observes that he has
  seen a greater wind generated by a blowing machine of this kind
  than could be produced by bellows ten or twelve feet long."

  [Illustration]

  Now, if, instead of the pedestal P, a wheel were placed in the
  condensing vessel, as in the figure, would not the water, in
  falling upon the wheel, be sufficiently dispersed to disengage
  the air at the same time that it drove the wheel, and would
  not the motion of the wheel be retarded by the density of the
  internal air?

  I do not apprehend that any considerable resistance would be
  offered by the internal air, and the motion of the wheel can be
  regulated by its load, so as to offer a sufficient resistance to
  the descending stream of water; and I, therefore, assume that
  the water, in its descent, would produce by means of the wheel,
  a power capable of raising a part of the water expended back
  again to the cistern; and this is the extent of the power of
  most of those machines which have been mistaken for perpetual
  motions by their projectors. But I have a blast of wind which
  is described as being of great force. Can this blast be in any
  way applied to raise the surplus water? I think I see the smile
  which the proposal will produce in those who deny the possibility
  of a perpetual motion. "A mere puff of wind!" is doubtless
  ejaculated from all sides. But let me tell these gentlemen
  that, though I may not know any method by which such blast can
  produce that effect, it does not, by any means, follow that the
  impossibility of the thing is thence to be presumed. Far from
  it; for such a conclusion rests upon the supposition that the
  powers and application of a blast of wind are fully known, and
  that no research or experience can add to our knowledge on that
  subject--assumptions which appear to me somewhat ridiculous.
  Allow me, for the sake of argument, to suppose that this blast
  instead of wind, had been a blast of steam. Time was when wise
  men would have smiled and said, "A puff of steam--a mere puff of
  steam!"--and had some one, more sanguine than the rest, attempted
  by its application to produce a motion, he would have applied it
  to the floatboards of a wheel, as in Branca's engine, and have
  been disappointed. It is not given to man to know when the powers
  of any great agent have been fully developed; and those who act
  upon such presumptions throw the greatest obstacles in the way of
  inquiry. But, to show the anti-perpetualists that within their
  own time since the commencement of the "Mechanics' Magazine," an
  addition has been made to our knowledge of the powers of a blast
  of wind, I have added a tube, G, to my figure, the proposed use
  of which I shall now describe.

  In a part of the "Mechanics' Magazine," published some time ago,
  there was described a novel mode of raising water in a tube by
  directing a stream of air over its mouth, thereby destroying the
  pressure of the atmosphere.

  I do not suppose it will rise to the height of the cistern as I
  have figured it; but it may still be a question whether it may
  not be accomplished by a series of short tubes, the bottom of
  the one being placed in the cistern into which the next below
  discharges its water, each being constructed with a blast and two
  valves, in the same manner as the single tube--namely, the valves
  _x_ (under water) and _y_, worked in such a manner by the arms
  K L, that the one may shut when the other opens. Presuming that
  the water will rise to the top of the tube when the blast is in
  action (_x_ open and _y_ shut), the water in the part of the tube
  between the blast and _y_ will be discharged into the cistern at
  the next motion of the valves--namely, when _x_ is shut and _y_
  opened, the blast, at the same time, being discontinued.


Device by Means of Buoyancy Through Media of Different Densities

An account of this appeared in "Mechanics' Magazine," 1825. The author
apparently had no great faith in the accomplishment of Perpetual
Motion, and yet it is manifest that he had not abandoned hope of
accomplishing it, and is still thinking along some line of attaining
it. It goes without saying that the device failed. The account
furnished, however, is as follows:

  The unsuccessful (but far from fruitless) search made to discover
  the "philosopher's stone," and the "elixir vitæ," were productive
  of most important and beneficial results in the kingdom of
  chemistry; so, by a parity of consequence, I am disposed to
  believe that from inquiry after the "perpetual motion" (though
  equally unsuccessful), a similar good will result to the
  mechanical world. * * I beg leave to offer the prefixed device.
  The point at which, like all the rest, it fails, I confess I
  did not (as I do now) plainly perceive at once, although it is
  certainly very obvious. The original idea was this--to enable a
  body which would float in a heavy medium and sink in a lighter
  one, to pass successively through the one to the other, the
  continuation of which would be the end in view. To say that
  valves cannot be made to act as proposed will not be to show the
  _rationale_ (if I may so say) upon which the idea is fallacious.

  The figure is supposed to be tubular, and made of glass, for the
  purpose of seeing the action of the balls inside, which float or
  fall as they travel from air through water and from water through
  air. The foot is supposed to be placed in water, but it would
  answer the same purpose if the bottom were closed.

  [Illustration]

  DESCRIPTION OF THE ENGRAVING.--No. 1, the left leg, filled with
  water from B to A. 2 and 3, valves, having in their centers very
  small projecting valves; they all open upwards. 4, the right
  leg, containing air from A to F. 5 and 6, valves, having very
  small ones in their centers; they all open downwards. The whole
  apparatus supposed to be air- and water-tight. The round figures
  represent hollow balls, which will sink one-fourth of their bulk
  in water (of course will fall in air); the weight, therefore, of
  three balls resting upon one ball in water, as at E, will just
  bring this top even with the water's edge; the weight of four
  balls will sink it under the surface until the ball immediately
  over it is one-fourth its bulk in water, when the under ball will
  escape round the corner at C, and begin to ascend.

  The machine is supposed (in the figure) to be in action, and
  No. 8 (one of the balls) to have just escaped round the corner
  at C, and to be, by its buoyancy, rising up to valve No. 3,
  striking first the small projecting valve in the center, which,
  when opened, the large one will be raised by the buoyancy of the
  ball; because the moment the small valve in the center is opened
  (although only the size of a pin's head), No. 2 valve will have
  taken upon itself to sustain the whole column of water from A to
  B. The said ball (No. 8) having passed through the valve No. 3,
  will, by appropriate weights or springs, close; the ball will
  proceed upwards to the next valve (No. 2), and perform the same
  operation there. Having arrived at A, it will float upon the
  surface three-fourths of its bulk out of water. Upon another
  ball in due course arriving under it, it will be lifted quite
  out of the water and fall over the point D, pass into the right
  leg (containing air), and fall to valve No. 5, strike and open
  the small valve in its center, then open the large one and pass
  through; this valve will then, by appropriate weights or springs,
  close, the ball will roll on through the bent tube (which is made
  in that form to gain time as well as to exhibit motion) to the
  next valve (No. 6), where it will perform the same operation,
  and then, falling upon the four balls at E, force the bottom one
  round the corner at C. This ball will proceed as did No. 8, and
  the rest in the same manner successively.


Device by Compressible and Distensible Bags in Liquid

In the year 1823, an account of a Perpetual Motion device was sent
to "Mechanics' Magazine" by some correspondent. This appears to have
considerable claim to ingenuity, though the correspondent states that
"it failed from friction." The figure and account furnished are as
follows:

  [Illustration]

  A A A A is a cistern of water, filled as high as B B. C C C C C C
  are six bladders, communicating by the tubes D D D D D D with
  the hollow axle E, which axle is connected with the bellows F by
  the pipe G. H is a crank connected with the crank I by the rod
  K. L is a saucer-wheel, M a pinion, N its shaft. O is a crank
  attached to the bellows F by the rod P. Q Q Q Q Q Q are valves
  with a projecting lever. R and S are two projecting knobs. T
  is a hole in the axle E, forming a communication with it and
  the lowermost bladder. The axle B being put in motion carried
  round the bladders and tables, and by the cranks H and I, and
  the connecting-rod K, caused the wheel L to revolve, which
  communicating a similar but accelerated motion to the pinion M,
  shaft N, and crank O, worked or blew the bellows F by the rod P;
  the air entered the axle E by the tube G, and passing through the
  hole in it at T, entered the lower bladder C by the tube D; this
  bladder being thus rendered lighter than the space it occupied,
  ascended, bringing the bladder behind it over the hole in the
  axle T in like manner, and which thereby gained an ascending
  power, producing a similar effect on the one behind it. When one
  of the bladders arrived at the knob S, the lever of the valve Q
  struck against it and opened the valve; when the bladder arrived
  at U and began to descend, its pressure on the water drove out
  the air and gave it a descending power; the knob R then closed
  the valve Q and prevented the entrance of any water into the
  bladder; by this contrivance three of the bladders were full and
  empty, according as they passed over the hole T or the knob S.


George Cunningham's Mercurial Pneumatic Device. Ireland. 1729

[Illustration]

Among the papers in the British Museum is one which purports to relate
to the Royal Society, and in that Royal Society volume it is number
32. It is quite amusing. The author explains that he is withholding
many precise details and measurements "such as workmen should follow in
making the engine. Intending no more here than the endeavor to satisfy
some others as well as myself, that there is really such a thing to be
found as that long-sought for Perpetual Motion, which is looked upon by
every one to be the true parent of the Longitude.--Description of the
Perpetual Motion":

  A, a cup nearly full of mercury.

  B, the height the mercury will rise by its own weight in--

  K, the main pipe, when--

  C, the lower cock is open.

  E, a hollow globe which must be capable of a greater quantity
  than the whole pipe K.

  F, the upper cock by which the mercury is filled into the engine
       and about 27 inches higher than the line B.

  D, the middle cock which, when open, lets the mercury fall upon
       the buckets of the wheel--

  G, and then passing down--

  I, a funnel which contracts itself at

  L, into a pipe which directs the mercury into the cup A.

  H, a case which entirely covers the wheel (being of the same
       metal, and of a piece with the pipe), through which the axis
       of the wheel passes to set another wheel agoing; so becom [ing]
       the principal mover in the clock or engine to be contrived.


_The Manner of Setting It to Work_

Stop the cock at C and fill mercury into the cup A, higher than the
line B; then stop the cock at D and turn in mercury at the cock F,
till K and E are full; stop the cock at F, very close, open C, first,
and then D, out of which the mercury will fall upon the buckets of the
wheel G, down the funnel I, L, into the cup A, and be pressed up K, by
the weight of the air, as in the barometer.


Why the Devices Described in this Chapter Failed to Work

The devices explained in the preceding chapter are of such complicated
and ridiculous structure that it is impossible to explain anything from
them. It is better to abandon them all and to discuss in a general way
why Perpetual Motion has not been, and cannot be, attained by devices
constructed on similar plans. An examination of the preceding devices
in this chapter shows that they depended ultimately upon the fact:

1. That air or some other gas is to be compressed by work done upon it
and that upon expanding it will do a greater amount of work than was
required for the compression, or

2. That a bag empty, or partially filled with air, or other gas, can be
easily immersed, and that if blown full of gas while immersed it will,
in its tendency to float, do more work than was required to immerse it,
or

3. That the weight of the atmosphere and its consequent pressure upon
vacua can be utilized to drive a piston, or compress a bag and by
some sort of means at the same time produce another vacua ready for a
similar operation, the loss of the driven piston, or the compressed bag
being utilized to drive machinery, if desired.

It is now believed by all scientific men that none of these things are
possible. In the first place, it is well known that compressed air
will do exactly the same work in regaining its former volume that was
expended upon it to compress it, and this with absolute exactness.
In compressing the gas with a piston the force exerted upon the rod
to drive the piston must be sufficient not only to compress the gas
but also to overcome the friction of the tight fitting piston, and
further, if the pressure on the rod be removed, the expanding gas will
deliver against the face of the piston exactly the force and energy
required to drive the piston for the compression, but not all of this
can be returned to any machinery driven by the piston-rod, for a part
will be lost in the friction of the tight-fitting parts. Thus here, as
elsewhere, there is an exact equivalent of energy a part of which is
consumed in friction, and only a part available for returned motion.
The same thing is true in compressing a bag, except that possibly
the bending of the fabric is less resistance than the friction of
the tight-fitting piston. Still, the bending of the fabric is some
resistance, and consequently the bag so expanding cannot return all
the energy required for its compression, the difference being the loss,
however slight, in the bending of the fabric of which the bag is made.

Again, let us admit that a dilated bag is easily immersed in water,
and that if inflated with air there will be considerable tendency to
rise, but how much energy is required for the inflation? It is manifest
that if it is immersed the weight of the water and its consequent
pressure will resist the attempted inflation, and must be overcome
before the inflation is complete. The deeper the immersion the more the
compression, and consequently the more work required for the inflation.
If a bag having a contents of one cubic foot were immersed a mile in
fresh water, and if it should be attempted to inflate it, the reader
will perhaps be surprised to know that the inflation would have to be
done against a pressure of substantially 2,400 pounds to the square
inch. It is simple that the deeper the bag is immersed the more work
it will do in rising to the surface, but it is equally plain that the
deeper it is immersed the more energy is required for its inflation. In
each case the work of inflating is exactly equal to the work returned
in rising to the surface, and there is not one whit to spare for
running machinery of any kind.

The third classes of devices above mentioned assume atmospheric
pressure, and a piston driven by atmospheric pressure. This is easily
attained, but in order for atmospheric pressure to drive a piston it
must only be on one side of the piston, and when the piston has been
driven what force and energy will be required to put it in a position
again such that there will be atmosphere on only one side, and a vacuum
into which it can retire, on the other side? It is easily answered. The
same work must be done, and the same work exactly, to put the piston
again in the position with the vacuum with equal dimensions into which
it can be driven by atmospheric pressure, that first drove it to occupy
the vacuum--exactly the same work, and no less and no more, except that
the amount lost by friction must be supplied in addition.



CHAPTER V

MAGNETIC DEVICES


A Magnetic Pendulum

Here we present a device for Perpetual Motion by magnetism, but we are
unable to give the inventor's name or his nativity. It seems to have
been brought forth in the early part of the nineteenth century, prior
to 1828. The description is as follows:

  Let A A, in the prefixed engraving, represent two magnets
  revolving on axes. Let B represent a larger magnet, hanging on
  an axis, pendulum fashion, between the two former. As the poles
  of the two smaller magnets lie in the same direction, the effect
  will be to draw the larger magnet towards that on the left hand,
  while it is at the same time repelled by that on the right; but
  while this is going on, the upper end of the large magnet raises
  by means of a guide wire, the tumbler D, which, just before the
  magnets come in contact, passes the perpendicular and falls over,
  carrying with it the lever connected with the two wheels C C, and
  causing them to perform a quarter revolution; these wheels are
  connected by lines with two small wheels fixed on the axles of
  the two magnets A A. While the former make a quarter revolution,
  the latter turn half round; consequently, the position of the
  magnets is reversed, and the same motions are then performed by
  the pendulum magnet being attracted and repelled in the opposite
  direction; and just before the magnets touch each other the
  arrangement is again instantly reversed.

  [Illustration]


Magnetic-Driven Wheel

Another plan for Perpetual Motion by magnetism appeared in the public
journals of England in 1828. The inventor states in effect that he
desires to get before the readers an

"Attempt at Perpetual Motion by Means of Magnetism, Applied in a New
Way."

His attempt as published is as follows:

  The object of the present communication is to lay before your
  readers an attempt at perpetual motion by means of magnetism
  applied somewhat differently to any that has yet been published
  in your Magazine.

  [Illustration]

  The above is a wheel of light construction, moving on friction
  wheels _in vacuo_; the rim is furnished with slips of
  steel--pieces of watch-spring will do. N N are two magnets,
  which, attracting the rim of the wheel, will render one side
  lighter and the other heavier, causing it to revolve _ad
  infinitum_: or to render it more powerful, let the steel rims
  be magnetized and fixed on the wheel with their north poles
  towards its center. Let two more magnets be added, as shown by
  the dotted lines: let these two, S S, be placed with their south
  poles nearest the rim of the wheel; and the other two, N N, with
  their north poles in that position. Now, as similar poles repel
  and opposite poles attract, the wheel will be driven round by
  attraction and repulsion acting conjointly on four points of its
  circumference. B B are blocks of wood to keep off the attraction
  of the magnets from that part of the wheel which has passed them.


Mackintosh's Experiment

F. S. Mackintosh, of England, in 1823, sought to accomplish Perpetual
Motion, and made the attempt here described. It was not made public
until 1836, when it was published in "Mechanics' Magazine." In the
meantime, the inventor had become convinced of the impossibility
of perpetual motion, as his comments on his own alleged invention
discloses.

(The classification in this book of Mackintosh's invention is somewhat
doubtful. The article as contributed in 1836 would as aptly be
classified under arguments against Perpetual Motion, Chapter XII. But,
in view of the fact that at the time of the invention the inventor
was seriously working at a scheme for the accomplishment of Perpetual
Motion, it has been decided to classify it under Magnetic Perpetual
Motion Devices.)

The published article was in the nature of a contribution from the
inventor, and is as follows:

  I herewith forward you a description of a machine which was
  constructed by me in the year 1823, with a view to produce a
  perpetual motion. With this machine and the studies necessarily
  connected with it, first originated the suspicion that the
  planets could not continue in motion unless they gradually
  approached the center of the attraction.

  In the first place, let us describe the machine. Fig. 1: A is
  a sectional view of the interior of the wheel, which is formed
  in two halves upon one shaft; each half or section is furnished
  with a projecting ledge and an opening is left between the two
  ledges sufficiently wide to admit of a magnet being introduced
  between them, by which arrangement the magnet may be brought as
  near to the ball as may be necessary (see Fig. 2). B is a magnet
  whose line of attraction acts at right angles with the line of
  gravity. C is an iron ball under the action of two forces. The
  magnet continually drawing the ball up the inclined plane within
  the wheel, and gravity continually drawing it to the bottom,
  by their united action it was supposed the wheel would revolve
  forever, or till it was worn out; upon the same principle that a
  wheel revolves by the animal force or muscular action of a mouse
  or squirrel, which carries it up the inclined plane, whilst it is
  continually drawn to the bottom by the action of gravity, thereby
  causing the wheel to revolve by the weight of its body. The
  model was taken from the earth's motion round the sun; and the
  following process of reasoning seemed to justify the assumption
  that the wheel would move on till it was worn out:

  "The earth is carried round the sun by the action of two forces,
  one of which is momentum, which is not, in reality, a force
  or cause of motion, but an effect derived from an original
  impulse; and that impulse or the momentum derived from it is
  not destroyed, because there is no resistance to the moving
  body--that is, there is no friction. Well, I cannot make this
  machine without having resistance to the motion--that is,
  friction; but to compensate for this I have two real forces, two
  causes of motion, each of them capable of imparting momentum to
  a body: they are both constant forces; and from one of them,
  the magnet, I can obtain any power that may be required within
  certain limits."

  [Illustration]

  This reasoning appeared conclusive, and the wheel was made; but
  when the magnet was applied instead of the ball rolling up the
  inclined plane, the wheel moved backwards upon its center. It
  occurred to me that by placing a small ratchet upon the wheel,
  as shown at D, this backward motion of the wheel on its center
  might be prevented, in which case the ball must roll up the
  inclined plane, and that a perpetual motion might then ensue;
  but this ratchet I never tried, having about that time begun to
  perceive that the idea of a perpetual mechanical motion, either
  on the earth or in the heavens, involves an absurdity; and that,
  therefore, the motions of the planets must necessarily carry them
  continually nearer and nearer to the center of attraction.

The above described device by Mr. Mackintosh brought forth the
following comment from R. Munro, which was published in 1836:

  The result of Mr. Mackintosh's essay at perpetual motion might
  be attributed to the avoidable friction caused by the manner in
  which the iron ball is placed in the wheel. Curious to try the
  experiment, I proceeded, and, with the view of diminishing the
  friction, I placed two wheels on the axis of the ball, but the
  result was precisely that described by Mr. Mackintosh. I next
  applied the ratchet, as suggested, but with no better effect; the
  ball rolled towards the magnet, but did not give the required
  motion to the wheel. It is not unlikely, then, that the present
  ingenious attempt will not be realized.


Spence's Device

John Spence, of Linlithgow, Scotland, was a shoemaker, but possessed
great mechanical ingenuity. He could not keep his mind from the subject
of mechanics. He devoted a great deal of time to designing mechanical
schemes for Perpetual Motion. An account of his efforts is taken from
"Percy Anecdotes."

The device was exhibited in Edinburgh and amazing to state it attracted
the attention of one of the greatest and most original scientists that
ever lived, Sir David Brewster.

It is from a letter written by Brewster, in 1818, to the "Annales de
Chimie," that we get a description of the Spence invention. The editor
of "Annales de Chimie," was evidently reluctant to publish any article
concerning Perpetual Motion, and only the great fame of Sir David
induced him to give space to the contribution. The article was first
published in France, but it has, with an introductory statement by the
editor, been translated into English, as follows:

  The reader will readily conclude that in publishing this article
  we are influenced solely by the great reputation of the learned
  contributor. Sir David writes from Edinburgh:

  [Illustration]

  I am almost afraid to inform you that at this moment in Edinburgh
  may be seen a machine, made by a shoemaker at Linlithgow, which
  realizes the perpetual motion. This effect is produced by two
  magnets A and B, acting alternately upon a needle _m n_, of which
  the point of attachment _n_ corresponds exactly with the axis
  around which turns the movable lever C D. When the needle _m n_
  has been attracted into the position _m´ n_ by the action of the
  magnet B, and C D is in consequence found in C´ D´, a _substance_
  connected with m n is interposed by mechanism between _m´ n_ and
  B. This substance has the property of intercepting, or rather of
  modifying the action of the magnet B, and this permits the other
  magnet A to draw the needle into the position _m´´ n_; but no
  sooner has it reached this point than a second plate or layer of
  the same substance places itself before magnet, and immediately B
  attracts anew the needle.

  [Illustration]

  The annexed figure exhibits a second form of the machine. A
  and B are two horse-shoe magnets, _a_ and _b_ the _mysterious
  substance_, and _m n_ the needle, which turns constantly with
  great rapidity. Mr. Playfair and Capt. Kater have inspected
  both of these machines, and are satisfied that they resolve the
  problem of _perpetual motion_.


Joannis Theisneri's Semi-Circle

An account of this invention has been preserved by Gaspar Schott in a
work entitled "Thaumaturgus Physicus, sive Magiae Universalis Naturae
et Artis," published in 1859. It is illustrated by the following figure:

[Illustration]

The inventor expected the operation of his device to be as follows: "A"
is a large magnet, elevated on a short pillar at the foot of which is a
straight inclined tube, "C" "F" the ends of which are connected with a
curved or semicircular tube "C", "D", "E", "F", as shown in the figure.

The weight at the lower extremity is supposed to ascend through the
curved tube by the attraction of the magnet "A" and upon reaching the
point "C" the supposition was that upon passing the point "C" the
attraction of the magnet "A" would be sufficient to hold it there * *
* back to the point "F" through the straight tube, and then be drawn
by the magnet through the curved tube to the point "C" and so on
perpetually.

The impracticability of the above device is manifest. At a point
between "D" and "E" it is plain the ball would have to ascend
perpendicularly and if the magnet exerts sufficient attraction to
elevate the weight at that point it would surely hold the weight at the
point "C", for at "C" the weight would be much nearer the magnet and
consequently much more strongly attracted.


Device of Dr. Jacobus

In the same work by Gaspar Schott from which an account of the
preceding device is obtained he gives an account of the device of Dr.
Jacobus.

Dr. Jacobus's scheme is illustrated by the following figure:

[Illustration]

It will be observed that the above figure shows a string of iron
balls "A" suspended on a grooved wheel "E" on an axle "C" between two
uprights "FF". At "H" lies a large lodestone, which is to attract the
balls at "D" and was expected by the inventor to cause the wheel to
rotate.



CHAPTER VI

DEVICES UTILIZING CAPILLARY ATTRACTION AND PHYSICAL AFFINITY


Ludeke and Wilckens's Device

In 1864, Johann Ernst Friedrich Ludeke, of London, and Daniel Wilckens,
of Surrey, applied for British patent on "Improvements in Motive Power
by Capillary Attraction." They describe their invention as follows:

  Our invention consists of improvements in motive power by
  capillary attraction constructed as follows:

  [Illustration]

  Figure 1 of the accompanying drawings represents in horizontal
  section a square case or cistern; this cistern is filled with
  water nearly to the top, and two wheels marked _a_, _a_, and
  _b_, _b_, are placed in the water in the cistern. By capillary
  attraction the water rises between the two wheels marked _x_,
  _x_, to a height above the level of the water in proportion to
  the distance of the wheels from each other at _x_, _x_. As the
  water rises between the wheels marked _x_, _x_, above its level,
  the weight of water between the wheels at _x_, _x_, will cause
  the wheels to continually revolve.

  Figure 2 represents the same as Figure 1, but in a vertical
  section. The said power may be obtained by wheels moved on axis,
  or by other apparatus by rise and fall in the water by vertical
  motion.


The Jurin Device

The device which we have designated "The Jurin Device," was not, in
fact, invented by Jurin. James Jurin furnished an account of the
invention to The Royal Society of London, and it appears in the reports
of that society published in 1720. The invention was by a friend of
Jurin's whose name he does not give in the account.

Jurin's account of his friend's invention is as follows:

  Some days ago a method was proposed to me by an ingenious friend
  for making a perpetual motion, which seemed so plausible, and
  indeed so easily demonstrable from an observation of the late Mr.
  Hawksbee, said to be grounded upon experiment, that though I am
  far from having any opinion of attempts of this nature, yet, I
  confess, I could not see why it should not succeed. Upon trial
  indeed I found myself disappointed. But as searches after things
  impossible in themselves are frequently observed to produce other
  discoveries, unexpected by the Inventor; so this Proposal has
  given occasion not only to rectify some mistakes into which we
  had been led, by that ingenious and useful member of the Royal
  Society above named, but likewise to detect the real principle,
  by which water is raised and suspended in capillary tubes, above
  the level.

  My friend's proposal was as follows:

  Fig. 1. Let A B C be a capillary siphon, composed of two legs
  A B, B C, unequal both in length and diameter; whose longer and
  narrower leg A B having its orifice A immersed in water, the
  water will rise above the level, till it fills the whole tube
  A B, and will then continue suspended. If the wider and shorter
  leg B C, be in like manner immersed, the water will only rise to
  same height as F C, less than the entire height of the tube B C.

  This siphon being filled with water and the orifice A sunk below
  the surface of the water D E, my friend reasons thus:

  Since the two columns of water A B and F C, by the supposition,
  will be suspended by some power acting within the tubes they are
  contained in, they cannot determine the water to move one way, or
  the other. But the column B F, having nothing to support it, must
  descend, and cause the water to run out at C. Then the pressure
  of the atmosphere driving the water upward through the orifice A,
  to supply the vacuity, which would otherwise be left in the upper
  part of the tube B C, this must necessarily produce a perpetual
  motion, since the water runs into the same vessel, out of which
  it rises. But the fallacy of this reasoning appears upon making
  the experiment.

  [Illustration]

  Exp. 1. For the water, instead of running out at the orifice C
  rises upwards towards F, and running all out of the leg B C,
  remains suspended in the other leg to the height A B.

  Exp. 2. The same thing succeeds upon taking the siphon out of
  the water, into which its lower orifice A had been immersed, the
  water then falling in drops out of the orifice A, and standing
  at last at the height A B. But in making these two experiments
  it is necessary that A G the difference of the legs exceed F C,
  otherwise the water will not run either way.

  Exp. 3. Upon inverting the siphon full of water, it continues
  without motion either way.

  The reason of all which will plainly appear, when we come to
  discover the principle, by which the water is suspended in
  capillary tubes.

  Mr. Hawksbee's observation is as follows:

  Fig. 2. Let A B F C be a capillary siphon, into which the water
  will rise above the level to the height C F, and let B A be the
  depth of the orifice of its longer leg below the surface of the
  water D E. Then the siphon being filled with water, if B A be
  not greater than C F, the water will not run out at A, but will
  remain suspended.

  This seems indeed very plausible at first sight. For since the
  column of water F C will be suspended by some power within the
  tube, why should not the column B A, being equal to, or less
  than the former, continue suspended by the same power.

  Exp. 4. In fact, if the orifice C be lifted up out of the water
  D E, the water in the tube will continue suspended, unless B A
  exceed F C.

  Exp. 5. But when C is never so little immersed in the water
  immediately the water in the tube runs out in drops at the
  orifice A, though the length A B be considerably less than the
  height C F.

  Mr. Hawksbee, in his book of Experiments, has advanced another
  observation, namely, that the shorter leg of a capillary siphon,
  as A B F C, must be immersed in the water to the depth F C, which
  is equal to the height of the column, that would be suspended in
  it, before the water will run out of the longer leg.

  Exp. 6. From what mistake this has proceeded, I cannot imagine;
  for the water runs out at the longer leg, as soon as the orifice
  of the shorter leg comes to touch the surface of the stagnant
  water, without being at all immersed therein.

Jurin's attitude concerning his friend's discovery is pleasing. He
appears to have had better judgment than to rush into print, or herald
forth that Perpetual Motion had been accomplished. Indeed, the account
as given to the Royal Society was that of an experiment and a failure.
Nevertheless, it presents an interesting point. Capillary Attraction,
however, creates no new energy. Adhesion is a force, and is often
quite a strong force in nature.

If a rod or tube be held by the hand at one end, and the other end
inserted in a liquid, it will be observed that in some instances,
depending upon the nature of the material of the rod or tube, and the
liquid, at the point of contact the liquid will slightly rise in the
tube and on the outside edges of the tube. In other instances it will
be depressed slightly at the same point. Whether it will be elevated or
depressed depends on whether the adhesion of the liquid to the material
of which the tube or rod is composed is greater than the cohesion of
the particles of the liquid.

If there be a depression it is manifest that the entire surface of the
liquid will be slightly elevated by reason of the depression. On the
contrary, if the liquid adheres to and creeps slightly upward on the
tube or rod, then it is manifest that the surface of the liquid will
come to rest slightly lower than though it did not so creep.

The net result finally gets back to the principle of flotation. The
immersion or insertion is a little more difficult in the case of
depression, and a little easier in the case of elevation. There is no
gain or loss of energy. It simply increases in one case, and diminishes
in the other case the amount of displacement, with all the resulting
mechanical phenomena.


Sir William Congreve

As stated in the preface of this work, pursuit of Perpetual Motion has
by no means been confined to mechanics and tradesmen. Many men eminent,
and even famous in professions, art and science have devoted much time
and thought to the subject. Among such eminent men is to be mentioned
Sir William Congreve, of England, a baronet. He was born 1772, and
died in 1828. He was an artillerist and an inventor, and was a son
of Lieutenant General Sir William Congreve; was distinguished as a
military man, as a member of parliament, and as a business man; was an
inventor of note, having invented a war rocket, a gun-recoil mounting,
a time-fuse, a parachute attachment for rockets, a hydro-pneumatic
canal lock sluice, a process for color painting, a new form of steam
engine, a method of consuming smoke, a clock which measured time
by a ball rolling down an inclined plane, besides other inventions
and discoveries. He published a large number of works on scientific
subjects.

It is not, therefore, surprising that whatever Sir William Congreve
said or did concerning any scientific or mechanical subject should have
attracted general attention.

He devised and made a Perpetual Motion Machine, which, like all others,
failed to work. We submit that his plan is peculiarly ingenious,
and we fail to see how, without a knowledge of the principles of
Conservation of Energy, the Congreve idea should not have appealed to
any one as reasonable, and its failure puzzling.

An account of the Congreve device and an explanation of his ideas
appeared in "The Atlas" in 1827, and the following description is taken
from the article appearing in "The Atlas":

  The celebrated Boyle entertained an idea that perpetual motion
  might be obtained by means of capillary attraction; and, indeed,
  there seems but little doubt that nature has employed this force
  in many instances to produce this effect.

  There are many situations in which there is every reason to
  believe that the sources of springs on the tops and sides of
  mountains depend on the accumulation of water created at certain
  elevations by the operation of capillary attraction, acting in
  large masses of porous material, or through laminated substances.
  These masses being saturated, in process of time become the
  sources of springs and the heads of rivers; and thus, by an
  endless round of ascending and descending waters, form, on the
  great scale of nature, an incessant cause of perpetual motion, in
  the purest acceptance of the term, and precisely on the principle
  that was contemplated by Boyle. It is probable, however, that any
  imitation of this process on the limited scale practicable by
  human art would not be of sufficient magnitude to be effective.
  Nature, by the immensity of her operations, is able to allow for
  a slowness of process which would baffle the attempts of man in
  any direct and simple imitation of her works. Working, therefore,
  upon the same causes, he finds himself obliged to take a more
  complicated mode to produce the same effect.

  To amuse the hours of a long confinement from illness, Sir
  William Congreve has recently contrived a scheme of perpetual
  motion, founded on this principle of capillary attraction, which,
  it is apprehended, will not be subject to the general refutation
  applicable to those plans in which the power is supposed to be
  derived from gravity only. Sir William's perpetual motion is as
  follows:

  [Illustration]

  Let A B C be three horizontal rollers fixed in a frame; _a a a_,
  etc., is an endless band of sponge, running round these rollers;
  and _b b b_, etc., is an endless chain of weights, surrounding
  the band of sponge, and attached to it, so that they must move
  together; every part of this band and chain being so accurately
  uniform in weight that the perpendicular side A B will, in all
  positions of the band and chain, be in equilibrium with the
  hypothenuse A C, on the principle of the inclined plane. Now, if
  the frame in which these rollers are fixed be placed in a cistern
  of water, having its lower part immersed therein, so that the
  water's edge cuts the upper part of the rollers B C, then, if the
  weight and quantity of the endless chain be duly proportioned to
  the thickness and breadth of the band of sponge, the band and
  chain will, on the water in the cistern being brought to the
  proper level, begin to move round the rollers in the direction
  A B, by the force of capillary attraction, and will continue so
  to move. The process is as follows:

  On the side A B of the triangle, the weights _b b b_, etc.,
  hanging perpendicularly alongside the band of sponge, the band
  is not compressed by them, and its pores being left open, the
  water at the point _x_, at which the band meets its surface,
  will rise to a certain height, _y_, above its level, and thereby
  create a load, which load will not exist on the ascending side
  C A, because on this side the chain of weights compresses the
  band at the water's edge, and squeezes out any water that may
  have previously accumulated in it; so that the band rises in a
  dry state, the weight of the chain having been so proportioned
  to the breadth and thickness of the band as to be sufficient to
  produce this effect. The load, therefore, on the descending side
  A B, not being opposed by any similar load on the ascending
  side, and the equilibrium of the other parts not being disturbed
  by the alternate expansion and compression of the sponge, the
  band will begin to move in the direction A B; and as it moves
  downwards, the accumulation of water will continue to rise, and
  thereby carry on a constant motion, provided the load at _x y_ be
  sufficient to overcome the friction on the rollers A B C.

  Now, to ascertain the quantity of this load in any particular
  machine, it must be stated that it is found by experiment that
  the water will rise in a fine sponge about an inch above its
  level; if, therefore, the band and sponge be one foot thick and
  six feet broad, the area of its horizontal section in contact
  with the water would be 864 square inches, and the weight of the
  accumulation of water raised by the capillary attraction being
  one inch rise upon 864 square inches, would be 30 lbs., which, it
  is conceived, would be much more than equivalent to the friction
  of the rollers.

  The deniers of this proposition, on the first view of the
  subject, will say, it is true the accumulation of the weight on
  the descending side thus occasioned by the capillary attraction
  would produce a perpetual motion, if there were not as much power
  lost on the ascending side by the change of position of the
  weights, in pressing the water out of the sponge.

  The point now to be established is, that the change in the
  position of the weights will not cause any loss of power. For
  this purpose, we must refer to the following diagram.

  [Illustration]

  With reference to this diagram, suppose _a a a_, etc., an endless
  strap, and _b b b_, etc., an endless chain running round the
  rollers; A B C not having any sponge between them, but kept
  at a certain distance from each other by small and inflexible
  props, _p p p_, etc., then the sides A B and C A would, in all
  positions of this system, be precisely an equilibrium, so as
  to require only a small increment of weight on either side to
  produce motion. Now, we contend that this equilibrium would still
  remain unaffected, if small springs were introduced in lieu of
  the inflexible props _p p p_, so that the chain _b b b_ might
  approach the lower strap _a a a_, by compressing these small
  springs with its weight on the ascending side; for although
  the centre of gravity of any portion of chain would move in a
  different line in the latter case--for instance, in the dotted
  line--still the quantity of the actual weight of every inch of
  the strap and chain would remain precisely the same in the
  former case, where they are kept at the same distance in all
  positions, as in the latter case, where they approach on the
  ascending side; and so, also, these equal portions of weights,
  notwithstanding any change of distance between their several
  parts which may take place in one case and not in the other,
  would in both cases rise and fall, though the same perpendicular
  space, and consequently the equilibrium, would be equally
  preserved in both cases, though in the first case they may rise
  and fall through rather more than in the second. The application
  of this demonstration to the machine described in Fig. 1, is
  obvious; for the compression of the sponge by the sinking of
  the weights on the ascending side, in pressing out the water,
  produces precisely the same effect as to the position and ascent
  of the weights, as the approach of the chain to the lower strap
  on the ascending side, in Fig. 2, by the compression of the
  springs; and consequently, if the equilibrium is not affected in
  one case--that is, in Fig. 2, as above demonstrated--it will not
  be affected in the other case, Fig. 1; and, therefore, the water
  would be squeezed out by the pressure of the chain without any
  loss of power. The quantity of weight necessary for squeezing
  dry any given quantity of sponge must be ascertained and duly
  apportioned by experiment. It is obvious, however, that whether
  one cubic inch of sponge required one, two, or four ounces
  for this purpose, it would not affect the equilibrium, since,
  whatever were the proportion on the ascending side, precisely
  the same would the proportion be on the descending side.

  This principle is capable of application in various ways, and
  with a variety of materials. It may be produced by a single
  roller or wheel. Mercury may also be substituted for water, by
  using a series of metallic plates instead of sponges; and, as the
  mercury will be found to rise to a much greater height between
  these plates, than water will do in a sponge, it will be found
  that the power to be obtained by the latter materials will be
  from 70 to 80 times as great as by the use of water. Thus, a
  machine, of the same dimensions as given above, would have a
  constant power of 2,000 lbs. acting upon it.

  We now proceed to show how the principle of perpetual motion
  proposed by Sir William Congreve may be applied upon one centre
  instead of three.

  In the following figure, _a b c d_ represents a drum-wheel or
  cylinder, moving on a horizontal axis surrounded with a band
  of sponge 1 2 3 4 5 6 7 8, and immersed in water, so that the
  surface of the water touches the lower end of the cylinder. Now
  then, if, as in Fig. 2, the water on the descending side _b_
  be allowed to accumulate in the sponge at _x_, while, on the
  ascending side D, the sponge at the water's edge shall, by any
  means not deranging the equilibrium, be so compressed that it
  shall quit the water in a dry state, the accumulation of water
  above its level at _x_, by the capillary attraction, will be a
  source of constant rotary motion; and, in the present case, it
  will be found that the means of compressing the sponge may be
  best obtained by buoyancy, instead of weight.

  For this purpose, therefore, the band of sponge is supposed to
  be divided into eight or more equal parts, 1 2 3 4, etc., each
  part being furnished with a float or buoyant vessel, _f_ 1,
  _f_ 2, etc., rising and falling upon spindles, _s s s_, etc.,
  fixed in the periphery of the drum; these floats being of such
  dimensions that, when immersed in water, the buoyancy or pressure
  upwards of each shall be sufficient to compress that portion of
  the sponge connected with it, so as to squeeze out any water it
  may have absorbed. These floats are further arranged by means of
  levers _l l l_, etc., and plates _p p p_, etc., so that, when
  the float _f_ No. 1 becomes immersed in the water, its buoyant
  pressure upwards acts not against the portion of the sponge No.
  1, immediately above it, but against No. 2, next in front of it;
  and so, in like manner, the buoyancy of _f_ No. 2 float acts on
  the portion of the sponge No. 3, and _f_ No. 3 float upon No. 4
  sponge.

  Now, from this arrangement it follows, that the portion of sponge
  No. 4, which is about to quit the water, is pressed upon by
  that float, which, from acting vertically, is most efficient in
  squeezing the sponge dry; while that portion of the sponge No. 1,
  on the point of entering the water, is not compressed at all from
  its corresponding float No. 8, not having yet reached the edge
  of the water. By these means, therefore, it will be seen that
  the sponge always rises in a dry state from the water on the
  ascending side, while it approaches the water on the descending
  side in an uncompressed state, and open to the full action of
  absorption by the capillary attraction.

  [Illustration]

  The great advantage of effecting this by the buoyancy of light
  vessels instead of a burthen of weights, as in Fig. 2, is that,
  by a due arrangement of the dimensions and buoyancy of the floats
  immersed, the whole machine may be made to float on the surface
  of the water, so as to take off all friction whatever from the
  centre of suspension. Thus, therefore, we have a cylindrical
  machine revolving on a single centre without friction, and having
  a collection of water in the sponge on the descending side,
  while the sponge on the ascending side is continually dry; and
  if this cylinder be six feet wide, and the sponge that surrounds
  it one foot thick, there will be a constant moving power of
  thirty pounds on the descending side, without any friction to
  counteract it.

  It has been already stated, that to perpetuate the motion of
  this machine, the means used to leave the sponge open on the
  descending side, and press it dry on the ascending side, must
  be such as will not derange the equilibrium of the machine when
  floating in water. As, therefore, in this case the effect is
  produced by the ascent of the buoyant floats _b_, to demonstrate
  the perpetuity of the motion, we must show that the ascent of the
  floats _f_ No. 1 and _f_ No. 3 will be equal in all corresponding
  situations on each side of the perpendicular; for the only
  circumstance that could derange the equilibrium on this system,
  would be that _f_ No. 1 and _f_ No. 3 should not in all such
  corresponding situations approach the centre of motion equally;
  for it is evident that in the position of the floats described in
  the above figure, if _f_ No. 1 float did not approach the centre
  as much as _f_ No. 3, the equilibrium would be destroyed, and the
  greater distance of _f_ No. 1 from the centre than that of f No.
  3 would create a resistance to the moving force caused by the
  accumulation of the water at _x_.

  It will be found, however, that the floats _f_ No. 1 and _f_ No.
  3 do retain equal distances from the centre in all corresponding
  situations, for the resistance to their approach to the centre
  by buoyancy is the elasticity of the sponge at the extremity
  of the respective levers; and as this elasticity is the same
  in all situations, while this centrifugal force of the float
  _f_ No. 1 is equal to that of the float _f_ No. 3, at equal
  distances from the perpendicular, the floats _f_ No. 1 and _f_
  No. 3 will, in all corresponding situations on either side of
  the perpendicular, be at equal distances from the centre. It is
  true, that the force by which these floats approach the centre
  of motion varies according to the obliquity of the spindles on
  which they work, it being greatest in the perpendicular position;
  but, as the obliquity of these spindles is the same at all equal
  distances from the perpendicular, and as the resistance of
  the ascent of the floats is equal in all cases, the center of
  buoyancy will evidently describe a similar curve on each side
  of the perpendicular; and consequently the equilibrium will be
  preserved, so as to leave a constant moving force at _x_, equal
  to the whole accumulation of water in the sponge. Nor will
  this equilibrium be disturbed by any change of position in the
  floats not immersed in the water, since, being duly connected
  with the sponge by the levers and plates, they will evidently
  arrange themselves at equal distances from the center, in all
  corresponding situations on either side.

  It may be said that the equilibrium of the band of sponge may be
  destroyed by its partial compression; and it must be admitted
  that the centre of gravity of the part compressed, according
  to the construction above described, does approach the center
  of motion nearer than the center of gravity of the part not
  compressed. The whole weight of the sponge is, however, so
  inconsiderable, that this difference would scarcely produce any
  sensible effect; and if it did, a very slight alteration in the
  construction, by which the sponge should be compressed as much
  outwards as inwards, would retain the center of gravity of the
  compressed part at the same distance from the center of motion as
  the center of gravity of the part not compressed.



CHAPTER VII

Liquid Air as a Means of Perpetual Motion


A few years ago air was liquefied. This was accomplished by a very high
compression accompanied by a very low temperature.

It is manifest that when liquid air is removed from the extremely
low temperature necessary for its liquefaction, and introduced into
ordinary atmospheric temperatures, it will exert a most tremendous
expansive force which can be utilized for driving machinery and thereby
producing heat or electricity, or for any other purpose for which force
is required. But, by the law of Conservation of Energy, the liquefied
air by expansion can yield no more energy than was required to extract
the heat from the air and compress it into the liquid state.

One enthusiastic individual who had worked in a plant for liquefying
air announced throughout the United States of America, and perhaps
throughout the civilized world, that he had a device by which the
expansive force of three pounds of liquid air could be made to liquefy
ten pounds, and that seven of the ten could be utilized for driving
machinery, or for any other purpose for which force is required, the
remaining three being utilized in the production of another ten pounds
of liquid air, and so on ad infinitum. He boldly announced that thereby
he had discovered an inexhaustible supply of energy at a nominal cost,
whereby we could all be warmed and have our machinery of all kinds
driven without the expense of gas, coal, fuel of any kind, wind, waves,
tides or streams. This enthusiastic individual produced considerable
excitement for a time, and then the public ceased to hear about either
him or his device. He dropped out of sight and his name sank into
oblivion. His claims were absurd, and the absurdity is readily apparent
to anyone versed in thermodynamics or familiar with the principles of
Conservation of Energy.

There was little excuse for his ever having made such pretentions or
for his pretentions ever to have been seriously listened to by any one;
for the principle of Conservation of Energy had years before been fully
established and heralded throughout the world.



CHAPTER VIII

Radium and Radio-Active Substances Considered as a Conceived Source of
Perpetual Motion


A few years ago when the remarkable properties of radium were
discovered it was thought by many that here at last was the long sought
solution of the problem of Perpetual Motion. Radium seemed to have the
power of maintaining its own temperature _permanently_ above that of
surrounding bodies. Many versed in the science of thermodynamics (heat
power) shook their heads in doubt. If, indeed, it were really true
that the substance, radium, or any other substance had the quality of
remaining permanently warmer than surrounding bodies without having
heat supplied to it, then, indeed, there was an inexhaustible supply of
heat, and consequently power.

Hon. R. J. Strutt (Lord Rayleigh), devised a radium clock to run on
this principle, consisting of a vacuum vessel in which was suspended
a radio-active substance contained in a tube. At the lower end of the
tube are two gold leaves as in an electroscope. Platinum wires extended
through the glass and touched the gold leaves. The other end of the
platinum wires are extended to connect with the earth. The radio-active
substance electrifies the gold leaves and causes them to be extended,
and upon being extended they come in contact with the platinum wires
and their charge of electricity is lost, being conducted through the
wires and dispersed in the earth, and the leaves losing their charge
fall by the force of gravity from the wires back to their position near
the tube containing the radio-active substance to be again charged,
to again move to and touch the platinum wires, and again lose their
charge; this process to go on indefinitely.

Here, indeed, was Perpetual Motion, except for the fact that further
and more refined experiments and investigations demonstrated that
radio-active substances are not permanently radio-active, but
gradually, though very slowly, lose their radio-activity just as a fire
will finally burn out, no matter how slowly it burns, or just as an
electric battery will finally lose its charge and become exhausted.

This loss, however, of radio-active energy in radio-active substances
is so slow that it is said the Strutt clock will run for over one
thousand years. But the fact that it will not run permanently, and
that the motion is the result of energy supplied by the radio-active
substance, and is not supplied by the mechanism itself, deprives it of
any right to be called a solution of the problem of self-motive power.

It should be noted that Hon. R. J. Strutt (Lord Rayleigh) of England,
who devised the radium clock, above mentioned, is not to be classed
with the ordinary Perpetual Motion enthusiast. He was, and is, in fact,
a man of very great scientific ability and attainments, and has to his
credit many actual and splendid achievements demonstrating him to be a
genius of the rarest and most exalted type. His radium clock is founded
on correct principles, and surely a clock that will run one thousand
years without having power supplied from an outside source is worth
while. It should be here also mentioned that the force derived from
radio-activity in the manner it is applied in the Strutt clock is very
slight, and the instrument necessarily extremely delicate.



CHAPTER IX

Perpetual Motion Devices Attempting Its Attainment by a Misconception
of the Relation of Momentum and Energy


The author, within twenty years last past, has had his attention
called by two different persons, each ignorant of the efforts of
the other, who were seeking to obtain Perpetual Motion by utilizing
certain physical facts concerning Momentum and Energy. These facts
and the principles out of which they grow are familiar to all who
understand thoroughly, even the rudiments of physics; but to persons
who are inclined to mechanics, but who have never had the advantages
of the presentation of clear principles, they are confusing, and it is
surprising that they have not become more fertile fields for Perpetual
Motion workers. However, we are unable to find any written or printed
account or description of a plan or device of that kind, and our
information is confined to instances that have been brought to our
personal observation, and concerning which the advice and counsel of
the author was sought.

The worker in each case was a man of more than ordinary natural
intelligence, and with a bent for mechanical pursuits and reflection.
Each had taken a course in what is conventionally called High School
Physics.

The idea in each case was so novel and interesting that we deem the
presentation worth while. They were so nearly alike that instead of
attempting to narrate what they said, we will endeavor in our own way
to present the idea, and then to give our explanation, showing wherein
lay their error.

The following definitions and laws of physics may be regarded as
established:


Momentum

_Momentum_ is the quantity of motion of a moving body, and is the
velocity multiplied by the weight.

Thus, a body weighing two pounds, moving at four feet per second, may
be represented as having a momentum of eight.

A body weighing two pounds moving at the rate of six feet per second
may be said to have a momentum of twelve.

A body weighing ten pounds moving at the rate of ten feet per second
will have a momentum of one hundred--and so on.

Now, a step further. A body in motion striking another body free to
move will lose part of its motion, and will impart some of its motion
to the body moved against. The aggregate momentum after the striking
is the same as before--that is to say--if a body weighing ten pounds
have a velocity of twenty feet per second, its momentum we will call
two hundred. Now, if in moving it strike another body either larger or
smaller its motion will be somewhat retarded, and the body struck will
possess some motion.

Multiply the weight of each by its motion after the striking, and it
will be found that the sum of the products is two hundred. This may
be illustrated by swinging balls like pendulums to cords of equal
length from a beam, having the arrangement such that balls of different
materials and sizes can be substituted at liberty. If a body be drawn
back parallel to the beam, and released so as to swing against another
swinging body, both will have motion. This motion will, in some cases
be a rebounding motion, as in the case of a small elastic body swinging
against and striking a larger elastic body, but in all cases the sum
total of the momentum after the impingement is the same as before.

The following statement of the law then, is deducible:

  _The Momentum_ of one body in motion may be made to impart
  momentum to another body, the amount of momentum lost by the
  former being exactly equal to that thus acquired by the latter.

Before leaving these remarks on momentum the reader should observe
carefully what momentum is and bear in mind it is the _quantity of
motion_ possessed by a moving body, and has to do only with _mass_ and
_velocity_--and takes no account of distance passed through.


Energy

Energy is the _capacity to do work_, and the energy of a moving body
is the amount of _work_ it will do, i. e., the _distance_ it will move
against a resistance by virtue of its tendency to move, before being
brought to a state of rest.

Now note, and note carefully, that the amount of _energy is
proportional_ to the mass, and to the _square_ of the velocity.

Note this carefully: Any body in motion _has both momentum and energy_.
Its momentum is proportional to its velocity; its energy to the
_square_ of its velocity. If the velocity be doubled, the momentum will
be doubled, but its energy quadrupled. If the velocity be trebled, its
momentum will be trebled, but its energy increased nine-fold.

It is important that the student get clearly what is meant by saying
that Energy is the _capacity to do work_, and is proportional to the
square of the velocity.

The capacity to do work means the capacity to move against resistance,
i. e., to overcome resistance. The word "work" being used in a purely
mechanical sense and in that sense it is used whether the result
accomplished is destructive or beneficial.

A revolving fly wheel will run machinery for some time after the
application of force has ceased. This is doing work, and represents
energy.

A bullet fired from a gun will accomplish destruction before having its
motion arrested. This is work--energy.

If a boy throw a ball into a snow bank, its motion will sink it into
the snow, but not far, the resistance of the snow will soon bring the
ball to rest. The ball overcomes resistance in passing through the snow
until it is brought to rest, and thus it does the _work_ of forcing
itself through the snow, and possesses the _energy_ necessary to do
that work.

The overcoming of the resistance of the air by a moving body is work.
A steamboat will move for some time in water after the steam has been
turned off. The overcoming of the resistance of the water is work, and
by virtue of the motion of the boat when the steam was turned off it
possessed the energy to do the work of forcing itself for some time
through the resistance of the water.

The Perpetual Motion worker in each case had reasoned himself into this
conclusion: That the same energy will impart the same _acceleration_
of velocity, regardless of the velocity at the beginning of the
application of energy. That the same amount of energy or work necessary
to impart to a body a velocity of ten feet per second will increase
that velocity to twenty feet per second, or from twenty feet per second
to thirty feet per second. In other words, that the same amount of
energy, and only the same amount of energy is required for a given
_increase_ in velocity without regard to the initial velocity. This
appears plausible, and almost self-evident. We believe the great
majority of people, other than mechanical engineers would, upon
presentation of the theory accept it as axiomatic, and as a matter of
course. The fallacy becomes manifest only from a critical and technical
examination of the Laws of Momentum and Energy.

The Perpetual Motion worker had learned from his text-books that if the
velocity be _doubled_, the energy would be _multiplied by four_. His
idea was to so arrange his mechanism that he would apply the amount of
energy to move a fly wheel free to revolve, from a position of rest to
a revolving velocity of ten revolutions per second. Then apply again
the _same amount of energy_, and accelerate that velocity from ten
revolutions per second to twenty revolutions per second. Thus, the
energy at the end of the second second would be four times what it was
at the end of the first second. But to make it so, only double the
amount of energy had been applied that had been expended at the end of
the first second. Thus, he reasoned, his machine was by virtue of its
structure, accumulating energy, and this energy could be used one-half
to continue the motion of his machine, and the other half to run other
machinery, or for any other purpose for which energy might be desired.

Wherein lies the fallacy of this supposition?

We will now endeavor to explain. And for the young student to get the
explanation fully, it will be necessary for him to pay the closest
attention to what we here state.

A force, for instance the pressure of the finger or the hand, equal to
one pound against a body free to move, will, we will say, move that
body in one second of time through a space of ten feet, and at the end
of that second the body will have a velocity of twenty feet. It is
manifest that at the end of the second the velocity will be twenty feet
per second for its initial velocity is zero, and its average velocity
ten feet per second, the acceleration being, of course, presumed
uniform.

Now, it is _not_ true as the Perpetual Motion worker had assumed that
the same energy--i. e., the same work that is required to increase
the velocity from zero to ten feet per second will increase the
velocity from ten feet per second to twenty feet per second, and _in
that assumption_ lay the fallacy of our friends who were thus seeking
Perpetual Motion.

The greater the velocity, the more energy is required to impart a given
acceleration. To increase the velocity from ten feet per second to
twenty feet per second, the applied force must continue through one
second of time, and more energy is required to follow a rapidly moving
body, and continue to apply to it a given force for one second than
would be required to follow and maintain the application of the same
force to a body moving more slowly--the _distance_ traveled is greater
in one case than in the other.

It must be plain that if the moving body have a velocity at the end of
the first second of twenty feet per second, it will, at the end of the
second second, with the same pressure (force) continued against the
same resistance, have a velocity of forty feet per second, and at the
end of three seconds have a velocity of sixty feet, and at the end of
four seconds a velocity of eighty feet, and so on.

Now, at the beginning of the second second it had a velocity of
twenty feet, and at the end of that second a velocity of forty feet.
It therefore, traveled through that second with an average velocity
of thirty feet and, of course, during the second second traveled
exactly thirty feet. It traveled ten feet the first second, and if it
traveled thirty feet the second, then in the two seconds it traveled
forty feet--four times as far as it traveled the first second. At the
beginning of the third second it had a velocity of forty feet, and
at the end of the third second a velocity of sixty feet. The average
velocity then for the third second would be one-half the sum of forty
feet and plus sixty feet--that is to say, it would be fifty feet, and
that would be the distance traveled during the third second. The first
second it traveled ten feet, the second second thirty feet, and the
third second fifty feet, making a total in three seconds of ninety
feet--that is to say, in three seconds it traveled nine times as far as
in one second.

It will be noticed from the above that the velocity is proportional to
the number of seconds, but that the distance traveled is proportional
to the _square_ of the number of seconds, and also proportional to the
square of the velocity.

Momentum is mass multiplied by velocity; energy is measured by the
distance through which a body will move against a given resistance.

Should you prop up one wheel of a carriage and revolve the wheel, then
with the pressure of the finger or the thumb on the hub as a brake,
stop it, it will be found that (omitting the effect of atmospheric
resistance), the wheel will make four times as many revolutions before
stopping with a doubled velocity; nine times as many with a trebled
velocity.

Falling bodies afford the most perfect illustration of the principle
of Momentum and Energy, and are so commonly used to illustrate those
principles that many students get the idea that the application of
those principles is confined to falling bodies, and do not realize that
they extend generally through the field of mechanics.

A falling body is, of course, acted upon by gravity with uniform force
equal to the weight of the falling body, and that force continues
to follow the falling body and to be applied uniformly and equally,
however slowly, or rapidly the body may be falling. And, omitting
atmospheric resistance, the body is absolutely free to move except
for its natural tendency to remain at rest, or at uniform velocity.
It is well known that a body falls (almost exactly) sixteen feet in
one second, and at the end of one second has a velocity of thirty-two.
During the second second it falls through a distance of forty-eight
feet, and during the third second a distance of eighty feet. In two
seconds it falls sixty-four feet, and in three seconds one hundred
twenty-eight feet, and so on. Thus, it will be observed that the
_velocity_ is proportional to the time during which it has fallen, but
that the distance fallen in any number of seconds is proportional to
the _square_ of the time.

This, indeed, is a property of numbers, and results from mathematical
law. If the reader will form a series of numbers, setting down any
number for the first term of the series, adding to it its double for
the second term, and adding to the second term double the first term
for the third, and adding double the first term to the third term for
the fourth, and so on--in other words, form any increasing arithmetical
series with double the first term for the common difference, he will
discover that the _sum of all the terms is equal to the first term
multiplied by the square of the number of terms_. Thus:

    1st Term   2nd Term   3rd Term   4th Term   5th Term
         5         15         25         35         45

In the above series the sum of the first two terms is 20, which is 4
times the first term. The sum of the first three terms, i. e., 5 + 15
+ 25 = 45-nine times the first term. The sum of the first four terms,
i. e., 5 + 15 + 25 + 35 = 80, sixteen times the first term, and so on.

It will thus be seen that Momentum and Energy are entirely different,
although co-related; that momentum relates to velocity, which includes
the element of time, whereas energy relates to the amount of work
done, and may be represented by a force operating against a certain
resistance, through a certain distance, entirely irrespective of time.
The energy is the same with the same force operating against the same
resistance, through the same distance whether the time consumed be
great or small. It takes as much energy in the aggregate to wind up a
bucket from the bottom of the well if done slowly as if done quickly.

It would seem hardly necessary to do so, and yet it is worth while
remarking that the amount of energy necessary to impart a given motion
is exactly the amount of Energy that will be required to arrest that
motion, and represents the amount of Energy possessed by the moving
body by virtue of its motion. Work done, i. e., Energy applied in
giving motion is there in that motion, ready to be returned in exactly
an equal quantity--no more--no less.

In all the considerations in this chapter no notice is taken of loss by
friction or atmospheric resistance. We are considering pure mechanics
and the laws governing them only. In actual mechanical devices it is
always necessary to make allowance for atmospheric, frictional and
other unavoidable resistances.



CHAPTER X

The Alleged Inventions of Edward Sommerset, Sixth Earl and Second
Marquis of Worcester, and of Jean Ernest Eli-Bessler (Councillor)
Orffyreus


More interest has been taken, and more has been said and written
concerning the claimed inventions of the men forming the subject of
this chapter than of all other Perpetual Motion devices known to
history. The reason is not difficult to explain. It was the rank and
eminence of the inventors and of others whom they induced to take
an interest in their inventions, and to proclaim them to the world.
Intrinsically, neither their claims nor their devices are entitled
to any more notice than are those of the humblest mechanic that ever
labored to attain Perpetual Motion. However, so much has been said
and written concerning them that they have an historical value and
interest. Then, too, the interest taken in their inventions brought
forth some splendid discussions which necessarily involve in a general
way, at least, the entire question of Self-Motive Power. The historical
interest attaching to their inventions and the discussions concerning
them, entitles them to more than a passing notice in this book.

They were not co-laborers; they were not even compatriots, nor
contemporaries. Worcester was an Englishman and Orffyreus a Frenchman,
though most of his labors were in what is now Germany. The former died
thirteen years before the latter was born.

Edward Sommerset, of England, Sixth Earl and Second Marquis of
Worcester, was born in the year 1601, and died in 1667. He was famous
not only for his noble birth and family rank, but for personal
attainments. He was the author of a work entitled "Century of Names
and Scantlings of Such Inventions as at Present I Can Call to Mind
Have Tried and Perfected" (1663), which has often been reprinted,
and is usually referred to simply as "Century Inventions." He was
very prominent in public life; was greatly interested in mechanical
experiments, and made valuable suggestions, inventions and improvements
in connection with the use of steam as a motive power.

Henry Dircks, who is so frequently mentioned in this book, wrote a
book which was published in 1865, entitled "Life, Times and Scientific
Labors of the Second Marquis of Worcester." The Marquis appears to
have been all his life greatly interested in science, mechanics and
mathematical contrivances. His first wife died in 1635, and it seems
probable that thenceforth he became and remained more than ever
devoted to mechanics, and sometime after that period announced a
successful Perpetual Motion machine, the gist of all known information
concerning which appears from the articles and discussions hereinafter
set forth in this chapter.

Jean-Ernest Eli-Bessler (Councillor) Orffyreus was born in 1680, near
Zittan, Alsace, France. He was a man of great ability and attained an
eminent place in public life. The title "Councillor," he acquired by
having been selected Councillor to the Prince of Hesse Castle. The
best information concerning him indicates that he was of very erratic
temperament, given to fits of melancholy and extreme anger. In early
life he was a student of theology and medicine, but his penchant was
really for mechanics. He claimed that in his search for whatever might
prove curious and valuable he had discovered Perpetual Motion, and that
between the years 1712 and 1719 he had made two successfully working
machines on his system. The following discussions disclose all that is
known of the claimed inventions of these two distinguished Perpetual
Motion workers.

The alleged inventions of the Marquis of Worcester is stated by him in
the 56th article of his book entitled "Century of Names and Scantlings
of Such Inventions as at Present I Can Call to Mind to Have Tried and
Perfected," and translated from the ancient English style in which his
book is written into modern style of English, reads as follows:

The inventor offers the accompanying sketch, with description of an
Hydraulic Mover, for communicating power to machinery, and recently
invented by him:--

  "To provide and make that all the weights of the descending side
  of a wheel, shall be perpetually farther from the center, than
  those of the mounting side, and yet equal in number and heft to
  the one side as the other. A most incredible thing, if not seen;
  but tried before the late King (of blessed memory) in the Tower
  by my directions, two extraordinary ambassadors accompanying his
  Majesty, and the Duke of Richmond, and Duke of Hamilton, with
  most of the Court attending him. The wheel was fourteen foot
  over, and had forty weights of fifty pounds apiece. Sir William
  Balfore, then Lieutenant of the Tower, can justify it, with
  several others. They all saw, that no sooner these great weights
  passed the diameter line of the lower side, but they hung a foot
  farther from the center; nor no sooner passed the diameter line
  of the upper side, but they hung a foot nearer. Be pleased to
  judge of the consequence."

In October of 1719, Orffyreus published a small book, or pamphlet,
both in German and Latin, entitled "Perpetual Motion Triumphant, by
Orffyreus." The book commences:

  It is a notorious fact that Perpetual Motion has not only been
  sought after by ingenious mathematicians and artists with more
  or less expense, but many have arisen here and there pretending
  that they have made the discovery. Nevertheless, it appears
  that to carry out this most subtle mechanical idea, namely, to
  make a dead material not only move itself, but lift weights and
  perform work, even the most profound mathematicians and the most
  learned people have continually fallen into error. It is no
  less notorious that those who have so sought, not only refuse
  their consent, but have set their seal on the discovery as an
  unsolvable problem.

On a subsequent page he proceeds thus:

  When I, at last, an unworthy man, was made an instrument in God's
  hands to solve this long-looked-for and valuable secret, and to
  give a representation, proposition and instruction on this rare
  invention; also to publish and propound it to all the world,
  no longer do I doubt, nay I presume, that as the discoverer I
  possess it, after many years of scrupulous doubts, much calumny
  and exasperation from all my enemies.

He speaks of his opponents under four divisions: First, the scientific
world; second, persons in high authority; third, the public in general;
and fourth, the press;--observing--

  Now my wish was to convince the world that this illiberal,
  rude and inhuman treatment was false, yet God's providence has
  brought to my help, protection and succour the mighty Prince Lord
  Charles, Landgrave of Hesse.

On a subsequent page he indulges in the following sycophantic
adulation of the Prince of Hesse Castle, and suggestion of the
description of his claimed device:

  It has not only pleased this mighty Prince to protect me against
  my numerous enemies, but also to give me house-room in his
  princely Castle of Weissenstein, near Cassel; to name me one of
  his most honored servants, and restore me in a measure all the
  honor and means that I had lost in my native country; wishing
  no doubt to give to Hessin Cassel the high honor which belonged
  to Saxony by right. In gratitude for all these gracious acts, I
  consented to give another example of my Perpetuum Mobile machine.
  I put all in fresh order, and began work in all possible haste,
  doing everything in the manner of those I had already made and
  destroyed, with only a few changes in the dimensions of the
  so-named turning-wheel. For as a grindstone may be called a
  wheel, so may the principal part of my machine be named. The
  outward part of this wheel is drawn over or covered with waxed
  linen in the form of a drum. This cylindrical basis was 12
  Rhenish feet in diameter, the thickness from 15 to 18 inches,
  the middle axle 6 feet long and 8 inches in thickness. It is
  supported in its movement on two pointed steel balance-pegs,
  each 1 inch thick; and the wheel is vertically suspended. The
  movement is modified by two pendulums, as shown in the engraving
  at the end of this book. The inward structure of the wheel is of
  a nature according to the laws of mechanical perpetual motion,
  so arranged that by disposed weights once in rotation they
  gain force from their own swinging, and must continue their
  movement as long as their structure does not lose its position
  and arrangement. Unlike all other automata, such as clocks or
  springs or other hanging weights which require winding up or
  whose duration depends on the chain which attaches them, on the
  contrary, these weights are the essential parts and constitute
  perpetuum mobile itself; as from them is received the universal
  movement which they must exercise so long as they remain out of
  the center of gravity; and when they come to be placed together,
  and so arranged one against another that they can never obtain
  equilibrium, or the _punctum quietus_ which they unceasingly seek
  in their wonderous speedy flight, one or other of them must apply
  its weight vertically to the axis, which in its turn will also
  move.

The author and inventor then suggests the following uses of his
machine: "raising weights, raising stampers, water," etc. He criticises
all critics of his scheme and denounces them as cunning rogues, and
fools who are contemptibly endeavoring to overthrow an incontestable
fact. He makes a quadrupled dedication of his device:

    1. To God,
    2. To the Public in General,
    3. To Men of Learning,
    4. To Himself as Discoverer,

and he very modestly suggests a method by which he could be approached
on the subject of selling the secret of his machine for one hundred
thousand rix-thalers, and points out the great importance to the public
of such an acquisition. The book contains a cut of his device with the
following very brief explanation:

  [Illustration]

  Number 1 shows the entire size of the wheel; 2, a cord wound
  round the principal axle; 3, the wheel or pulley to guide the
  cord; 4, the cord passed through a window and over 5, another
  pulley; 6, the box of stones raised or lowered; 7, the lock
  to prevent motion; 8, the pendulum with three weights; 9, a
  winch-handle acting on the pendulum; and 10, shows above and
  below transparent, so that the machine stands clear and can be
  moved about.

In 1720 the following article was contributed to and published in the
"Gentleman's Magazine," concerning the Orffyrean Wheel:

  MR. URBAN: Being an admirer of improvements in mechanics and
  desirous of seeing the perpetual motion discovered, I was much
  pleased on reading, some time ago, an account of the automaton
  constructed by Orffyreus in two letters, one from Professor 's
  Gravesande to Sir Isaac Newton, the other from Baron Fischer
  to Dr. Desaguliers, with the testimonial of the Landgrave of
  Hesse-Cassel (who had seen the inside of it) in favor of its
  construction. To which are added some remarks by William Kenrick,
  the writer of the pamphlet, who takes that opportunity to propose
  a subscription for a similar machine, which he says he has
  contrived and denominated a Rotator.

  It is much to be lamented that the learned did not examine
  more strictly into the merit of Orffyreus's wheel; but,
  on the contrary, being prepossessed with a notion of the
  impracticability of the perpetual motion, suffered it to be
  neglected, and at last destroyed by the hands of a disappointed
  mechanic, who, with unwearied application and steady
  perseverance, had brought it to perfection. I wish we may not
  again let slip an opportunity of becoming acquainted with an
  invention, which, when made public, will reflect honor on the
  inventor, and be of the utmost utility to the world. Such, I
  would hope, is the rotator mentioned by W. Kenrick; for, unless
  his discovery were real, I cannot think that he would have taken
  the liberty to express himself as he does in p. 26, etc., "The
  inventor flatters himself that, if the contents of the foregoing
  pages are seriously attended to, and it be farther considered,
  that not a penny of the proposed premium is required, till the
  subscribers are fully satisfied of the reality and utility of the
  invention, his proposal will not be treated with so mortifying
  a neglect as that of Orffyreus." Again he says, "If it does not
  supply the place of a first mover, at the expense only of the
  construction and repair of a simple wheel subject to very little
  friction, and that in all such engines and machines, even from
  the slightest piece of clockwork to the waterworks of Marli or
  London-bridge, he expects nothing for his discovery, but to stand
  exposed to the contempt that will be justly thrown on him for
  having so miserably misspent his time, and frivolously engaged
  the attention of the public."

  Now, I think that W. Kenrick's proposals are very fair; and
  should be glad to be informed, whether any attention has been
  paid to them, and whether Sir Isaac Newton took any notice of the
  letter addressed to him by Professor Gravesande. I shall consider
  it as a favor if any correspondent will oblige me with an answer
  to these particulars.

      A CONSTANT READER.

In 1721 Rev. Dr. J. T. Desaguliers, LL.D., F.R.S., contributed to an
English periodical entitled "Philosophical Transactions," the following
article concerning the device of the Marquis of Worcester, and the
Orffyrean Wheel:

  REMARKS ON SOME ATTEMPTS MADE TOWARDS A PERPETUAL MOTION; BY THE
    REVEREND DR. DESAGULIERS, F.R.S.

  The wheel at Hesse-Cassel, made by Monsieur Orffyreus, and by
  him called a perpetual motion, has, of late, been so much talked
  of on account of its wonderful phenomena, that a great many
  people have believed it to be actually a self-moving engine;
  and accordingly have attempted to imitate it as such. Now, as a
  great deal of time and money is spent in those endeavours, I was
  willing (for the sake of those that try experiments with that
  view) to show that the principle which most of them go upon is
  false, and can by no means produce a perpetual motion.

  They take it for granted that if a weight descending in a wheel
  at a determined distance from the center, does, in its ascent,
  approach nearer to it; such a weight in its descent will always
  preponderate and cause a weight equal to it to rise, provided it
  comes nearer the center in its rise; and accordingly as itself,
  rises, will be overbalanced by another weight equal to it; and,
  therefore, they endeavour by various contrivances to produce that
  effect as if the consequence of it would be a perpetual motion.

  But I shall show that they mistake one particular case of a
  general theorem, or rather a corollary of it, for the theorem
  itself. The theorem is as follows:

  THEOR.--If one weight in its descent does, by means of any
  contrivance, cause another weight to ascend with a less momentum
  or quantity of motion than itself, it will preponderate and raise
  the other weight.

  COR. 1.--Therefore, if the weights be equal, the descending
  weight must have more velocity than the ascending weight, because
  the momentum is made up of the weight multiplied into the
  quantity of matter.

  COR. 2.--Therefore, if a leaver or balance have equal weights
  fastened or hanging at its ends, and the brachia be ever so
  little unequal that weight will preponderate which is farthest
  from the center.

  SCHOLIUM.--This second corollary causes the mistake; because
  those who think the velocity of the weight is the line it
  describes, expect that that weight shall be overpoised, which
  describes the shortest line, and, therefore, contrive machines to
  cause the ascending weight to describe a shorter line than the
  descending weight. As for example, in the circle A D B _a_ (Fig.
  3) the weights A and B being supposed equal, they imagine that if
  (by any contrivance whatever) whilst the weight A describes the
  arc A _a_, the weight B is carried in any arc, as B _b_, so as to
  come nearer the center in its rising than if it went up the arc
  B D; the said weight shall be overpoised, and consequently, by a
  number of such weights a perpetual motion will be produced.

  This is attempted by several contrivances, which all depend
  upon this false principle; but I shall only mention one which
  is represented by Fig. 4, where a wheel having two parallel
  circumferences, has the space between them divided into cells,
  which being curved, will (when the wheel goes round) cause
  weights placed loose in the said cells to descend on the side A
  at the outer circumference of the wheel, and on the side D to
  ascend in the line B _b b b_, which comes nearer the center and
  touches the inner circumference of the wheel. In a machine of
  this kind the weights will indeed move in such a manner if the
  wheel be turned round, but will never be the cause of the wheel's
  going round. Such a machine is mentioned by the Marquis of
  Worcester in his "Century of Inventions," in the following words,
  No. 56:

  [Illustration]

  "To provide and make that all the weights of the descending side
  of a wheel shall be perpetually farther from the center than
  those of the mounting side, and yet equal in number and heft to
  the one side as the other. A most incredible thing, if not seen;
  but tried before the late King (of blessed memory) in the Tower
  by my directions, two extraordinary ambassadors accompanying his
  Majesty, and the Duke of Richmond, and Duke of Hamilton, with
  most of the court attending him. The wheel was fourteen foot
  over and had forty weights of fifty pounds a piece. Sir William
  Balfore, then Lieutenant of the Tower, can justify it with
  several others. They all saw that no sooner these great weights
  passed the diameter line of the lower side, but they hung a foot
  farther from the center; nor no sooner passed the diameter line
  of the upper side, but they hung a foot nearer. Be pleased to
  judge of the consequence."

  [Illustration]

  Now the consequence of this and such like machines, is nothing
  less than a perpetual motion; and the fallacy is this: The
  velocity of any weight is not the line which it describes in
  general, but the height that it rises up to or falls from, with
  respect to its distance from the center of the earth. So that
  when the weight (Fig. 3) describes the arc A _a_, its velocity is
  the line A C, which shows the perpendicular descent (or measures
  how much it is come nearer to the center of the earth), and
  likewise the line B C denotes the velocity of the weight B, or
  the height that it rises to when it ascends in any of the arcs
  B _b_, instead of the arc B D: so that in this case whether the
  weight B in its ascent be brought nearer the center or not, it
  loses no velocity which it ought to do in order to be raised up
  by the weight A. Nay, the weight in rising nearer the center of
  a wheel may not only lose of its velocity, but be made to gain
  velocity in proportion to the velocity of its counterpoising
  weights that descend in the circumference of the opposite side
  of the wheel; for if we consider two radii of the wheel, one
  of which is horizontal, and the other (fastened to and moving
  with it) inclined under the horizon in an angle of 60 degrees
  (Fig. 5) and by the descent of the end B of the radius B C, the
  radius C D by its motion causes the weight at D to rise up the
  line _p_ P, which is in a plane that stops the said weight from
  rising in the curve D A, that weight will gain velocity, and in
  the beginning of its rise it will have twice the velocity of the
  weight at B; and consequently, instead of being raised, will
  overpoise, if it be equal to the last mentioned weight. And this
  velocity will be so much the greater in proportion as the angle
  A C D is greater, or as the plane P _p_ (along which the weight
  D must rise) is nearer to the center. Indeed, if the weight at B
  (Fig. 3) could, by any means, be lifted up to β, and move in the
  arc β _b_, the end would be answered; because then the velocity
  would be diminished and become β C.

  [Illustration]

  EXPERIMENT (Fig. 5).--Take the leaver B C D, whose brachia
  are equal in length, bent in an angle of 120 degrees at C and
  moveable about that point as its center: in this case a weight of
  two pounds hanging at the end of B of the horizontal part of the
  leaver will keep in equilibrio a weight of four pounds hanging
  at the end D. But if a weight of one pound be laid upon the end
  D of the leaver, so that in the motion of D along the arc _p_ A,
  this weight is made to rise up against the plane P _p_ (which
  divides in half the line A C equal to C B) the said weight will
  keep in equilibrio two pounds at B, as having twice the velocity
  of it when the leaver begins to move. This will be evident, if
  you let the weight 4 hang at D, whilst the weight 1 lies above
  it: for if then you move the leaver the weight 1 will rise four
  times as fast as the weight 4.

  [Illustration]

In 1770 Dr. William Kenrick published "A Lecture on the Perpetual
Motion." In it he has the following to say concerning the alleged
inventions of the Marquis of Worcester, and Councillor Orffyreus, and
Perpetual Motion in general. The following excerpts of and comments on
the lecture are taken verbatim from Dircks:

  The mere exhibition of a self-moving machine without a display
  of its mechanism, or the principles on which its motion is
  begun and continued, could produce no conviction. The fate of
  Orffyreus and his machine is a proof of this. Scarce fifty years
  ago that whimsical mechanician exhibited a perpetual motion at
  Hesse Cassel, the constancy of whose operation was experienced
  for many weeks under the most exact caution of the Landgrave of
  that Principality, whose testimony of such operation, as well
  as in favor of its construction (to the secret of which he was
  admitted), was given in the most explicit and determinate form.
  And yet, because Orffyreus could not display the mechanism
  without the previous assurance of a premium of 200,000 florins
  (near twenty thousand pounds), or because he would not or could
  not discover the principles on which it acted, his pretensions
  were neglected, his machine was destroyed by his own hands,
  and his life made a sacrifice to the chagrin attending his
  disappointment. Twenty years had he racked his brains for
  invention, and expended a patrimonial competence with parsimony
  in prosecuting his design. And when success inspired the hope of
  reward, he found his ingenuity suspected of imposture, and his
  industry rewarded with contempt.

  Whether any of his successors in the same pursuit will meet with
  a better fate is at length to be determined. One species of our
  predecessor's merit, however, I (adds Dr. Kenrick) presume myself
  at least entitled to, that of perseverance; it being now fifteen
  years since I first engaged in this undertaking, which I have
  since pursued with almost unremitted assiduity, and that not
  only at a considerable waste of time and expense, but under the
  constant mortification of hearing it equally ridiculed by those
  who do know, and by those who do not know, anything of the matter.

  It is, indeed, generally supposed, and as confidently affirmed,
  that the mathematicians have published demonstrations of the
  impossibility of a perpetual motion. But I can safely take upon
  me to affirm that no such demonstration was ever published by
  any. Within these twelve years past the mathematicians who deny
  the possibility of a perpetual motion have been repeatedly and
  publicly called upon, both in the foreign and English prints, to
  produce a single instance of these demonstrations. They have not
  done it. They might have produced, indeed, the demonstrations of
  Huygens, De la Hire, and others to prove, as Desaguliers very
  properly expresses it the fallacy of the schemes of most of the
  pretenders to the perpetual motion. They proved nothing more;
  and this was so far unnecessary in that the fallacy evidently
  appeared in the discovery of the principle on which they were
  founded.

  This was done in the last century by the celebrated Marquis
  of Worcester, in the presence of the King and his Court, at
  the Tower, by the exhibition of a wheel so contrived that in
  revolving on its axis it carried up several weights nearer its
  center on one side than they descended on the other. The scheme
  was plausible and to appearance practicable; but, though the
  wheel was polite enough to turn about while his Majesty was
  present, it could not be prevailed upon to be so complaisant
  in his absence. The mathematicians avenged themselves of the
  short triumph of the mistaken Marquis, but were equally mistaken
  themselves in thinking they had routed the problem or that
  in hunting down the jackal they had destroyed the lion. The
  perpetual motion survived; it had still its advocates; Professor
  Gravesande and John Bernouille maintained its practicability,
  the former giving his testimony in favor of Orffyreus's machine,
  after a long and scrutinous examination. It is not twelve
  years since this testimony was republished by Dr. Allaman, the
  present Professor of Natural Philosophy at Leyden, whose own
  opinion, given at the same time, is also greatly in favor of
  the discovery. It is even some years later that a dissertation
  still more in its favor, written, if I am not mistaken, by
  the celebrated De Gorter of Petersburg, appeared in the
  "Philosophical Transactions" of Haarlem. My end is not to amuse
  or persuade, but, with due deference, to inform and convince. To
  remove every cause of objection, I must beg leave to expatiate
  somewhat at large on the theory of this discovery. It is with
  the more propriety I presume on this method, as the discovery
  to which I pretend has not been (as frequently happens) the
  effect of mechanical accident, but the premeditated result of
  mathematical reasoning and physical experiment. I shall proceed
  to elucidate the principal arguments _a priori_, that prove
  the practicability of a perpetual motion to be the necessary
  consequence of the known and established laws of nature.

Having proceeded thus far, he opens his lecture at page 7 with the
introduction; and first "On the Nature of Motion in General," which,
in fourteen pages, being more metaphysical than mechanical, affords
no extractable matter for our present object. Part I is "On the Cause
and Effect of Motion." This elementary part is needlessly labored and
elaborated through 27 pages. In the course of his remarks he states:

  The discovery of a perpetual motion, says De la Hire, would be to
  discover a body at once heavier and lighter than itself. But this
  is not a fair state of the question. It is not necessary that
  all the parts of a perpetually-moving machine should be attached
  to, and inseparable from each other; which they must be, to
  constitute one gravitating body of a determinate weight.

He proceeds to consider the nature of the circulation of the blood,
pneumatic pressure, the steel-yard, real and relative weight, and
spiral action. Again, we have Hobbes, Locke, and Stewart, in the same
sentence with such language as--"I could almost as readily impute
ingenuity to vegetables and fossils--to the sensitive plant and the
loadstone--as mediation to muscles, or cogitabundity to cockles,
periwinkles and rock oysters!" In conclusions he says:

  I have endeavoured to make it appear that motion is the
  mechanical effect of the physical action of the primary elements;
  that the direction of motion only comes within the province of
  animal intellect; that the vital system is supported by mere
  mechanic motion, kept up by the elasticity of the solids and
  the gravity of the fluids composing the animal body; that by
  the same means a more simple inanimate system or machine may be
  framed which may have the same property of continued action (or,
  as it is called, self-motion). And this is all that is, or can
  be, expected of a perpetual motion; the momentum of which may be
  increased to any degree, according to the weight of the bodies
  employed and the work required to be done.

The second part of this lecture commences with a Proem of thirteen
pages:

  I am induced (he says) to trespass farther by extending in like
  manner the subsequent divisions of it; making the second and
  third parts of my printed syllabus the topics of the present
  reading, and reserving the last part, with the concluding
  experiment, to the third and final lecture.

  I pretend merely to the investigation of the general principles
  of mechanics, and even to illustrate these so far only as I
  conceive they relate to the immediate object of my lecture,
  the discovery of an artificial perpetual motion; leaving the
  application of such principles, in the solution of particular
  phenomena, or the construction of particular machines, to such as
  make the different arts and sciences their peculiar study.

He very prudently ends, observing:

  But I beg pardon, gentlemen, for the length of this digressive
  introduction, and shall proceed to the more immediate subject of
  my lecture.

Section 1 of this lecture is "On the Composition and Combination of
Motion." After discussing, in his own peculiar style, mechanical
principles of motion, he adds:

  It would require a volume, and that not a small one, to
  illustrate these subjects and support them by the necessary
  demonstrations and experiments. Should Providence give me life
  and health, therefore, they (his auditors) shall have it. Indeed,
  I have already spent some years in preparing such a volume for
  the press.

He is very prolix on gravity and motion, then commences Section 2 "On
the Communication and Dissipation of Motion." Five pages are occupied
in discussing motion, in popular language, in the course of which he
remarks:

  And as to the imperfectly elastic bodies, their power of
  retaining or communicating motion depends entirely on their
  _vis inertiae_ and weight; nor can they on any occasion
  whatever communicate a greater momentum to another body than
  they themselves possess. It is sufficient for the purpose of a
  perpetual motion that they can do this. And, indeed, here all the
  difficulty lies, viz., in the means of communicating the momentum
  or moving force of a heavy body to a light one. Now, the most
  virulent opponents to the practicability of perpetual motion
  have never pretended to demonstrate the impracticability of this
  communication. The _quomodo_, or means of effecting it, being
  the point in dispute. It is to this discovery that I pretend; and
  to show that my pretensions are well grounded, have taken the
  liberty to invite you to this lecture.

The lectures appear to have been illustrated by a plate having two
figures of a simple apparatus used to demonstrate the action of a
spring and two unequal weights; also an inflexible ruler suspended
between two unequal balls--with both he experimented before his
auditors; but the engraving is wanting in the edition now used. In
conclusion, he observes:

  You see, gentlemen, I am purposely provided here with a very
  simple and clumsy apparatus. The perpetual motion does not need
  the assistance of friction wheels, or depend on the niggling
  nicety of tooth and pinion. If the practical part of my discovery
  be not superior to the manual dexterity of a village carpenter or
  country smith, I am satisfied. There will be no great discernment
  required to comprehend the design they are to put in execution.
  You will permit me, however, at present, to defer what I have
  farther to offer on the subject to another opportunity.

In 1770 Dr. Kenrick published a quarto-pamphlet concerning the
Orffyrean Wheel, and in the pamphlet appears the following regarding
a letter from Prof. Gravesande to Sir Isaac Newton, and a letter from
Baron Fischer to Dr. Desaguliers:

  _A Letter from Professor 's Gravesande to Sir Isaac Newton,
    Concerning Orffyreus's Wheel_

SIR: Doctor Desaguliers has doubtless shown you the letter that Baron
Fischer wrote to him some time ago about the wheel of Orffyreus; which
the inventor affirms to be a perpetual motion. The landgrave, who is
a lover of the sciences and fine arts, and neglects no opportunity to
encourage the several discoveries and improvements that are presented
him, was desirous of having this machine made known to the world, for
the sake of public utility. To this end he engaged me to examine it;
wishing that, if it should be found to answer the pretensions of the
inventor, it might be made known to persons of greater abilities, who
might deduce from it those services which are naturally to be expected
from so singular an invention. You will not be displeased, I presume,
with a circumstantial account of this examination; I transmit you,
therefore, a detail of the most particular circumstances observable
on an exterior view of a machine, concerning which the sentiments of
most people are greatly divided, while almost all the mathematicians
are against it. The majority maintain the impossibility of a perpetual
motion, and hence it is that so little attention has been paid to
Orffyreus and his invention.

For my part, however, though I confess my abilities inferior to those
of many who have given their demonstrations of this impossibility;
yet I will communicate to you the real sentiments with which I
entered on the examination of this machine. It is now more than
seven years since I conceived I discovered the paralogism of those
demonstrations, in that, though true in themselves, they were not
applicable to all possible machines; and have ever since remained
perfectly persuaded it might be demonstrated that a perpetual motion
involved no contradiction; it appearing to me that Leibnitz was wrong
in laying down the impossibility of the perpetual motion as an axiom.
Notwithstanding this persuasion, however, I was far from believing
Orffyreus capable of making such a discovery, looking upon it as an
invention not to be made (if ever) till after many other previous
discoveries. But since I have examined the machine, it is impossible
for me to express my surprise.

The inventor has a turn for mechanics, but is far from being a profound
mathematician, and yet his machine has something in it prodigiously
astonishing, even though it should be an imposition. The following
is a description of the external parts of the machine, the inside of
which the inventor will not permit to be seen, lest any one should
rob him of his secret. It is a hollow wheel, or kind of drum, about
fourteen inches thick and twelve feet diameter; being very light, as
it consists of several crosspieces of wood framed together; the whole
of which is covered over with canvas, to prevent the inside from being
seen. Through the center of this wheel or drum runs an axis of about
six inches diameter, terminated at both ends by iron axes of about
three-quarters of an inch diameter upon which the machine turns. I
have examined these axes and am firmly persuaded that nothing from
without the wheel in the least contributes to its motion. When I turned
it but gently, it always stood still as soon as I took away my hand;
but when I gave it any tolerable degree of velocity, I was always
obliged to stop it again by force; for when I let it go, it acquired in
two or three turns its greatest velocity, after which it revolved for
twenty-five or twenty-six times in a minute. This motion it preserved
some time ago for two months, in an apartment of the castle: the door
and windows of which were locked and sealed so that there was no
possibility of fraud. At the expiration of that term indeed his serene
highness ordered the apartment to be opened, and the machine to be
stopped, lest, as it was only a model, the parts might suffer by so
much agitation. The landgrave being himself present on my examination
of this machine, I took the liberty to ask him, as he had seen the
inside of it, whether after being in motion for a certain time no
alteration was made in the component parts; or whether none of those
parts might be suspected of concealing some fraud: on which his serene
highness assured me to the contrary, and that the machine was very
simple.

You see, sir, I have not had any absolute demonstration, that the
principle of motion which is certainly within the wheel, is really a
principle of perpetual motion; but at the same time it cannot be denied
me that I have received very good reasons to think so, which is a
strong presumption in favor of the inventor. The landgrave hath made
Orffyreus a very handsome present, to be let into the secret of the
machine, under an engagement nevertheless not to discover, or to make
any use of it before the inventor may procure a sufficient reward for
making his discovery public.

I am very sensible, sir, that it is in England only the arts and
sciences are so generally cultivated as to afford any prospect of the
inventor's acquiring a reward adequate to this discovery. He requires
nothing more than the assurance of having it paid him in case his
machine is found to be really a perpetual motion; and as he desires
nothing more than this assurance till the construction of the machine
be displayed and fairly examined before such assurance be given him.
Now, sir, as it would conduce to public utility as well as to the
advancement of science, to discover the reality or the fraud of this
invention, I conceive the relation of the above circumstances could not
fail of being acceptable. I am, etc.

In the same book appear the following animadversions by Prof. Allaman,
on the neglect of Orffyreus's invention:

  We see that the testimony of M. 's Gravesande was as advantageous
  as possible to Orffyreus, not having seen the interior of
  the machine, he could form no other judgment; however, that
  extraordinary man was not contented, for in consequence of the
  examination Orffyreus broke the machine into pieces. By the
  accounts of M. 's Gravesande, Baron Fischer and the testimony
  of the Landgrave it appears clear that the wheel was not moved
  by any exterior agent. Orffyreus is, however, accused of being
  an impostor, of having imposed on the good faith of the prince,
  deceived M. 's Gravesande and all those who examined his machine.
  His own servant deposed against him and said that she was made
  to turn the wheel, and thus he has fallen into contempt; and
  everyone who protected him, is ashamed of him. M. de Crousaz, who
  was at that time at the court of Cassel, writes a letter to M.
  's Gravesande dated February 3, 1729, in these terms:--'First,
  Orffyreus is a fool; Second, It is impossible that a fool can
  have discovered what such a number of clever people have searched
  for without success; Third, I do not believe in impossibilities;
  Fourth, One can easily imagine that persons keep a secret from
  which they are to receive benefit, but this fellow, hoping
  only to receive reputation, allows it to be tarnished by an
  accusation which he has in his power to disprove, if false;
  Fifth, The servant who ran away from his house, for fear of being
  strangled, has in her possession, in writing, the terrible oath
  that Orffyreus made her swear; Sixth, He only had to have asked,
  in order to have had this girl imprisoned, until he had time
  to finish his machine; Seventh, They publish that the machine
  is going to be exhibited, when suddenly those who advertise it
  become silent; Eighth, It is true there is a machine at his
  house, to which they give the name of perpetual motion, but that
  cannot be removed; it is much smaller, and differs from the
  first, inasmuch as it only turns one way.

  This is what makes Orffyreus and his machine to be suspected; can
  it be that M. 's Gravesande was so mistaken as to be his dupe?
  Let us read what he himself says in answer to M. Crousaz, which
  I have found among my papers, without date:--"I have deferred
  replying to you until I had found a paper which I wrote the day
  after I examined Orffyreus' machine, for although I remember well
  all that passed, I believe that a paper, written the day after
  the examination, and communicated to my Lord and all those who
  were with him, must have more weight.

  "This is what I heard; they say that a servant under oath, turned
  Orffyreus' machine, being placed in an adjoining room.

  "I know well that Orffyreus is a fool, but I ignore that he is
  an impostor; I have never decided whether his machine is an
  imposture or not, but this I know as certainly as anything in
  the world, that if the servant says the above, she tells a great
  falsehood.

  "My Lord the Landgrave in the presence of the Baron Fischer,
  Architect of the Emperor, and other persons at my request,
  showed the supports of the machine; we saw the axles uncovered;
  I examined the plates or brasses on which the axles rested and
  in that examination there did not appear the slightest trace of
  communication with the adjoining room. I remember very distinctly
  the whole of the circumstances of that examination, which put
  Orffyreus in such a rage with me, that the day after he broke
  his machine in pieces, and wrote on the wall that, it was the
  impertinent curiosity of Professor 's Gravesande which was the
  cause. I read this myself the following year, and the result of
  the examination is clearly explained in the paper of which I
  spoke to you.

  "They told me several circumstances on the testimony of the
  servant, but I pay little attention to what a servant can say
  about machines, perhaps in turning her master's roast-jack
  she thought she saw a perpetual motion. If you know anything
  concerning this matter I shall feel much pleasure if you would
  communicate it."

  It is difficult to determine what to believe about this machine.
  It seems to me, however, that on examining minutely the for and
  against Orffyreus we can come to these conclusions: 1. That
  Orffyreus was evidently mad, as M. 's Gravesande and M. de
  Crousaz both affirm; his machinery broken at different times
  without either reason or necessity prove this. But his was a
  sort of madness we do not often see: a folly fixed only on
  certain objects, and merits more the name of fantasticalness or
  whimsicalness; this kind of folly is often accompanied by much
  genius, and when persons of this disposition apply themselves
  solely to one subject, as it appears he did, it is not surprising
  to find them making discoveries which had escaped the sagacity
  of wiser people. Thus I do not wish to agree with M. de Crousaz,
  that it is incredible that a madman, such as Orffyreus should
  have found out something that learned men have searched for
  unsuccessfully. Added to this he is mistaken in saying that
  Orffyreus could hope for no other reward for his secrets than
  mere reputation: for he expected a considerable profit seeing
  that he demanded for it 200,000 florins. 2. No exterior agent
  moved the machine; if it were a servant that moved it, would it
  not have been apparent to eyes so searching as those that made
  the examination, or to the Landgrave, who had seen the interior
  of the machine? Besides how can any one imagine that a wheel
  of so great a volume could have been moved by such a cause,
  a cause which would act simply on the axle in crossing the
  supports, and which must have been so small as to have escaped
  the most rigorous examination? 3. If the servant has not been
  paid to depose against Orffyreus, what does her testimony prove?
  Only that her master made her believe that by turning a little
  wheel, she moved the whole machine, and we can fancy a singular
  character, such as he was might have done this to prevent the
  curiosity of those who sought to penetrate his secret; M. 's
  Gravesande's opinion of this strange character is such that he
  doubts not his whimsicalness prevented him from making a new
  machine. 4. It must be confessed that this wheel was a very
  remarkable mechanical phenomenon, and this is all we can say,
  not knowing more than the preceding details; it were too much
  temerity to say that this invention was a perpetual motion, as
  much as it would be wrong to call it an imposture, seeing that no
  exterior agent was employed.

  Dr. Kenrick proceeds to state that:--The celebrated John
  Bernoulli, speaking of the above demonstration, in a letter
  to the author, remarks that it is very just; the principle
  assumed necessarily involving an augmentation of force, _viz._,
  a perpetual motion. But this, continues he, is no more than
  Leibnitz had long before demonstrated in his dispute with Papin
  and others.

  Having thus occupied twenty-three pages in fencing himself
  with a screen against the ridicule he appears to have so much
  dreaded, and reasonably anticipated from the many authors he
  had himself similarly treated in the "London Review," we are
  informed that,--An accidental conversation, many years ago, on
  the spot where Orffyreus exhibited his machine, awakened the
  author's curiosity and directed his attention to an object which
  he has ever since occasionally pursued. The experiments he has
  made, even so long since as the year 1761, convinced him so far
  of the reality of Orffyreus' discovery, that he applied for
  letters-patent to secure an exclusive right to the construction
  of a similar machine; which he had contrived and denominated A
  ROTATOR. Before his patent, however, was expedited, he reflected
  that, though the model he had constructed might serve to remove
  the prejudices of the public, it was not so well calculated as
  it might be, to answer the practical purposes of so important
  a discovery. To the improvement of the Rotator, therefore, has
  he long since dedicated all the time and attention he could
  possibly spare from his other, more immediately necessary,
  pursuits.

  Nothing can be more flimsy than the statement here made, and the
  next sentence would seem to explain the true state of the case.
  He proceeds: "Not that he believes he has contrived quite so many
  different machines as Orffyreus did, though he has been almost as
  many years engaged in the like undertaking; he has, nevertheless,
  both contrived and constructed a considerable number, many of
  them useless as costly, except indeed as they served to assist
  him in completing his invention."

  His invention, however, was _not_ complete; the very model of it
  was unsatisfactory. Like Orffyreus, he had spent nearly twenty
  years, making numerous, and some costly, machines. He no doubt
  had his own misgivings, and wished to reimburse himself for the
  great outlay he must have incurred during that long period,
  before the bubble finally burst! However, poor man, he died nine
  years after publishing this elaborate advertising prospectus,
  which concludes: "Such bodies corporate, private companies or
  individuals, as are interested in the construction or use of
  considerable mechanical engines, or are disposed to encourage
  the present discovery, may receive any further information they
  require, on applying to the inventor, WILLIAM KENRICK, Charles
  street, St. James's Square, March 1, 1770."

In 1803, Dr. Charles Hutton, LL.D., and F. R. S., contributed in
a brief work entitled, "Recreations in Mathematics and Natural
Philosophy," gave the following notice to the Orffyrean Wheel:

  The perpetual motion has been the quicksand of mechanicians, as
  the quadrature of the circle, the trisection of an angle, etc.,
  have been that of geometricians: and as those who pretend to have
  discovered the solution of the latter problems are in general
  persons scarcely acquainted with the principles of geometry,
  those who search for, or imagine they have found, the perpetual
  motion, are always men to whom the most certain and invariable
  truths of mechanics are unknown.

  It may be demonstrated, indeed, to all those capable of reasoning
  in a sound manner on those sciences, that a perpetual motion
  is impossible: for, to be possible, it is necessary that the
  effect should become alternately the cause, and the cause the
  effect. It would be necessary, for example, that a weight raised
  to a certain height by another weight, should in its turn
  raise the second weight to the height from which it descended.
  But, according to the laws of motion, all that a descending
  weight could do, in the most perfect machine which the mind
  can conceive, is to raise another in the same time to a height
  reciprocally proportional to its mass. But it is impossible to
  construct a machine in which there shall be neither friction nor
  the resistance of some medium to be overcome; consequently at
  each alternation of ascent and descent, some quantity of motion,
  however small, will always be lost: each time, therefore, the
  weight to be raised will ascend to a less height; and the motion
  will gradually slacken, and at length cease entirely.

  [Illustration]

  A moving principle has been sought for, but without success,
  in the magnet, in the gravity of the atmosphere, and in the
  elasticity of bodies. If a magnet be disposed in such a manner
  as to facilitate the ascension of a weight, it will afterwards
  oppose its descent. Springs, after being unbent, require to be
  bent by a new force equal to that which they exercise; and the
  gravity of the atmosphere, after forcing one side of the machine
  to the lowest point, must be itself raised again, like any other
  weight, in order to continue its action.

  We shall, however, give an account of various attempts to obtain
  a perpetual motion, because they may serve to show how much some
  persons have suffered themselves to be deceived on this subject.

  [Illustration]

  Fig. 52, plate 12, represents a large wheel, the circumference of
  which is furnished, at equal distances, with levers, each bearing
  at its extremity a weight, and movable on a hinge, so that in
  one direction they can rest upon the circumference, while on the
  opposite side, being carried away by the weight at the extremity,
  they are obliged to arrange themselves in the direction of the
  radius continued. This being supposed, it is evident that when
  the wheel turns in the direction _a b c_, the weights A B and C
  will recede from the centre; consequently, as they act with more
  force, they will carry the wheel towards that side; and as a new
  lever will be thrown out, in proportion as the wheel revolves, it
  thence follows, say they, that the wheel will continue to move in
  the same direction. But, notwithstanding the specious appearance
  of this reasoning, experience has proved that the machine will
  not go; and it may indeed be demonstrated that there is a
  certain position in which the centre of gravity of all these
  weights is in the vertical plane passing through the point of
  suspension, and that therefore it must stop.

  The case is the same with the following machine, which it would
  appear ought to move also incessantly. In a cylindric drum, in
  perfect equilibrium on its axis, are formed channels as seen in
  Fig. 53, which contain balls of lead, or a certain quantity of
  quicksilver. In consequence of this disposition, the balls or
  quicksilver must, on the one side, ascend by approaching the
  centre; and on the other must roll towards the circumference. The
  machine then ought to turn incessantly towards that side.

  A third machine of this kind is represented in Fig. 54. It
  consists of a kind of wheel formed of six or eight arms,
  proceeding from a centre, where the axis of motion is placed.
  Each of these arms is furnished with a receptacle in the form
  of a pair of bellows, but those on the opposite arms stand in
  contrary directions, as seen in the figure. The movable top of
  each receptacle has affixed to it a weight, which shuts it in
  one situation and opens it in the other. In the last place, the
  bellows of the opposite arms have a communication by means of a
  canal, and one of them is filled with quicksilver.

  These things being supposed, it is visible, that the bellows
  on the one side must open, and those on the other must shut;
  consequently the mercury will pass from the latter into the
  former, while the contrary will be the case on the opposite side.

  It might be difficult to point out the deficiency of this
  reasoning; but those acquainted with the true principles of
  mechanics will not hesitate to bet a hundred to one that the
  machine, when constructed, will not answer the intended purpose.

  [Illustration]

  The description of a pretended perpetual motion, in which
  bellows, to be alternately filled with and emptied of
  quicksilver, were employed, may be seen in the "Journal des
  Savans" for 1685. It was refuted by Bernouilli and some others,
  and it gave rise to a long dispute. The best method which the
  inventor could have employed to defend his invention would have
  been to construct it, and show it in motion; but this was never
  done.

  We shall here add another curious anecdote on this subject. One
  Orffyreus announced, at Leipsic, in the year 1717, a perpetual
  motion, consisting of a wheel which would continually revolve.
  This machine was constructed for the Landgrave of Hesse Cassel,
  who caused it to be shut up in a place of safety, and the door to
  be sealed with his own seal. At the end of forty days, the door
  was opened, and the machine was found in motion. This, however,
  affords no proof in favor of a perpetual motion; for as clocks
  can be made to go a year without being wound up, Orffyreus's
  wheel might easily go forty days, and even more.

  The result of this pretended discovery is not known. We are
  informed that an Englishman offered 80,000 crowns for this
  machine; but Orffyreus refused to sell it at that price: in this
  he certainly acted wrong, as there is reason to think he obtained
  by his invention, neither money, nor even the honor of having
  discovered the perpetual motion.

  The Academy of Painting at Paris possessed a clock which had
  no need of being wound up, and which might be considered as
  a perpetual motion, though it was not so. But this requires
  some explanation. The ingenious author of this clock employed
  the variations in the state of the atmosphere for winding up
  his moving weight. Various artifices might be devised for this
  purpose; but this is no more a perpetual motion than if the
  flux and reflux of the sea were employed to keep the machine
  continually going; for this principle of motion is exterior to
  the machine, and forms no part of it.

  But enough has been said on this chimera of mechanics. We
  sincerely hope that none of our readers will ever lose themselves
  in the ridiculous and unfortunate labyrinth of such a research.

  To conclude, it is false that any reward has been promised by the
  European Powers to the person who shall discover the perpetual
  motion; and the case is the same in regard to the quadrature of
  the circle. It is this idea, no doubt, that excites so many to
  attempt the solution of these problems; and it is proper they
  should be undeceived.

The foregoing, we believe, are sufficient to disclose the gist of
all that is known, and all that has been said concerning the claimed
inventions of the distinguished Marquis and the distinguished
Councillor. It is manifest from reading the above that Dircks himself,
as well as nearly all the other eminent persons quoted above, felt
an extreme delicacy in stating their honest belief concerning the
claims of the distinguished inventors. That delicacy arose from their
deference to the rank and prominence of the Marquis and the Councillor.
The author of this book is not thus encumbered, and has no such regard
for family or official rank, and feels at liberty to say exactly what
he thinks.

No one now actually believes that either the Marquis or the Councillor
ever made a wheel or machine that actually furnished its own
motive-power. Those who believe in the impossibility of Perpetual
Motion, of course, do not admit the possibility of such a thing. Those
who may still believe in the possibility of Perpetual Motion devices
admit, as they must, that had either of these discoveries actually
been made it would have supplanted steam, electricity, wind, water
and all other forms of power for driving machinery, and, indeed, for
furnishing heat. And, yet, the above articles and comments show that
the contemporaries of the Marquis and the Councillor, and subsequent
writers on their claims sought to find excuses and explanations
consistent with their good faith and their claims. We do not accuse
either one of them of vicious falsehood, but the truth is that when the
Marquis of Worcester wrote that "all the weights of the descending side
of a wheel shall be perpetually farther from the centre than those of
the mounting side, and yet equal in number and heft to the one side as
the other. A most incredible thing, if not seen; but tried before the
late King (of blessed memory) in the Tower by my directions," etc., he
meant, if he meant anything, to convey the idea that he had constructed
such a machine, and had exhibited it before King Charles I, and when
Orffyreus wrote "The inward structure of the wheel is of a nature
according to the laws of mechanical perpetual motion, so arranged that
by disposed weights once in rotation they gain force from their own
swinging and must continue their movement as long as their structure
does not lose its position and arrangement," he meant, as clearly
appears from the entire context of what he wrote, to convey the idea
that he had constructed a wheel capable of moving perpetually by virtue
of the arrangement of its own parts until it should wear out. Neither
one spoke the truth. Each knew that he had done no such thing as he
claimed to have done. He probably thought the solution so near at hand
that he could safely announce it to the world, and when called upon for
a demonstration could produce the finished working article.

The author of this book has known many Perpetual Motion workers so
confident and so enthusiastic that unhampered with extreme discretion,
they announced that they were near enough to the solution of this
ages-old puzzle that they were certain of success. A little less
discretion, with the slightest disregard or even carelessness about
the absolute truth could have easily led them to announce that they
had such a working machine. The author has indeed known a few such
announcements. It is therefore, not surprising that in the history of
Perpetual Motion labors, instances can be found where the tireless, but
enthusiastic worker being full of confidence, and not secretive, and
with the least bit of human carelessness about the truth have announced
the actual discovery and successful operation of the machine. We will
undertake to say that there have been thousands of just such instances
during the last three or four centuries, probably tens of thousands. It
is probable that such an instance could be found in every township in
the United States. It is not, therefore, surprising that two instances
can be found in persons of sufficient personal eminence to give
credence and weight to their stories. Such we conceive the facts with
reference to the Marquis and the Councillor. Each thought what he told
when telling it to be a harmless stretch of the truth, and felt sure
that he could protect himself by a very little added perfection to his
device. How many many Perpetual Motion devices have been perfect and
ready for successful operation except for "one little thing," which the
inventor felt sure of finding.

The Marquis and Councillor by their little indiscretion, and their
puerile carelessness about the truth, each made himself neither famous,
nor infamous, but ridiculous in history.



CHAPTER XI

Conservation of Energy--A Discussion of the Relation of the Doctrine of
Conservation of Energy, and the Possibility of Perpetual Motion


_Conservation of Energy_ is a doctrine to the effect that energy, like
matter, is indestructible, and, except by the infinite, can neither be
created nor destroyed; that the sum total of all Energy in the world
remains constant; that it may manifest itself in different forms, as
heat, magnetism, electricity, mechanical motion, vaporization, but that
the sum total remains the same.

Nothing could be more satisfactorily proved than this doctrine, and,
yet, like Newton's theory of universal gravitation the proof does
not amount to a mathematical demonstration. Mathematics demonstrates
the conformity of the doctrine of universal gravitation, and of
Conservation of Energy with all known natural processes and observed
phenomena; but mathematics does not otherwise prove the Universality of
Gravitation nor Conservation of Energy.

Writing on this subject of proof, with reference to gravitation, the
late and eminent Simon Newcomb says:

  "It may be inquired, is the induction which supposes gravitation
  universal so complete as to be entirely beyond doubt? We reply
  that within the solar system it certainly is. The laws of motion
  as established by observation and experiment at the surface of
  the earth must be considered as mathematically certain. Now, it
  is an observed fact that the planets in their motion deviate from
  straight lines in a certain way. By the first law of motion, such
  deviation can be produced only by a force; and the direction
  and intensity of this force admit of being calculated once that
  the motion is determined. When thus calculated, it is found to
  be exactly represented by one great force constantly directed
  toward the sun, and smaller subsidiary forces directed toward
  the several planets. Therefore, no fact in nature is more firmly
  established than is that of universal gravitation, as laid down
  by Newton, at least within the solar system."

It will thus be observed that the theory of Universal Gravitation is
not by scientific men claimed to have been mathematically demonstrated,
but its proof is regarded as resting upon its conformity with known
natural phenomena. The same thing is true of Conservation of Energy.
Scientists and mathematicians do not claim proof of this doctrine other
than by its universal coincidence with all natural manifestations, and,
yet its proof rests upon such a solid structure of coincidence and
conformity with all known things in nature, that now all scientific
research begins with its assumption, and with the exclusion of the
possibility of Perpetual Motion.

It is not within the purview of this work to give a history of the
origin and establishment in science of the doctrine. While, as
heretofore noted in this book, a number of scientists of the past few
centuries are shown by their reflections to have had a measure of
appreciation of its ultimate effect, and to have applied that effect
in their scientific researches, there is no evidence that they ever
dreamed of its establishment as a basic fact of science. The real
establishment and acceptance of the doctrine dates not much over a
half century back. Since that time many scientists have in their
researches and writings contributed to its evolution and formation. The
experiments of Joule, of England, and the generalizations of Helmholtz,
of Germany, are entitled to special mention.

Scientists are naturally and necessarily conservative. So many
startling pseudo-scientific facts are announced, that every startling
scientific theory, before it is accepted, is submitted to the most
careful and crucial tests. No modern scientist will announce a
scientific fact as having been demonstrated until the demonstration is
complete and fortified with repeated tests of mathematical rigidity,
and as long as there remains a phenomenon that does not conform to the
supposed theory, acceptance and promulgation will be withheld. It is,
therefore, not surprising that the doctrine of Conservation of Energy
has been thoroughly intrenched as an established indisputable and
accepted fact of science, less than a single generation.

The student of natural science should be warned against the common
error of supposing that the discovery of a scientific fact or theory,
means demolition of the old theories. The rule is the other way. New
theories are additional information to the world, and usually conform
to, and are built upon what was known before. Conservation of Energy
was generalized from previously known facts conformed to them and
reflexively elucidated them, and left them standing clearer than before.

The proof that Conservation of Energy conforms to all other known
phenomena of nature has been aided, and hastened by the refinement
of scientific instruments by which forms of energy such as heat,
electricity, and magnetism can be more delicately measured and
determined than ever before, and if instruments for measuring and
determining the amount of energy in its various forms were as crude
as they were even a single century ago, it is probable Conservation
of Energy would still be the undiscovered foundation of all natural
phenomena.

Let us now consider a few well-known facts which it has been determined
positively by the most delicate instruments, prove and illustrate the
doctrine of Conservation of Energy.

Resistance to motion, or which is the same thing, motion against
resistance, is always accompanied by heat. This developed heat is not
always readily perceptible to our sense of touch. A stone, ball or
other object thrown through the air has its motion gradually arrested
by the air. Heat is developed, but the heat is distributed through
so much air and the object thrown is heated so little that this
development of heat was not known until scientifically discovered.
Where the resistance is friction, the development of heat is quite
perceptible, and has always been well known. Suppose a coin be
rubbed on a cloth or blotter. Heat is developed both in the coin and
the blotter--the more vigorous the rubbing--i. e., the more energy
expended, the greater the heat. Science has determined that the
developed heat is exactly proportional to the expended energy. Every
machinist knows that in turning a tap on a bolt where the threads are
rusty so that it turns only with the application of great force, a
considerable amount of heat is readily developed. The heat developed is
proportional to the energy expended in turning the tap.

A wheel revolving on a spindle will develop heat exactly proportional
to the resistance the spindle offers to the wheel turning upon it.
Thus, we often see smoke and a blaze rising from the spindles of the
car wheels where oil is lacking, and they turn with difficulty.

Every farmer knows that if a buggy wheel turns with difficulty for want
of lubrication, or for any other reason, the spindle will heat, expand
and lock the wheel, so that it will often either grind out the boxing
or slide on the ground. Whereas, if the parts be kept lubricated so
that less energy is required to turn the wheel on the spindle, there
is no perceptible heat developed, but in all cases heat is developed
to some extent, and the heat developed is exactly proportional to the
energy necessary to force the revolution.

With heat we can boil water and make steam under a pressure, and with
the steam under a pressure we can run an engine, and with the engine
make heat by friction, or make electric current that can produce heat.
Carry this proposition back to the fuel box, and knowing the amount
of heat developed by the burning of a certain quantity of fuel, it is
found that, counting the heat that rises in the air through the smoke
stack, the heat that is radiated from the boiler, the heat that is
carried away in warmed ashes, the heat that exists in the steam after
it is exhausted from the cylinder, and all other heat expended whether
utilized in driving the machinery or going to waste, the sum total is
in every case equal to the heat developed by the fuel box combustion.
The most striking thing about all this is that when the steam goes into
the cylinder where it is cooled as it expands and drives the pistons,
the heat _thus lost by the expanding steam is the exact equivalent of
the mechanical energy realized against the piston head_. Not all of the
energy that is realized at the piston head is delivered to the driving
shaft. Some of it is lost in the friction of the piston rings wearing
against the cylinder lining; some, of course, is lost in friction at
the journals connecting with the driving shaft. It is usual in counting
engine efficiency to count the amount of energy delivered to the belt,
or to the driving shaft, and because of the frictional resistance of
the pistons working in the cylinder, there is always found a little
discrepancy between the energy represented by the cooling of the steam
in the cylinder and the energy delivered to the belt, or the driving
shaft.

It is quite surprising how much energy a small amount of heat
represents if it could all be converted into the obvious forms of
energy. Owing to the great waste suffered in all modern machinery, heat
represents much more energy than is ordinarily supposed, in the absence
of exact knowledge. One would hardly think it possible that the amount
of heat that will raise the temperature of one pound (almost exactly
one pint) of water, one single degree (Fahrenheit) is the equivalent of
energy required to elevate one pound seven hundred seventy-eight feet
high against the force of gravity. Yet, such is the case. This was one
of the demonstrations of the immortal Joule. It was he who enabled us
to cross the bridge with calculations from mechanical force and motion
to heat. He stated the equivalent to be seven hundred seventy-two feet,
but more delicate instruments than could be had in his day have shown
a slight discrepancy in his calculations, and it is now known to be
almost exactly seven hundred seventy-eight feet. Thus, if the Falls of
Niagara be considered as being one hundred sixty feet high, the energy
developed by the descent is only the equivalent of the heat necessary
to raise the temperature of the water about one-fifth of one degree. A
modern railroad locomotive does well to realize to the driving rod two
per cent of the total energy developed in the fuel box. An ordinary
thrasher engine realizes no more than one per cent. The very best steam
engines known in large stationary plants do not realize as much as
fifteen per cent.

The amount of heat necessary to raise the temperature of one pound of
water one degree is taken as a standard for heat measurement, and is
known as a British Thermal Unit--nearly always in scientific works
abbreviated to B. T. U. The common standard of energy is the amount
of energy or work necessary to elevate one pound one foot against the
force of gravity. This in scientific works is usually referred to as
the foot-pound.

From what is said above it is manifest that one B. T. U. is the
equivalent of seven hundred seventy-eight foot-pounds, and vice versa.

The _amount_ of energy must not be confused with the _rate_ of
expending energy, or doing work. The horse-power is the common
measurement of the rate of delivery of energy or of doing work and is
equivalent to 33,000 foot-pounds per minute. It is what one horse can
do, and continue doing several hours with reasonable ease. For a short
time a horse can exert several horse-power.

Remember, and remember always that heat and electricity are just as
much forms of energy as the motion of concrete objects.

We have introduced the above statement of equivalents for the purpose
of enabling us to present a few fundamental facts more clearly than
could otherwise be done.

Everyone knows that if paddles be revolved rapidly in a vessel
containing a liquid, such as a churn, or the like, the liquid will
offer considerable resistance to their motion, the amount of
resistance depending upon the nature of the liquid, and the rapidity of
the motion.

Our scientific instruments have determined the fact to be that the
B. T. U. developed in the liquid and on the paddles is the exact
equivalent to the foot-pounds of energy required to drive the paddles,
i. e., the number of B. T. U. is 778 times the number of foot-pounds.

An engine is run with steam--the engine drives an electric generator.
Electricity is developed. This electricity is conducted over a wire to
a motor. It is always found that not as much energy can be derived from
the motor as is supplied from the generator to the wire. Where is the
loss?

It is found that the loss is in the resistance of the wire to the
current, and that the wire is warmed--possibly not sufficient to be
perceptible to the ordinary sense of touch, and, yet, it is warmed to
some extent, and the B. T. U., developed in, and radiated away by the
wire, amounts precisely and exactly to the difference in foot-pounds
between the energy supplied to the wire at one end of the wire, and the
energy supplied by the wire at its other end.

Capillary Attraction is one form of motion by which liquids are
elevated and carried considerable distance. The moisture is taken from
the earth and carried up the trunks of trees, and out through their
limbs to their leaves. This cannot be done without force and energy,
but where is the heat? It has been determined and proven that there is
an expenditure of heat in doing that work, and that the expenditure of
heat is precisely equivalent to the work done. It is hardly believable
that there is a loss of heat by coal oil or water, or other liquid
performing the work of ascending the wick, and yet, science has
determined that that work is only done at the expense of that other
form of energy--heat.

If an object falls a distance of twenty feet, and it strikes one end of
a lever having two arms of equal length, and at the other end of the
lever there be a ball of equal weight, the other ball will be thrown
upward twenty feet, less an allowance for the resistance of the air
in the descent and ascent, and for the frictional resistance of the
motion of the lever. It would throw a ball of twice the weight half the
height by adjusting the levers properly. Or, it would throw a ball of
one-third the weight three times as high, and so on.

A ball rolling down an inclined plane is found to have a velocity, and
consequently a striking force, and an energy equal to that acquired
in falling the vertical distance of its descent, due allowance being
made for the resistance offered to its rolling motion. It makes no
difference whether the incline be great or small, the velocity, the
energy are the same as though it had fallen perpendicularly through the
same vertical distance.

Instances and illustrations can be multiplied indefinitely. Millions
of tests have been made by scientific men, and the basic fact of
Conservation of Energy is found true everywhere. That fact is that
energy cannot be created. So much as is given is returned in some other
form, or else in the form of heat, but in some form, precisely the
equivalent is always found to exist.

One of the most beautiful experiments is with the pendulum. Imagine
a nail or peg driven into a wall and projecting out--say six inches
from the wall. Hang a pendulum four feet long--let the pendulum swing
parallel to the wall in the annexed figure. Let "A" represent the
point from which the pendulum is suspended. Draw the pendulum back to
C, and release it. Its lowest descent in the swing will be at B. It
will swing to D, and a line connecting D & C is exactly horizontal,
showing that the energy represented by the motion of the pendulum at
B was sufficient to elevate it to the point D. Now, on a line on the
wall downward from where the nail or peg is driven into the wall, let
there be made holes into which a nail or peg can be inserted, and
suppose a peg be driven at the point F. If now pendulum be released
at C, it will be found that when the cord strikes F the pendulum will
swing to the point J, which is on the horizontal line D C. It makes no
difference where the interrupting peg or nail be placed, the pendulum
will rise to the same horizontal from which it was released. It is
said that this was one of Gallileo's experiments. If so, it is another
example of the masterly force and originality of his genius, and shows
that he subconsciously had some appreciation of the basic facts of the
now accepted doctrine of Conservation of Energy.

[Illustration]

We believe it is useless to multiply instances further, to illustrate
the doctrine of Conservation of Energy, and show the character of proof
upon which it rests. There is no fact in nature, but what in the hands
of modern science appears to conform to this doctrine. A few years ago
when radio-active properties were first discovered it was thought that
it was an exception, but even that has been found to conform to this
wonderful generalized doctrine.

If the doctrine of Conservation of Energy be true about which there
seems to be no doubt, then all hopes of ever attaining Perpetual Motion
must cease, for the idea of Perpetual Motion is predicated and has
its foundation upon the creation of energy. The mechanism must give
more energy than is imparted to it. It must make energy, and this in
the light of the generalized truth of Conservation of Energy is an
impossibility. We might as well talk about making substance, and the
creation of substance, or the creation of energy either one is not
an attribute of man. It is an attribute to be accredited only to the
infinite, and can not be conceived as an attribute of the finite.



CHAPTER XII

Will Perpetual Motion Ever Be Accomplished?


The antiquity of the problem of Perpetual Motion, and the countless
attempts by clever and ingenious minds to accomplish its solution, and
the uniform failure of such attempts is no proof at all, scientifically
speaking, that Perpetual Motion is an impossibility. If there be
scientific proof that Perpetual Motion is unattainable, that proof must
be found elsewhere than in the number of attempts and the universality
of failures, or in the number or eminence of the people who believe it
to be impossible.

Dircks in his work printed in 1861, being "A History of the Search for
Self-Motive Power, During the 17th 18th and 19th Centuries," says on
the subject:

"The subject of Perpetual Motion opposes paradox to paradox. It is
viewed both as being most simple and most difficult to find. The
learned justify both its possibility and impossibility. Many mechanics
believe it possible * * * Its pursuit always commences in confidence,
only to end in doubt. * * *

We think a careful perusal of all that has been gathered respecting
Perpetual Motion clearly establishes that much remains to be done to
prove the impossibility of practically solving this knotty problem; and
that a full demonstration of the difficulties that environ it is worthy
of being attempted, even by the most exalted mathematicians. It is not
requisite that they should descend to the level of the most ordinary
minds, but leave it for others to reduce their elaborated reasonings on
the subject to some generally comprehensible form. We fear the proposal
partakes too much of the difficulty of proving a negative; but still,
as the attempt has been made by celebrated savants, and is generally
considered insufficient; and as data may have been wanting, which we
conceive a collection of the chief known examples will supply; we
recommend the consideration of this matter to all geometers. * * *

In a mathematical point of view, we think this subject is far
from being exhausted; and, after what has been advanced, may very
properly be considered as claiming grave considerations. And that,
scientifically examined, it is a mark of mere shallowness and
querulousness to attempt the substitution of ridicule and satire for
the more difficult, but consistent course of sound, close reason and
argument, such as the wonted sobriety and severity of scientific
criticism accords to its investigations generally."

At the time of the publication of Dircks's work from which the above
quotation is taken (1861), the doctrine of Conservation of Energy
had not been announced and accepted as an established generalization
of a scientific fact, and it is apparent was not understood by him.
Dircks's statement "as data may have been wanting, which we conceive
a collection of the chief known examples will supply," shows that he
misconceived the nature of the problem of proving the impossibility of
Perpetual Motion. If, however, the principle of Conservation of Energy
is a true scientific fact, the impossibility of self-motive power
follows as an inevitable scientific corollary, and the ignis fatuus
hope of attaining Perpetual Motion which has deluded so many bright
minds is forever destroyed and demolished.

A perusal of the arguments against Perpetual Motion made by thinking
men with scientific minds even though long before the thorough
establishment of the doctrine of transmutation and Conservation of
Energy, discloses the fact that those arguments in fact depend finally
on the principle now known and designated Conservation of Energy.

It is amusing to note in reading the arguments on the subject by our
greatest philosophers, Newton, Gallileo, Huyghens, and Descartes, that
while they lived and labored long before Conservation of Energy in
its generalized form was known, or announced, they seemed to have a
perception that energy could not be created; that energy must produce
an effect commensurate with its own activity; that the existence of
energy in one body is proof positive that some agency furnished and
lost an exact equivalent of that energy. In other words, these men in
reasoning on specific problems presented to them, and on the problem of
Perpetual Motion in particular, appear to have appreciated and applied
in their reasonings, the principle of Conservation of Energy.

Men who have worked at the problem of Perpetual Motion before the
establishment of the doctrine of Conservation of Energy, and men
who still work at the problem, who, through lack of opportunity
have not become familiar with that doctrine, are not to be blamed
or thought stupid because of that folly, but those who knowing that
principle, or being in a situation to know it, must be mechanically
and mathematically stupid not to realize that Perpetual Motion and
Conservation of Energy are irreconcilable, and that both cannot be
possibilities. In this day when the principle of Conservation of Energy
is taught in the High Schools of the United States, and in every other
civilized country in the world, it is not surprising that fewer people
work on Perpetual Motion than formerly, and that public interest in
the subject is waning, as waning it surely is.

A generation ago, however, this principle was not known and taught, and
the state of the world's learning was at such a stage that many even
scientific minds thought Perpetual Motion possible, and worked for its
attainment.

The principle of Conservation of Energy as applied to all Perpetual
Motion devices can be stated as follows: There can be no mechanical
effect without an equal mechanical cause. Energy--i. e., the capacity
to do work, can only be imparted by an equal amount of work done. It
therefore follows axiomatically that Perpetual Motion is possible only
if and when a machine be produced that runs absolutely without friction
and absolutely without atmospheric resistance, or the resistance of
bending of cords, or other like mechanical resistance. If there be such
resistance, then the energy imparted to the machine will be diminished
by that resistance, with the result that the machine can only yield the
amount of energy imparted, less the energy required to overcome such
resistance. That no machine can be built free of such resistance is
patent to even a tyro in mechanics.

It will be interesting here, and perhaps more interesting than useful,
to add some of the arguments quoted by Dircks and reproduced in his
work for and against the possibility of Perpetual Motion. They have
little scientific value at this time, as they were all made by men who
were unfamiliar with the decisive principle of Conservation of Energy.
Nevertheless, for their historical interest we offer a few:


The Possibility of Perpetual Motion Denied Remarks of Dr. Papin on a
French Contrivance

In 1665, Dr. Papin, Fellow of the Royal Society, brought before the
Royal Society of London, a paper concerning a French contrivance for
Perpetual Motion. The following excerpt will illustrate and explain the
contrivance:

  The paper printed in French, and containing contrivance for
  perpetual motion, being set down in such a manner that can hardly
  be understood but by those that are much acquainted with such
  descriptions, I have endeavored to explain it as follows:

  Let D E F be a pair of bellows forty inches long, that may be
  opened by removing the part F from E; let them be exactly shut
  everywhere but at the aperture E; and let a pipe E G, twenty
  or twenty-two inches long, be soldered to the said aperture E,
  having its other end in a vessel G, full of mercury, and placed
  near the middle of the bellows.

  A is an axis for the bellows to turn upon.

  B, a counterpoise fastened to the lower end of the bellows.

  C, a weight with a clasp to keep the bellows upright.

  [Illustration]

  Now, if we suppose the bellows opened only to one-third or
  one-fourth, standing upright, and full of mercury, it is plain
  that the said mercury, being forty inches high, must fall, as in
  the Torricellian experiment, to the height of about twenty-seven
  inches, and, consequently, the bellows must open towards F, and
  leave a vacuity there. This vacuity must be filled with the
  mercury ascending from G through the pipe G E, the said pipe
  being but twenty-two inches long; by this means the bellows must
  be opened more and more, till the mercury continuing to ascend
  makes the upper part of the bellows so heavy that the lower part
  must get loose from the clasp C, and the bellows should turn
  quite upside down; but the vessel G being set in a convenient
  place, keeps them horizontal, and the part F engageth there in
  another clasp C; then the mercury, by its weight, runs out from
  the bellows into the vessel G through the pipe E G, and the
  bellows must shut closer and closer until the part E F comes to
  be so light that the counterpoise B is able to make the part F
  get loose from the clasp C; then the bellows come to be upright
  again; the mercury left in them falls again to the height of
  twenty-seven inches, and, consequently, all the other effects
  will follow as we have already seen, and the motion will continue
  forever. Thus much for the French author.

  [Illustration]

  Upon this it is to be observed, that the bellows can never be
  opened by the internal pressure, unless the said pressure be
  stronger then the external; now, in this case, the weight of the
  atmosphere doth freely press up the outward part of the bellows,
  but it cannot come at the inward part but through the pipe G E,
  which, containing twenty-two perpendicular inches of mercury,
  does counterpoise so much of the weight of the atmosphere, so
  that this being supposed to be twenty-seven inches of mercury,
  it cannot press the inward part of the bellows but with weight
  equivalent to five perpendicular inches of mercury. From this
  we may conclude, that the pressure of the atmosphere, being
  weakened within the bellows more then it can be helped by the
  mercury contained in the same, as may easily be computed, the
  said bellows standing upright must rather shut then open. Thus,
  without losing any labor and charges in trying, people may be
  sure that the thing can never do.


Two "Certain" Plans for (Not) Producing Perpetual Motion

In 1834, the following article was contributed to "Mechanics'
Magazine." The contributor was very frank, and presents some splendid
suggestions for Perpetual Motion workers. His article is as follows:

  Very few young mechanicians escape being seduced into an attempt
  to produce a perpetual movement, by making gravitation counteract
  itself. They are not contented with being told by older men,
  that a cause can never be made to exceed its own power; yet
  gravitation is expected by them to lift up on one side more
  weight than sinks on the other, with some percentage of friction
  into the bargain. Nature, however, is too true to itself to be
  so taken in by all or any of the multitudes of various ways
  the inventive genius of man has contrived, and still keeps
  contriving, to circumvent her immutable laws, with no other
  effect than to render the case so complicated as to puzzle the
  judgment of the inventors, which ends usually in their firm
  belief that they have outwitted nature instead of themselves. I
  acknowledge that in my youth I was one of this class, and, for
  the benefit of the young, I beg to present you with two _certain_
  plans for producing perpetual motion, and compelling gravity to
  be frolicsome, and do more work than she ought.

  Let A (Fig. 1) be a cistern full of oil or water, above 4 feet
  deep. Let B be a wheel; freely suspended within it, on its axle,
  let there be four wide glass tubes, 40 inches long, _c c c c_,
  having large bulbs, holding, say a pint, blown at the closed
  end. Fill these tubes with mercury, fix on an Indian-rubber ball
  or bladder, that will hold a pint, to each of them at the open
  end, and let them be attached round the wheel, as exhibited in
  the figure. As the pressure of 40 inches of mercury will exceed
  the atmospheric pressure, and also that of the four-foot column
  of water, when the Indian-rubber bottle is lowest, and the tube
  erect, at D, the mercury will fill it, leaving a vacuum in the
  glass bulb above. On the opposite side the mercury will fill the
  glass bulb, and the Indian-rubber bottle will be pressed flat,
  as will also be the case in the two horizontal tubes. Now, it is
  evident that the two horizontal tubes exactly balance each other;
  but the tube D, with its bulb swelled out, displaces a pint of
  water more than its opposite tube, and hence will attempt to rise
  with the force of about one pound; and each tube, when it arrives
  at the same position, must produce the same result, the wheel
  must have a continual power, equal to about one pound, with a
  radius of two feet.--Q. E. D.

  Let Fig. 2 represent a light drum of wood--one-half of which is
  inserted into a cleft in a water-cistern A, which fits it, and
  from which the water is prevented from escaping by a strip of
  leather, which the water presses against the drum, and which thus
  operates as a valve, without much friction (especially if oil be
  substituted for water in the cistern). Now, as this drum is much
  lighter than water, it must ever attempt to swim, and thus, in
  perpetually rising, cause the drum to revolve forcibly round its
  axle.--Q. E. D.

  [Illustration]

  I tried this last method thirty years ago, but it was so
  obstinate as not to move one inch at my bidding, though it
  obviously is proved, to demonstration, that it ought to have
  gone on swimmingly. I have just heard that an Italian gentleman
  has hit upon the same plan; so it seems that the mania is not
  confined to England.

The article above quoted elicited a varied correspondence on the
subject of self-motive power. The editor finally made the following apt
and happy remark concerning the two "Certain" plans:

  We think our correspondent, S. F., has entirely misconceived the
  scope of the playful account, given in our last number, of two
  plans of perpetual motion. The object of the writer seems to have
  been, to impress on the minds of young mechanicians the folly of
  wasting their time in vain endeavors to render the effects of
  causes greater than the causes themselves; or, in other words,
  to gain power out of nothing--a process without limit or value,
  were it not cut short by the want of all limit to its folly; and
  this he could not, perhaps, have done in any way so well, as by
  exhibiting a couple of infallible perpetual movers that would
  not stir at all, though they bade as fair for it as any of their
  kindred.


Article by Rev. John Wilkins

Rev. John Wilkins of England, born 1614; died 1672, published a work
called "Mathematical Magic," in which he discoursed scientifically and
technically on efforts that had been made up to that time to attain
Perpetual Motion. His work shows great scholarship, diligent search,
and a thorough knowledge of mathematics and mechanics. Considering the
state of scientific knowledge at the time when he lived and worked, his
insight into scientific subjects is truly remarkable.

Considering the state of scientific learning in his day, his
observations on the subject of Perpetual Motion show him to have
possessed really a great scientific and analytical mind. Of all those
who wrote or thought extensively on the subject in that century we
regard what he had to say as being the most worthy of reproduction.
The following excerpt from "Mathematical Magic," will give the reader
an idea of his course of reasoning and conclusions on the subject of
self-motive power:

  CHAP. IX.--_Of a Perpetual Motion--The seeming facility and real
    difficulty of any such contrivance--The several ways whereby it
    hath been attempted, particularly by Chemistry._

  It is the chief inconvenience of all the automata
  before-mentioned, that they need a frequent repair of new
  strength, the causes whence their motion does proceed being
  subject to fail, and come to a period; and, therefore, it
  would be worth our enquiry to examine whether or no there may
  be made any such artificial contrivance, which might have the
  principle of moving from itself so that the present motion should
  constantly be the cause of that which succeeds.

  This is that great secret in art which, like the Philosopher's
  Stone in Nature, has been the business and study of many more
  refined wits for divers ages together; and it may well be
  questioned whether either of them as yet have ever been found
  out; though if this have, yet like the other, it is not plainly
  treated of by any author.

  Not but there are sundry discourses concerning this subject, but
  they are rather _conjectures_ than _experiments_. And though many
  inventions in this kind may at first view bear a great show of
  probability, yet they will fail, being brought to trial, and will
  not answer in practice what they promised in speculation. Any one
  who has been versed in these experiments must needs acknowledge
  that he has been often deceived in his strongest confidence;
  when the imagination has contrived the whole frame of such an
  instrument, and conceives that the event must infallibly answer
  its hopes, yet then does it strangely deceive in the proof and
  discovers to us some defect which we did not before take notice
  of.

  Hence it is that you shall scarce talk with any one who has never
  so little smattering in these arts, but he will instantly promise
  such a motion as being but an easy achievement, till further
  trial and experience has taught him the difficulty of it. There
  being no enquiry that does more entice with the _probability_ and
  deceive with the _subtilty_.

  I shall briefly recite the several ways whereby this has been
  attempted, or seems most likely to be effected, thereby to
  contract and facilitate the enquiries of those who are addicted
  to these kind of experiments; for when they know the defects of
  other inventions, they may the more easily avoid the same or the
  like in their own.

  The ways whereby this has been attempted may be generally reduced
  to these three kinds:

  1. By Chemical Extractions. 2. By Magnetical Virtues. 3. By the
  Natural Affection of Gravity.

  1. The discovery of this has been attempted by chemistry.
  Paracelsus and his followers have bragged that by their
  separations and extractions they can make a little world which
  shall have the same perpetual motions with this microcosm, with
  the representation of all meteors, thunder, snow, rain, the
  courses of the sea in its ebbs and flows, and the like. But these
  miraculous promises would require as great a faith to believe
  them as a power to perform them; and though they often talk of
  such great matters:

  At nusquam totos inter qui talia curant, Apparet ullus, qui re
  miracula tanta Comprobet--

  yet we can never see them confirmed by any real experiment; and
  then, besides, every particular author in that art has such
  a distinct language of his own (all of them being so full of
  allegories and affected obscurities), that 'tis very hard for any
  one (unless he be thoroughly versed amongst them) to find out
  what they mean, much more to try it.

  One of these ways (as I find it set down) is this: Mix five
  ounces of ☿ with an equal weight of ♃; grind them together with
  ten ounces of sublimate; dissolve them in a cellar upon some
  marble for the space of four days, till they become like oil
  olive; distil this with fire of chaff, or driving fire, and it
  will sublime into a dry substance; and so, by repeating of these
  dissolvings and distillings, there will be at length produced
  divers small atoms, which, being put into a glass well luted and
  kept dry, will have a perpetual motion.

  I cannot say anything from experience against this; but I think
  it does not seem very probable, because things that are forced
  up to such vigorousness and activity as these ingredients seem to
  be by their frequent sublimings and distillings, are not likely
  to be of any duration. The more any thing is stretched beyond
  its usual nature, the less does it last; violence and perpetuity
  being no companions. And then, besides, suppose it is true, yet
  such a motion could not well be applied to any use, which will
  needs take much from the delight of it.

  Amongst the chemical experiments to this purpose may be reckoned
  up that famous motion invented by Cornelius Dreble, and made for
  King James; wherein was represented the constant revolutions of
  the sun and moon, and that without the help either of springs
  or weights. Marcellus Vranckhein, speaking of the means whereby
  it was performed, he calls it _Scintillula animae magneticae
  mundi, seu astralis et insensibilis spiritus_; being that grand
  secret for the discovery of which those dictators of philosophy,
  Democritus, Pythagoras, Plato, did travel unto the Gymnosophists
  and Indian Priests. The author himself, in his discourse upon
  it, does not at all reveal the way how it was performed. But
  there is one Thomas Tymme who was a familiar acquaintance of his,
  and did often pry into his works (as he professes himself), who
  affirms it to be done thus: By extracting a fiery spirit out of
  the mineral matter, joining the same with his proper air, which
  included in the axletree (of the first moving wheel), being
  hollow, carried the other wheels, making a continual rotation,
  except issue or vent be given in this hollow axletree, whereby
  the imprisoned spirit may get forth.

  What strange things may be done by such extractions I know not,
  and, therefore, dare not condemn this relation as impossible;
  but I think it sounds rather like a chemical dream than a
  philosophical truth. It seems this imprisoned spirit is now
  set at liberty, or else is grown weary, for the instrument
  (as I have heard) has stood still for many years. It is here
  considerable that any force is weakest near the center of a
  wheel; and therefore, though such a spirit might of itself have
  an agitation, yet 'tis not easily conceivable how it should
  have strength enough to carry the wheels about with it. And
  then, the absurdity of the author's citing this, would make one
  mistrust his mistake. He urges it as a strong argument against
  Copernicus; as if, because Dreble did thus contrive in an engine
  the revolution of the heavens and the immovableness of the earth,
  therefore it must needs follow that 'tis the heavens which are
  moved, and not the earth. If his relation were no truer than his
  consequence, it had not been worth the citing.


  CHAP. XIII.--_Concerning several attempts of contriving a
    Perpetual Motion, by Magnetical Virtues._

  The second way whereby the making of a perpetual motion has
  been attempted, is by Magnetical Virtues, which are not without
  some strong probabilities of proving effectual to this purpose;
  especially when we consider that the heavenly revolutions (being
  as the first pattern imitated and aimed at in these attempts)
  are all of them performed by the help of these qualities. This
  great orb of earth, and all the other planets, being but as so
  many magnetical globes, endowed with such various and continual
  motions as may be most agreeable to the purposes for which they
  were intended. And, therefore, most of the authors who treat
  concerning this invention, do agree that the likeliest way to
  effect it, is by these kind of qualities.

  It was the opinion of Pet. Peregrinus, and there is an example
  pretended for it in Bettinus (apiar. 9, progym. 5, pro. 11) that
  a magnetical globe, or terella, being rightly placed upon its
  poles, would of itself have a constant rotation, like the diurnal
  motion of the earth. But this is commonly exploded as being
  against all experience.

  Others think it possible so to contrive several pieces of steel
  and loadstone that, by their continual attraction and expulsion
  of one another, they may cause a perpetual revolution of a wheel.
  Of this opinion were Taisner, Pet. Peregrinus, and Cardan, out
  of Antonius de Fantis. But D. Gilbert, who was more especially
  versed in magnetical experiments, concludes it to be a vain and
  groundless fancy.

  But amongst all these kinds of inventions, that is most likely,
  wherein a loadstone is so disposed that it shall draw unto it on
  a reclined plane a bullet of steel, which steel, as it ascends
  near to the loadstone, may be contrived to fall down through
  some hole in the plane, and so to return unto the place from
  whence at first it began to move; and, being there, the loadstone
  will again attract it upwards till coming to this hole, it will
  fall down again; and so the motion shall be perpetual, as may be
  more easily conceivable by this figure:

  [Illustration]

  Suppose the loadstone to be represented at A B, which, though it
  have not strength enough to attract the bullet C directly from
  the ground, yet may do it by the help of the plane E F. Now, when
  the bullet is come to the top of this plane, its own gravity
  (which is supposed to exceed the strength of the loadstone) will
  make it fall into that hole at E; and the force it receives in
  this fall will carry it with such a violence unto the other end
  of this arch, that it will open the passage which is there made
  for it, and by its return will again shut it; so that the bullet
  (as at the first) is in the same place whence it was attracted,
  and, consequently, must move perpetually.

  But, however, this invention may seem to be of such strong
  probability, yet there are sundry particulars which may prove it
  insufficient; for--

  1. This bullet of steel must first be touched, and have its
  several poles, or else there can be little or no attraction
  of it. Suppose C in the steel to be answerable unto A in the
  stone, and to B; in the attraction C D must always be directed
  answerable to A B, and so the motion will be more difficult; by
  reason there can be no rotation or turning round of the bullet,
  but it must slide up with the line C D, answerable to the axis
  A B.

  2. In its fall from E to G, which is _motus elementaris_, and
  proceeds from its gravity, there must needs be a rotation of it;
  and so 'tis odds but it happens wrong in the rise, the poles
  in the bullet being not in the same direction to those in the
  magnet; and if in this reflux it should so fall out, that D
  should be directed towards B, there should be rather a flight
  than an attraction, since those two ends do repel, and not draw
  one another.

  3. If the loadstone A B have so much strength, that it can
  attract the bullet in F, when it is not turned round, but does
  only slide upon the plane, whereas its own gravity would rowl
  it downwards; then it is evident the sphere of its activity
  and strength would be so increased when it approaches much
  nearer, that it would not need the assistance of the plane,
  but would draw it immediately to itself without that help; and
  so the bullet would not fall down through the hole, but ascend
  to the stone, and, consequently, cease its motion: for, if the
  loadstone be of force enough to draw the bullet on the plane, at
  the distance F B, then must the strength of it be sufficient to
  attract it immediately unto itself, when it is so much nearer
  as E B. And if the gravity of the bullet be supposed so much
  to exceed the strength of the magnet, that it cannot draw it
  directly when it is so near, then will it not be able to attract
  the bullet up the plane, when it is so much further off.

  So that none of all these magnetical experiments, which have
  been as yet discovered, are sufficient for the effecting of
  a perpetual motion, though these kind of qualities seem most
  conducible unto it; and perhaps, hereafter, it may be contrived
  from them.


  CHAP. XIV.--_The seeming probability of effecting a Continual
  Motion by Solid Weights in a Hollow Wheel or Sphere._

  The third way whereby the making of a perpetual motion has been
  attempted is by the Natural Affection of Gravity; when the
  heaviness of several bodies is so contrived, that the same motion
  which they give in their descent, may be able to carry them up
  again.

  But (against the possibility of any such invention) it is thus
  objected by Cardan:--All sub-lunary bodies have a direct motion
  either of ascent or descent; which, because it does not refer to
  some term, therefore cannot be perpetual, but must needs cease
  when it is arrived at the place unto which it naturally tends.

  I answer, though this may prove that there is no natural motion
  of any particular heavy body which is perpetual, yet it does not
  hinder, but that it is possible from them to contrive such an
  artificial revolution as shall constantly be the cause of itself.

  Those bodies which may be serviceable to this purpose are
  distinguishable into two kinds:

  1. Solid and consistent; as weights of metal, or the like.

  2. Fluid or sliding; as water, sand, etc.

  Both these ways have been attempted by many, though with very
  little or no success. Other men's conjectures in this kind you
  may see set down by divers authors. It would be too tedious to
  repeat them over, or set forth their draughts.

  I shall only mention two new ones, which (if I am not
  over-partial) seem altogether as probable as any of these kinds
  that have been yet invented; and, till experience had discovered
  their defect and insufficiency, I did certainly conclude them to
  be infallible.

  The first of these contrivances was by solid weights being placed
  in some hollow wheel or sphere, unto which they should give a
  perpetual revolution; for, as the philosopher has largely proved,
  only a circular motion can properly be perpetual.

  But, for the better conceiving of this invention, it is requisite
  that we rightly understand some principles in Trochilicks, or the
  art of wheel instruments; as, chiefly, the relation betwixt the
  parts of a wheel and those of a balance; the several proportions
  in the semi-diameter of a wheel being answerable to the sides
  in a balance, where the weight is multiplied according to its
  distance from the center.

  [Illustration]

  Thus, suppose the center to be at A, and the diameter of
  the wheel, D C, to be divided into equal parts (as is here
  expressed), it is evident, according to the former ground, that
  one pound at C will equiponderate to five pound at B, because
  there is such a proportion betwixt their several distances from
  the center. And it is not material whether or no these several
  weights be placed horizontally; for though B do hang lower than
  C, yet this does not at all concern the heaviness; or though the
  plummet C were placed much higher than it is at E, or lower at
  F, yet would it still retain the same weight which it had at C;
  because these plummets (as in the nature of all heavy bodies),
  do tend downwards by a straight line; so that their several
  gravities are to be measured by that part of the horizontal
  semi-diameter, which is directly either below or above them.
  Thus, when the plummet C shall be moved either to G or H, it will
  lose one-third of its former heaviness, and be equally ponderous
  as if it were placed in the balance at No. 3; and if we suppose
  it to be situated at I or K, then the weight of it will lie
  wholly upon the center, and not at all conduce to the motion of
  the wheel on either side; so that the straight lines which pass
  through the divisions of the diameter may serve to measure the
  heaviness of any weight in its several situations.

  These things thoroughly considered, it seems very possible and
  easy for a man to contrive the plummets of a wheel, that they may
  be always heavier in their fall, than in their ascent; and so,
  consequently, that they should give a perpetual motion to the
  wheel itself; since it is impossible for that to remain unmoved
  as long as one side in it is heavier than the other.

  For the performance of this, the weights must be so ordered: 1.
  That in their descent they may fall from the center, and in their
  ascent may rise nearer to it. 2. That the fall of each plummet
  may begin the motion of that which should succeed it, as in the
  following diagram:

  Where there are sixteen plummets, eight in the inward circle,
  and as many in the outward. (The inequality being to arise from
  their situation, it is therefore most convenient that the number
  of them be even.) The eight inward plummets are supposed to be
  in themselves so much heavier than the other, that in the wheel
  they may be of equal weight with those above them, and then the
  fall of these will be of sufficient force to bring down the
  other. For example, if the outward be each of them four ounces,
  then the inward must be five; because the outward is distant from
  the center five of those parts whereof the inward is but four.
  Each pair of these weights should be joined together by a little
  string or chain, which must be fastened about the middle, betwixt
  the bullet and the center of that plummet which is to fall first,
  and at the top of the other.

  [Illustration]

  When these bullets, in their descent, are at their farthest
  distance from the center of the wheel, then shall they be
  stopped, and rest on the pins placed to that purpose; and
  so, in their rising, there must be other pins to keep them
  in a convenient posture and distance from the center, lest,
  approaching too near unto it, they thereby become unfit to fall
  when they shall come to the top of the descending side.

  This may be otherwise contrived with some different
  circumstances, but they will all redound to the same effect. By
  such an engine it seems very probable that a man may produce
  perpetual motion; the distance of the plummets from the center
  increasing with weight on one side, and their being tied to one
  another, causing a constant succession in their falling.

  But now, upon experience, I have found this to be fallacious;
  and the reason may sufficiently appear by a calculation of the
  heaviness of each plummet, according to its several situation;
  which may easily be done by those perpendiculars that cut
  the diameter (as was before explained, and is here expressed
  in five of the plummets on the descending side). From such a
  calculation it will be evident, that both the sides of this
  wheel will equiponderate; and so consequently, that the supposed
  inequality whence the motion should proceed, is but imaginary
  and groundless. On the descending side, the heaviness of each
  plummet may be measured according to these numbers (supposing the
  diameter of the wheel to be divided into twenty parts, and each
  of those sub-divided into four):

  _The Outward Plummets._    _The Inward Plummets._

       7.0  }                    1.0  }
      10.0  }  The sum 24.       7.2  }  The sum 19.
       7.0  }                    7.2  }
                                 3.0  }

  On the ascending side, the weights are to be reckoned according
  to these degrees:

  _The Outward._               _The Inward._

       1.3  }                  4.1  }
       7.2  }                  7.0  }  The sum 19.
       9.0  }  The sum 24.     5.2  }
       5.3  }                  2.1  }
       0.0  }

  The sum of which last numbers is equal with the former, and
  therefore both the sides of such a wheel in this situation will
  equiponderate.

  If it be objected, that the plummet A should be contrived to pull
  down the other at B, and then the descending side will be heavier
  than the other; for answer to this, it is considerable--

  1. That these bullets towards the top of the wheel, cannot
  descend till they come to a certain kind of inclination.

  2. That any lower bullet hanging upon the other above it, to pull
  it down, must be conceived, as if the weight of it were in that
  point where its string touches the upper; at which point this
  bullet will be of less heaviness in respect of the wheel, than if
  it did rest in its own place; so that both the sides of it, in
  any kind of situation, may equiponderate.


  CHAP. XV.--_Of composing, a Perpetual Motion by Fluid
    Weights--Concerning Archimedes his Water Screw--The great
    probability of accomplishing this enquiry by the help of that,
    with the fallibleness of it upon experiment._

  That which I shall mention as the last way, for the trial of
  this experiment, is by contriving it in some Water Instrument;
  which may seem altogether as probable and easy as any of the
  rest; because that element, by reason of its fluid and subtle
  nature (whereby, of its own accord, it searches out the lower
  and more narrow passages), may be most pliable to the mind of
  the artificer. Now, the usual means for the ascent of water is
  either by suckers or forces, or something equivalent thereunto;
  neither of which may be conveniently applied unto such a work as
  this, because there is required unto each of them so much or more
  strength, as may be answerable to the full weight of the water
  that is to be drawn up; and then, besides, they move for the most
  part by fits and snatches, so that it is not easily conceivable,
  how they should conduce unto such a motion, which, by reason of
  its perpetuity, must be regular and equal.

  But, amongst all other ways to this purpose, that invention of
  Archimedes is incomparably the best, which is usually called
  _Cochlea_, or the Water Screw; being framed by the helical
  revolution of a cavity about a cylinder. We have not any
  discourse from the author himself concerning it, nor is it
  certain whether he ever writ anything to this purpose; but if he
  did, yet, as the injury of time hath deprived us of many other of
  his excellents works, so likewise of this amongst the rest.

[Near five pages are occupied in describing the use of this screw, and
the form and manner of making it; then follows:]

  The true inclination of the screw being found, together with
  the certain quantity of water which every helix does contain;
  it is further considerable, that the water by this instrument
  does ascend naturally of itself, without any violence or labor;
  and that the heaviness of it does lie chiefly upon the centers
  or axis of the cylinder, both its sides being of equal weight
  (said Ubaldus); so that, it should seem, though we suppose each
  revolution to have an equal quantity of water, yet the screw
  will remain with any part upwards, according as it shall be
  set, without turning itself either way; and, therefore, the
  least strength being added to either of its sides should make
  it descend, according to that common maxim of Archimedes--any
  addition will make that which equiponderates with another to tend
  downwards.

  But now, because the weight of this instrument and the water
  in it does lean wholly upon the axis, hence is it (said
  Ubaldus) that the grating and rubbing of these axes against the
  sockets wherein they are placed, will cause some ineptitude
  and resistency to that rotation of the cylinder; which would
  otherwise ensue upon the addition of the least weight to any one
  side; but (said the same author) any power that is greater than
  this resistency which does arise from the axis, will serve for
  the turning of it round.

  These things considered together, it will hence appear how a
  perpetual motion may seem easily contrivable. For, if there were
  but such a water-wheel made on this instrument, upon which the
  stream that is carried up may fall in its descent, it would turn
  the screw round, and by that means convey as much water up as is
  required to move it; so that the motion must needs be continual,
  since the same weight which in its fall does turn the wheel is,
  by the turning of the wheel, carried up again.

  Or, if the water, falling upon one wheel, would not be forcible
  enough for this effect, why then there might be two or three, or
  more, according as the length and elevation of the instrument
  will admit; by which means the weight of it may be so multiplied
  in the fall that it shall be equivalent to twice or thrice that
  quantity of water which ascends; as may be more plainly discerned
  by the following diagram:

  [Illustration]

  Where the figure L M, at the bottom, does represent a wooden
  cylinder with helical cavities cut in it, which at A B is
  supposed to be covered over with tin plates, and three
  water-wheels upon it, H I K; the lower cistern, which contains
  the water, being C D. Now, this cylinder being turned round, all
  the water which from the cistern ascends through it, will fall
  into the vessel at E, and from that vessel being conveyed upon
  the water-wheel H, shall consequently give a circular motion to
  the whole screw. Or, if this alone should be too weak for the
  turning of it, then the same water which falls from the wheel H,
  being received into the other vessel F, may from thence again
  descend on the wheel I, by which means the force of it will be
  doubled. And if this be yet unsufficient, then may the water
  which falls on the second wheel I, be received into the other
  vessel G, and from thence again descend on the third wheel at
  K; and so for as many other wheels as the instrument is capable
  of. So that, besides the greater distance of these three streams
  from the center or axis by which they are made so much heavier,
  and besides that the fall of this outward water is forcible and
  violent, whereas the ascent of that within is natural--besides
  all this, there is thrice as much water to turn the screw as is
  carried up by it.

  But, on the other side, if all the water falling upon one wheel
  would be able to turn it round, then half of it would serve with
  two wheels, and the rest may be so disposed of in the fall as to
  serve unto some other useful delightful ends.

  When I first thought of this invention, I could scarce forbear,
  with Archimedes, to cry out εὕρηκα, εὕρηκα {heurêka, heurêka};
  it seeming so infallible a way for the effecting of a perpetual
  motion that nothing could be so much as probably objected
  against it; but, upon trial and experience, I find it altogether
  insufficient for any such purpose, and that for these two reasons:

  1. The water that ascends will not make any considerable stream
  in the fall.

  2. This stream, though multiplied, will not be of force enough to
  turn about the screw.

  1. The water ascends gently, and by intermissions; but it falls
  continually, and with force; each of the three vessels being
  supposed full at the first, that so the weight of the water in
  them might add the greater strength and swiftness to the streams
  that descend from them. Now, this swiftness of motion will cause
  so great a difference betwixt them that one of these little
  streams may spend more water in the fall than a stream six times
  bigger in the ascent, though we should suppose both of them to
  be continuate; how much more, then, when as the ascending water
  is vented by fits and intermissions, every circumvolution voiding
  so much as is contained in one helix; and, in this particular,
  one that is not versed in these kind of experiments may be easily
  deceived.

  But, secondly, though there were so great a disproportion, yet,
  notwithstanding, the force of these outward streams might well
  enough serve for the turning of the screw, if it were so that
  both its sides would equiponderate the water being in them (as
  Ubaldus had affirmed). But now, upon farther examination, we
  shall find this assertion of his to be utterly against both
  reason and experience. And herein does consist the chief mistake
  of this contrivance; for the ascending side of the screw is made,
  by the water contained in it, so much heavier than the descending
  side, that these outward streams, thus applied, will not be of
  force enough to make them equiponderate, much less to move the
  whole, as may be more easily discerned by this figure:

  Where A B represents a screw covered over, C D E one helix or
  revolution of it, C D the ascending side, E D the descending
  side, the point D the middle; the horizontal line C F showing how
  much of the helix is filled with water, viz., of the ascending
  side, from C the beginning of the helix, to D the middle of it;
  and on the descending side, from D the middle, to the point G,
  where the horizontal does cut the helix. Now, it is evident that
  this latter part, D G, is nothing near so much, and consequently
  not so heavy as the other, D C; and thus is it in all the other
  revolutions, which, as they are either more or larger, so will
  the difficulty of this motion be increased. Whence it will appear
  that the outward streams which descend must be of so much force
  as to countervail all that weight whereby the ascending side in
  every one of these revolutions does exceed the other. And though
  this may be effected by making the water-wheels larger, yet then
  the motion will be so slow that the screw will not be able to
  supply the outward streams.

  [Illustration]

  There is another contrivance to this purpose, mentioned by
  Kircher de Magnete, 1, 2, p. 4, depending upon the heat of the
  sun and the force of winds; but it is liable to such abundance of
  exceptions that it is scarce worth the mentioning, and does by no
  means deserve the confidence of any ingenious artist.

  Thus have I briefly explained the probabilities and defects of
  those subtle contrivances whereby the making of a perpetual
  motion has been attempted. I would be loath to discourage the
  enquiry of any ingenious artificer by denying the possibility
  of effecting it with any of these mechanical helps; but yet (I
  conceive) if those principles which concern the slowness of the
  power in comparison to the greatness of the weight were rightly
  understood and thoroughly considered, they would make this
  experiment to seem, if not altogether impossible, yet much more
  difficult than otherwise, perhaps, it will appear. However, the
  inquiring after it cannot but deserve our endeavors, as being one
  of the most noble amongst all these mechanical subtilties. And,
  as it is in the fable of him who dug the vineyard for a hidden
  treasure, though he did not find the money, yet he thereby made
  the ground more fruitful, so, though we do not attain to the
  effecting of this particular, yet our searching after it may
  discover so many other excellent subtilties as shall abundantly
  recompense the labor of our inquiry.

  And then, besides, it may be another encouragement to consider
  the pleasure of such speculations, which do ravish and sublime
  the thoughts with more clear angelical contentments. Archimedes
  was generally so taken up in the delight of these mathematical
  studies of this familiar siren (as Plutarch styles them) that he
  forgot both his meat and drink, and other necessities of nature;
  nay, that he neglected the saving of his life, when that rude
  soldier, in the pride and haste of victory, would not give him
  leisure to finish his demonstration. What a ravishment was that,
  when, having found out the way to measure Hiero's crown, he
  leaped out of the bath, and (as if he were suddenly possessed)
  ran naked up and down, crying εὕρηκα, εὕρηκα {Greek: heurêka,
  heurêka}! It is storied of Thales that, in his joy and gratitude
  for one of these mathematical inventions, he went presently
  to the Temple, and there offered up a solemn sacrifice; and
  Pythagoras, upon the like occasion, is related to have sacrificed
  a hundred oxen; the justice of Providence having so contrived
  it, that the pleasure which there is in the success of such
  inventions should be proportioned to the great difficulty and
  labor of their inquiry.


The Paradoxical Hydrostatic Balance

The following was contributed to an English scientific journal in 1831,
the name of the author of the article is unknown to us, but here is
what he wrote:

  [Illustration]

  This hydrostatic balance, like the compound balance of
  Desaguliers, may be introduced to illustrate the impossibility of
  perpetual motion by a weight removed from the centre of a wheel.

  Take the hollow-rimmed wheel A B; let it be air-tight and half
  filled with water. Let C be the axle; at B place a hollow ball
  loaded to near sinking. Such a wheel, however fine its axle
  may be, or however well lubricated, will not make a single
  revolution, though the weight B occupies that part at which every
  deluded perpetual-motionist is desirous it should be placed;
  concluding that, by such an arrangement, the production of
  another Orffyrean wheel must be inevitable.


Discussion by P. Gregorio Fontana

P. Gregorio Fontana was professor of higher mathematics at the Royal
University of Pavia, in the Province of Lombardy, Italy. In 1786 he
published what he designated "Examination of a New Argument in Favor of
Perpetual Motion." In part he says:

  1. A vertical wheel (Fig. 2) divided in two halves by a vertical
  plane which passes through its diameter F O, has the half F P O
  immersed in water under the level M N, and the other half wholly
  out of the water, being cut off in F O by a peculiar mechanism
  from all communication with the reservoir, the exterior half
  of the wheel being F Q O; this turns freely round on an axle
  passing through the centre C. Now the wheel being specifically
  lighter than the water, the immersed part F P O comes with a
  continual rotation to the top with a force equal to the excess
  of the weight of a volume of water corresponding to the immersed
  portion, over the weight of the immersed portion; which rotation
  passing through the centre of gravity of the exterior part, and
  consequently out of the centre C, obliges the wheel to turn
  around C.

  Such being the case, the question to be asked is whether the
  wheel has itself a perpetual motion, as may be judged at first
  sight.

  [Illustration]

  2. To reply adequately, it is at first necessary to know what
  effect is produced on the wheel by the horizontal pressure which
  the water exercises on the semi-circumference F L O.

  Having taken for this purpose, a part P _p_, and having drawn to
  the diameter the ordinate P. R, _p r_, and marked the radius P C,
  and from it P G perpendicular to the radius C L, which determines
  the quadrant O L, the distance of the lowest point O from the
  level of the water will be = _b_, the semi-diameter of the wheel
  = _a_, C R = _x_, and the specific gravity of the water = 1; the
  perpendicular pressure against the part P _p_ = P _p_ . R D,
  which resolved in two, one horizontal P R, the other vertical
  P G, gives the proportion

    PG : PR :: P_p_ . RD : (P_p_ . PR . RD) / (PG).

  Thence the horizontal pressure against P _p_, and = (P _p_ .
  P R . R D .) / (P G), that is to say P _p_ . P R = R _r_ . P G,
  the given horizontal pressure is found to be = R _r_ . R D =
  (_b_ - _x_) _d_ _x_, and which, multiplied by R D, giving _b_
  - _x_, becomes the momentum of the pressure relatively to M N
  = (_b_ - _x_)² _d_ _x_, and the sum of the momenta of pressure
  exercised upon the indefinite arc, O P = _f_ (_b_ - _x_)² _d_ _x_
  = -(1/3)(_b_ - _x_)³ + the side. And since acting together such
  momenta equal _x_, there comes the side = (1/3)_b_³; and as the
  already-given sum of the momenta = (1/3)(_b_³ - (_b_ - _x_)³) =
  _b² x_ - _b x_² + (1/3)_x_³. Whence, taking _x_ = 2_a_, the sum
  of all the momenta of the horizontal pressure exercised on the
  whole semi-circumference O L F of the wheel, will be = 2_b_²_a_
  - 4_b_ _a_² + (8/3)_a_³, and dividing that sum by the whole
  horizontal pressure, that is to say by _f_(_b_ - _x_)_d_ _x_ =
  (1/2)(_b_² - (_b_ - _x_)²) = _b_ _x_ - (1/2)_x_² = 2_b_ _a_ -
  2_a_², gives _x_ = 2_a_, we have the formula

    (2_b_² - 4_b_ _a_ + (8/3)_a_³) / (2_b_ _a_ - 2_a_²) =
    (_b_² - 2_b_ _a_ + (4/3)_a_²) / (_b_ - _a_) =
    ((_b_ - _a_)² + (1/3)_a_²) / (_b_ - _a_) =
    _b_ - _a_ + ((2/3)_a_²) / (_b_ - _a_),

  which represents the distance of the level M N from the result
  of all the horizontal pressure against the circumference, which
  distance exceeds D C, and consequently the direction of the
  result passes from below the centre C of the wheel to a distance
  from the said centre, which is = ((1/3)_a_²)/(_b_ - _a_).

  If this distance be multiplied by the result of all the
  horizontal pressure, that is, by 2_a_.(_b_ - _a_); there is
  obtained (2/3)_a_³ for the momentum of the force which tends to
  make the wheel revolve from L towards O. This being established,
  it is known that the force which causes the half of the wheel
  F L G to revolve vertically to the top (calling _g_ the specific
  gravity of the wheel) is = (1 - _g_) F C O L, and which force
  passes through the center of gravity of F L O. And consequently
  the gravity of any circular segment divided by the half of the
  radius, is distant from the centre of the circle by a quantity
  equal to the twelfth of the cube of the chord divided by the
  segment; and therefore the centre of gravity of the semicircle
  F C O L, will be distant from the centre C by the quantity
  (1/12)8_a_³/(E C O L) = (2/3)_a_³/(E C O L). Consequently the
  momentum of this force tending to make the wheel revolve from O
  towards L will

    be = (2/3_a_³)/(E C O L) . (1 - _g_)(E C O L) = 2/3(1 - _g_)_a_³.

  But moreover a certain momentum will be derived from the other
  half F Q O of the wheel, which being out of the water, tends by
  its own weight downwards with a force = _g_ . (E C O Q) = _g_ .
  (E C O L), which multiplied by the distance (2/1_a_³)/(E C O L)
  of the centre of gravity of the semicircle F Q O from the centre
  of the wheel gives as a momentum of force tending to turn the
  wheel from O to L the quantity 2/3_g_ _a_³. Thus the whole
  momentum to make the wheel turn from O to L, will be 2/3(1 -
  _g_)_a_³, + 2/3_g_ _a_³ = 2/3_a_³, that is to say the same that
  is found to turn the wheel in the opposite direction, viz., from
  L to O, and thence the wheel remains perfectly motionless.

  3. Cor. I. If the wheel were specifically heavier than the water,
  one would not be able to conceive in that case any motion from L
  to O, as seemed probable in the former supposition. Since, then,
  the momentum of the force, which turns vertically downwards the
  portion of the wheel F C O L, and tends to make it revolve from L
  to O is = 2/3(_g_ - 1)_a_³ to which momentum should be added a
  certain portion of the horizontal pressure, that is to say 2/3,
  and thus is obtained the whole momentum 2/3_g_ _a_³, tending
  to cause the wheel to turn from L to O; and to which momentum
  precisely, is equal such of the weight of the half F C O Q as
  tends to give to the wheel a contrary revolution, that is, from O
  to L.

  3. Cor. II. If the wheel in place of being a circular plane were
  a zone bounded by two concentric peripheries (Fig. 3), then
  from the sum of the horizontal pressure of the water against
  the exterior periphery should be taken the sum of the opposite
  horizontal pressure against the other interior semi-periphery
  of the zone. So calling _a_ the greater radius of the zone, and
  λ its breadth, the sum of the first horizontal pressure is =
  2_a_(_b_ - _a_) and the sum of the second = 2(_a_ - λ)(_b_ - λ) -
  (_a_ - λ) = 2(_a_ - λ)(_b_ - _a_). Then subtract the latter from
  the former and there remains 2(_b_ - _a_)λ for the sum of the
  whole pressure, which acts upon the zone (_sic_) of the half of
  the wheel immersed in the fluid in a direction tending from the
  outside to the interior of the wheel.

  Moreover the sum of the momenta of all the horizontal pressure on
  the exterior circumference relatively to the level

  M N is = 2_b_ _a_ - 4_b_ _a_ + 8/3_a_³.

  And similarly the sum of the momenta of the horizontal pressure
  opposite, on the interior semi-circumference, relatively to the
  given level is = 2(_b_ - λ)² - (_a_ - λ) - 4(_b_ - λ) × (_a_ -
  λ)² + 8/3(_a_ - λ)³.

  Subtracting this sum from the preceding, there remains the sum
  of the momenta acting on the zone of the half-wheel from the
  exterior to the interior = 2_b_² _a_ - 4_b_ _a_² + 8/3_a_³ -
  2(_b_ - λ)² (_a_ - λ) + 4(_b_ - λ) (_a_ - λ)² - 8/3(_a_ - λ)³ -
  2_b_² λ - 4_b_ _a_ λ + 4_a_² λ - 2_a_ λ² + 2/3λ³ = 2λ (_b_(_b_
  - _a_) - _b_ _a_ + 2_a_² - _a_λ + 1/3λ²) = 2λ ((_b_ - _a_)(_b_
  - _a_) + _a_² - _a_λ + 1/3λ²) Then dividing this sum of the
  momenta by the sum of the pressure there will be 2λ(((_b_ -
  _a_)(_b_ - _a_) + _a_² - _a_λ + 1/3λ²)/(2λ(_b_ - _a_))) = _b_
  + _p_ (_a_(_a_² - _a_λ + 1/3λ²)/(_b_ - _a_)) the distance of
  the center of the pressure from the level of the fluid, that
  is, to the distance of the result of all the pressure from that
  level. From this it is evident that the center of pressure falls
  under the center of the wheel, C, to the distance (_a_² - _a_λ +
  1/3λ²)/(_b_ - _a_) .

  Whence multiplying this distance by the result of the pressure,
  or by 2λ(_b_ - _a_), we obtain 2λ(_a_² - _a_λ + 1/3λ²) to express
  the momentum of the horizontal pressure of the water, directed to
  make the wheel turn from L to O.

  Now the momentum with which the vertical impulse of the fluid
  tends to make the semicircle F C O L turn from O to L (supposing
  the wheel not with a simple zone, but with a circular plane) is
  = 2/3_a_³. Likewise the momentum of the impulse of the fluid to
  cause the internal semicircle V C I G from O to L is - 2/3(_a_
  - λ)³. Then taking this second momentum from the first, the
  momentum of the zone from the fluid V G I O L F to give the wheel
  an impulse from O to L will be = 2/3(_a_³ - (_a_ - λ)³) = 2λ(_a_²
  - _a_λ + 1/3λ²) which is precisely the momentum with which the
  horizontal pressure of the fluid to impress on the wheel an
  impulse in the opposite direction, that is to say from L to O.
  Consequently from the pressure of the fluid the wheel cannot
  have any motion around its center.

  The weight of the wheel itself, by which the half-zone immersed
  in the water tends to make the wheel turn from L to O, and the
  half which is out of the water, to make it turn in the reverse
  direction, such a weight, I say, cannot induce any motion of
  rotation, and both halves remain in equilibrium around the center
  C.


Article by William Nicholson

William Nicholson was born in London in 1753; died in 1815. He was a
scientist of note, and a writer of scientific subjects. In 1797 he
established in London and continued publishing until 1814, a periodical
entitled "Journal of Natural Philosophy, Chemistry and the Arts,"
known, however, throughout the civilized world as "Nicholson's Journal."

A Perpetual Motion device of Dr. Conradus Schwiers, in 1790, and the
Richard Varley device, in 1797, described at page 132 et seq., ante,
had attracted a great deal of attention, and were the occasion of
much discussion. A consequent increased interest in the subject of
self-moving mechanism was thus created.

Mr. Nicholson, whose scientific attainments were recognized by all, was
asked to publish an article on the subject. His article appeared in
his publication, "Nicholson's Journal," and is as follows:


  _On the Mechanical Projects for Affording a Perpetual Motion_

  In consequence of the notice taken of Mr. Varley's attempt to
  produce a perpetual motion, I have been requested by several
  correspondents to state how far the mechanical scheme for which
  Dr. Conrad Schwiers took out a patent in the year 1790, for
  the same object may be worthy of attention. I have, on that
  occasion, mentioned the difficulties which have prevented any
  clear general demonstration of the absurdity of this pursuit
  from being produced, though it has not been difficult to show
  the fallacy of the individual plans. It does not, indeed, seem
  easy to enunciate the scheme itself. What in universal terms is
  the thing proposed to be done? Is it to cause a body to act in
  such a manner that the reaction shall be greater than the action
  itself, and by that means generate force by the accumulation of
  the surplus? Or, can the motion communicated be greater than
  that lost by the agent? Since these positions are evidently
  contrary to the physical axioms called the laws of nature, and
  frictions and resistances would speedily destroy all motions of
  simple uniformity, it may be presumed that 's Gravesande, who
  thought that all the demonstrations of the absurdity of schemes
  for perpetual motion contained paralogism, would have stated the
  proposition under different terms. But without entering upon this
  apparently unprofitable disquisition, it may be useful, as well
  as entertaining, to make a few observations on the mechanical
  contrivances which depend on a mistaken deduction from the
  general theorem respecting the balance, among which that of Dr.
  Schwiers must be classed.

  There is no doubt but numerous arrangements have been made, and
  still are labored at by various individuals, to produce a machine
  which shall possess the power of moving itself perpetually,
  notwithstanding the inevitable loss by friction and resistance of
  the air. Little, however, of these abortive exertions has been
  entered upon record. The plans of Bishop Wilkins, the Marquis of
  Worcester, and M. Orffyreus, are all which at this time occur to
  my recollection.

  [Illustration]

  There is no doubt but the celebrated Wilkins was a man of
  learning and ability. His essay towards a real character and a
  philosophical language is sufficient to render his name immortal.
  Twenty years before the appearance of that work he published
  his "Mathematical Magic," namely, in the year 1648, containing
  295 pages, small octavo, which, from the number of copies still
  in being, I suppose to have been a very popular treatise. It is
  in this work that I find, among other contrivances for the same
  purpose, a wheel carrying sixteen loaded arms, similar to that
  delineated in Fig. 4, plate 15, in which, however, for the sake
  of simplicity, I have drawn but six. Each lever, A B C D E F,
  is movable through an angle of 45 degrees, by a joint near the
  circumference of the wheel, and the inner end or tail of each
  is confined by two studs or pins, so that it must either lie in
  the direction of a radius, or else in the required position of
  obliquity. If the wheel be now supposed to move in the direction
  E F, it is evident that the levers A B C D, by hanging in the
  oblique position against the antecedent pins, will describe a
  less circle in their ascent than when, on the other side, they
  come to descend in the positions E F. Hence, it was expected that
  the descending weights, having the advantage of a longer lever,
  would always predominate. Dr. Wilkins, by referring the weights
  to an horizontal diameter, has shown that in his machine they
  will not. A popular notion of this result may also be gathered
  from the figure, where there are three weights on the ascending
  and only two on the descending side; the obliquity of position
  giving an advantage in point of number, equal to what the other
  side may possess in intensity. Or, if this contrivance were to be
  strictly examined, on the supposition that the levers and weights
  were indefinitely numerous, the question would be determined by
  showing that the circular arcs A K, H I, are in equilibrio with
  the arcs A G, G L.

  The simplest method of examining any scheme of this kind with
  weights, consists in inquiring whether the perpendicular ascents
  and descents would be performed with equal masses in equal times.
  If so, there will be no preponderance, and, consequently, no
  motion. This is clearly the case with the contrivance before us.

  The Marquis of Worcester, who will ever be remembered as the
  inventor of the steam engine, has described a perpetual motion in
  the fifty-sixth number of his "Century of Inventions," published
  in the year 1655, and since reprinted in 1767 by the Foulis's at
  Glasgow. His words were as follows:

  "To provide and make, that all the weights of the descending side
  of a wheel shall be perpetually further from the center than
  those of the mounting side, and yet equal in number and heft to
  the one side as the other. A most incredible thing if not seen,
  but tried before the late King (of blessed memory) in the Tower
  by my directions, two extraordinary ambassadors accompanying his
  Majesty, and the Duke of Richmond and Duke Hamilton, with most of
  the Court attending him. The wheel was fourteen feet over, and
  forty weights of fifty pounds apiece. Sir William Balfour, then
  Lieutenant of the Tower, can justify it with several others. They
  all saw that no sooner these great weights passed the diameter
  line of the lower side, but they hung a foot further from the
  center; nor no sooner passed the diameter line of the upper side,
  but they hung a foot nearer. Be pleased to judge the consequence."

  [Illustration]

  Desaguliers, in his "Course of Experimental Philosophy," Vol.
  I, page 185, has quoted this passage, and given a sketch of a
  pretended self-moving wheel, similar to Fig. 5, plate 15, as
  resembling the contrivance mentioned by the Marquis of Worcester.
  The description of this last engineer agrees, however, somewhat
  better with the contrivance Fig. 4. It must, of course, be a
  mistake in terms, when he says the weight receded from the center
  at the lower diameter and approached towards it at the upper:
  the contrary being, in fact, necessary to afford any hope of
  success; and accordingly in the quotation it is so stated. I am,
  therefore, disposed to think that Fig. 5 represents the wheel
  of Orffyreus at Hesse Cassel, much talked of about the year
  1720, and which probably was made to revolve, during the time
  of exhibition, by some concealed apparatus. It consists of a
  number of cells or partitions, distinguished by the letters of
  the alphabet, which are made between the interior and exterior
  surfaces of two concentric cylinders. The partitions being
  placed obliquely with respect to the radius, a cylindrical or
  spherical weight placed on each, it is seen from the figure,
  that these weights will lie against the inner surface of the
  larger cylinder whenever the outer end of the bottom partition
  of any cell is lowest; and, on the contrary, when that extremity
  is highest, the weight will rest on the surface of the interior
  cylinder. Let the wheel be made to revolve in the direction
  A B C; the weights in C D E F G H I being close to the external
  circle, and the weights K L M A B close to the inner, for the
  reasons last mentioned. As the cell B descends, its weight
  will likewise run out, at the same time that the weight in
  the cell I will run in in consequence of its partition being
  elevated. By the continuation of this process, since all the
  weights on the descending side pass down at a greater distance
  from the center, while those of the ascending side rise for a
  considerable part of their ascent at a less distance from the
  same point, it is concluded that the wheel will continue to
  maintain its motion. On this, however, it is to be remarked that
  the perpendicular ascent and descent are alike, both in measure
  and in time of performance; and that the familiar examination,
  even to those who know little of such subjects, is sufficient
  to show that the preponderance is not quite so palpable as at
  first it appears. For the weights G and F, H and E, I and D
  are evidently in equilibrio, because at the same horizontal
  distance from the center; and if the favorable supposition that
  the weight B has already run out be admitted, it will then
  remain a question whether these two exterior weights, B and C,
  can preponderate over the four inner weights, K L M A. The more
  accurate examination of this particular contrivance will lead to
  the following theorem: In two concentric circles, if tangents be
  drawn at the extreme points of a diameter of the smaller, and
  continued till they intersect the larger, the common center of
  gravity of the arc of the greater circle included between the
  tangents and of the half periphery of the smaller circle on the
  opposite side of the diameter, will be the common center of the
  circles. If, therefore, the balls were indefinitely numerous and
  small, the supposed effective parts of the wheel (Fig. 5) would
  be in equilibrio, as well as the parts beneath the horizontal
  tangent of the inner circle.

  Fig. 6 represents the contrivance of Dr. Schwiers, which, in
  a periodical publication, in other particulars respectable,
  has been said to continue in motion for weeks and even months
  together. There is not the smallest probability that it should
  continue in motion for half a minute, or nearly as long as
  a simple wheel would retain part of its first impulse. The
  external circle denotes a wheel carrying a number of buckets,
  A B I L, etc. C represents a toothed wheel, on the same axis
  which drives a pinion D; and this last drives another pinion
  E upon the axis of a lanthorn, or wheel intended to work a
  chain-pump with the same number of buckets as in the larger wheel
  A B I. The lanthorn G is made of such a size as to receive the
  buckets _a b i l_ with a due velocity. K represents a gutter
  through which a metallic ball, contained in the bucket _m_, may
  run and lodge itself in the bucket A of the wheel. Each of the
  buckets of the wheel, B I L M, which are below the gutter, is
  supplied with a metallic ball, and so likewise are the ascending
  buckets, _a b i l m_, of the chain-pump. As the pump supplies
  the wheel, it is again supplied at M, where the balls fall into
  its ascending buckets. Now, it is presumed that the balls in the
  wheel I suppose on account of their distance from the center of
  motion, will descend with more than sufficient force to raise
  those on the chain, and, consequently, that the motion will be
  perpetual.

  The deception in this contrivance has much less seduction than
  in the two foregoing, because it is more easily referred to the
  simple lever. This, like the others, exhibits no prospect of
  success, when tried by the simple consideration of the quality
  of the ascent and descent in the whole time of the rotation
  of a single ball. It may also be shown from the principles of
  wheel-work, which are familiar to artisans, that whatever is
  gained by the excess of the diameter of the great wheel beyond
  that of the wheel C, is again lost by the excess of the lanthorn
  A beyond the pinion E.

  [Illustration]

  The fundamental proposition of the simple lever or balance,
  that equal bodies at an equal distance from the fulcrum will
  equiponderate, but that at unequal distances the most remote
  will descend, has, in these and numberless other instances, led
  mechanical workmen and speculators to pursue this fruitless
  inquiry with labor and expense often ill-afforded, and with a
  degree of anxiety and infatuation which can hardly be conceived
  by those who have never suffered the pain of hope long deferred.
  For this reason chiefly, it has appeared desirable and useful
  to treat the subject in a familiar way without descending to
  those expressions of contempt, which ignorance, harmless to all
  but itself, is surely not entitled to. If such reasoners were
  well convinced that the power of a machine is to be estimated
  by the excess of motion referred to the perpendicular, without
  any regard to the apparent center of the machine, and that
  in machines very little compounded it is possible to produce
  effects directly contrary to the rule which is true of the simple
  lever, they would probably renounce many flattering projects,
  grounded only on the supposition of its universality. Desaguliers
  contrived an apparatus in which two equal weights may be placed
  at any distance whatever from the center of motion, and still
  continue in equilibrio. Fig. 3 represents this instrument. A D
  denotes a balance with equal arms, and E F another of the same
  dimensions. These move on the centers B and C, and are connected
  by the inflexible rods A E and D F; the motion being left free
  by means of joints at the corners. Across the rods A D, E F, are
  fixed two bars, I K, L M. Now, it is unnecessary to show that the
  weight G will describe exactly the same line or circular arc,
  when the levers are moved into the position _a d f e_, or any
  other position, as it would have described in case it had been
  suspended at A, or K, or E; and that it is of no consequence in
  this respect at what part of the line A E or I K it be fixed.
  The same observations are true of the weight H on the other
  side. And accordingly it is found that these equal weights may
  be suspended anywhere on the lines I K and L M without altering
  their equilibrium.

  [Illustration]

  By this contrivance it is most evidently proved to those who
  are totally unacquainted with the theory, that weights do not
  preponderate in compound engines on account of their distance
  from the center. Several contrivances may be made to the same
  effect. The following combination of wheel-work presented
  itself to me as one which would most probably be mistaken for a
  perpetual motion. (Fig. 2, plate 15.) The five circles represent
  the same number of wheels of equal diameter and number of teeth,
  acting together. The middle wheel A is fixed between two upright
  pillars, so that it cannot revolve. The other four wheels are
  pinned in a frame H I, in which they can revolve, and through
  which the axis of A likewise passes. From the extremity of the
  axis of D, and also of _d_, proceed the horizontal levers H K and
  I L, which are equal, and point in the same direction parallel
  to the plane of the wheels. At the extremity of these arms hang
  the equal weights P and _p_. Let it now be imagined that the
  end I of the frame is depressed, the wheel B will turn round by
  the reaction of the fixed wheel A in the same direction as H I,
  and it will make one revolution in the same time relative to
  the frame, or two with regard to absolute space, by reason of
  its being carried round. The action of B upon D will produce a
  rotation relative to the frame in the opposite direction during
  the same time. Instead, therefore, of two revolutions like the
  wheel B, this wheel D, with regard to absolute space, will not
  revolve at all, and in every position of the apparatus the arm
  I L will continue horizontal, and point the same way. For similar
  reasons the arm H K will retain its position. Consequently, it is
  seen that the descending weight will move at a great horizontal
  distance from the center N, while the ascending weight rises
  very near that center. But there will, not on this account,
  be a perpetual motion: for the action of the levers H K and
  I L upon the frame H I, by means of the toothed wheels, will,
  in the detail, be found precisely alike, and in the general
  consideration of the motions of P and _p_, the opposite motions
  in the circle E F G will be accurately the same.

  [Illustration]

  It has always been considered as essential to a perpetual motion
  that it should be derived from some energy which is not supposed
  to vary in its intensity. Such are the inertia, the gravity or
  magnetism of bodies. For an occasional or periodical variation of
  intensity in any force is evidently productive of motion, which
  requires only to be accumulated or applied, and the apparatus
  for applying it cannot be considered as a machine for perpetual
  motion. Neither in strictness can any machine whose motion is
  derived from the rotation of the earth, and the consequent change
  of seasons and rotation of events, be so considered, because
  it does not generate, but only communicates. The perpetual
  flow of rivers; the vicissitudes of the tides; the constant,
  periodical and variable winds; the expansions and contractions
  of air, mercury, or other fluids, by daily or other changes of
  temperature; the differences of expansions in metals, by the
  same change; the rise and fall of the mercury in the barometer;
  the hygrometric changes in the remains of organized beings, and
  every other mutation which continually happens around us, may be
  applied to give motion to mills, clocks, and other engines, which
  may be contrived to endure as long as the apparatus retains its
  figure.

Mr. Nicholson's article, published above, shows, if nothing else
had ever shown, the fact that he was endowed with a real scientific
mind. It also shows what is still most interesting--that his mind
anticipated and that he had a subconscious conception of the principle
of Conservation of Energy.

In 1824 and 1825 there was published in London a mechanical journal
called "The Artisan"; or "Mechanic's Instructor." In one of the issues
the following occurred on the subject of Perpetual Motion:

  Perpetual motion is a motion which is supplied and renewed from
  itself without the intervention of any external cause: to find
  a perpetual motion, or to construct a machine which shall have
  such a motion, is a subject which has engaged the attention of
  mathematicians for more than 2,000 years; though none perhaps
  have prosecuted it with so much zeal and hopes of ultimate
  success as some of the speculative philosophers of the present
  age.

  Infinite are the schemes, designs, plans, engines, wheels, etc.,
  to which this longed-for perpetual motion has given birth;
  and it would not only be endless but ridiculous to attempt to
  give a detail of them all, especially as none of them deserve
  particular mention, since they have all equally proved abortive;
  and it would rather partake of the nature of an affront than a
  compliment, to distinguish the pretenders of this discovery, as
  the very attempting of the thing conveys a very unfavorable idea
  of the mental powers of the operator.

  For among all the laws of matter and motion, we know of none
  which seems to afford any principle or foundation for such an
  effect. Action and reaction are allowed to be ever equal; and a
  body which gives any quantity of motion to another, always loses
  just so much of its own; but, under the present state of things,
  the resistance of the air, and the friction of the parts of
  machines, necessarily retard every motion.

  To keep the motion going on, therefore, there must either be a
  supply from some foreign cause, which, in a perpetual motion, is
  excluded.

  Or, all resistance from the friction of the parts of matter must
  be removed; which necessarily implies a change in the nature of
  things.

  For by the second law of motion the changes made in the motions
  of bodies are always proportional to the impressed moving force,
  and are produced in the same direction with it; no motion, then,
  can be communicated to any engine, greater than that of the first
  force impressed.

  But, on our earth, all motion is performed in a resisting fluid,
  namely, the atmosphere, and must, therefore, of necessity, be
  retarded; consequently, a considerable quantity of its motion
  will be spent on the medium. Nor is there any engine or machine
  wherein all friction can be avoided; there being in nature no
  such thing as exact smoothness or perfect congruity; the manner
  of the cohesion of the parts of bodies, the small proportion
  which the solid matter bears to the vacuities between them, and
  the nature of those constituent particles not admitting it.

  Friction, therefore, will also, in time, sensibly diminish the
  impressed or communicated force; so that a perpetual motion can
  never follow, unless the communicated force be so much greater
  than the generating force as to supply the diminution occasioned
  by all these causes; but the generating force cannot communicate
  a greater degree of motion than it had itself. Therefore, the
  whole affair of finding a perpetual motion comes to this, viz.,
  to make a weight heavier than itself, or an elastic force
  greater than itself; or, there must be some method of gaining a
  force equivalent to what is lost by the artful disposition and
  combination of the mechanical powers: to this last point then,
  all endeavors are to be directed; but how, or by what means such
  a force can be gained, is still a mystery!

  The multiplication of powers or forces avails nothing; for what
  is gained in power is lost in time; so that the quantity of
  motion still remains the same.

  The whole science of mechanics cannot really make a little power
  equal or superior to a larger; and wherever a less power is found
  in equilibrio with a greater--as, for example, twenty-five pounds
  with one hundred--it is a kind of deception of the sense; for
  the equilibrium is not strictly between one hundred pounds and
  twenty-five pounds moving (or disposed to move) four times as
  fast as the one hundred pounds.

  A power of ten pounds moving with ten times the velocity of one
  hundred pounds would have equalled the one hundred in the same
  manner; and the same may be said of all the possible products
  equal to one hundred: but there must still be one hundred pounds
  of power on each side, whatever way they may be taken, whether in
  matter or in velocity.

  This is an inviolable law of nature; by which nothing is left to
  art, but the choice of the several combinations that may produce
  the same effects.

  The only interest that we can take in the projects which have
  been tried for procuring a perpetual motion must arise from the
  opportunity that they afford of observing the weakness of human
  reason.

  For a better instance of this can scarcely be supplied than to
  see a man spending whole years in the pursuit of an object,
  which a single week's application to sober philosophy would have
  convinced him was unattainable.

  But for the satisfaction of those who may not be convinced of the
  impossibility of attaining this grand object, we shall add a few
  observations on the subject of a still more practical nature than
  the above.

  [Illustration]

  The most satisfactory confutation of the notion of the
  possibility of a perpetual motion is derived from the
  consideration of the properties of the center of gravity; it is
  only necessary to examine whether it will begin to descend or
  ascend when the machine moves, or whether it will remain at rest.
  If it be so placed that it must either remain at rest or ascend,
  it is clear, from the laws of equilibrium, that no motion derived
  from gravitation can take place; if it may descend, it must
  either continue to descend forever with a finite velocity, which
  is impossible, or it must first descend and then ascend with a
  vibratory motion, and then the case will be reducible to that of
  a pendulum, where it is obvious that no new motion is generated,
  and that the friction and resistance of the air must soon destroy
  the original motion.

  One of the most common fallacies by which the superficial
  projectors of machines for obtaining a perpetual motion have
  been deluded, has arisen from imagining that any number of
  weights ascending by a certain path on one side of the center of
  motion, and descending on the other at a greater distance, must
  cause a constant preponderance on the side of the descent; and
  for this purpose weights have been made to slide or roll along
  grooves or planes, which lead them to a more remote part of the
  wheel, from whence they return as they ascend, as represented in
  the following figure: Or they have been fixed on hinges which
  allow them to fall over at a certain point so as to become more
  distant from the center; but it will appear on the inspection
  of such a machine that although some of the weights are more
  distant from the center than others, yet there is always a
  proportionally smaller number of them on that side on which they
  have the greater power; so that these circumstances precisely
  counterbalance each other.

  We have heard it proposed to attach hollow arms to a wheel by
  joints or hinges at the circumference, and to fill these arms
  with quicksilver or small balls instead of the plan represented
  by the above figure; but though we have never heard of it having
  been tried, we are perfectly convinced that it would end as all
  other attempts have done; that is, in a total failure.


The Possibility of Perpetual Motion Asserted

The enthusiastic earnestness with which the subject of Perpetual
Motion was formerly discussed is illustrated by the fact that the Holy
Scriptures were dragged in to support arguments on the proposition.

The following is a verbatim copy of an article published in an English
scientific magazine in 1829:

  "Notice to Perpetual Motion Seekers."--The following is a literal
  copy of a communication which we have received under this head.
  We publish it for the benefit of all concerned: "Perpetual Motion
  Seekers! see Coloss., ch. ii., v. 8--'Beware lest any man spoil
  you, through philosophy and vain deceit, after the tradition of
  men, after the rudiments of the world.' Ye are making the words
  of God of none effect by your traditions in publishing these
  things to the world. How can such toys and baubles as these be
  perpetual? See Malachi, ch. iv., v. 1--'For behold the day cometh
  that shall burn as an oven; and all the proud, yea, all that do
  wickedly, shall be as stubble.' Here is the end of them. I, the
  undersigned, have to inform the public, the model for making
  perpetual motion is to be found in that too much neglected book
  of models, the Bible. I called upon the Lord, and he showed it
  to me. I said, 'Lord, shall I show this unto them? This was the
  answer to me: See Isaiah, ch. xli., v. 29--'Behold, they are all
  vanity; their works are nothing.' I said, 'Lord, be pleased to
  show me some more about it.' 'Bring forth your strong reasons,
  saith the King of Jacob.'--Isaiah, ch. xli., v. 21. This was the
  answer: See Isaiah, ch. xli., v. 14--'Fear not, thou worm Jacob.
  * * Behold, I will make thee a new sharp threshing instrument
  having teeth; thou shalt thresh the mountains, and beat them
  small, and shall make the hills as chaff.' See also Jeremiah,
  ch. vii., v. 9--'The wise men are ashamed; they are dismayed and
  taken,' etc. See also Jeremiah, ch. ix., v. 12--'Who is the wise
  man that may understand this?' If there is not a wise and learned
  man who can show this, there is a deaf and unlearned man that
  will, by the blessing of God, set it forth to you. I am that deaf
  and unlearned man, George Lovatt, Stafford.

  "P. S.--Mr. Editor: I have told you what I was commanded to do.
  See Ezekiel, ch. iii., v. 4 to the end. Now, see thou forget it
  not; let those models which come from the Word of God have the
  first place.--Joshua, ch. xxiv., v. 15."


John Bernoulli's Dissertation on Perpetual Motion

John Bernoulli was born in 1667, and died in 1748. He belonged to the
famous Belgian family bearing the name. His family seems to have been
peculiarly prolific in men of great genius for mathematics and science.
Almost any encyclopedia with any pretense for thoroughness will
mention and give the sketch of the life of from five to nine members of
the Bernoulli family.

John Bernoulli possessed perhaps the greatest genius of any bearing the
name for pure mathematics and pure mechanics. He was a contemporary
of such men as Leibnitz, Euler and Newton, a co-laborer with the two
former, but never conceded the merits of Newton. He was of a peculiar
disposition, of intense likes and dislikes and among his peculiarities
it may be mentioned that he harbored an unreasonable hatred toward a
worthy and deserving son.

In 1742 he wrote a work entitled "Dissertation on Effervescence and
Fermentation." To this work he added an appendix entitled "Concerning
Artificial Perpetual Motion." The appendix translated into English and
as published by Dircks, is as follows:

  Scarcely had I finished this dissertation, when, attentively
  considering the nature of precipitation and secretion, briefly
  explained in the last pages, there accidentally occurred to me
  a mode of constructing, by means of some continually flowing
  liquid, the much-talked of and long-desired Perpetual Artificial
  Motion; and this as a completion to my work, on account of the
  affinity of the subject, I now propose for the consideration of
  the learned.

  No one need be told how eagerly for a length of time this same
  Perpetual Motion has been sought after by the most celebrated
  men, how ardently desired; what indeed have they not contrived?
  To what expense have they not gone? How many machines have they
  not constructed? But all in vain.

  The secret desire of this Perpetual Motion still perplexes and
  torments many, and excites their minds to such a degree that we
  see the ears and minds of learned men carried away by it; yet
  many philosophers reject the idea, unanimously asserting that
  Perpetual Motion cannot be communicated and cannot be invented;
  which opinion is nevertheless not of any weight, seeing that they
  rashly judge that no one should be listened to who boasts of
  having found out such a thing; and their reasons (as I confess)
  do not suffice to convince me; for I do not hesitate to assert
  not only that Perpetual Motion may be discovered, but that it has
  now actually been discovered, as will be confessed by any one
  who reads these lines; and what is this labor to many? does not
  Nature herself (who is never said not to operate by mechanical
  laws) indicate Perpetual Motion to be possible? To recall but one
  instance, what is the constant flux and reflux of the rivers and
  seas but Perpetual Motion? Does it not all belong to Mechanics?
  Therefore, you must confess that it does not exceed the limits of
  mechanical laws, and is not impossible; what then hinders that
  following Nature in this, we should be able perfectly to imitate
  her? as indeed I shall so conclude, by declaring to these the
  possibility of Perpetual Motion and the manner of obtaining it;
  and lest thou come to an adverse conclusion, or regard it as a
  Titanic enterprise, I pray that thou mayest first well weigh the
  thing, or, if it so please thee, put its truth to the test of
  experience.

  First of all the following must be premised:

  1. If there are two fluids of different density, the weights of
  which respectively are in the ratio G to L; the altitudes of
  cylinders of equal weight, and having the same base, will be in
  the ratio L to G.

  2. Therefore, if the altitude A C of one fluid contained in the
  vessel A D to be the altitude E F of the other fluid contained in
  an open tube, as L to D; the fluids so placed will remain at rest.

  [Illustration]

  3. Therefore, if A C to E F be in a greater ratio than L to
  G, the fluid in the tube will ascend; or if the tube be not
  sufficiently long, the fluid will escape by the orifice E. (These
  are proved by Hydrostatics.)

  4. It is possible to have two fluids of different gravity, which
  are capable of being mixed one with the other.

  5. It is possible to have a filter, strainer or other separator,
  by means of which the lighter fluid may be separated from the
  heavier.


  _Construction_

  These being pre-supposed, I construct Perpetual Motion in the
  following manner:

  Let two fluids of different gravity and capable of mixing
  together (which is possible by Hyp. 4) be taken in any
  quantities, in equal quantities, if desired; let the ratios of
  their gravities be first determined, which suppose as G to L, the
  heavier to the lighter; and being mixed, let a vessel, A D, be
  filled to A.

  This having been done, let a tube be taken, open at both ends
  E F; and of such a length that A C : E F > 2 L : G + L; and
  the orifice F stopped, or rather filled with a filter or some
  substance separating the lighter fluid from the heavier (as is
  possible also by Hyp. 5); when the tube filled in this manner
  with fluid is immersed to the bottom of the vessel C D; I say
  that the fluid will continually ascend by the orifice of the tube
  F, and by the orifice E will fall into the fluid below.


  _Demonstration_

  Because the orifice of the tube F is occupied by a filter (by
  Constr.) which separates the lighter fluid from the heavier;
  it follows, that if the tube be immersed to the bottom of
  the vessel, the fluid lighter by itself, which is mixed with
  the heavier fluid, must ascend in the tube, and as it will
  ascend above the surface of the surrounding fluid as A C :
  E F = 2 L : G + L : which is (by Const.) A C : E F > 2 L :
  G + L, it necessarily follows (by Hyp. 3) that the lighter
  liquid, through the orifice E, will fall in the vessel below;
  there it again mixes with the heavier (by Hyp. 4); and then,
  penetrating the filter, ascends again into the tube, and escapes
  by the upper orifice. So, therefore, the flow is continued
  perpetually.--Q. E. D.


  _Corollary_

  Hence a reason may easily be given, why water from the depths of
  the ocean, ascending into the summits of the mountains, bursts
  from them in the form of rivers and flows again into the ocean;
  so does Nature offer to us the spectacle of perpetual motion.

  Hence I say, they do not well explain who allege that the water
  ascends to these heights through the pores of the earth, as a
  fluid ascends in narrow tubes above the surface of the fluid
  surrounding; for if such were the explanation of the thing, they
  would never be able to demonstrate it; for the water so raised
  to a height from the bosom of the earth, falls again, whereas
  we see that the fluid in these narrow tubes, although slightly
  elevated above the surrounding surface, never issues from their
  orifices and falls into the fluid below. The following is then
  the more feasible explanation. It is known that water in which
  much salt is held in solution is heavier than fresh water; now
  sea-water, as is sufficiently evident from the taste, contains
  many saline particles; consequently it is heavier than spring or
  river water; so that it is credible that the earth acts like a
  filter through the pores of which only fresh water can pass, the
  saline particles being left behind, and this increases the weight
  of the water; the fresh water must ascend much higher on account
  of the immense profundity of the ocean, as it is forced to the
  highest peaks of the mountains by the presence of the sea-water;
  and thence, not being able to ascend any higher, it falls in
  rivers.


P. Christopher Scheiner

That an earnest belief in the possibility of Perpetual Motion has not
been confined entirely to scientific tyros and enthusiastic dreamers,
is sufficiently attested by the fact that a respectable number of
eminent scientists, many of whom had done great service in their
scientific labors, have believed in such possibility.

Among these is to be mentioned P. Christopher Scheiner, a German,
born 1575, and died 1650. He was a mechanic of note; in his day made
valuable additions to what was known of light and optics, invented the
Pantagraph, discovered solar spots, besides benefiting mankind by many
other distinguished fruits of his genius.

The subject of Perpetual Motion claimed some of his attention. He
wrote in defense of its possibility. The substance of what he said,
translated into English, is as follows:

  Let the centre of the universe then, or of gravity, be A, and the
  gnomon A B C, of which the extremity A is pierced and traversed
  by an axis going through the centre of the world, so that it may
  turn and revolve freely and easily around the said centre; to
  the other extremity of the gnomon, C, let a phial full of water
  be attached.

  The weight C will turn around the centre A and will first come
  to D, thence to E, thence to F and G; then it will return to C,
  having described a complete circle, C D E F G; then it will again
  move to D, E, F, etc., and so perpetually, since there is no
  reason for its stopping in any point of the circle rather than in
  another.

  [Illustration]

  That indeed the weight C affixed to the gnomon will move from C
  to D, is proved by daily experience, by which it is established
  that a gnomon so contrived and placed erect on any flat space,
  will not be able to stand, but the arm B C, C preponderating,
  will move towards D.

  It may in the second place be proved, that if, on the other hand,
  another arm B G be added to the gnomon, equal in weight and
  similar to the other, the whole G B C A will remain motionless
  in equilibrium; therefore the arm B G being taken away and
  equilibrium being destroyed, the arm B C must move in the
  opposite direction.

The above, from Scheiner, called forth the following from Schott, who
was also an eminent mathematician:

  Whether there could be a perpetual artificial motion around the
  centre of the earth?

  [Illustration]

  We have treated this question in our Hydraulico-pneumatic
  Mechanics, Part 2, Class 2, Machine 13, not however universally,
  but only in one particular case, that of the Gnomon of Scheiner.
  For P. Christopher Scheiner, in "Mathematical Disquisitions,"
  in Number XV., Corollary 4, asserts Perpetual Artificial Motion
  not to be repugnant to Nature, and attempts to prove it in the
  following manner. Let a gnomon of a certain weight A B C be
  suspended around A, the centre of the universe, and bound to the
  beam D F, which is supported by the columns D F and E G and turns
  at the pole D or E; or let it be fixed at the poles, but the
  gnomon revolving at A.

  These being the conditions, I say that the gnomon A B C will
  revolve from C to H and towards I, thence will return to C,
  thence to H as before, and so on perpetually. The cause of this
  continual motion is the forcible suspension; for the whole gnomon
  preponderates in C on account of the perpendicular tangent B A;
  which effect becomes more marked if a globe of iron S be supposed
  suspended at C. As therefore the whole of this mass, as well
  from the supports of the balance as from the momentary diameter,
  hangs suspended at C, and the vertex A, on account of the firm
  beam D E, cannot fall from the centre of the universe; it comes
  to pass that all points as well of the globe S, as of the gnomon
  A B C, with a continual motion turn round A; but because, by the
  line B A in the fixed point A, they are held from falling to the
  centre; therefore the greatest force of that tendency is exerted
  in the line B, and induces it to inclination; which inclination
  on account of the continuous solidity of the gnomon cannot be
  at all abated, so that the whole impetus is exerted either at
  the point A about the movable beam or at the movable poles of
  the beam D and E; which poles being free in their sockets D and
  E, abandon themselves to the motion of Nature, and thus do not
  in any wise hinder a perpetual circular motion. What indeed is
  self-evident in this, reason confirms, and daily experience in
  statics manifests. For if a short gnomon stand either on the
  terrestrial superficies M N, O P, or Q R; it will always fall
  towards the part C, or N, by the preponderating portion M K C;
  which is manifested in daily experiments.

  Thence it is evident that if the gnomon were entire, the force
  which it exerts at N would pass into the line B A still hanging
  over the centre. And this is one argument. The other is from
  the contrary. For if an equal and similar gnomon were attached
  towards the part D, then the whole mass hanging on its centre
  would remain in equilibrium and there would be no motion;
  consequently the one half being taken away, the other would
  necessarily move according to the laws and experience of statics.
  If the shortened gnomon M B C N were bound only to the point M,
  the rest being left free, it would certainly revolve, and in the
  same case, the point C would describe almost a semicircular arc
  till, coming down to a perpendicular position, it would there
  remain.

  Now as the force of the entire gnomon falls in the vertex A,
  there would be an entire and perpetual revolution around A. Much
  more would this be the case if on the centre C stood either the
  small curve A C L A or the larger one A K C, or finally the globe
  S alone, hanging from two iron rods A B and B C, or from one
  arc, A N C. From this, therefore, it may be demonstrated that a
  perpetual circular motion is possible.

In 1825, the following was contributed to and published in "Mechanics'
Magazine." We are unable to give the name of the contributor, but he
writes in encouragement of Perpetual Motion. The gist of his article is
as follows:

  We can now, however, soar above the clouds, explore the depths of
  the ocean, and skim over its surface. * * * And be it remembered
  that we owe these and many other advantages to a few persevering
  individuals who were, in all probability, stigmatized as
  chimerical visionaries by those who seem to have an unconquerable
  propensity to condemn everything above the level of their own
  understanding.

  If by perpetual motion nothing more is meant than the putting
  in motion some of the most durable substances with which we
  are acquainted, in such a manner as to ensure a continuance of
  motion as long as those substances will resist the effects of
  time and friction, I do not despair of seeing it accomplished.
  * * * [He thinks there is] reasonable ground to hope that the
  time is not far distant when even this impossibility must yield
  to persevering ingenuity. In the present state of public opinion
  with regard to its practicability, it would be looked upon as an
  empty boast, were I to assert that the discovery is already made.


T. H. Pasley

T. H. Pasley in 1824, contributed an article to "Mechanics' Magazine,"
asserting the possibility of Perpetual Motion. The following excerpts
give the substance of his article:

  I feel no hesitation in standing up in support of this grand
  desideratum,--this almost forsaken friend of science,--whether
  the thing be practicable or not.

  On the contrary, "Persevere" should be every one's advice; to do
  so, or discontinue, every one's own pleasure. And why should the
  impossibility of anything be pronounced unless it be established
  wherein the limits of possibility consist?

  It is puerile in the extreme to be foretelling defeat when
  so many other objects may be gained by the highly laudable
  pursuit, perhaps of greater advantage to society at large than
  the discovery in question. * * * In a word, were the perpetual
  motion discovered tomorrow, it would be wise of all the
  governments of the world to offer a very high reward for some
  species of discovery that would be universally sought after,
  although it might never be found out. * * * The effects of
  industry are--enlargement of the mind, accumulation of knowledge,
  and rendering ourselves ignorant of the torments which idleness
  and dulness always engender. * * * In the next place, there
  are no solid grounds for the assertion that the discovery of
  a perpetual motion is an impossibility. In the present state
  of human knowledge respecting the powers of nature, it is not
  demonstrable one way or another. * * * The study of what relates
  to the perpetual motion has this great advantage, that it
  directs to the discovery of error as well as of truth; whereas,
  what are they which are called truths of science at present but
  vacillating human opinions, or erroneous assumptions of what
  we call natural causes? What are they but such as consist in
  mere assumption, sanctioned by time, and admitted by existing
  authorities in science, and of course generally acquiesced in,
  without previous investigation?

  So far, then, from being guided in our decision respecting what
  is possible by the "unerring laws of nature," by "mathematical
  demonstration," and by "experimental proofs," we are continually
  misled by an erroneous faith in the nonentity, attraction.

  On such an imperfect knowledge of the causes of phenomena, who
  should say he knows what can or what cannot be discovered?


Article From Pamphleteer

In the "Pamphleteer," published in London, the following by a
correspondent whose name we cannot give was published in March of 1822:

"A few words inducing towards the discovery of Perpetual Motion, perhaps
the actual discovery thereof:"

      London, March, 1822.

  What is meant by the term "Perpetual Motion?" Is it supposed
  that there is an undiscovered substance in the world, that will
  of itself perpetually move, with as little apparent cause as
  that which actuates the needle in becoming motionless in one
  particular position? Or, is it to be found in the combined
  reaction of mechanical powers?

  The first idea is stamped with a degree of probability, by the
  mystery of the needle; yet I imagine the latter is relied on
  with the greater confidence of mankind, and is the pith of the
  following few words:

  It is well known that the weight of a pendulum will almost regain
  the level from which it descended, losing a little space at every
  vibration, until it becomes motionless; if of itself it could
  exceed or even regain the level, doubtless it would become a
  perpetual motion.

  To find a power that will aid the motion of the pendulum, and
  in conjunction renew its strength, is what is wanted to create
  perpetual motion.

  What I shall endeavor to explain will at least induce towards the
  discovery of this power.

  The principal parts of the machinery about to be shown are in
  number three:

  A vibrating pendulum.

  A revolving pendulum, and

  A tubular lever.

  A vibrating pendulum in motion describes a segment of a circle,
  and returns on the same segment, and at every vibration its
  described segment decreases.

  A revolving pendulum is composed of two or more pendulums, united
  at their lighter extremities, there revolving on an axis, the
  heavier extremities being placed at equal distances in the outer
  circle: this, I believe, is what is termed a fly-wheel when
  affixed to hand-mills, etc.

  The tubular lever is the chief instigator of the whole, and must
  contain a weight apportioned to the weights of the two pendulums.

  Fix the lever on a cross axis; thus, on an axis within a circle,
  the circle on an axis at opposite angles, thereby is given to
  each extremity of the lever a revolving power of motion; attach
  one extremity of the lever to the outer circle of a revolving
  pendulum, the other extremity confine within the bar of the
  vibrating pendulum; thus combined, the effect to be produced when
  put in motion will be this:

  The two pendulums will guide the motion of the lever, which
  then partakes of the power of a pendulum, giving fresh impulse
  at every vibration of the pendulum, and every half revolution
  of the revolving pendulum; for, as each extremity of the lever
  rises, the weight within falls to the opposite extremity, and
  gives fresh impulse to the whole: thus (if my idea is correct)
  will be produced motion perpetual--that is to say, perpetual so
  long as the materials of which it is made will hold together. I
  have given this short description merely by way of example, as I
  believe there are several ways of combining these three powers,
  so as to produce perpetual motion, if my idea on the subject is
  correct.

  The lever may contain mercury or a solid orb of heavy substance;
  and if the tube be exhausted of air the weight will pass more
  freely, and certainly increase the power of the lever.


J. Welch

In 1825 the following article was published in "Mechanics' Magazine,"
having been contributed by J. Welch:

  Those who condemn the notion altogether seem to have taken but
  a very confined view of the subject. What they say about mere
  matter is right enough; but they seem to forget that there are
  other active agents in nature which possess wonderful powers,
  that have nothing to do with either bulk, weight, or form. Such
  are electricity, magnetic attraction, capillary attraction,
  and the irregular pressure of the atmosphere. The powers of
  electricity are great, and, indeed, it seems to be the _primum
  mobile_ that gives life and motion to the animated part of the
  creation. Dr. Franklin shows us how to give a circular coated
  plate, revolving on an axle, sufficient power to roast a chicken,
  merely by once changing (charging?) it. Could not a plate of this
  kind be made to turn a small electrical apparatus, so situated as
  to keep the charge in the plate always at its maximum? The whole
  might be kept dry by having it enclosed in a glass case.

  It has often been attempted to give motion to a wheel by the
  power of a loadstone, but hitherto without effect; no substance
  in nature being found to have the power, by interposition, of
  cutting off its attractive property. Still I think it should
  be further investigated. Is a small piece of steel in the form
  of a wedge as strongly attracted at the smaller end as at the
  thicker? And would not twenty or thirty pieces of steel, of that
  form, placed round the circumference of a circle, the point of
  one towards the head of the other, cause a magnet placed in the
  centre, to revolve in the direction in which their points lie? I
  think, perhaps not; but still such experiments should be tried.

  In capillary attraction we have a power that at once raises
  fluids above their level. It is this which carries the oil up
  the wick of a lamp as fast as the flame consumes it. Water and
  other fluids rise through cotton even quicker than oil; and he
  who can contrive to collect them as they arrive at the top will
  discover perpetual motion. Would not water run constantly through
  a siphon, one leg of which was made of a collection of capillary
  tubes, and the other in the usual way? or would the water above
  and below the tubes neutralize and destroy their power?

  I now come to the pressure of the atmosphere, a thing easily
  understood. * * * Make a cast-iron barometrical tube, with a top
  sufficiently large to contain 2 cwt. of mercury; invert it in a
  basin large enough to contain 2 or 3 cwt. more, and let a piece
  of iron of 10 or 12 stones weight float on the mercury in this
  basin, so as to rise and fall along with it at every change of
  the weather. We have here both motion and power. The motion,
  indeed, will sometimes stand still, but then it can easily be
  regulated, and made a constant quantity in the machine to be
  attached. I have no doubt but clocks, etc., may be made to derive
  their chiming principle from a contrivance of this nature.


Article From Mechanics' Magazine

In 1831, the following article was contributed by an unknown
correspondent to, and published in "Mechanics' Magazine":

    "Yes; we shall conquer! All those dangers past
    Will serve to enrich the future story."

  The application to the subject, on my part, has been accompanied
  by continual experimental elucidations of the subjects
  considered, and comparisons of these with the axioms, theorems,
  and demonstrations of one of the best authorities, if I may be
  allowed so to call my favorite author, Emerson, whose _I says_
  are generally correct.

  I disagree with Mr. B., and do trust that even a perpetual motion
  seeker might deserve encouragement, if it be found that such a
  character may exist in a person who is not so ignorant of first
  principles as Mr. B. supposes _all_ are who have this bias;
  especially if it be found that the person's researches have been
  connected with subjects of a more tangible nature, relating to
  the improvement of the useful arts, and particularly to some
  modern inventions of high importance that are not perfectly
  correct in their construction.

  In this article, Mr. B. advises those who are misspending their
  time in this pursuit, to consider the question in its most simple
  form, divested of more complicated operations, which simple form
  is that of a pulley accurately constructed so as to reduce the
  resistance to motion as much as possible. He says, "it will be
  found, as long as the weights are equal," there will be no motion
  produced, but wherever the weights are placed they will remain;
  and to produce vertical motion in the smallest degree, it will
  be necessary to add a weight to one of the former to create a
  preponderancy. This weight he calls the mechanical loss, and an
  insurmountable bar to perpetual motion, etc. We need not follow
  Mr. B. to his conclusion, as I think this insurmountable bar
  can be easily removed; and I shall be able to show that this
  equilibrium, for such it merely is, can be destroyed without
  adding to one of the weights, or absolutely taking from the
  other; though this may virtually be considered to be the case,
  inasmuch as we can at least produce an effect on the system as
  if the weight were reduced. Mr. B. says, under this arrangement,
  "wherever the weights are placed they will remain, unless an
  addition is made to one of them." We will therefore suppose the
  following diagram to represent the arrangement on a small scale,
  delicately constructed.

  [Illustration]

  A B are the two weights connected to each other by the string
  passing over the pulley, and being nicely equalized in their
  weight, here would, of course, be an equilibrium on the principle
  of the lever. But take a flat piece of wood, such as a ruler,
  and place it obliquely in a way so as not to interfere with
  the pulley _m_ in the direction _d_, and then bring the weight
  to impinge upon it in a way so as not to move the weight A
  _m_, C _d_, the least, or alter its position. What will be
  the consequence? Some would say, why, the weight A would then
  descend, and cause the weight B to ascend. But I should rather
  say, the reaction of the plane when acted on by the weight B,
  having destroyed the equilibrium of the forces, motion takes
  place. Now, if we attribute this motion to the reaction of the
  plane on the weight, though we will not go so far as to say
  motion is generated, yet if we say, by this simple arrangement
  the equilibrium is destroyed and motion takes place, the least
  we can admit is, that motion is communicated to the system, and
  that by the agency of part of the machine itself, the apparatus
  employed being considered as such. Then, why so much objection
  to the term self-moving machine in limited sense? But I will not
  dispute about words, which are but the images of things, and
  images may be strangely distorted by the medium through which
  they are received--of which distorting mediums, there is none
  equal to that of prejudice in favor of abstract notions--which
  notions perhaps, if rigidly examined, would be found to have no
  foundation in facts or in common sense.

  Another demonstrator of the impossibility of perpetual motion,
  is Mr. Mackinnon (see "Mechanical Magazine," Vol. 1, Page 363).
  As no doubt the different attempts to produce, or communicate,
  continued and perpetual motion, at least, such as are often
  brought forward by persons unacquainted with the science of
  mechanics, are generally to those who are acquainted with that
  science, if not absolutely ridiculous, yet of a nature to excite
  a smile at their futility: still there are a few (perhaps a
  very few) who entertain an opinion that such a thing is not
  impracticable, and who have, from practical experience as well
  as study, acquired a tolerable insight into the laws of nature
  (so far as relate to this subject); who in their turn cannot
  help smiling at the weak reasoning of some other would-be
  philosophers, who gravely give their dictum in the case. In
  this class I include Mr. Mackinnon, who very gravely goes to
  work to prove, etc., and flatters himself he shall, if rightly
  understood, help to prevent much future waste of time on the
  subject. He then goes on to give us his definition of inertia, by
  which he informs us that a body in a state of rest will remain so
  until it is moved (wonderful!)--that it cannot move itself--that
  it has not that power--and that no mechanical contrivance can
  give it that power. (How profound!)



SUMMARIZED TABLE OF CONTENTS


                                                                Page
  Introduction                                                     3

  Contents                                                       5-6

  Preface                                                       7-10

  Introductory Essay                                           11-21


  CHAPTER I--DEVICES BY MEANS OF WHEELS AND WEIGHTS--

    Wilars De Honecort; A Repetition of Wilars Honecort's
      plan; Leonardo da Vinci; A. Capra's Device; The Device
      of Dixon Vallance; Furman's Device; Schirrmeister's
      "Mechanical Movement;" James Ferguson's Device; B.
      Belidor's Device; Desagulier's Proposition on the
      Balance; John Haywood's Device; Explanation of the
      Failure of Wheels and Weights Devices to Accomplish
      Perpetual Motion                                         22-67


  CHAPTER II--DEVICES BY MEANS OF ROLLING WEIGHTS AND INCLINED
    PLANES--

    Device by Mercury in Inclined Glass Tube and Heavy Ball
      on Inclined Plane; Series of Inclined Planes; Devices
      by Oscillating Trough and Cannon Balls; Unpublished
      Inclined Plane and Weights Devices Noted by the Author   68-75


  CHAPTER III--HYDRAULIC AND HYDRO-MECHANICAL DEVICES--

    Enbon and Anderson's Pump; Device of "Ed. Vocis
      Rationis;" Böckler's Plates; John Linley's Hydraulic
      Device; Device of Author of the "Voice of Reason;" An
      Italian Device; P. Valentine Stansel's Device; Vogel's
      Device; A Water Wheel-Driven Pump; "A Journeyman
      Mechanic's" Device; James Black's Device; Archimedean
      Screw and Liquid; John Sims's Problem; A Perpetual
      Pump, by an Unknown Inventor; Explanation of the
      Failure of Hydraulic and Hydro-Mechanical Devices to
      Accomplish Perpetual Motion                             76-117


  CHAPTER IV--PNEUMATIC, SIPHON AND HYDRO-PNEUMATIC DEVICES--

    The Hydrostatical Paradox; Pickering's Device; Stuckey's
      Device; Prof. George Sinclair's Device; Jacob Brazill's
      Device; Läserson's Device; Von Rathen & Ellis' Device;
      Richard Varley's Device; Siphon and Funnel Device;
      Orchard's Vacuum Engine; Robert Copland's Device;
      Eaton's Perpetual Siphon; Legge's Hydro-Pneumatic
      Power Device; Waterblowing Machine; Device by Means of
      Buoyancy Through Media of Different Densities; Device
      by Compressible and Distensible Bags in Liquid; George
      Cunningham's Mercurial Pneumatic Device; Explanation of
      the Failure of Pneumatic, Siphon and Hydro-Pneumatic
      Devices to Accomplish Perpetual Motion                 118-162


  CHAPTER V--MAGNETIC DEVICES--

    A Magnetic Pendulum; Magnetic-Driven Wheel; Mackintosh's
      Experiment; Spence's Device; Joannis Theisneri's
      Semi-Circle; Device of Dr. Jacobus                     163-174


  CHAPTER VI--DEVICES UTILIZING CAPILLARY ATTRACTION AND PHYSICAL
    AFFINITY--

    Ludeke & Wilcken's Device; the Jurin Device; Sir William
      Congreve, Notice of; His Perpetual Motion Devices and
      Writings                                               175-194


  CHAPTER VII--LIQUID AIR AS A MEANS OF PERPETUAL MOTION--

    Liquefaction of Air; Explanation of Conservation of
      Energy Applied to; Perpetual Motion by Means of Liquid
      Air Pompously Heralded; Failure Explained              195-196


  CHAPTER VIII--RADIUM AND RADIO-ACTIVE SUBSTANCES CONSIDERED AS A
    CONCEIVED SOURCE OF PERPETUAL MOTION--

    Perpetual Emanation of Energy; Radium Clock by Lord
      Rayleigh (Hon. R. J. Strutt); Lord Rayleigh Not a
      Perpetual Motion Worker but Thoroughly Scientific      197-199


  CHAPTER IX--PERPETUAL MOTION DEVICES ATTEMPTING ITS ATTAINMENT BY
    A MISCONCEPTION OF THE RELATION OF MOMENTUM AND ENERGY--

    Works of Tyros Known to Author; Momentum Defined,
      Differentiated, Measured and Explained; Energy
      Defined, Differentiated, Measured and Explained;
      Explanation by Author of Common Misconception of the
      Relation of Momentum and Energy and Attempts to thus
      Realize Perpetual Motion; the Fallacy Explained by
      Illustrations of Energy Required for and Represented
      by Acceleration and Retardation of Velocity; Property
      of Numbers Relating to; Arithmetical Progression
      Illustration                                           200-211


  CHAPTER X--THE ALLEGED INVENTIONS OF EDWARD SOMMERSET, SIXTH EARL
    AND SECOND MARQUIS OF WORCESTER, AND OF JEAN ERNEST ELI-BESSLER
    (COUNCILLOR) ORFFYREUS--

    Intense Interest Caused by; Notice of Marquis of
      Worcester and Councillor Orffyreus and Periods in
      Which They Lived; Description by Marquis of Worcester
      of the Essentials of His Claimed Inventions; Excerpts
      From Remarks of Councillor Orffyreus on His Claimed
      Invention; Dedication by Councillor Orffyreus to God,
      the Public, to Men of Learning and to Himself as the
      Discoverer; Article Concerning the Orffyrean Wheel
      Published 1720 in Gentlemen's Magazine; Criticism by "A
      Constant Reader" of Attitude of W. Kenrick Concerning
      the Orffyrean Wheel; Article by Rev. J. T. Desagulier
      Concerning the Device of Marquis of Worcester and the
      Orffyrean Wheel; Excerpt from Dr. William Kenrick's
      Lecture on Perpetual Motion; De la Hire's Remarks
      Concerning Perpetual Motion; Letter from Prof. 's
      Gravesande to Sir Isaac Newton; Animadversions of Prof.
      Alliman on the Neglect of the Orffyrean inventions;
      Dr. Charles Hutton's Scientific Works and Notice of
      the Orffyrean Wheel; Remarks by the Author on the
      Historical Celebrity of These Inventions               212-255


  CHAPTER XI--CONSERVATION OF ENERGY. A DISCUSSION OF THE RELATION
    OF THE DOCTRINE OF CONSERVATION OF ENERGY, AND THE POSSIBILITY
    OF PERPETUAL MOTION--

    Statement of Doctrine of Conservation of Energy; Upon
      What Proof of Doctrine Rests; Not Mathematically
      Proved; Conforms to Natural Phenomena; Multiplied
      Illustrations; Inter-changeability and Convertibility
      of Heat with Mechanical and Other Forms of Energy;
      Explanation of Heat and Energy Units, and Their
      Relative Equivalents; British Thermal Unit, Foot-Pound
      and Horse-Power and Their Mutual Relationship
      Explained; Further Illustrations; Galileo's Famous
      Pendulum Experiment; Apparent Anticipation of the
      Principle of Conservation of Energy                    256-269


  CHAPTER XII--WILL PERPETUAL MOTION EVER BE ACCOMPLISHED?--

    The Antiquity of the Problem; Remarks by Dircks, Newton,
      Galileo, Huyghens and Descartes; Generalizations
      of; Remarks by Author Concerning the Possibility of
      Perpetual Motion. Comments from Other Sources:

      1 Denying the Possibility of Perpetual Motion,--Article
        by Dr. Papin; Article by Rev. John Wilkins; Article
        Based on Paradoxical Hydrostatical Balance; Article
        by P. Gregorio Fontana; Article by William Nicholson;
        Article Published in "The Artisan"; Article Published
        in "Mechanic's Magazine."

      2 Asserting the Possibility of Perpetual
        Motion,--Scriptural Argument; Article by John
        Bernoulli; Article by P. Christopher Scheiner;
        Article by T. H. Pasley; Article Published in "The
        Pamphleteer"; Article by J. Welch; Article Published
        in "Mechanic's Magazine"                             270-357



INDEX


                                                                    Page

  Air (See Liquid Air).

  "A Journeyman Mechanic's" Device,                                   99

  Allaman's Animadversions on the Neglect of Orffyreus's
      Inventions,                                                    239

  Anderson & Enbom's Pump,                                            76

  Archimedean Screw and Liquid, Device by Means of,                  104

  "Artisan, The," Article Published in,                              329


  Bags in Liquid, Compressible and Distensible, Device by Means of,  155

  Bellidor, B., His Account of Perpetual Motion Device,               46

  Bernoulli, John, Notice of,                                        336
    Arguments Supporting Possibility of Perpetual Motion,            336

  Black, James, His Device,                                          102

  Böckler, George Andrew, His Plates,                                 81

  Buoyancy Through Media of Different Densities,                     151

  Brewster, Sir David, Edited Lectures of James Ferguson,             44
    In Appendix to Ferguson's Lectures Gives Description of
        "Water-Blowing Machine",                                     148
    Is Attracted by Spence's Device, and Writes Letter Affording
        Description of Same,                                         170

  British Patents,                 58; 120; 121; 125; 127; 129; 132, 140

  British Thermal Unit Defined and Explained,                        264


  Cannon Balls and Oscillating Trough,                                71

  Capillary Attraction and Physical Affinity, Devices by Means of
      (See Table of Contents),                                         5

  Capra, A., His Device,                                              32

  Compressible and Distensible Bags in Liquid,                       155

  Congreve, Sir William, Notice of;
    His Perpetual Motion Devices,                                    182

  Conservation of Energy, Its Relation to Possibility of Perpetual
      Motion (See Table of Contents),                                  5
    Considered with Reference to Perpetual Motion,                   269
    Proof and Illustration of,                                       200
    Anticipated by Newton, Galileo, Huyghens and Descartes,          272

  Copland, Robert, His "Improved Method of Gaining Power",           140

  Cunningham, George, His "Mercurial Pneumatic Device",              157


  "Darius Green and His Flying Machine",                              16

  Desagulier, Rev. J. T., Proposition on the Balance,                 47
    Article of, Concerning the Device of Marquis of Worcester and
        the Orffyrean Wheel,                                         222

  Dircks, Henry, Title Page Mention,                                   3
    His Books Mentioned,                                               7
    Comments by Author on His Works,                                   8
    Information Furnished by, Rearranged,                              9
    His Classification of Devices,                                    19
    His "Life, Times and Scientific Labors of the Second Marquis of
        Worcester",                                                  213
    Excerpt from,                                                    228
    His Statement Concerning Arguments For and Against the
       Possibility of Perpetual Motion,                              270
    Arguments by Others For and Against the Possibility of Perpetual
        Motion, Published by Dircks, Copied in This Work,            274


  Eaton's Perpetual Siphon,                                          145

  "Ed. Vocis Rationis," His Device,                                   78

  Ellis, George Henry (See Rathen & Ellis).

  Energy (See Momentum and Energy).

  Energy, Conservation of (See Conservation of Energy).

  Energy and Heat Convertible and Commensurable,                     262

  Energy Defined, Explained and Distinguished from Momentum,         203

  Enbom and Anderson's Pump,                                          76

  Explanation by Author of Failure of Hydraulic and Hydro-Mechanical
        Devices,                                                     112
    of the Failure of Pneumatic, Siphon and Hydro-Pneumatic
        Devices,                                                     159
    of the Failure of Momentum and Energy Devices,                   206
    of Failure of Wheels and Weights Devices,                         61


  Failures (See Explanation of Failures).

  Ferguson, James; "Peasant Boy Philosopher," His Device,             43

  Fontana, P. Gregorio, Notice of; His Arguments on the
      Impossibility of Perpetual Motion,                             306

  Foot-Pound, Defined and Explained,                                 265

  Furman, George H., "A New and Improved Motor," U. S. Patent,        36


  Gallileo, His Pendulum Experiment,                                 267

  Gravesande, Prof. S., Letter to Sir Isaac Newton,                  236


  Haywood, John, His Device,                                          58

  Heat and Energy Convertible and Commensurable,                     261

  Helmholtz, Notice of,                                              258

  Honecort, Willars de, Account of His Device,                        22

  Horse-Power, Defined and Explained,                                264

  Hydro-Pneumatic Devices (See Table of Contents),                     5

  Hydrostatical Paradox,                                             118

  Hydrostatical Paradoxical Balance, Article on,                     305

  Hydraulic and Hydro-Pneumatic Devices (See Table of Contents),       5


  Inclined Planes and Rolling Weights (See Table of Contents),         5

  Inclined Planes and Weights Devices, Unpublished. Noted by the
      Author,                                                         73

  Inclined Planes, Series of,                                         69

  Italian Device, An,                                                 92

  Introductory Essay,                                                 11


  Jacobus, Dr., His Magnetic Device,                                 173

  Joule, Notice of,                                                  258

  Jurin's Device,                                                    176


  Kenrick, Dr. William, His Remarks Concerning the Inventions of the
      Marquis of Worcester and Councillor Orffyreus and Perpetual
      Motion in General,                                             228


  Langley, Prof. Samuel P., His Attempts and Labors at Heavier Than
      Air Flight,                                                     14

  Lardner, Ignatius, Attempts to Show Impossibility of Crossing Ocean
      With Steam Power,                                               14

  Leonardo da Vinci (See Vinci).

  Läserson, Louis Diodor, His "Improvements in Production of Motive
      Power",                                                        127

  Legge's Hydro-Pneumatic Power Device,                              146

  Linley, John, His Hydraulic Device,                                 87

  Liquid Air, as a Means of Perpetual Motion,                        195

  Lord Rayleigh (See Rayleigh).


  Mackintosh, F. S., Experiment by,                                  166

  Magnetic Devices (See Table of Contents),                            5

  Magnetic-Driven Wheel,                                             164

  Magnetic Pendulum,                                                 163

  Magnetic Semi-Circle,                                              172

  Mechanic, A Journeyman (See "A Journeyman Mechanic").

  Mechanics' Magazine, Article Published in,                    278, 353

  Media of Different Densities, Devices by Means of Buoyancy
      Through,                                                       151

  Mercurial Pneumatic Device (See Cunningham, George).

  Mercury, Inclined Glass Tube and Ball,                              68

  Momentum, Defined, Explained and Distinguished from Energy,        201

  Momentum and Energy, Account and Explanation of Perpetual Motion
      Devices by Means of,                                           205

  Momentum and Energy, Distinguished and Considered; Attempted
      Devices for Perpetual Motion by Means of (See Table of
      Contents),                                                       5

  Munro, R., Comments on Mackintosh's Experiment,                    169


  Newcomb, Simeon, Notice of,                                         15

  Newton, Sir Isaac, Mention of,                                135, 220
      Letter to from Prof. 's Gravesande,                            236

  Nicholson, William, Notice of,                                     315
    His Article Against the Possibility of Perpetual Motion,         316


  Orchard's Vacuum Engine,                                           137

  Orffyreus, Jean Ernest Eli Bessler (Councillor), His Perpetual
      Motion Labors (See Table of Contents),                           5
    Remarks of Author Concerning Claims of,                          252


  Papin, Dr., Argument by Against the Possibility of Perpetual
      Motion,                                                        275

  Pasley, T. H., Article by,                                         347

  "Pamphleteer, The," Article Published in,                          349

  Paradox, Hydrostatical,                                            118

  Patents, U. S. (See U. S. Patents); Patents, British (See British
      Patents).

  "Peasant Boy Philosopher" (See Ferguson, James).

  Pendulum, Gallileo's Experiment with,                              268

  Perpetual Motion Defined,                                           11

  Perpetual Pump,                                                    109

  Perpetual Motion, Its Possibility Considered with Reference to
      Conservation of Energy,                                        269

  Perpetual Motion, Consideration of Its Possibility,                270
    Arguments Against Its Possibility--Article by Dr. Papin,         275
    Article by Rev. John Wilkins,                                    281
    Article Based on Paradoxical Hydrostatical Balance,              305
    Article by P. Gregorio Fontana,                                  306
    Article by William Nicholson,                                    316
    Article Published in "The Artisan,"                              329
    Article Published in "Mechanic's Magazine,"                      278

    Arguments Maintaining Its Possibility--Scriptural Arguments,     335
    Article by John Bernoulli,                                       336
    Article by P. Christopher Scheiner,                              342
    Article by T. H. Pasley,                                         347
    Article Published in "The Pamphleteer,"                          349
    Article by J. Welch,                                             351
    Article Published in "Mechanic's Magazine,"                      353

  Physical Affinity and Capillary Attraction, as a Means of Perpetual
      Motion (See Table of Contents),                                  5

  Pickering, Peter, His "Atmospheric Engine",                        120

  Pneumatic Devices (See Table of Contents),                           5

  Preface,                                                             7

  Proposition on the Balance (See Desagulier, Rev. J. T.)


  Radium and Radio-Active Substances as a Means of Perpetual Motion
      (See Table of Contents),                                         5

  Rayleigh, Lord, His Radium Clock, Notice of,                  197, 199

  Rangley's Patent Roller Pump, Adaptation of,                        97

  Rathen and Ellis's Device,                                         129

  Rationis, Ed. Vocis (See "Ed. Vocis Rationis").

  Rolling Weights and Inclined Planes as a Means of Perpetual Motion
      (See Table of Contents),                                         5

  Scheiner, P. Christopher, Notice of; Argument by Supporting
      Possibility of Perpetual Motion,                               342

  Schirrmeister, Charles, His "Mechanical Movement",                  38

  Schott, Gaspar, Mention of in Connection with Perpetual
      Motion,                                                   172, 173

  Scriptural Argument,                                               335

  Self-Motive Power Defined,                                          11

  Semi-Circle, Magnetic,                                             172

  Siphon Device for Perpetual Motion (See Table of Contents).

  Sims, John, His Perpetual Motion Problem,                          106

  Sinclair, Prof. George, His Pneumatic Device,                      124

  Siphon, Eaton's Perpetual,                                         145

  Siphon and Funnel Device,                                          135

  Sleigh, Burrowes, Willcocks Arthur, His Perpetual Motion Labors,   111

  Sleigh, William Willcocks, His Perpetual Motion Labors,            110

  Sommerset, Edward (Marquis of Worcester) (See Table of Contents),    5

  Spence, John, Notice of; His Magnetic Device,                      170

  Stansel, P. Valentine, Device of,                                   95

  Strutt, Hon. R. J. (See Rayleigh).

  Stuckey, William Henry, His "Pneumatic Engine",                    121


  Theisneri, Joannis, His Magnetic Semi-Circle,                      172

  Trough, Oscillating and Cannon Balls,                               71


  U. S. Patents,                                              36, 38, 76


  Vacuum Engine, Orchard's,                                          137

  Vallance, Dixon, His Device,                                        34

  Varley, Richard, His "New Perpetual Moving Power",                 132

  Vinci, Leonardo da, Notice of,                                      27
    His Perpetual Motion Labors,                                  29, 32

  "Voice of Reason," Device by Author of,                             88

  Vogel, A. F., His "Hydrostatic General Mobile",                     96


  Water Blowing Machine,                                             147

  Water-Wheel Driven Pump,                                            97

  Welch, J., Article by,                                             351

  Wheel, Magnetic Driven (See Magnetic-Driven Wheel).

  Wheels and Weights Devices (See Table of Contents),                  5

  Wilckens (See Ludeke and Wilckens).

  Wilkins, Rev. John, Argument Denying Possibility of Perpetual
      Motion,                                                        281

  Worcester, Marquis of (Edward Sommerset) (See Sommerset).


  X-Ray Machine, Notice of,                                           16



Transcribers' Notes:


In Unicode and HTML versions of this eBook, Greek words are shown in
Greek and then in Transcribers' English transliterations that are
enclosed in {curly braces}. Only the transliterations are shown in
Latin-1 and ASCII versions of this eBook. Individual Greek letters used
in equations and lists are shown either as actual Greek letters or in
similar Latin characters, depending on the version of this eBook. Also
see later note about alchemy symbols.

Accent mark errors in Greek text have been remedied.

Inconsistent spelling and punctuation have been retained, as this book
quotes many sources.

Simple typographical errors were corrected.

Ambiguous hyphens at the ends of lines were retained.

The original book copied illustrations from various sources and did
not change the Figure numbers. This eBook retains those original
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Text usually spells "Galileo" as "Gallileo"; both forms have been
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Mathematical equations have been expressed here in linear form.
Accuracy of their transcriptions is questionable. Multiplication was
indicated in various ways and has not been changed or standardized.

Page 73: "phraseology" was printed as "praseology".

Page 76: "1882" was printed as "182".

Page 222: "misspent" was printed as "mispent".

Page 229: "perseverance" was printed as "perserverance".

Page 220 and others: "'s Gravesande" was the person's name.

Page 241: Removed unmatched double quote mark following "it only turns
one way."

Page 252: Removed unmatched double quote mark following "should be
undeceived."

Page 268: "horizontal from which" was printed as "form".

Page 284: ☿ is the alchemy symbol for Mercury; ♃ is the alchemy symbol
for tin (and for Jupiter).

Page 288: "attracted" was printed as "attraced".

Page 313: The _p_ near the end of the equation shortly before "the
distance of the" appeared to be only partly printed and may be a
different symbol.

Page 326: "preponderate" was printed as "perponderate".





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