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Title: Physics
Author: Cope, Thomas Darlington, 1880-1964, Turton, Charles Mark, 1861-1937, Tower, Willis Eugene, 1871-, Smith, Charles Henry, 1861-1926
Language: English
As this book started as an ASCII text book there are no pictures available.
*** Start of this LibraryBlog Digital Book "Physics" ***
PHYSICS
TOWER, SMITH, TURTON,
AND
COPE
[Illustration: (_See p.441_)
THREE-COLOR PRINTING
_Y._ Yellow impression; negative made through a blue-violet filter. _R._
Crimson impression; negative made through a green filter. _RY._ Crimson
on yellow. _B._ Blue impression; negative made through a red filter.
_YRB._ Yellow, crimson, and blue combined; the final product. (Courtesy
of Phototype Engraving Co., Philadelphia.)]
PHYSICS
BY
WILLIS E. TOWER, M. SCI. (Univ. of Illinois)
HEAD OF THE DEPARTMENT OF PHYSICS, ENGLEWOOD
HIGH SCHOOL, CHICAGO
CHARLES H. SMITH, M. E. (Cornell)
HEAD OF THE DEPARTMENT OF PHYSICS AND ASSISTANT
PRINCIPAL, HYDE PARK SCHOOL, CHICAGO
CHARLES M. TURTON, A. M. (Syracuse)
HEAD OF THE DEPARTMENT OF PHYSICS, BOWEN
HIGH SCHOOL, CHICAGO
IN COLLABORATION WITH
THOMAS D. COPE, Ph.D. (Pennsylvania)
ASSISTANT PROFESSOR OF PHYSICS, UNIVERSITY
OF PENNSYLVANIA
BASED UPON
PRINCIPLES OF PHYSICS
BY
TOWER, SMITH and TURTON
WITH 7 PLATES AND 448 OTHER ILLUSTRATIONS
PHILADELPHIA
P. BLAKISTON'S SON & CO.
1012 WALNUT STREET
COPYRIGHT, 1920, BY P. BLAKISTON'S SON & CO.
PREFACE
In the preparation of this text, the _pupil_, his experience, needs, and
interests have been constantly kept in mind. The order of topics,
illustrations, and problems have been selected with the purpose of
leading the _pupil_ into a clear understanding of the physical phenomena
continually taking place about him.
The recommendations and conclusions reached by the "New Movement in the
Teaching of Physics" have been incorporated into the book as a whole.
These conclusions indicate that the most efficient teaching in physics
involves a departure from the quantitative, mathematical methods of
presentation that were in general use a dozen or more years ago, toward
a method better adapted to the capabilities, interests, and requirements
of the young people in our physics classes.
The older methods are effective with a portion of the student body which
has the greater mathematical ability and training, but they discourage a
large majority of the pupils who are not gifted or prepared for severe
mathematical analysis. For this reason, many of the more difficult
mathematical demonstrations often given in physics texts are omitted.
Most of the problems involve only the units employed in practical
every-day measurements.
The portions of Mechanics that are ordinarily so difficult for the
average pupil are not taken up until he has covered considerable ground
with which he is more or less familiar and not until he has become
somewhat accustomed to the methods of study and the technical terms of
the subject.
The pupil comes to the study of physics with a great number of
experiences and impressions of physical phenomena continually occurring
about him. In recognition of this fact, it has been thought best to
consider first the explanation of common things well known to all
pupils, such as the diffusion of gases, evaporation of liquids,
expansion of bodies when heated, and capillary action. Since the
molecular theory of matter is now supported by so many conclusive
evidences, we have not hesitated to make free use of it in the early
chapters. The applications of this theory are extremely helpful in
explaining every-day phenomena. Our experience shows that beginners in
physics understand and apply this theory without difficulty.
The illustrations and drawings have been selected from a pedagogical
rather than a spectacular point of view. Practically all of them are
new. The problems and exercises have been selected for the distinct
purpose of illustrating the principles taught in the text and for their
practical applications.
Many direct applications to common every-day experiences are given in
order to connect the subject matter with the home environment and daily
observation of physical phenomena. Some phenomena are mentioned without
detailed explanation as it is felt that the presentation of these
subjects in this manner is better for this grade of student than a
complete analysis.
Some of the special features of the text may be briefly summarized as
follows:
(A) _Simplicity of presentation_ is emphasized. The methods of attack,
the illustrations and examples employed in developing the subjects are
particularly adapted to beginners in physics.
(B) The text is divided into some _seventy-seven sections_, each
containing material enough for one recitation.
(C) Each of these sections is summarized by a list of _important topics_
which point out to the pupil the principles and subject matter requiring
most careful attention. The lists of important topics are also of
assistance to the teacher in assigning recitations.
(D) The _problems and practical exercises_ emphasize physical principles
as distinguished from mathematical training. A list of exercises is
placed at the end of the several sections. They are in sufficient number
to permit testing at many points and of a choice of problems by
teachers.
The authors wish to express their appreciation for suggestions and
helpful criticisms to many who have read the text in manuscript or
proof. Especially to Professor A. P. Carman of the University of
Illinois and his associate, Professor F. R. Watson, who have gone
carefully over the whole text; and to Mr. Chas. M. Brunson, Scott High
School, Toledo, Ohio, Mr. Frank E. Goodell, North High School, Des
Moines, Iowa, and to Mr. Walter R. Ahrens, Englewood High School,
Chicago, for assistance in reading the proofs. Also to Mr. W. H.
Collins, Jr., Bowen High School, Chicago, who supervised the preparation
of drawings for the diagrams and figures; and to many firms and
individuals that have courteously furnished material for illustrations.
WILLIS E. TOWER.
CHARLES H. SMITH.
CHARLES M. TURTON.
ON THE STUDY OF PHYSICS
When a pupil begins the study of Physics he has in his possession many
bits of knowledge which are fundamental in the science. He has learned
to throw a ball and can tell how a thrown ball moves. He has drawn out
nails with a claw hammer. He has seen wood float and iron sink. He has
sucked liquids up through straws. In his mother's kitchen, he sees water
as ice, liquid, and steam. On a wintry day he reads the temperature on a
thermometer. He sees sparks fly from car wheels when the brakes are
applied. He has played with a horseshoe magnet, and has found the north
by means of a compass. The telephone, the electric light and the motor
he sees, and perhaps uses, many times a day. He dresses before a mirror,
focuses his camera, watches the images at a moving picture show, and
admires the colors of the rainbow. He has cast stones into water to
watch the ripples spread, has shouted to hear the echo, and perhaps
plays some musical instrument. These, and a thousand other things, are
known to the intelligent and normal boy or girl who has reached the age
at which the study of Physics is properly begun.
To a great extent even the terms used in the science are familiar to the
beginner. He speaks of the horse-power of an engine, reads
kilowatt-hours from the meter in the cellar, and may know that
illuminating gas costs one dollar per thousand "cubic feet." "Ampere"
and "volt" are words he frequently hears and sees.
When he takes up the study of Physics, the attitude of the student
toward these familiar things and words must undergo a change. Casual
information about them must be changed to sound knowledge, purposely
acquired. Hazy notions about the meanings of words must be replaced by
exact definitions. Bits of knowledge must be built into a structure in
which each fact finds its proper place in relation to the others.
The only agent which can accomplish these changes is the student
himself. He must consciously and purposely seek the truth and must
reflect upon it until he sees it in its relation to other truth. Upon
him, and upon him alone, rests the final responsibility for the success
or failure of his study.
But the student is not without assistance. In his teacher he finds a
guide to stimulate, to direct, and to aid his efforts, and a critic to
point out wherein his efforts have failed and wherein they have
succeeded. Weights, measures, and other apparatus are furnished to
enable him to answer for himself questions which have arisen in his
studies.
In addition to these the student has his text book, his teacher for his
hours of private study. A good text book is an inspiring teacher in
print. It directs attention to things familiar to the student through
long experience, and inspires him to make a closer scrutiny of them. It
invites him to observe, to analyze, to compare, to discover likenesses
and differences in behavior. It questions him at every turn. Its ever
repeated challenge reads, "Weigh and consider." It furnishes him needed
information that he cannot otherwise acquire. It satisfies his desire to
know, "By whom, where, when, and how was this first discovered?"
The student of Physics must never forget that he is studying not pages
of text but the behavior and properties of iron, water, mica, moving
balls, pumps, boiling liquids, compressed air, mirrors, steam engines,
magnets, dynamos, violins, flutes, and a host of other things. His
studies should, whenever possible, be made first hand upon the things
themselves. The text is an aid to study, never a substitute for the
thing studied.
It is an excellent plan for each student to select some one thing for
special study, the telephone for example. By observation, experiment,
and reading, he may acquire a large amount of valuable information about
such a subject while pursuing his course in Physics. Every part of the
science will be found to bear some relation to it.
The student who takes up the study of Physics in the way suggested will
find himself at the end of a year of study in possession of much new and
valuable knowledge about the physical world in which he lives. By virtue
of this knowledge he will be better able to enjoy the world, to control
it, and to use it.
THOMAS D. COPE.
PHILADELPHIA.
CONTENTS
CHAPTER I. INTRODUCTION AND MEASUREMENT. PAGE
(1) Introduction 1
(2) States of Matter 4
(3) The Metric System 8
CHAPTER II. MOLECULAR FORCES AND MOTIONS.
(1) Molecular Motions in Gases 13
(2) Molecular Motions in Liquids 18
(3) Molecular Forces in Liquids 21
(4) Molecular Forces in Liquids and Solids 27
(5) Molecular Forces in Solids 31
CHAPTER III. MECHANICS OR LIQUIDS.
(1) Liquid Pressure 36
(2) Transmission of Liquid Pressure 41
(3) Archimedes' Principle 47
(4) Density and Specific Gravity 52
CHAPTER IV. MECHANICS OF GASES.
(1) Weight and Pressure of the Air 55
(2) Compressibility and Expansibility of the Air 62
(3) Pneumatic Appliances 66
CHAPTER V. FORCE AND MOTION.
(1) Force, how Measured and Represented 79
(2) Motion. Newton's Laws 85
(3) Resolution of Forces 96
(4) Moment of Force and Parallel Forces 99
(5) Gravitation and Gravity 103
(6) Falling Bodies 109
(7) The Pendulum 115
CHAPTER VI. WORK AND ENERGY.
(1) Work and Energy 119
(2) Power and Energy 123
(3) The Lever and Simple Machines 129
(4) Wheel and Axle and Pulley 136
(5) Efficiency and the Inclined Plane 142
(6) Friction and its Uses 147
(7) Water Power 152
CHAPTER VII. HEAT, ITS PRODUCTION AND TRANSMISSION.
(1) Sources and Effects of Heat 159
(2) Temperature and Expansion 162
(3) Expansion of Gases, Liquids and Solids 167
(4) Modes of Transmitting Heat 173
(5) Convection, Heating and Ventilation 179
(6) The Moisture in the Air, Hygrometry 191
(7) Evaporation 196
CHAPTER VIII. HEAT AND WORK.
(1) Heat Measurement and Specific Heat 200
(2) Heat and Changes of State 205
(3) Heat and Work 212
(4) Heat Engines 222
CHAPTER IX. MAGNETISM.
(1) General Properties of Magnets 228
(2) Theory of Magnetism, Magnetic Fields 232
(3) The Earth's Magnetism 238
CHAPTER XI. STATIC ELECTRICITY.
(1) Electrification and Electrical Charges 243
(2) Electric Fields and Electrostatic Induction 247
(3) Electric Theories, Distribution and Electric Charges 252
(4) Potential, Capacity, and the Electric Condenser 257
(5) Electrostatic Generators 262
CHAPTER XI. ELECTRIC CURRENTS PRODUCED BY VOLTAIC
CELLS.
(1) Electrical Currents and Circuits 267
(2) The Simple Voltaic Cell and its Action 270
(3) Practical Voltaic Cells 274
CHAPTER XII. MAGNETIC EFFECTS OF ELECTRIC CURRENTS,
AND ELECTRICAL MEASUREMENTS.
(1) The Magnetic Effect of Electric Currents 279
(2) Electrical Measurements 289
(3) Ohm's Law and Electrical Circuits 298
(4) Grouping of Cells and Measuring Resistance 302
CHAPTER XIII. CHEMICAL AND HEAT EFFECTS OF ELECTRIC
CURRENTS.
(1) The Chemical Effect of Electric Currents 307
(2) The Storage Battery and Electric Power 312
(3) The Heat Effect of Electric Currents 318
CHAPTER XIV. INDUCED CURRENTS.
(1) Electromagnetic Induction 326
(2) The Dynamo and the Motor 335
(3) The Induction Coil and the Transformer 343
(4) The Telephone 349
CHAPTER XV. SOUND.
(1) Sound, Source, Speed, Media 354
(2) Waves and Wave Motion 357
(3) Intensity and Pitch of Sound 363
(4) Musical Scales and Resonance 368
(5) Interference, Beats, Vibration of Strings 374
(6) Tone Quality, Vibrating Plates and Air Columns 384
CHAPTER XVI. LIGHT.
(1) Rectilinear Propagation of Light 388
(2) Photometry and Law of Reflection 393
(3) Mirrors and Formation of Images 400
(4) Refraction of Light 410
(5) The Formation of Images by Lenses 416
(6) Optical Instruments 423
(7) Color and Spectra 430
(8) Nature of Light 442
CHAPTER XVII. INVISIBLE RADIATIONS.
(1) Electric waves and Radioactivity 448
CHAPTER XVIII. WIRELESS TELEPHONY AND ALTERNATING
CURRENTS.
(1) Wireless Telephony 460
(2) Alternating Currents 466
INDEX 487
PHYSICS
CHAPTER I
INTRODUCTION AND MEASUREMENT
(1) INTRODUCTION
=1. Physics, an Explanation of Common Things.=--Many students take up
the study of physics expecting to see wonderful experiments with the "X"
rays, wireless telegraphy, dynamos, and other interesting devices.
Others are dreading to begin a study that to them seems strange and
difficult, because they fear it deals with ideas and principles that are
beyond their experience and hard to comprehend.
Each of these classes is surprised to learn that _physics is mainly an
explanation of common things_. It is a study that systematizes our
knowledge of the forces and changes about us; such as the pull of the
earth, the formation of dew, rain and frost, water pressure and pumps,
echoes and music, thermometers and engines, and many other things about
us with which people are more or less familiar. Physics is like other
school subjects, such as mathematics and language, in having its own
peculiar vocabulary and methods of study; these will be acquired as
progress is made in the course.
The most useful habit that the student of physics can form is that of
connecting or relating each _new idea_ or _fact_ that is presented to
him to _some observation_ or _experience_ that will illustrate the new
idea. This relating or connecting of the new ideas to one's own personal
experience is not only one of the best known means of cultivating the
memory and power of association, but it is of especial help in a subject
such as physics, which deals with the systematic study and explanation
of the facts of our every-day experience.
=2. Knowledge--Common and Scientific.=--This leads to the distinction
between _common knowledge and scientific knowledge_. We all possess
common knowledge of the things about us, gained from the impressions
received by our senses, from reading, and from the remarks of others.
_Scientific_ knowledge is attained when the bits of common knowledge are
connected and explained by other information gained through study or
experience. That is, common knowledge becomes scientific, when it is
_organized_. This leads to the definition: _Science is organized
knowledge_.
Common knowledge of the forces and objects about us becomes scientific
only as we are able to make accurate measurements of these. That is,
science is concerned not only in _how_ things work, but even more in
_how much_ is involved or results from a given activity. For example, a
scientific farmer must be able to compute his costs and results in order
to determine accurately his net profits. The business man who is
conducting his business with efficiency knows accurately his costs of
production and distribution.
This book is written in the hope that it will make more scientific the
student's common knowledge of the forces and changes in the world about
him and will give him many ideas and principles that will help him to
acquire the habit of looking from effects to their natural causes and
thus tend to develop what is called the _scientific habit of thought_.
=3. Hypothesis, Theory, and Law.=--Three words that are frequently used
in science may be mentioned here: _hypothesis_, _theory_, and _law_. An
hypothesis is a supposition advanced to explain some effect, change, or
condition that has been observed. For example, the Nebular Hypothesis of
which many high-school students have heard, is an attempt to explain the
origin of the sun, the earth, the planets, and other solar systems.
A theory is an hypothesis which has been tested in a variety of ways and
which seems to fit the conditions and results so that it is generally
accepted as giving a satisfactory explanation of the matter in question.
The Molecular Theory of Matter which states that matter of all kinds is
composed of very small particles called molecules (see Art. 6), is a
familiar example of a theory.
A theory becomes a law when it may be definitely proved. Many laws are
expressed in mathematical language, e.g., the law of gravitation. (See
Art. 88.) Many of the laws of physics are illustrated by laboratory
experiments, which show in a simple way just what the law means.
Exercises
Explain what is meant by the following terms and expressions:
1. Common knowledge.
2. Scientific knowledge.
3. Science.
4. Topics in physics.
5. Scientific habit of thought.
6. Value of relating new ideas to former experiences.
7. Hypothesis.
8. Theory.
9. Law.
(2) THE STATES OF MATTER
=4. Physics Defined.=--In the study of any science or field of
knowledge, it is helpful to have a basis for grouping or classifying the
facts studied. In physics we are to study the objects, forces, and
changes about us, to understand them and their relations to one another.
Accordingly, physics, dealing with the material world about us, is often
defined as _the science of matter and energy_, _matter_ being _anything
that occupies space_ and _energy_ the _capacity for doing work_. This
definition of physics while not strictly accurate is sufficiently
comprehensive for our present purpose.
=5. The Three States of Matter.=--Our bodies are _matter_ since they
occupy space. Further, they possess _energy_ since they are able to do
work. In beginning the study of physics it will simplify our work if we
study one of these topics before the other. We will therefore begin with
matter and consider first its three states.
Some bodies are _solid_; as ice, iron, wax. Others are _liquid_; as
water, mercury, oil. Still others are in the state of _gas_; as steam,
air, and illuminating gas. Further we notice that the same substance may
be found in any one of the three states. For example water may be either
ice, water or steam; that is, either a solid, a liquid, or a gas.
Most persons have heard of _liquid air_ and possibly some know of _ice
air_, _i.e._, air cooled until it not only liquefies, but is solidified.
On the other hand, iron may be melted and, if heated hot enough, may be
turned into iron vapor. In fact most substances by heating or cooling
sufficiently may be changed into any one of the three states.
Before defining the three states, let us consider the _structure_ of
matter. This may help us to answer the question: How is it possible to
change a hard solid, such as ice, into a liquid, water, and then into
an invisible gas like steam? This is explained by the molecular theory
of matter.
=6. The Molecular Theory of Matter.=--It is believed that all bodies are
made up of very small particles called _molecules_, and that these
instead of being packed tightly together like square packages in a box,
are, strange as it may seem, very loosely packed even in solids and do
not _permanently_ touch their neighbors. The size of these molecules is
so minute that it has been estimated that if a drop of water could be
magnified to the size of the earth, the molecules magnified in the same
proportion would be in size between a baseball and a football. The air
and all other gases are believed to be made up of molecules in _rapid
motion_, striking and rebounding continually from one another and from
any objects in contact with the gas.
=7. States of Matter Defined.=--These ideas of the structure of matter
assist us in understanding the following definitions: _A solid is that
state of matter in which the molecules strongly cling together and tend
to keep the same relative positions_. (This of course follows from the
tendency of a solid to retain a definite form.) _A liquid is that state
of matter in which the molecules tend to cling together, yet move about
freely._ Hence a liquid takes the form of any vessel in which it is
placed. _A gas is that state of matter in which the molecules move about
freely and tend to separate indefinitely._ Hence a gas will fill any
space in which it is placed.
=8. Effect of Heat on Matter.=--It is further believed that when a body
is heated, that the action really consists in making its molecules move
or vibrate faster and faster as the heating progresses. This increase of
motion causes the molecules to push apart from one another and this
separation of the molecules causes an expansion of the body whether it
be solid, liquid, or gas. Fig. 1 shows the expansion of air in an air
thermometer. Fig. 2 shows the expansion of a solid on heating.
[Illustration: FIG. 1.--When the bulb is heated, the air within expands
forcing down the water in the tube.]
=9. Physical and Chemical Changes.= A change of state such as the
freezing or boiling of water is called a _physical_ change, for this
change has not affected the identity of the substance. It is water even
though it has become solid or gaseous. Heating a platinum wire red hot
is also a physical change for the wire when on cooling is found to be
the same substance as before. Further if salt or sugar be dissolved in
water the act of _solution_ is also a physical change since the
identical substance (salt or sugar) is in the solution and may be
obtained by evaporating the water.
[Illustration: FIG. 2 (_a_) represents a straight bar made of a strip of
brass and a strip of iron riveted together and attached to a handle.
Upon heating the compound bar in a gas flame, the brass expands faster
than the iron causing the bar to bend toward the latter as in Fig. 2
(_b_).]
If some sugar, however, is heated strongly, say in a test-tube, it is
found to blacken, some water is driven off and on cooling _some black
charcoal is found in the tube instead of the sugar_. This action which
has resulted in a _change in the nature of the substance_ treated is
called a _chemical_ change. To illustrate further, if some magnesium
wire is heated strongly in a flame, it burns, giving off an intense
light and when it cools one finds it changed to a light powdery
substance like ashes. Chemical changes, or those that change the nature
of the substance affected, are studied in _chemistry_. In _physics_ we
have to do only with physical changes, that is, with those changes that
do not affect the nature of the substance.
Important Topics
1. Physics defined.
2. The three states of matter; solid, liquid, gas.
3. Molecular theory of matter.
4. Physical and chemical changes.
Exercises
Write out in your own words your understanding of:
1. The structure of matter.
2. Some of the differences between solids, liquids, and gases.
3. How to change solids to liquids and gases and _vice versa_.
4. The reason for the changes of size of a body on heating.
5. Why cooling a gas tends to change it to a liquid or a solid.
6. The actual size of molecules.
Which of the following changes are chemical and which physical?
Give reasons.
1. Melting of ice.
2. Burning of a candle.
3. Production of steam.
4. Falling of a weight.
5. Drying of clothes.
6. Making an iron casting.
7. Decay of vegetables.
8. Sprouting of seeds.
9. Flying an aeroplane.
10. Growth of a plant.
11. Grinding of grain.
12. Sawing a board.
13. Pulverizing stone.
14. Making toast.
15. Sweetening tea or coffee with sugar.
16. Burning wood or gas.
(3) THE METRIC SYSTEM
=10. The Metric System.=--In order to study the three states of matter
with sufficient exactness it is necessary to employ a system of
measurement. The system universally employed by scientists is called
_The Metric System_. In many respects it is the most convenient for all
purposes. Every student should therefore become familiar with it and
learn to use it. At the present time, not only do scientists everywhere
use it, but many countries have adopted it and use it in common
measurements. It was legalized in the United States in 1866. The metric
system was originated by the French Academy of Sciences during the
latter part of the 18th century. There were so many different systems of
weights and measures in use, each country having a system of its own,
that commerce was much hindered. It was therefore decided to make a
system based upon scientific principles. The length of the earth's
quadrant passing from the equator to the pole was determined by
surveying and computation. One-ten-millionth of this distance was
selected as the unit of length and called a _meter_. Accurate copies of
this meter were made and preserved as standards.
Later surveys have shown that the original determination of the earth's
quadrant was not strictly accurate; so that after all the meter is not
exactly one-ten-millionth of the earth's quadrant.
=11. The Standard Meter.=--The standard unit of _length_ in the metric
system is the _meter_. It is the distance, at the temperature of melting
ice, between two transverse parallel lines ruled on a bar of platinum
(see Fig. 3), which is kept in the Palace of the Archives in Paris.
Accurate copies of this and other metric standards are also kept at the
Bureau of Standards at Washington, D. C. Fig. 4 shows the relation
between the inch and the centimeter (one-hundredth of a meter).
=12. Units and Tables in the Metric System.=--The metric unit of _area_
commonly used in physics is the _square centimeter_.
[Illustration: FIG. 3--The standard meter.]
The standard unit of _volume_ or capacity is the _liter_. It is a cube
one-tenth of a meter on each edge. It is equal to 1.057 quarts. It
corresponds, therefore, to the quart in English measure.
[Illustration: FIG. 4.--Centimeter and inch scales.]
The standard unit of _mass_ is the _kilogram_. It is the mass of 1 liter
of pure water at the temperature of its greatest density, 4°C. or
39.2°F.
The three principal units of the metric system, the _meter_, the
_liter_, and the _kilogram_, are related to one another in a simple
manner, since the liter is a cube one-tenth of a meter in each dimension
and the kilogram is the mass of a liter of water. (See Fig. 5.)
The metric system is a _decimal_ system that is, one unit is related to
another unit in the ratio of _ten_ or of some power of ten. This is
indicated by the following tables:
_Metric Table of Length_
10 millimeters (mm.) equal 1 centimeter.
10 centimeters (cm.) equal 1 decimeter.
10 decimeters (dm.) equal 1 meter.
10 meters (m.) equal 1 dekameter.
10 dekameters (Dm.) equal 1 hectometer.
10 hectometers (hm.) equal 1 kilometer.
10 kilometers (km.) equal 1 myriameter.
The measures commonly used are the _centimeter_, _meter_ and
_kilometer_.
_Metric Table of Mass_ (_or Weight_)
10 milligrams (mg.) equal 1 centigram.
10 centigrams (cg.) equal 1 decigram.
10 decigrams (dg.) equal 1 gram.
10 grams (g.) equal 1 dekagram.
10 dekagrams (Dg.) equal 1 hectogram.
10 hectograms (hg.) equal 1 kilogram.
10 kilograms (kg.) equal 1 myriagram.
The masses commonly used are the _milligram_, _gram_ and _kilogram_.
Notice in these tables the similarity to 10 mills equal 1 cent, 10 cents
equal 1 dime, 10 dimes equal 1 dollar, in the table of United States
money.
Other tables in the metric system are built upon the same plan. Learn
the prefixes in order thus: milli, centi, deci, deka, hecto, kilo,
myria. The first three prefixes are Latin numerals and represent
divisions of the unit. The last four are Greek numerals and represent
multiples. In these tables, milli means 1/1000, centi means 1/100, deci
means 1/10, deka means 10, hecto, 100, kilo, 1000, myria, 10,000. Two
other prefixes are sometimes used, _micro_ which means 1/1,000,000; as
microfarad or microvolt, and _meg_ which means 1,000,000, as megohm
meaning 1,000,000 ohms.
=13. Advantages of the Metric System.=--_First_, it is a decimal system;
_second_, the same form and prefixes are used in every table; _third_,
the standards of length (meter), volume (liter), and mass (kilogram)
bear a simple relation to one another. This simple relation between the
three standard units may be given thus: _first_, the liter is a cubic
decimeter, and _second_, the kilogram is the mass of a liter of water.
(See Fig. 5) Since the liter is a cubic decimeter, the length of one
side is 10 cm. The liter therefore holds 1000 ccm. (10 × 10 × 10).
Therefore, 1 liter = 1 cu. dm. = 1000 ccm. and since 1 liter of water
has a mass of 1 kg. or 1000 g., then 1000 ccm. of water has a mass of
1000 g., or _1 ccm. of water has a mass of 1 g._
[Illustration: FIG. 5.--One liter of the water has a mass of one
kilogram.]
The following table of equivalents gives the relation between the most
common English and metric units. Those marked (*) should be memorized.
(*) 1 meter = 39.37 inches. 1 cu, in. = 16.387 ccm.
(*) 1 inch = 2.54 cm. 1 cu. ft. = 28315 cm.
1 foot = 30.48 cm. 1 cu. m. = 1.308 cu. yd.
1 mile = 1.609 km. (*) 1 liter = 1.057 qt.
1 sq. in. = 6.45 sq. cm. (*) 1 kg. = 2.204 lbs.
1 sq. cm. = 0.155 sq. in. 1 g. = 15.44 grains.
1 sq. m. = 1.196 sq. yd. 1 lb. = 0.4536 kg.
1 acre = 0.405 ha. 1 oz. = 28.35 g.
1 hectare = 2.45 acres. 1 g. = 0.0353 oz.
THE C. G. S. SYSTEM. Scientists have devised a plan for expressing any
measurement in terms of what are called the _three fundamental units of
length_, _mass_, and _time_. The units used are the _centimeter_, the
_gram_ and the _second_. Whenever a measurement has been reduced to its
equivalent in terms of these units, it is said to be expressed in
_C.G.S._ units.
Important Topics
1. The metric system; how originated.
2. Units; meter, liter, kilogram.
3. Metric tables.
4. Advantages of the metric system.
5. Equivalents.
6. The C.G.S. system.
Exercises
1. Which is cheaper, milk at 8 cents a quart or 8 cents a liter? Why?
2. Which is more expensive, cloth at $1.00 a yard or at $1.00 a meter?
Why?
3. Which is a better bargain, sugar at 5 cents a pound or 11 cents a
kilogram? Why?
4. Express in centimeters the height of a boy 5 ft. 6 in. tall.
5. What is the length of this page in centimeters? In inches?
6. What is the mass of a liter of water? Of 500 ccm.? Of 1 ccm.?
7. From Chicago to New York is 940 miles. Express in kilometers.
8. A 10-gallon can of milk contains how many liters?
9. What will 100 meters of cloth cost at 10 cents a yard?
10. What will 4 kg. of beef cost at 15 cents a pound?
11. What will 5-1/2 lbs. of mutton cost at 40 cents a kilogram?
12. How can you change the state of a body? Give three methods.
13. Correct the statement 1 ccm. = 1 g.
14. How many liters in 32 quarts?
CHAPTER II
MOLECULAR FORCES AND MOTIONS
(1) EVIDENCES OF MOLECULAR MOTION IN GASES
=14. Size of Molecules.=--The difference between solids, liquids, and
gases has been explained as due to the different behavior of molecules
in the three states of matter. That is, in solids they cling together,
in liquids they move freely, and in gases they separate. At this time we
are to consider the _evidences_ of molecular motion in gases. It must be
kept in mind that molecules are exceedingly small. It has been said that
if a bottle containing about 1 ccm. of ordinary air has pierced in it a
minute opening so that 100,000,000 molecules (a number nearly equal to
the population of the United States) pass out every second, it would
take, not minutes or hours, but nearly 9000 years for all of the
molecules to escape. The number of molecules in 1 ccm. of air at 0°C.
and 76 cm. pressure has been calculated by Professor Rutherford to be
2.7 × 10¹⁹. It is evident that such minute particles cannot be seen or
handled as _individuals_. We must judge of their size and action by the
results obtained from experiments.
=15. Diffusion of Gases.=--One line of evidence which indicates that a
gas consists of moving particles is the rapidity with which a gas having
a strong odor penetrates to all parts of a room. For example, if
illuminating gas is escaping it soon diffuses and is noticed throughout
the room. In fact, the common experience of the diffusion of gases
having a strong odor is such that we promptly recognize that it is due
to motion of some kind. The gas having the odor consists of little
particles that are continually hitting their neighbors and are being
struck and buffeted in turn until the individual molecules are widely
scattered. When cabbage is boiled in the kitchen soon all in the house
know it. Other illustrations of the _diffusion_ of gases will occur to
anyone from personal experience, such for instance as the pleasing odor
from a field of clover in bloom.
The following experiment illustrates the rapid diffusion of gases.
[Illustration: FIG. 6_a_.--Diffusion of gases.]
[Illustration: FIG. 6_b_.--Effusion of gases.]
Take two tumblers (see Fig. 6_a_), wet the inside of one with a few
drops of strong ammonia water and the other with a little
hydrochloric acid. Cover each with a sheet of clean paper. Nothing
can now be seen in either tumbler. Invert the second one over the
first with the paper between, placing them so that the edges will
match. On removing the paper it is noticed that both tumblers are
quickly filled with a cloud of finely divided particles, the two
substances having united chemically to form a new substance,
ammonium chloride.
On account of their small size, molecules of air readily pass through
porous solids, cloth, unglazed earthenware, etc. The following
experiment shows this fact strikingly. (See Fig. 6_b_.)
A flask containing water is closed by a rubber stopper through
which pass the stem of a glass funnel and a bent glass tube that
has been drawn out to a small opening (_J_). The funnel has
cemented in its top an inverted porous clay jar (_C_), over the top
of the latter is placed a beaker (_B_). A piece of flexible rubber
tubing (_H_) leading from a hydrogen generator is brought up to the
top of the space between the jar and the beaker. When hydrogen gas
is allowed to flow into the space between _C_ and _B_, the level of
the water in _W_ is seen to lower and a stream of water runs out at
_J_ spurting up into the air.
On stopping the flow of hydrogen and removing _B_, the water falls
rapidly in _J_ and bubbles of air are seen to enter the water from
the tube. (The foregoing steps may be repeated as often as
desired).
This experiment illustrates the fact that the molecules of some
gases move faster than those of some other gases. Hydrogen
molecules are found to move about four times as fast as air
molecules. Hence, while both air and hydrogen molecules are at
first going in opposite directions through the walls of _C_, the
hydrogen goes in much faster than the air comes out. In consequence
it accumulates, creates pressure, and drives down the water in _W_
and out at _J_. On removing _B_, the hydrogen within the porous cup
comes out much faster than the air reënters. This lessens the
pressure within, so that air rushes in through _J_. This experiment
demonstrates not only the fact of molecular motion in gases but
also that molecules of hydrogen move much faster than those of air.
(This experiment will work with illuminating gas but not so
strikingly.)
Careful experiments have shown that the speed of ordinary air molecules
is 445 meters or 1460 ft. per second; while hydrogen molecules move at
the rate of 1700 meters or 5575 ft. or more than a mile per second.
=16. Expansion of Gases.=--Gases also possess the property of indefinite
expansion, that is, if a small quantity of gas is placed in a vacuum,
the gas will expand immediately to fill the entire space uniformly. This
is shown by an experiment with the air pump. On raising the piston the
air follows instantly to fill up the space under it. As the air is
removed from the receiver of an air pump the air remaining is uniformly
distributed within.
=17. How Gases Exert Pressure.=--It is further found that air under
ordinary conditions exerts a pressure of about 15 lbs. to the square
inch. In an automobile tire the pressure may be 90 lbs. and in a steam
boiler it may be 200 lbs. or more to the square inch.
How is the pressure produced? The molecules are not packed together
solidly in a gas, for when steam changes to water it shrinks to about
1/1600 of its former volume. Air diminishes to about 1/800 of its volume
on changing to liquid air. The pressure of a gas is not due then to the
gas filling all of the space in which it acts, but is due rather to the
_motion_ of the molecules. The blow of a single molecule is
imperceptible, but when multitudes of molecules strike against a surface
their combined effect is considerable. In fact, this action is known to
produce the pressure that a gas exerts against the walls of a containing
vessel. Naturally if we compress twice as much gas into a given space
there will be twice as many molecules striking in a given time, which
will give twice as much pressure.
If gas is heated, it is found that the heat will cause a swifter motion
of the molecules. This will also make the molecules strike harder and
hence cause the gas to expand or exert more pressure.
=17a. Brownian Movements.=--Direct photographic evidence of the motion
of molecules in gases has been obtained by studying the behavior of
minute drops of oil suspended in stagnant air. Such drops instead of
being at rest are constantly dancing about as if they were continually
receiving blows from many directions. These motions have been called
_Brownian Movements_ (see Fig. 7).
It has been proved that these movements are due to the blows that these
small drops receive from the swiftly moving molecules of the gas about
them. If the drops are made smaller or the gas more dense, the movements
increase in intensity. These effects are especially marked at a pressure
of 0.01 of an atmosphere.
[Illustration: FIG. 7.--Photograph of Brownian movement. This record is
prepared by the aid of Siedentopf's ultra-microscope and a plate moving
uniformly across the field from left to right.]
Important Topics
It is assumed that air and all gases are made up of molecules in rapid
motion; that this motion is dependent upon temperature and pressure.
Evidence of this is shown by (a) diffusion, (b) expansion, (c) pressure.
Brownian Movements.
Questions
1. What is the molecular (kinetic) theory of gases?
2. What three kinds of evidence help to confirm the theory?
3. What have you seen that seems to show that a gas consists of
molecules in motion?
4. How many meters long is a 10-ft. pole?
5. A 50-kg. boy weighs how many pounds?
6. What are three advantages of the metric system?
7. What will 12 qts. of milk cost at 8 cents a liter?
8. A cube 1 meter each way will contain how many cubic centimeters? How
many liters? What will a cubic meter of water weigh?
(2) MOLECULAR MOTION IN LIQUIDS
=18. Diffusion of Liquids.=--From the evidence given in Arts. 14-17, (a)
of diffusion of odors, (b) of the continued _expansion_ of air in the
air pump, and (c) of the pressure exerted by a gas in all directions,
one may realize without difficulty that a _gas consists of small
particles in rapid motion_. Let us now consider some of the evidence of
molecular motion in liquids. If a little vinegar is placed in a pail of
water, all of the water will soon taste sour. A lump of sugar in a cup
of tea will sweeten the entire contents. This action is somewhat similar
to the diffusion of gases but it takes place much more slowly. It is
therefore believed that the motion of liquid molecules is much slower
than that of gas molecules.
Again, if a dish of water is left standing in the open air in fine
weather, within a few days the dish will become dry though no one has
taken anything from it. We say the water has _evaporated_. What was
liquid is now _vapor_. If we were to observe carefully any dish of water
we would find that it continually loses weight on dry days. That is,
there is a constant movement of the molecules of water into the air.
This movement of the molecules is explained as follows. There appear to
be in the dish of water some molecules that by moving back and forth
acquire a greater velocity than their neighbors; when these reach the
surface of the liquid, some vibration or movement sends them flying into
the air above. They are now vapor or gas molecules, flying, striking,
and rebounding like the air molecules. Sometimes on rebounding, the
water molecules get back into the water again. This is especially apt to
happen when the air is damp, _i.e._, when it contains many water
molecules. Sometimes the air over a dish becomes _saturated_, as in the
upper part of a corked bottle containing water. Although molecules are
continually leaving the surface of the water they cannot escape from the
bottle, so in time as many molecules must return to the water from the
space above as leave the water in the same time. When this condition
exists, the air above the water is said to be _saturated_. On very damp
days the air is often saturated. The explanation above shows why wet
clothes dry so slowly on such a day (See Arts. 166-7 on Saturation.)
=19. Cooling Effect of Evaporation.= We have seen that warming a gas
increases its volume. This expansion is due to the increased motion of
the warmed molecules. Now the molecules that escape from a liquid when
it evaporates are naturally the fastest moving ones, _i.e._, the hottest
ones. The molecules remaining are the slower moving ones or colder
molecules. The liquid therefore becomes colder as it evaporates, unless
it is heated. This explains why water evaporating on the surface of our
bodies cools us. In evaporating, the water is continually losing its
warm, fast moving molecules. The _cooling effect_ of evaporation is,
therefore an evidence of molecular motion in liquids.
[Illustration: FIG. 8.--Osmosis Shown by carrot placed in water.]
=20. Osmosis.=--If two liquids are separated by a membrane or porous
partition, they tend to pass through and mix. This action is called
osmose, or _osmosis_.
Such a movement of liquid molecules in osmosis may be illustrated
by filling a beet or carrot that has had its interior cut out to
form a circular opening (see Fig. 8) with a thick syrup. The
opening is then closed at the top with a rubber stopper through
which passes a long glass tube.
If the carrot is immersed in water, as in Fig. 8, a movement of
water through the porous wall to the interior begins at once. Here,
as in the experiment of the hydrogen and air passing through the
porous cup, the lighter fluid moves faster. The water collecting in
the carrot rises in the tube. This action of liquids passing
through porous partitions and mingling is called _osmosis_.
Gases and liquids are alike in that each will _flow_. Each is therefore
called a _fluid_. Sometimes there is much resistance to the flow of a
liquid as in molasses. This resistance is called _viscosity_. Alcohol
and gasoline have little viscosity. They are _limpid_ or _mobile_. Air
also has some viscosity. For instance, a stream of air always drags some
of the surrounding air along with it.
Important Topics
1. Liquids behave as if they were composed of small particles in motion.
2. This is shown by (1) Diffusion, (2) Solution, (3) Evaporation, (4)
Expansion, (5) Osmosis.
Exercises
1. Give an example or illustration of each of the five evidences of
molecular motion in liquids.
2. When is air saturated? What is the explanation?
3. Why does warming a liquid increase its rate of evaporation?
4. Air molecules are in rapid motion in all directions. Do they enter a
liquid with a surface exposed to the air? Give reason.
5. What are some of the inconveniences of living in a saturated
atmosphere?
6. Fish require oxygen. How is it obtained?
(3) MOLECULAR FORCES IN LIQUIDS
=21. Cohesion and Adhesion.=--In liquids "the molecules move about
freely yet tend to cling together." This tendency of molecules to cling
together which is not noticeable in gases is characteristic of =liquids=
and especially of =solids=. It is the cause of the viscosity mentioned
in the previous section and is readily detected in a variety of ways.
For instance, not only do liquid molecules cling together to form drops
and streams, but they cling to the molecules of solids as well, as is
shown by the wet surface of an object that has been dipped in water. The
attraction of like molecules for one another is called _cohesion_, while
the attraction of =unlike molecules= is called _adhesion_, although the
force is the same whether the molecules are alike or unlike. It is the
former that causes drops of water to form and that holds iron, copper,
and other solids so rigidly together. The adhesion of glue to other
objects is well known. Paint also "sticks" well. Sometimes the "joint"
where two boards are glued together is stronger than the board itself.
The force of attraction between molecules has been studied carefully.
The attraction acts only through very short distances. The attraction
even in liquids is considerable and may be measured. The cohesion of
water may be shown by an experiment where the force required to pull a
glass plate from the surface of water is measured.
[Illustration: FIG. 9.--The water is pulled apart.]
Take a beam balance and suspend from one arm a circular glass
plate, Fig. 9. Weigh the plate and its support. Adjust the glass
plate so that it hangs horizontally and just touches the surface of
clean water, the under side being completely wet. Now find what
additional weight is required to raise the glass plate from the
water.
Just as the plate comes from the water its under side is found to be
wet. That is, _the water was pulled apart_, and the plate was not pulled
from the water. The cohesion of the water to itself is not so strong as
its adhesion to the glass.
The cohesion of liquids is further shown by the form a drop of liquid
tends to take when left to itself. This is readily seen in small drops
of liquids. The spherical shape of drops of water or mercury is an
example. A mixture of alcohol and water in proper proportions will just
support olive oil within it. By carefully dropping olive oil from a
pipette into such a mixture, a drop of the oil, an inch or more in
diameter suspended in the liquid, may be formed. It is best to use a
bottle with plane or flat sides, for if a round bottle is used, the
sphere of oil will appear flattened.
[Illustration: FIG. 10 _a_.
FIG. 10 _b_.
FIGS. 10 _a_ AND _b_.--Surface tension of a liquid film.]
=22. Surface Tension.=--The cohesion of liquids is also indicated by the
tendency of films to assume the smallest possible surface. Soap bubble
films show this readily. Fig. 10 _a_ represents a circular wire form
holding a film in which floats a loop of thread. The tension of the
film is shown in Fig. 10 _b_ by the circular form of the loop after the
film within it has been pierced by a hot wire, Fig. 11 shows a
rectangular wire form with a "rider." The tension in the film draws the
rider forward.
[Illustration: FIG. 11.--The rider is drawn forward.]
[Illustration: FIG. 12.--Surface tension causes the pointed shape.]
A soap bubble takes its spherical shape because this form holds the
confined air within the smallest possible surface. A drop of liquid is
spherical for the same reason. Many illustrations of the tension in
films may be given. Users of water colors notice that a dry camel's-hair
brush is bushy. (Fig. 12 _A_). When in water it is still bushy. (Fig. 12
_B_.) But when it is taken from the water and the excess is shaken from
it, it is pointed as in Fig. 12 _C_. It is held to the pointed shape by
the tension of the liquid film about the brush.
[Illustration: FIG. 13.--A needle depresses the surface when floating.]
The surface of water acts as if covered by a film which coheres more
strongly than the water beneath it. This is shown by the fact that a
steel needle or a thin strip of metal may be floated upon the surface of
water. It is supported by the surface film. (See Fig. 13.) If the film
breaks the needle sinks. This film also supports the little water bugs
seen running over the surface of a quiet pond in summer. The surface
film is stronger in some liquids than in others. This may be shown by
taking water, colored so that it can be seen, placing a thin layer of it
on a white surface and dropping alcohol upon it. Wherever the alcohol
drops, the water is seen to pull away from it, leaving a bare space over
which the alcohol has been spread. This indicates that the alcohol has
the weaker film. The _film of greasy benzine is stronger_ than the film
of the pure material. If one wishes to remove a grease spot and places
pure benzine at the center of the spot, the stronger film of the greasy
liquid will pull away from the pure benzine, and spread out, making a
larger spot than before, while if pure benzine is placed _around the
grease spot_, the greasy liquid at the center pulls away from the pure
benzine, drawing more and more to the center, where it may be wiped up
and the grease entirely removed.
[Illustration: FIG. 14.--The molecule at _A_ is held differently from
one within the liquid.]
=23. Explanation of the Surface Film.=--Beneath the surface of a liquid
each molecule is attracted by all the other molecules around it. It is
attracted equally in all directions. Consequently the interior molecules
move very easily over each other in any direction. A molecule at the
surface, as at _A_, Fig. 14, is not attracted _upward_ by other liquid
molecules. Its freedom of motion is thereby hindered with the result
that a molecule at the surface behaves differently from one beneath the
surface. The surface molecules act as if they form an elastic skin or
membrane upon the liquid surface.
[Illustration: FIG. 15.--Capillary attraction in tubes.]
=24. Capillarity.=--A striking action of the surface film of a liquid is
seen in the rise of liquids in tubes of small bore when the liquid
_wets_ them. If the liquid _does not wet_ the tube, as when mercury is
placed in glass, the liquid is depressed. It is found in general that:
_Liquids rise in capillary tubes when they wet them and are depressed in
tubes which they do not wet; the smaller the diameter of the tube the
greater the change of level._ (See Fig. 15.) This action is explained as
follows: The molecules of a liquid have an attraction for each other and
also for the sides of a tube. The former is called "cohesion for
itself," the latter is called "adhesion for the sides of the containing
vessel." If the cohesion for itself is greater than the adhesion for the
side of the containing vessel, the liquid is pulled away from the side
and is depressed. If the adhesion is greater, the liquid is elevated.
This action is called "capillary action" from the Latin word
(_capillus_) signifying hair, since it shows best in fine hairlike
tubes.
There are many common illustrations of capillary action: oil rising in a
wick; water rising in a towel or through clothes; ink in a blotter, etc.
The minute spaces between the fibers composing these objects act as fine
tubes. If cloth is treated with a preparation which prevents water from
adhering to its fibers, the material will not be wet when water is
poured upon it, because the water will not run in between the fibers; a
surface film spreads over the cloth so that no water enters it.
_Cravenette cloth_ has been treated in this way and hence is waterproof.
The action of this film may be shown by the following experiment.
Dip a sieve of fine copper gauze in melted paraffin, thus coating
each wire so that water will not adhere to it. Water may now be
poured into the sieve, if a piece of paper is first laid in it to
break the force of the water. On carefully removing the paper the
surface film of the water will prevent the passage of the water
through the sieve.
=25. Capillary Action in Soils.=--The distribution of moisture in the
soil depends largely upon capillary action. When the soil is compact the
minute spaces between the soil particles act as capillary tubes, thus
aiding the water to rise to the surface. As the water evaporates from
the surface more of it rises by capillary action from the damper soil
below. Keeping the soil loose by cultivation, makes the spaces between
the particles too large for much capillary action, thus the moisture is
largely prevented from rising to the surface.
In the semi-arid regions of the West "_dry farming_" is successfully
practised. This consists in keeping the surface covered with a "dust
mulch" produced by frequent cultivation. In this way the moisture is
kept below the surface, where it can be utilized during the hot dry
summer by the roots of growing plants.
Important Topics
1. Attractive forces between liquid molecules.
2. Cohesion (like molecules); adhesion (unlike molecules).
3. Special effects of this force are classified as (a) capillary action,
and (b) surface tension.
Exercises
1. What evidence of capillary action have you seen outside of the
laboratory?
2. What is the explanation for capillary action?
3. Where are surface films found?
4. What are three common effects of surface films?
5. Explain why cravenette cloth sheds water.
6. If a circular glass disc 10 cm. in diameter requires 50 grams of
force to draw it from the water, what is the cohesion of water per
square centimeter?
7. What is the weight in grams of 1 ccm. of water? of a liter of water?
8. Name five examples of adhesion to be found in your home.
9. Under what conditions will a liquid wet a solid and spread over it?
10. When will it form in drops on the surface?
11. Explain the proper procedure for removing a grease spot with
benzine.
12. What difference is there between a liquid and a fluid?
13. Why cannot a "soap bubble" be blown from pure water?
14. Which are larger, the molecules of steam or those of water? Why?
15. Why is the ground likely to be damp under a stone or board when it
is dry all around?
16. Why does any liquid in falling through the air assume the globule
form?
17. Give three examples of capillary attraction found in the home. Three
out of doors.
18. Why does cultivation of the soil prevent rapid evaporation of water
from the ground?
(4) EVIDENCES OF MOLECULAR FORCES IN LIQUIDS AND SOLIDS
=26. Solutions.=--A crystal of potassium permanganate is placed in a
liter of water. It soon dissolves and on shaking the flask each portion
of the liquid is seen to be colored red. The dissolving of the
permanganate is an illustration of the attraction of the molecules of
water for the molecules of the permanganate. We are familiar with this
action in the seasoning of food with salt and sweetening with sugar.
Water will dissolve many substances, but in varying degrees, _i.e._, of
some it will dissolve much, of others, little, and some not at all.
Further, different liquids have different solvent powers. Alcohol will
dissolve resin and shellac, but it will not dissolve gum arabic, which
is soluble in water. Benzine dissolves grease. Beeswax is not dissolved
by water, alcohol or benzine, but is soluble in turpentine.
It is found that the _temperature_ of the liquid has a marked effect
upon the amount of substance that will dissolve. This is an indication
that the _motions_ of the molecules are effective in solution. It
appears that dissolving a solid is in some respects similar to
evaporation, and just as at higher temperatures more of the liquid
evaporates, because more of the molecules will escape from the liquid
into the air above, so at higher temperatures, more molecules of a solid
will detach themselves through greater vibration and will move into the
liquid.
Further, just as an evaporating liquid may saturate the space above it
so that any escape of molecules is balanced by those returning, so with
a dissolving solid, the liquid may become _saturated_ so that the
solution of more of the solid is balanced by the return of the molecules
from the liquid to the solid condition.
=27. Crystals and Crystallization.=--This return from the liquid to the
solid state, of molecules that are in solution, is especially noticeable
when the solution is cooling or evaporating and hence is losing its
capacity to hold so much of the solid. On returning to the solid, the
molecules attach themselves in a definite manner to the solid portion,
building up regular solid forms. These regular forms are _crystals_. The
action that forms them is called _crystallization_.
Each substance seems to have its own _peculiar form of crystal_ due to
the manner in which the molecules attach themselves to those previously
in place. The largest and most _symmetrical crystals are_ those in which
the molecules are deposited slowly with no disturbance of the liquid.
Beautiful crystals of alum may be obtained by dissolving 25 g. of alum
in 50 ccm. of hot water, hanging two or three threads in the solution
and letting it stand over night. The thread fibers provide a foundation
upon which crystals grow.
When a _solution_ of a solid evaporates, the molecules of the _liquid_
escape as a gas, the molecules of the _solid_ remain accumulating as
crystals. This principle has many uses: (a) sea water is purified by
_evaporating the water and condensing the vapor_, which of course forms
pure water. (b) water is forced down to _salt_ beds where it dissolves
the salt. The brine is then raised and evaporated, leaving the salt in
the evaporating pans.
=28. Absorption of Gases by Solids and Liquids.=--If a piece of
heated charcoal is placed in a test-tube containing ammonia gas,
inverted in mercury, the ammonia is seen to disappear, the mercury
rising to take its place. The ammonia has been absorbed by the
charcoal, the gas molecules clinging closely to the solid. The
charcoal being very porous presents a large surface to the action
of the gas.
This experiment indicates that attraction exists between gas molecules
and other molecules. Many porous substances have this power of absorbing
gases. We have all noticed that butter has its flavor affected by
substances placed near it.
That _liquids absorb gases_ is shown by slowly heating cold water in a
beaker. Small bubbles of air form on the sides and rise before the
boiling point is reached. Ammonia gas is readily absorbed in water, the
bubbles disappearing almost as soon as they escape into the water from
the end of the delivery tube. _Household ammonia_ is simply a solution
of ammonia gas in water. On warming the solution of ammonia the gas
begins to pass off; thus, warming a liquid tends to drive off any gas
dissolved in it.
_Soda water_ is made by forcing carbon dioxide gas into water under
strong pressure. When placed in a vessel open to the air the pressure is
lessened and part of the gas escapes. The dissolved gas gives the
characteristic taste to the beverage.
Important Topics
1. The solution of solids is increased by heating.
2. The solution of gases is decreased by heating.
3. Pressure increases the quantity of gas that can be dissolved in a
liquid.
4. The attraction (cohesion) of molecules of a dissolved solid for each
other is shown by crystallization.
Exercises
1. How do fish obtain oxygen for breathing?
2. Why does warming water enable it to dissolve more of a salt?
3. Why does warming water lessen the amount of a gas that will stay in
solution?
4. Will water absorb gases of strong odor? How do you know?
5. Name three solvents. Give a use for each.
6. What liquids usually contain gases in solution? Name some uses for
these dissolved gases.
7. What is the weight of a cubic meter of water?
8. Name three substances obtained by crystallization.
9. How is maple sugar obtained?
10. Name five crystalline substances.
(5) EVIDENCE OF MOLECULAR FORCES IN SOLIDS
=29. Differences between Solids and Gases.=--In studying gases, it is
seen that they behave as if they were composed of small particles in
rapid motion, continually striking and rebounding, and separating to
fill any space into which they are released. This action indicates that
there is practically no attractive force between such molecules.
Between the molecules of a solid, however, the forces of attraction are
strong, as is shown by the fact that a solid often requires a great
force to pull it apart; some, as steel and iron, show this property in a
superlative degree, a high-grade steel rod 1 cm. in diameter requiring
nearly 9 tons to pull it apart. Tests show that the breaking strengths
of such rods are directly proportional to their areas of cross-section.
That is, twice the area has twice the breaking strength.
[Illustration: FIG. 16.--Elasticity of bending.]
=30. Elasticity.=--Fully as important as a knowledge of the breaking
strengths of solids, is the knowledge of what happens when the forces
used are not great enough to break the rods or wires.
Take a wooden rod (as a meter stick) and clamp one end to the table
top, as in Fig. 16. At the other end hang a weight. Fasten a wire
to this end so that it projects out in front of a scale. Add
successively several equal weights and note the position of the
wire each time. Remove the weights in order, noting the positions
as before. The rod will probably return to the first position.
This simple experiment illustrates a characteristic of solids: that of
changing shape when force is applied and of returning to the original
shape when the force is removed. This property is called _elasticity_.
Tests of elasticity are made by subjecting wire of different materials
but of the same dimensions to the same tension. The one changing least
is said to have the greatest _elastic force_ or elasticity. If greater
forces are applied to the wire and then removed, one will finally be
found that will permanently stretch the wire so that it will not return
exactly to the former length. The wire has now passed its _elastic
limit_ and has been permanently stretched.
Just as there are great differences between the _elastic forces_ of
different substances, so there are great differences in the _limits of
elasticity_. In some substances the limit is reached with slight
distortion, while others are _perfectly elastic_ even when greatly
stretched. India rubber is an example of a body having _perfect_
elasticity through wide limits. Glass has great _elastic force_ but its
_limit_ of _elasticity_ is soon reached. Substances like India rubber
may be said to have great "_stretchability_," but little elastic force.
In physics, elasticity refers to the elastic force rather than to
ability to endure stretching.
=31. Kinds of Elasticity.=--_Elasticity may be shown in four ways_:
_compression_, _bending_ or _flexure_, _extension_ or _stretching_,
_twisting_ or _torsion_. The first is illustrated by squeezing a rubber
eraser, the second by an automobile spring, the third by the stretching
of a rubber band, the fourth by the twisting and untwisting of a string
by which a weight is suspended.
_There are two kinds of elasticity_: (1) elasticity of form or shape;
(2) elasticity of volume. Gases and liquids possess elasticity of
volume, but not of shape, while solids may have both kinds. Gases and
liquids are perfectly elastic because no matter how great pressure may
be applied, as soon as the pressure is removed they regain their former
volume. No solid possesses perfect elasticity, because sooner or later
the limit of elasticity will be reached.
=32. Hooke's Law.=[A]--On examining the successive movements of the end
of the rod in Art. 30, we find that they are approximately equal.
Carefully conducted experiments upon the elasticity of bodies have shown
that the changes in shape are _directly proportional_ to the forces
applied, provided that the limit of elasticity is not reached. This
relation, discovered by Robert Hooke, is sometimes expressed as follows:
"_Within the limits of perfect elasticity, all changes of size or shape
are directly proportional to the forces producing them._"
[A] A law is a statement of a constant mode of behavior. It is
often expressed in mathematical language.
=33. Molecular Forces and Molecular Motions.=--If a solid is compressed,
on releasing the pressure the body regains its former shape if it has
not been compressed too far. This indicates that at a given temperature
the "molecules of a solid tend to remain at a fixed distance from each
other, and resist any attempt to decrease or increase this distance."
This raises the question, Why does not the cohesion pull the molecules
tightly together so that compression would be impossible? The reason is
that heat affects the size of solid bodies. On lowering the temperature,
bodies do contract, for as soon as the temperature is lowered the
vibration of the molecule is lessened. On raising the temperature the
molecules are pushed farther apart.
The size of a body, then, is the result of a balance of opposing forces.
The attractive force between the molecules pulling them together is
_cohesion_, while the force which pushes them apart is due to the
motions of the molecules. Raising the temperature and thus increasing
the motion causes expansion; lowering the temperature decreases the
molecular motion and so causes contraction. If an outside force tries to
pull the body apart or to compress it this change of size is resisted by
either cohesion or molecular motion.
=34. Properties of Matter.=--Many differences in the physical properties
of solids are due to differences between the cohesive force of different
kinds of molecules. In some substances, the attraction is such that they
may be rolled out in very thin sheets. Gold is the best example of this,
sheets being formed 1/300,000 of an inch thick. This property is called
_malleability_. In other substances the cohesion permits it to be drawn
out into fine threads or wire. Glass and quartz are examples of this.
This property is called _ductility_. In some, the cohesion makes the
substance excessively _hard_, so that it is difficult to work or scratch
its surface. The diamond is the hardest substance known. Some substances
are _tough_, others _brittle_. These are tested by the ability to
withstand sudden shocks as the blow of a hammer.
Important Topics
1. Molecular forces in solids; (_a_) adhesion, (_b_) cohesion.
2. Elasticity, Hooke's Law.
3. Contraction on cooling.
4. Malleability, ductility, hardness, brittleness, etc.
Exercises
1. Give an illustration of Hooke's Law from your own experience.
2. What devices make use of it?
3. Do solids evaporate. Give reasons.
4. When iron is welded, is cohesion or adhesion acting?
5. When a tin basin is soldered, is cohesion or adhesion acting?
6. Sometimes a spring is made more elastic by _tempering_ and made soft
by _annealing_. Look up the two terms. How is each accomplished?
7. Review the definitions: solid, liquid, and gas. Why do these
definitions mean more to you now than formerly?
8. If a wire is stretched 0.3 cm. on applying 4 kg. of force, what force
will stretch it 0.75 cm? Explain.
9. How long will it take under ordinary conditions for a gas molecule to
cross a room? Give reasons for your answer.
10. What is meant by the elastic limit of a body?
11. Without reaching the elastic limit, if a beam is depressed 4 mm.
under a load of 60 kg., what will be the depression under a load of 400
kg.? Of 600 kg.?
12. Name three substances that possess elasticity of volume.
13. Give three examples of each; elasticity of (1) compression, (2)
stretching, (3) torsion, (4) flexure.
Review Outline: Introduction and Molecules
Physics; definition, topics considered, physical and chemical changes.
Science; hypothesis, theory, law. Knowledge; common, scientific.
Matter; three states, molecular theory. Mass, weight, volume.
Metric system; units, tables, equivalents, advantages.
Evidences of molecular motions; gases (3), liquids (5), solids (3).
Evidences of molecular forces; liquids (3), solids (many) special
properties such as: elasticity, tenacity, ductility, hardness, etc.
Hooke's law; applications.
CHAPTER III
MECHANICS OF LIQUIDS
(1) THE GRAVITY PRESSURE OF LIQUIDS
=35. Pressure of Liquids against Surfaces.=--The sight of a great ship,
perhaps built of iron and floating on water, causes one to wonder at the
force that supports it. This same force is noticed when one pushes a
light body, as a cork, under water. It is quite evident in such a case
that a force exists sufficient to overcome the weight of the cork so
that it tends to rise to the surface. Even the weight of our bodies is
so far supported by water that many persons can float.
[Illustration: FIG. 17.--Water forces the card against the chimney.]
The following experiment provides a means of testing this force:
If an empty can is pushed down into water, we feel at once the
force of the liquid acting against the object and tending to push
it upward. It may be noticed also that so long as the can is not
completely submerged the deeper the can is pushed into the water
the greater is the upward force exerted by the liquid.
We may test this action in various ways: a simple way is to take a
cylindrical lamp chimney, press a card against its lower end and
place it in the water in a vertical position. The force of the
water will hold the card firmly against the end of the chimney.
(See Fig. 17.) The amount of force may be tested by dropping shot
into the tube until the card drops off. At greater depths more shot
will be required, showing that the force of the water increases
with the depth. Or one may pour water into the chimney. It will
then be found that the card does not drop until the level of the
water inside the chimney is the same as on the outside. That is,
before the card will fall off, the water must stand as high within
the chimney as without no matter to what depth the lower end of the
chimney is thrust below the surface of the water.
=36. Law of Liquid Pressure.=--As there is twice as much water or shot
in the chimney when it is filled to a depth of 10 cm. as there is when
it is filled to a depth of 5 cm. the force of the water upward on the
bottom must be twice as great at a depth of 10 cm. as at a depth of 5
cm. Since this reasoning will hold good for a comparison of forces at
any two depths, we have the law: "_The pressure exerted by a liquid is
directly proportional to the depth_."
The amount of this force may be computed as follows: First, the card
stays on the end of the tube until the _weight_ of water from above
equals the force of the water from below, and second, the card remains
until the water is at the same _height_ inside the tube as it is
outside. Now if we find the weight of water at a given depth in the
tube, we can determine the force of the water from below. If for
instance the chimney has an area of cross-section of 12 sq. cm. and is
filled with water to a depth of 10 cm., the volume of the water
contained will be 120 ccm. This volume of water will weigh 120 g. This
represents then, not only the weight of the water in the tube, but also
the force of the water against the bottom. In a similar way one may
measure the force of water against any horizontal surface.
=37. Force and Pressure.=--We should now distinguish between _force_ and
_pressure_. Pressure refers to the force acting against _unit area_,
while force refers to the action against the whole surface. Thus for
example, the atmospheric _pressure_ is often given as 15 pounds to the
square inch or as one kilogram to the square centimeter. On the other
hand, the air may exert a _force_ of more than 300 pounds upon each side
of the hand of a man; or a large ship may be supported by the _force_ of
thousands of tons exerted by water against the bottom of the ship.
In the illustration, given in Art. 36, the upward _force_ of the water
against the end of the tube at a depth of 10 cm. is computed as 120
grams. The _pressure_ at the _same_ depth will be 10 grams per sq. cm.
What will be the pressure at a depth of 20 cm.? at a depth of 50 cm.? of
100 cm.? Compare these answers with the law of liquid pressure in Art.
36.
=38. Density.=--If other liquids, as alcohol, mercury, etc., were in the
jar, the chimney would need filling to the same level outside, with the
_same_ liquid, before the card would fall off. This brings in a factor
that was not considered before, _that of the mass[B] of a cubic
centimeter of the liquid_. This is called the _density_ of the liquid.
Alcohol has a density of 0.8 g. per cubic centimeter, mercury of 13.6 g.
per cubic centimeter, while water has a density of 1 g. per cubic
centimeter.
[B] The _mass_ of a body is the _amount of matter in it_, the
_weight_ is the _pull of the earth upon it_.
=39. Liquid Force against Any Surface.=--To find the force exerted by a
liquid against a surface we must take into consideration the area of the
surface, and the height and the =density= of the liquid above the
surface. The following law, and the formula representing it, which
concisely expresses the principle by which the force exerted by a liquid
against any surface may be computed, should be memorized:
_The force which a liquid exerts against any surface, equals the
area of the surface, times its average depth below the surface of
the liquid, times the weight of unit volume of the liquid._
Or, expressed by a formula, _F = Ahd_. In this formula, "F" stands for
_the force which a liquid exerts against any surface_, "A" _the area
of the surface_, "h," for _the average depth (or height) of the liquid
pressing on the surface_, and "d", for _the weight of unit volume of the
liquid_. This is the first illustration in this text, of the use of a
formula to represent a law. Observe how accurately and concisely the law
is expressed by the formula. When the formula is employed, however, we
should keep in mind the law expressed by it.
We must remember that a liquid presses not only downward and upward but
sideways as well, as we see when water spurts out of a hole in the side
of a vessel. Experiments have shown that at a point the pressure in a
fluid is the same in all directions, hence the rule given above may be
applied to the pressure of a liquid against the side of a tank, or boat,
or other object, provided we are accurate in determining the _average
depth of the liquid_; The following example illustrates the use of the
law.
_For Example_: If the English system is used, the area of the
surface should be expressed in square feet, the depth in feet and
the weight of the liquid in pounds per cubic foot. One cubic foot
of water weighs 62.4 lbs.
Suppose that a box 3 ft. square and 4 ft. deep is full of water.
What force will be exerted by the water against the bottom and a
side?
From the law given above, the force of a liquid against a surface
equals the product of the _area_ of the surface, the _depth_ of the
liquid and its weight per unit volume, or using the formula, _F =
Ahd_. To compute the downward force against the bottom we have the
area, 9, depth, 4, and the weight 62.4 lbs. per cubic foot. 9 × 4 ×
62.4 lbs. = 2246.4 lbs. To compute the force against a side, the
area is 12, the average depth of water on the side is 2, the weight
62.4, 12 × 2 × 62.4 lbs. = 1497.6 lbs.
Important Topics
1. Liquids exert pressure; the greater the depth the greater the
pressure.
2. Difference between force and pressure.
3. Rules for finding upward and horizontal force exerted by a liquid. _F
= Ahd._
4. Weight, mass, density.
Exercises
1. What is the density of water?
2. What force is pressing upward against the bottom of a flat boat, if
it is 60 ft. long, 15 ft. wide and sinks to a depth of 2 ft. in the
water? What is the weight of the boat?
3. If a loaded ship sinks in the water to an average depth of 20 ft.,
the area of the bottom being 6000 sq. ft., what is the upward force of
the water? What is the weight of the ship?
4. If this ship sinks only 10 ft. when empty, what is the weight of the
ship alone? What was the weight of the cargo in Problem 3?
5. What is the liquid force against one side of an aquarium 10 ft. long,
4 ft. deep and full of water?
6. What is the liquid force on one side of a liter cube full of water?
Full of alcohol? Full of mercury? What force is pressing on the bottom
in each case?
7. What depth of water will produce a pressure of 1 g. per square
centimeter? 10 g. per square centimeter? 1000 g. per square centimeter?
8. What depth of water will produce a pressure of 1 lb. per square inch?
10 lbs. per square inch? 100 lbs. per square inch?
9. What will be the force against a vertical dam-breast 30 meters long,
the depth of the water being 10 meters?
10. A trap door with an area of 100 sq. dcm. is set in the bottom of a
tank containing water 5 meters deep. What force does the water exert
against the trap door?
11. What is the force on the bottom of a conical tank, filled with
water, the bottom of which is 3 meters in diameter, the depth 1.5
meters?
12. If alcohol, density 0.8 were used in problem 11, what would be the
force? What would be the depth of alcohol to have the same force on the
bottom as in problem 11?
13. What is the pressure in pounds per square inch at a depth of 1 mile
in sea water, density 1.026 grams per cc.?
14. Find the force on the sides and bottom of a rectangular cistern
filled with water, 20 ft. long, 10 ft. wide, and 10 ft. deep?
15. Find the force on the bottom of a water tank 14 ft. in diameter when
the water is 15 ft. deep, when full of water.
16. Find the force on one side of a cistern 8 ft. deep and 10 ft.
square, when full of water.
17. Find the force on a vertical dam 300 ft. long and 10 ft. high, when
full of water.
18. Find the pressure at the bottom of the dam in question 17.
19. Why are dams made thicker at the bottom than at the top?
20. A ship draws 26 ft. of water, _i.e._, its keel is 26 ft. under
water. What is the liquid force against a square foot surface of the
keel? Find the pressure on the bottom.
(2) TRANSMISSION OF LIQUID PRESSURE
=40. Pascal's Principle.=--Liquids exert pressure not only due to their
own weight, but when confined, may be made to transmit pressure to
considerable distances. This is a matter of common knowledge wherever a
system of waterworks with connections to houses is found, as in cities.
The transmission of liquid pressure has a number of important
applications. The principle underlying each of these was first
discovered by Pascal, a French scientist of the seventeenth century.
Pascal's Principle, as it is called, may be illustrated as follows:
Suppose a vessel of the shape shown in Fig. 18, the upper part of
which we may assume has an area of 1 sq. cm., is filled with water
up to the level _AB_. A pressure will be exerted upon each square
centimeter of area depending upon the depth. Suppose that the
height of _AB_ above _CD_ is 10 cm., then the force upon 1 sq. cm.
of _CD_ is 10 g., or if the area of _CD_ is 16 sq. cm., it receives
a force of 160 g.
[Illustration: FIG. 18.--The force increases with the depth.]
If now a cubic centimeter of water be poured upon _AB_ it will
raise the level 1 cm., or the head of water exerting pressure upon
_CD_ becomes 11 cm., or the total force in _CD_ is 16×11 g.,
_i.e._, each square centimeter of _CD_ receives an additional force
of 1 g. _Hence the force exerted on a unit area at_ _AB_ _is
transmitted to every unit area within the vessel._
The usual form in which this law is expressed is as follows: _Pressure
applied to any part of a confined liquid is transmitted unchanged, in
all directions, and adds the same force to all equal surfaces in contact
with the liquid_.
[Illustration: FIG. 19.--The force is proportional to the area.]
The importance of this principle, as Pascal himself pointed out, lies in
the fact that by its aid we are able to exert a great force upon a large
area by applying a small force upon a small area of a confined liquid,
both areas being in contact with the same liquid. Thus in Fig. 19 if the
area of the surface _CD_ is 2000 times the area of the surface _AB_,
then 1 lb. applied to the liquid on _AB_ will exert or sustain a force
of 2000 lbs. on _CD_.
=41. Hydraulic Press.=--An important application of Pascal's principle
is the _hydraulic press_. See Fig. 20. It is used for many purposes
where great force is required, as in pressing paper or cloth, extracting
oil from seeds, lifting heavy objects, etc. Many high school pupils have
been seated in a _hydraulic chair_ used by a dentist or barber. This
chair is a modified hydraulic press.
[Illustration: FIG. 20.--Cross-section of a hydraulic press.]
The hydraulic press contains two movable pistons, _P_ and _p_ (see Fig.
20). The larger of these, _P_, has a cross-sectional area that may be
100 or 1000 times that of the smaller. The smaller one is moved up and
down by a lever; on each upstroke, liquid is drawn in from a reservoir,
while each down-stroke forces some of the liquid into the space about
the large piston. Valves at _V_ and _V´_ prevent the return of the
liquid. If the area of _P_ is 1,000 times that of _p_, then the force
exerted by _P_ is 1000 times the force employed in moving _p_. On the
other hand, since the liquid moved by the small piston is distributed
over the area of the large one, the latter will move only 1/1000 as far
as does the small piston. The relation between the motions of the two
pistons and the forces exerted by them may be stated concisely as
follows: The _motions_ of the two _pistons_ of the hydraulic press are
inversely proportional to the forces exerted by them. The
_cross-sectional areas_ of the two pistons are, on the other hand,
directly proportional to the forces exerted by them.
An application of Pascal's principle often employed in cities is the
hydraulic elevator. In this device a long plunger or piston extends
downward from the elevator car into a cylinder sunk into the earth,
sometimes to a depth of 300 ft. Water forced into this cylinder pushes
the piston upward and when the water is released from the cylinder the
piston descends.
Fig. 21 represents another form of hydraulic elevator, where the
cylinder and piston are at one side of the elevator shaft. In this
type, to raise the elevator, water is admitted to the cylinder
pushing the piston downward.
=42. Artesian Wells.=--Sometimes a porous stratum containing water in
the earth's crust is inclined. Then if there are impervious strata (see
Fig. 22), both above and below the water-bearing one, and the latter
comes to the surface so that rain may fill it, a well sunk to the
water-bearing stratum at a point where it is below the surface will
usually give an artesian well, that is, one in which the water rises to
or above the surface. Many are found in the United States.
[Illustration: FIG. 21.--A hydraulic freight elevator.]
[Illustration: FIG. 22.--Conditions producing an artesian well.]
[Illustration: FIG. 23.--A standpipe.]
=43. Standpipes and Air Cushions.=--Many who have lived in cities where
water is pumped into houses under pressure know that the water pressure
is changed when several faucets are opened at the same time. Again, if
several persons are using a hose for sprinkling, the pressure may be
lessened so as to be insufficient to force the water above the first
floor. In order to allow for these changes some flexibility or spring
must be introduced somewhere into the water-pipe system. Water is
nearly incompressible and if no means were employed to take care of the
pressure changes, the sudden stopping and starting of the flow would
cause serious jars and start leaks in the pipes. Two common devices for
controlling sudden changes in the water pressure are the _standpipe_ and
the _air cushion_.
The _standpipe_ is simply a large vertical tube connected to the
water mains from which and into which water readily flows. When
many faucets are opened the water lowers; when most faucets are
closed the water rises, giving a simple automatic control of the
surplus water and a supply of water for a short time during a
shut-down of the pumps. Standpipes are often used in towns and
small cities. Fig. 23 represents the standpipe at Jerome, Idaho.
The _air cushion_ (Fig. 24) is a metal pipe or dome filled with air
attached to a water pipe where sudden changes in pressure are to be
controlled. At many faucets in a city water system such an air
cushion is employed. It contains air; this, unlike water, is easily
compressible and the confined air when the tap is suddenly closed
receives and checks gradually the rush of water in the pipe. Even
with an air cushion, the "pound" of the water in the pipe when a
tap is suddenly closed is often heard. If air cushions were not
provided, the "water hammer" would frequently crack or break the
pipes.
[Illustration: FIG. 24.--The short pipe above the faucet contains air
forming an air cushion.]
Important Topics
1. Pascal's law.
2. Hydraulic press.
3. Artesian wells.
4. Standpipes and air cushions.
Exercises
1. Where have you _seen_ an air cushion? Describe it and its use.
2. Where have you _seen_ an hydraulic press? Why and how used?
3. Where have you _seen_ hydraulic elevators? What moves them?
4. Where do you know of liquids under pressure? Three examples.
5. What is the pressure in water at a depth of 1500 cm. Express in grams
per square centimeter and in kilograms per square centimeter.
6. What head[C] of water is required to give a pressure of 200 g. per
square centimeter? 2 kg. per square centimeter?
[C] "Head" is a term used to express the vertical height of water
in pipes.
7. What _pressure_ will be produced by a "head" of water of 20 meters?
8. If 1728 cu. in. of water are placed in a vertical tube 1 sq. in. in
cross section to what height would the water rise? It would give how
many feet of _head_?
9. What would the water in problem 8 weigh? What pressure would it
produce at the bottom, in pounds per square inch? From this, compute how
many feet of "head" of water will produce a pressure of 1 lb. per square
inch.
10. Using the result in problem 9, what "head" of water will produce a
pressure of 10 lbs. per square inch? 100 lbs. per square inch?
11. From the result in 9, 100 ft. of "head" of water will produce what
pressure? 1000 ft. of "head?"
12. If the diameter of the pump piston in a hydraulic press is 2 cm. and
that of the press piston 50 cm. what will be the force against the
latter if the former is pushed down with a force of 40 kg.?
(3) ARCHIMEDES' PRINCIPLE
=44. A Body Supported by a Liquid.=--Among the applications of the force
exerted by a liquid upon a surface, Archimedes' Principle is one of the
most important.
Most persons have noted that a body placed in water is partly or wholly
supported by the force of the water upon it. A stone held by a cord and
lowered into water is felt to have a part of its weight supported,
while a piece of cork or wood is wholly supported and floats.
The human body is almost entirely supported in water, in fact, many
people can easily float in water. It was the consideration of this fact
that led the Greek philosopher Archimedes to discover and state the
principle that describes the supporting of a body in a liquid.
[Illustration: FIG. 25.--Theoretical proof of Archimedes' principle.]
=45. Archimedes' Principle.=--"_A body immersed in a liquid is pushed up
by a force equal to the weight of the liquid that it displaces._" The
proof for this law is simply demonstrated. Suppose a cube, _abcd_, is
immersed in water (Fig. 25). The upward force on _cd_ is equal to the
weight of a column of water equal to _cdef_. (See Art. 39.) The downward
force upon the top of the cube is equal to the weight of the column of
water _abef_. Then the net upward force upon the cube, that is, the
upward force upon the bottom less the downward force upon the top, or
the buoyant force exerted by the liquid is exactly equal to the weight
of the displaced water _abcd_.
=46. Law of Floating Bodies.=--This same reasoning may be applied to any
liquid and to any body immersed to any depth below the surface of the
liquid. If the body weighs more than the displaced liquid it will sink.
If it weighs less than the displaced liquid it will float or rise in the
water. A block of wood rises out of the water in which it floats until
its own weight just equals the weight of the water it displaces. From
this we have the law of floating bodies.
_A floating body displaces its own weight of the liquid in which it
floats._
[Illustration: FIG. 26.--A floating body displaces its own weight of
water.]
To test the law of floating bodies, take a rod of light wood 1 cm.
square and 30 cm. long (Fig. 26). Bore out one end and fill the opening
with lead and seal with paraffin so that the rod will float vertically
when placed in water. Mark upon one side of the rod a centimeter scale,
and dip the rod in hot paraffin to make it waterproof. Now find the
weight of the stick in grams and note the depth to which it sinks in
water in centimeters. Compute the weight of the displaced water. It will
equal the weight of the rod.
=47. Applications of Archimedes' Principle.= There are numerous
applications of Archimedes' Principle and the law of floating bodies.
=(a) To Find the Weight of a Floating Body: Problem.=--A boat 20
ft. long and with an average width of 6 ft. sinks to an average
depth of 3 ft. in the water. Find the weight of the boat. What
weight of cargo will sink it to an average depth of 5 ft.?
=Solution.=--The volume of the water displaced is 20 × 6 × 3 cu.
ft. = 360 cu. ft. Since 1 cu. ft. of water weighs 62.4 lbs., 360 ×
62.4 lbs. = 22,464 lbs., the weight of water displaced. By the law
of floating bodies this is equal to the weight of the boat. When
loaded the volume of water displaced is 20 ft. × 6 × 5 ft. which
equal 600 cu. ft. 600 × 62.4 lbs. = 37,440 lbs. This is the weight
of the water displaced when loaded. 37,440 lbs. - 22,464 lbs. =
14,976 lbs., the weight of the cargo.
=(b) To Find the Volume of an Immersed Solid: Problem.=--A stone
weighs 187.2 lbs. in air and appears to weigh 124.8 lbs. in water.
What is its volume?
=Solution.=--187.2 lbs. - 124.8 lbs. = 62.4 lbs., the buoyant force
of the water. By Archimedes' Principle, this equals the weight of
the displaced water which has a volume of 1 cu. ft. which is
therefore the volume of the stone.
=(c) To Find the Density of a Body:= The density of a body is
defined as the mass of unit volume.
We can easily find the mass of a body by weighing it, but the
volume is often impossible to obtain by measurements, especially of
irregular solids.
Archimedes' Principle, however, provides a method of finding the volume
of a body accurately by weighing it first in air and then in water (Fig.
27), the apparent loss in weight being equal to the weight of the
displaced water. One needs only to find the volume of water having the
same weight as the loss of weight to find the volume of the body.
If the metric system is used, 1 ccm. of water weighs 1 g., and the
volume is numerically the same as the loss of weight.
[Illustration: FIG. 27.--A method of weighing a body under water.]
Important Topics
1. Archimedes' Principle.
2. Law of floating bodies.
3. The applications of Archimedes' Principle are to determine (a) the
weight of a floating body; (b) the volume of an immersed solid, and (c)
the density of a body.
Exercises
1. Look up the story of Archimedes and the crown. Write a brief account
of it.
2. Why is it easier for a fat man to float in water than for a lean
one?
3. A fish weighing 1 lb. is placed in a pail full of water. Will the
pail and contents weigh more than before adding the fish? Why?
4. Why can a large stone be lifted more easily while under water than
when on the land?
5. Why does the air bubble in a spirit level move as one end of the
instrument is raised or lowered?
6. Why does a dead fish always float?
7. A ship is built for use in fresh water. What will be the effect on
its water line when passing into the ocean?
8. Why can small bugs walk on water while large animals cannot?
9. If an object weighing 62.4 lbs. just floats in water, what weight of
water does it displace? What volume of water is displaced? What is the
volume of the body?
10. What is the volume of a man who just floats in water if he weighs
124.8 lbs.? If he weighs 187.2 lbs.?
11. An object weighing 500 g. just floats in water. What is its volume?
How much water does a floating block of wood displace if it weighs 125
lbs.? 125 g.? 2 kg.? 2000 kg.?
12. A flat boat 10 × 40 ft. in size will sink how much in the water when
10 horses each weighing 1250 lbs. are placed on board?
13. A ship 900 ft. long and 80 ft. average width sinks to an average
depth of 25 ft. when empty and 40 ft. when loaded. What is the weight of
the ship and of its load?
14. Will a 1000 cc. block sink or float in water if it weighs 800 g.? If
it weighs 1200 g.? Explain.
15. If a 1000 cc. block of metal weighing 1200 g. is placed in the water
in mid ocean what will become of it?
16. Prove Archimedes' Principle by use of the principles of liquid
pressure.
17. An irregular stone, density 2.5 g. per ccm. displaces 2 cu. ft. of
water. What is its weight? Its apparent weight in water?
18. Will the depth to which a vessel sinks in water change as she sails
from Lake Ontario into the Atlantic Ocean? Why?
19. If the density of sea water is 1.0269 g. per cubic centimeter and
that of ice 0.918 g. per ccm., what portion of an iceberg is above
water?
20. In drawing water from a well by means of a bucket, why is less force
used when it is under water than when entirely above?
21. A stone which weighs 300 lbs. can be lifted under water with a force
of 150 lbs. What is the volume of the stone?
22. The average density of the human body is 1.07 grams per c.c. How
much water will a man who weighs 150 lbs. displace when diving? How much
when floating?
(4) DENSITY AND SPECIFIC GRAVITY
=48. Density.=--The density of a substance is often used as a test of
its purity. Archimedes in testing King Hiero's crown to find out if it
were made of pure gold determined first its density. It is by such tests
that the purity of milk, of alcohol, of gold, and a great variety of
substances is often determined.
Knowledge of methods of finding density is of value to everyone and
should be included in the education of every student. _The density of a
substance is the mass of unit volume of the substance._ In the metric
system, for example, the density of a substance is the mass in grams per
1 ccm. Taking water, 1 ccm. weighs 1 gr. or its density is therefore 1
g. to the cubic centimeter. A cubic centimeter of aluminium weighs 2.7
g. Its density therefore is 2.7 g. per ccm.
=49. Specific Gravity.=--_Specific gravity is the ratio of the weight of
any volume of a substance to the weight of an equal volume of water._
Its meaning is not quite the same as that of density, since specific
gravity is always a _ratio_, _i.e._, an _abstract_ number, as 2.7.
Density of a substance is a _concrete_ number, as 2.7 grams per ccm. In
the metric system the density of water is one gram per cubic centimeter,
therefore we have:
Density (g. per ccm.) = (numerically) specific gravity.
In the English system, the density of water is 62.4 pounds per cubic
foot, therefore in this system we have:
Density (lbs. per cu. ft.) = (numerically) 62.4 × sp. gr.
=50. Methods for Finding Density and Specific Gravity=
=(a) Regular Solids.=--Solids of regular shapes such as cubes, spheres,
etc., whose volumes may be readily found by measurement, may be weighed.
The mass divided by the volume gives the density, or _D = Mμ/v_.
=(b) Irregular Solids.=--with these the volume cannot be found by
measurement but may be obtained by Archimedes' Principle. Weigh the
solid first in the air and then in water. The apparent loss of weight
equals the weight of the equal volume of water displaced. From this the
volume may be found. And then the
density equals mass/volume; the specific gravity =
wt. in air / wt. of equal volume of water = wt. in air / ((wt. in air) -
(wt. in water))
mass
density equals ------; the specific gravity =
volume
wt. in air wt. in air
---------------------------- = -----------------------------
wt. of equal volume of water ((wt. in air) - (wt. in water))
=(c) Solids Lighter than Water.=--This will require a sinker to hold the
body under water. Weigh the solid in air (_w_). Weigh the sinker in
water (_s_). Attach the sinker to the solid and weigh both in water
(w´). The specific gravity equals
(wt. of solid in air)/(loss in wt. of solid in water) or _w/((w +
s) - w´)_
wt. of solid in air _w_
--------------------------- or ------------
loss of wt. of solid in water (_w + s_) - _w´_
The apparent loss of weight of the solid is equal to the sum of its
weight in air plus the weight of the sinker in water, less the combined
weight of both in water.
=(d) The Density of a Liquid by a Hydrometer.=--One may also easily find
the density of any liquid by Archimedes' Principle. If one takes the rod
described in Art. 46, and places it in water, the number of cubic
centimeters of water it displaces indicates its weight in grams. On
placing the rod in another liquid in which it floats, it will of course
displace its own weight and the height to which the liquid rises on the
scale gives the volume. By dividing the _weight_ of the rod as shown by
its position in _water_ by the _volume_ of the _liquid_ displaced we
obtain the density of the liquid. Commercial hydrometers for testing the
density of milk, alcohol and other liquids are made of glass of the form
shown in Fig. 28. The long narrow stem permits small differences in
volume to be noticed, hence they are more accurate than the rod
described in the preceding paragraph. For convenience this rod contains
a paper scale, so that when the height of the liquid on the stem is
noted, the density is read at once.
[Illustration: FIG. 28.--A hydrometer used to find the density of a
liquid.]
=Density of Liquids by Loss of Weight.= Weigh a piece of glass in air
(_W_{a}_), in water (_W_{w}_), and in the liquid to be tested (_W_{l}_).
Then (_W_{a}_ - _W_{w}_)gives the weight of the water displaced.
And (_W_{a}_ - _W_{l}_) gives the weight of the liquid displaced.
Hence, (_W_{a}_ - _W_{l}_)/(_W_{a}_ - _W_{w}_) equals the specific
gravity of the liquid.
Important Topics
1. Definitions of density and specific gravity.
2. Methods of finding density: (a) regular solids; (b) irregular solids;
(c) solids lighter than water; (d) liquids by hydrometer; (e) liquids by
loss of weight.
Exercises
_Note._--Consider that 1 cu. ft. of water weighs 62.4 lbs. Consider that
1 ccm. of water weighs 1 g.
1. What is meant by the statement that a block of wood has a specific
gravity of 0.6?
2. Considering that the density of the human body is the same as that of
water, what is the volume of a 125-lb. boy? Of a 250-lb. man? Of a
62.4-lb. boy? What is the volume of your body?
3. How is the weight of large ships found? Give an example.
4. Mention three cases where determinations of density are important.
5. A body weighs 40 g. in air, 15 g. in water, 5 g. in an acid. Find (a)
the density of the body; (b) its volume; (c) density of the acid.
6. If the specific gravity of a horse is 1, what is the volume of a
horse weighing 500 kg.? Of one weighing 1248 lbs.?
7. A weighted wooden box sinks to a depth of 20 cm. in water and 24 cm.
in alcohol, and to a depth of 18 cm. in brine. What is the density of
the alcohol and of the brine?
8. A glass stopper weighs in the air 25 g., in water 15 g., in oil 18 g.
Find the density and volume of the stopper. Find the density of the oil.
9. What would a cubic foot of wood weigh if the specific gravity were
0.5.?
10. The specific gravity of aluminum is 2.7. Find the weight of a cubic
foot of it.
11. A block of wood weighs 40 g. A piece of lead appears to weigh 70 g.
in water. Both together appear to weigh 60 g. in water. Find the density
of the wood.
12. A stone weighs 30 g. in air, 22 g. in water, and 20 g. in salt
water. Find the density of the salt water.
13. Will iron sink in mercury? Why?
14. A submarine boat weighing 200 tons must have what volume in order to
float?
15. Find the weight of 2 cu. ft. of copper from its density.
16. What is the weight in water of a mass whose specific gravity is 3.3
and whose weight is 50 kg.?
17. A block of granite weighs 1656 lbs.; its volume is 10 cu. ft., what
is its density?
18. If the specific gravity of hard coal is 1.75 how would you determine
how many tons of coal a bin would hold?
19. A hollow copper ball weighs 2 kg. What must be its volume to enable
it to just float in water?
20. A mass having a volume of 100 ccm. and a specific gravity of 2.67 is
fastened to 200 ccm. of wood, specific gravity 0.55. What will the
combination weigh in water?
21. A block weighing 4 oz. in air is tied to a sinker which appears to
weigh 14 oz. in water. Both together appear to weigh 6 oz. in water.
What is the specific gravity of the block?
CHAPTER IV
MECHANICS OF GASES
(1) WEIGHT AND PRESSURE OF THE AIR
=51. Weight of Air.=--It is said that savages are unaware of the
presence of _air_. They feel the _wind_ and hear and see it moving the
leaves and branches of the trees, but of air itself they have little
conception.
To ordinary observers, it seems to have no weight, and to offer little
resistance to bodies passing through it. That it has weight may be
readily shown as follows: (See Fig. 29.) If a hollow metal sphere, or a
glass flask, provided with tube and stopcock, be weighed when the
stopcock is open, and then after the air has been exhausted from it by
an air pump, a definite loss of weight is noticeable.
[Illustration: FIG. 29.--Proof that air has weight.]
If the volume of the sphere is known and it is well exhausted of air, a
fair approximation of the weight of air may be obtained. Under
"_standard conditions_," which means _at the freezing temperature_ and a
barometric pressure of 76 cm., a liter of air weighs 1.293 g. while 12
cu. ft. of air weigh approximately 1 lb.
=52. Pressure of Air.=--Since air has weight it may be supposed to exert
pressure like a liquid. That it does so may be shown in a variety of
ways.
If a plunger fitting tightly in a glass cylinder be drawn upward, while
the lower end of the tube is under water, the water will rise in the
tube (Fig. 30). The common explanation of this is that the water rises
because of "suction." The philosophers of the ancient Greeks explained
it by saying that "nature abhors a vacuum," and therefore the water
rises. Neither explanation is correct. It was found in 1640 that water
would not rise in a pump more than 32 ft. despite the fact that a vacuum
was maintained above the water. Galileo was applied to for an
explanation. He said, "evidently nature's horror of a vacuum does not
extend above 32 ft." Galileo began tests upon "the power of a vacuum"
but dying left his pupil Torricelli to continue the experiment.
Torricelli reasoned that if water would rise 32 ft., then mercury, which
is 13.6 times as dense as water, would rise about 1/13 as much. To test
this, he performed the following famous experiment.
[Illustration: FIG. 30.--Air pressure forces the liquid up the tube.]
=53. Torricelli's Experiment (1643).=--Take a glass tube about 3 ft.
long, sealed at one end, and fill it with mercury. Close the end with
the finger and invert, placing the end closed by the finger under
mercury in a dish (Fig. 31). Remove the finger and the mercury sinks
until the top of the mercury is about 30 in. above the level of the
mercury in the dish. Torricelli concluded that the rise of liquids in
exhausted tubes is due to the pressure of the atmosphere acting on the
surface of the mercury in the dish.
To test this, place the tube with its mercury upon the plate of an air
pump and place a tubulated bell jar over the apparatus so that the tube
projects through a tightly fitting stopper. (See Fig. 32.) If the air
pressure is the cause of the rise of mercury in the tube, on removing
the air from the bell jar the mercury should fall in the tube. This is
seen to happen as soon as the pump is started. It is difficult to remove
all the air from the receiver so the mercury rarely falls to the same
level in the tube as in the dish. A small tube containing mercury is
often attached to air pumps to indicate the degree of exhaustion. Such
tubes are called _manometers_.
[Illustration: FIG. 31.--Torricelli's experiment.]
[Illustration: FIG. 32.--The mercury drops as the air is removed.]
=54. The Amount of Atmospheric Pressure.=--Torricelli's experiment
enables us to compute readily the pressure of the atmosphere, since it
is the atmospheric pressure that balances the column of mercury in the
tube. By Pascal's Law, the pressure of the atmosphere on the surface of
the mercury in the dish is transmitted as an exactly equal pressure on
the mercury column in the tube at the same level as the mercury
outside.
This pressure, due to the air, must balance the weight of the column of
mercury in the tube. It therefore equals the weight of the column of
mercury of unit cross-section. The average height of the column of
mercury at sea-level is 76 cm. Since the weight of 1 cc. of mercury is
13.6 grams, the pressure inside the tube at the level of the surface of
the mercury in the dish is equal to 1 × 76 × 13.6 or 1033.6 g. per
square centimeter. Therefore the _atmospheric pressure_ on the surface
of the mercury in the dish is 1033.6 g. per square centimeter,
approximately _1 kg. per square centimeter or 15 lbs. per square inch_.
=55. Pascal's Experiment.=--Pascal tested in another way the action of
atmospheric pressure upon the column of mercury by requesting his
brother-in-law, Perrier, who lived near a mountain, to try the
experiment on its top. Perrier found that on ascending 1000 meters the
mercury fell 8 cm. in the tube. Travelers, surveyors, and aviators
frequently determine the altitude above sea-level by reading the
barometer, an ascent of 11 meters giving a fall of about 1 mm. in the
mercury column, or 0.1 in. for every 90 ft. of ascent.
[Illustration: FIG. 33.--A standard barometer.]
_56. The Barometer._--The modern barometer (Fig. 33), consists of a
Torricellian tube properly mounted. Reading a barometer consists in
accurately reading the height of the mercury column. This height varies
from 75 to 76.5 cm. or 29 to 30 in. in localities not far from the
sea-level. The atmospheric pressure varies because of disturbances in
the atmosphere. It is found that these disturbances of the atmosphere
pass across the country from west to east in a somewhat regular manner,
hence a series of readings of the barometer may give reliable
information of the movement of these disturbances and so assist in
forecasting the weather. The weather Bureau has observations taken at
the same moment at various stations over the country. These observations
form the basis for the daily forecast of the weather.
[Illustration: FIG. 34.--An aneroid barometer]
Another form of barometer in common use is the _Aneroid Barometer_
(Fig. 34). Its essential parts are a cylindrical air-tight box with
an elastic corrugated cover. Inside the box is a partial vacuum.
This makes the cover very sensitive to slight changes of pressure.
The motion of the top of the box is conveyed by a series of levers
to an indicating hand which moves over a dial. This barometer can
be made so sensitive as to indicate the change of air pressure from
a table top to the floor. It is much used by travelers, explorers,
surveying parties and aviators, since the mercurial barometer is
inconvenient to carry.
Important Topics
1. _Weight_ and _Pressure_ of air in English and metric units. How
shown. Evidences.
2. Work of Galileo, Torricelli, and Perrier.
3. Barometer: construction, action, mercurial, aneroid.
[Illustration: FIG. 35.--Air pressure keeps the water In the tumbler.]
[Illustration: FIG. 36.--Cross-section of a modern drinking fountain.]
Exercises
1. Do you think Archimedes' Principle applies to the air? Does Pascal's
Law? Why?
2. Find the downward pressure of the mercury in a barometer tube if the
cross-section is 1 sq. cm. and the height 75 cm. at the level of the
mercury surface in contact with the air. (The density of mercury is 13.6
grams per cc.)
3. What is the weight of the air in a room if it is 10 × 8 × 4 meters?
4. What weight of air is in a room 10 × 15 × 10 ft.?
5. When smoke rises in a straight line from chimneys, is it an
indication of a high or low barometric pressure? Why?
6. Why does a tumbler filled with water and inverted in a dish with its
rim under water remain full?
7. If the barometer tube is inclined the mercury remains at the same
horizontal level. How can this be explained?
8. When the mercurial barometer stands at 76 cm., how high would a water
barometer stand? Explain.
9. Explain why it is possible for one to suck soda water through a tube?
10. Fill a tumbler with water. Place a sheet of paper over the top and
invert. The paper clings to the tumbler and prevents the water from
escaping. Explain. (See Fig. 35.)
11. Why must a kerosene oil can have two openings in order to allow the
oil to flow freely?
12. Explain the action of the modern drinking fountain (Fig. 36).
(2) COMPRESSIBILITY AND EXPANSIBILITY OF THE AIR
=57. Effect of Pressure on Liquids and Gases.=--Both classes of fluids,
liquids and gases, have many characteristics in common. Both are
composed of molecules that move freely; hence both _flow_. At any point
within a fluid the _pressure is the same in all directions_. Archimedes'
Principle applies, therefore, to both liquids and gases.
We now come to an important _difference_ between liquids and gases.
_Liquids_ are _practically incompressible_. "So much so, that if water
is subjected to a pressure of 3000 kg. per sq. cm., its volume is
reduced only about one-tenth." Gases show a very different behavior from
liquids on being subjected to pressure. They may readily be compressed
to a small fraction of their volume as is noticed on inflating a
pneumatic tire. A gas has also the _ability to spring back_ to a larger
volume as soon as the pressure is released, as when a cork is driven
from a pop gun. Not only is compressed air able to expand, but air
under ordinary conditions will expand if it is released in a space where
the pressure is less.
Hollow bodies, animals and plants, are not crushed by atmospheric
pressure, because the air and gases contained within exert as much force
outward as the air exerts inward.
=58. Boyle's Law.=--The relation between the volume and pressure of a
gas was first investigated by Robert Boyle in the seventeenth century.
The experiment by which he first discovered the law or the relation
between the volume and the pressure of a gas is briefly described as
follows:
[Illustration: FIG. 37 _a_.
FIG. 37 _b_.
FIGS. 37 _a_ AND 37 _b_.--Boyle's law apparatus.]
A glass tube is bent in the form of the capital letter J, the short
arm being closed. A little mercury is poured in to cover the bend.
(See Fig. 37 _a_.) Since the mercury is at the _same level in both
arms_, the pressure in (_A_) is the same as in (_B_). Mercury is
now poured into (_A_) until it stands in the long tube at a height
above that in (B) which is equal to the height of the mercury
column of the barometer. (See Fig. 37 _b_.) The air in (_BC_) is
now under a pressure of two atmospheres (one atmosphere is due to
the mercury column). On measurement the air in (_BC_) will be found
to have just one-half of its original volume.
Thus doubling the pressure to which a gas is subjected reduces its
volume to one-half. Tripling the pressure, reduces the volume to
one-third and so on.
Careful experiments reveal the following law: _The volume of a given
mass of gas at constant temperature is inversely proportional to the
pressure to which it is subjected_.
This law is often expressed mathematically. _P/P´ = V´/V_, or _PV =
P´V´_. Since doubling the pressure reduces the volume one-half, it
doubles the density. Tripling the pressure triples the density. We
therefore have _P/P´ = D/D´_ or the density of a gas directly
proportional to its pressure.
[Illustration: FIG. 38.--Height and density of the air.]
=59. Height of the Atmosphere.=--From its properties of _compression_
and _expansion_, the air varies in density and pressure as one ascends
in it. At a height of 3 miles the pressure is reduced to about one-half.
This is an indication that one-half of the air is below this level.
Balloonists have gone to a height of 7 miles, Glaser and Coxwell in
England in 1862 and Berson in France in 1901. The atmosphere has been
explored to a height of 30,500 meters (18.95 miles) by sending up
self-registering barometers in small balloons which burst at great
altitudes. A parachute protects the instruments from breakage from too
rapid fall. This height of 30,500 meters was reached by a balloon sent
up by William R. Blair, at Huron, South Dakota, September 1, 1910.
At a height of 35 miles, the density is estimated at 1/30,000 of its
value at sea-level. (See Fig. 38.) It is believed that some rarefied air
exists for a considerable distance above this point, some estimates
placing the extent at 100 miles, and others from 200 to 500 miles.
Evidences of some air at such heights are shown by: (a) the height at
which meteors first appear, (b) the height of the Aurora Borealis, and
(c), the distance that the sun is below the horizon when the last traces
of color disappear from the sky in the evening.
Although the exact limits of the atmosphere are unknown, the weight of a
column of air 1 sq. cm. in cross-section, and extending _upward as high
as the atmosphere_, may be accurately computed. For this column of air
exactly balances the column of mercury in the tube of the barometer.
Below sea-level, the air increases rapidly in density and it is
estimated that at a depth of 35 miles, the density of the air would be a
thousand times that at the earth's surface, or more than that of water.
Important Topics
1. Evidence of compressibility of gases and incompressibility of
liquids.
2. Boyle's Law. Proof, applications.
3. Extent of the atmosphere--three evidences.
Exercises
1. Mention three illustrations of the compressibility and expansibility
of air that you know from your own experience.
2. Increasing the pressure increases the amount of a gas that will be
absorbed by a liquid? Explain this. Have you ever observed this fact?
Where?
3. If a toy balloon containing 2000 ccm. of gas at the earth's surface
where the barometer reading is 76 cm., rises to an elevation where the
barometer reads 54 cm., the balloon will tend to expand to what volume?
Explain. Will it attain this volume?
4. If a gas is compressed, it changes in temperature. How do you explain
this?
5. What change in temperature will occur when compressed air is allowed
to expand? Explain.
6. Air blowing up a mountain side has its pressure lessened as it
approaches the top. How will this affect the temperature? Why? What may
result from this change in temperature? Explain.
7. To what pressure must 500 ccm. of air be subjected to compress it to
300 ccm. the barometer reading at first being 75 cm. Explain.
[Illustration: FIG. 39.--The air pump.]
(3) PNEUMATIC APPLIANCES
=60. The Air Pump.=--The air pump is used to remove air or other gases
from a closed vessel. It was invented about 1650 by Otto Von Guericke,
burgomaster of Magdeburg, Germany. One form of air pump is shown in
Fig. 39. _C_ is a cylinder within which slides a tightly fitting piston.
_R_ is the vessel from which the air is to be exhausted. _r_ and _u_ are
valves opening upward. The action of the pump is as follows:
On pushing the piston down, the air in _C_ is compressed. This opens
valve _r_ allowing the confined air to escape above the piston. The
piston is then raised making the space in _C_ a partial vacuum. The
pressure in _R_ now being greater than in _C_, _u_ is pushed up and the
air from _R_ rushes into _C_, until the pressure is equalized. On
pushing down the piston again, valve _u_ closes and the process is
repeated until the pressure in _R_ is no longer able to raise the valve
_u_. Some air pumps are so constructed that the valves are opened and
closed automatically by the movement of the piston. With these pumps a
higher degree of rarefaction can be obtained.
Air is often partially exhausted from receivers or vessels by the use of
a filter pump or _aspirator_. A stream of water flowing through a
constriction causes a reduced pressure, draws in air and carries it
away, and thus produces a partial vacuum. See Fig. 40 for a section of
the device.
[Illustration: FIG. 40.--An aspirator.]
=61. The Condensing Pump.=--This is like the exhaust pump except that
its valves are reversed. It is used in compressing illuminating gases
into cylinders for use in lighting vehicles, stereopticons, Pintsch
lights, gas light buoys, etc., and also for compressing air to operate
air brakes, pneumatic hammers and drills, and for other uses.
The common condensing pump is the kind used for inflating tires. (See
Fig. 41.) In this, a loosely fitting metal piston is attached to a disc
of leather somewhat larger than the cylinder. This device is called a
_cup valve_. On raising the piston, air rushes in from the top past the
valve, but on pushing the piston down, the valve is pressed tightly
against the sides of the cylinder and prevents the escape of any air.
The compressed air pushes open a valve on the tire and enters it. This
valve closes as soon as the pressure is lessened from outside. It is
well to notice in all of these pumps that _two_ valves are used. One
holds the air already secured while the other opens for a new supply.
Both valves are never open at the same time.
[Illustration: FIG. 41.--Condensing pump used in inflating tires.]
=62. Water Pumps.--The Common Lift Pump.= This, the simplest pump for
raising water, consists of a cylinder _C_ (Fig. 42) connected by a pipe
_R_ to a supply of water as a cistern or well. A valve opening upward is
placed at the bottom of the cylinder over the entrance to the pipe. In
the cylinder is a tightly fitting piston connected by a rod to a lever
for ease in action. The piston contains a valve opening upward. In
operating this pump water is usually first poured into the cylinder to
"prime" it. This helps to close the valves and prevents air leaking past
them. When the piston is lowered the lower valve closes, the air in the
cylinder being compressed pushes the upper valve open and passes above
the piston. On raising the piston the upper valve closes. This forms a
partial vacuum in the cylinder.
The air pressing on the surface of the water below forces the water and
air that may be in the tube upward through the lower valve to fill this
partial vacuum.
When the cylinder becomes filled with water, this is lifted out on the
up-stroke, whence its name, "lift pump." Since the atmospheric pressure
at sea-level can only support a column of water about 34 ft. high, the
lower valve must be within this distance of the water surface. In actual
practice the limit is about 27 ft. In deeper wells, the cylinder and
valves are placed so that they are within 25 or 27 ft. of the surface of
the water in the well, a long piston rod reaching above the surface of
the ground and connected to a pump handle operates the piston. A
discharge pipe extends from the cylinder to the surface of the ground
above.
[Illustration: FIG. 42.--The common lift pump.]
[Illustration: FIG. 43.--A force pump with an air chamber (_A_).]
=63. The Force Pump.=--The force pump is used to deliver water under
pressure either for spraying or to an elevated reservoir. The piston is
solid, the second valve being placed at the entrance of the discharge
pipe. (See Fig. 43.) The action is the same as that of the lift pump,
with this exception; the piston in its down stroke forces the water out
through the discharge pipe, the velocity depending upon the pressure
exerted.
A force pump is usually provided with an air chamber which is connected
with the discharge pipe. On the down stroke of the piston, water is
forced into the air chamber. This compresses the air it contains. The
compressed air reacts and exerts pressure on the water forcing it out in
a steady stream.
Force pumps are used in deep wells, being placed at the bottom.
The pumps used in city water works, fire engines, and all steam pumps,
are force pumps. (See Fig. 44.)
[Illustration: FIG. 44.--A steam pump used on a fire engine.]
=64. The Siphon.=--The siphon is a tube used to convey a liquid from one
level over an elevation to a lower level by atmospheric pressure. It is
used to remove liquids from tanks or vessels that have no opening at the
bottom.
The siphon cannot be completely understood until one has mastered the
laws of the flow of liquids. The following is offered as an incomplete
explanation of its behavior. Consider the siphon to be full of water
and closed at _d_ (Fig. 45). Atmospheric pressure on _a_ will hold the
siphon full if _ab_ does not exceed 34 feet. If _d_ is opened the water
falls out with a speed equal to that acquired in falling from the level
of _a_ to that of _d_. This speed is acquired by all the water in the
siphon and results in a drop in pressure throughout it. The pressure at
_a_ inside the siphon becomes less than the pressure at the same level
outside as soon as the water starts flowing. The water in the vessel
then flows into the siphon and out at _d_. This flow continues as long
as there is a fall from the free surface of the water in the vessel to
the outlet at _d_.
[Illustration: FIG. 45.--Cross-section of a siphon.]
[Illustration: FIG. 46.--The Cartesian diver.]
=65. The Cartesian Diver.=--This is a device which illustrates at the
same time transmission of pressure by liquids, Archimedes' principle,
and compressibility of gases. It was invented by Des Cartes (1596-1650).
As ordinarily made, it is a hollow glass image with a small opening in
the foot. It contains air and water in such amounts that the average
density of image and contents is slightly less than that of water. It is
placed in a tall glass jar filled with water and covered with tightly
stretched rubber tissue. (See Fig. 46.) By pressing on the rubber cover
the diver may be made to sink, since the air and water transmit the
pressure on the cover which compresses the air inside the figure
admitting some water to it, thus making the diver more dense than
water. By varying the pressure it can be made to sink, rise, or remain
stationary at will.[D] A small vial can be used instead of the image.
[D] The position of a submarine in or under water is controlled in
a similar manner.
=66. Hydraulic Ram.=--The hydraulic ram (see Fig. 47) is an automatic
device that is much used for raising water from springs to houses
located on higher ground. Water flows through the pipe _A_ through the
opening at _B_. The pressure closes the valve at _B_. The increased
pressure in the pipe due to the closing of _B_ opens the valve _C_ and
some of the water flows into the air chamber _D_. This reduces the
pressure against the valve _B_ so that it drops and allows a little
water to escape. Just as this happens, valve _C_ closes. The pressure in
the pipe then closes _B_ and forces water past _C_. This action being
continually repeated, the air in _D_ becomes so compressed that it has
elastic force enough to raise the water in a steady stream to a height
of many feet.
[Illustration: FIG. 47.--Cross-section of a hydraulic ram.]
=67. The Balloon.=--Since air is a fluid, Archimedes' principle applies
to it as well as to liquids. Therefore any object in the air is lifted
up by a force equal to the weight of the air it displaces. The object
will rise, if it weighs less than this displaced air and will continue
to rise until both weights are equal.
_The Balloon_ (Fig. 48) rises because it weighs less than the air it
displaces, and therefore it is pushed up by the heavier air, the
"lifting power" being the difference between its weight and that of the
air displaced. The neck at the bottom is left open to allow for
expansion of the gas. When the aeronaut wishes to descend, he opens a
valve at the top allowing some of the gas to escape.
[Illustration: FIG. 48.--Winner of international championship race,
Paris, 1913.]
_Hydrogen_ is the lightest gas, weighing 0.09 kg. per cubic meter, and
so gives the greatest lifting power, but as it is expensive to make,
coal gas, density 0.75 kg. per cubic meter, is ordinarily employed.
Helium has recently been used to fill military balloons because it
cannot be set on fire.
_The Parachute_ (Fig. 49) is an umbrella-shaped device for use in
descending from a balloon. After falling a few seconds it opens, the
large surface exposed to the air causing it to descend slowly. The hole
in the top keeps the parachute upright by allowing the air to escape
through it, thus relieving the pressure.
[Illustration: FIG. 49.--A parachute.]
[Illustration: FIG. 50.--Cross-section of a Westinghouse air brake.]
=68. The Air Brake.=--Compressed air is used to do work in many
machines, such as pneumatic drills, hammers, and air brakes. The
Westinghouse air brake (Fig. 50) uses air at a pressure of about 70 lbs.
to the square inch. The essential parts as shown are a reservoir _R_,
the brake cylinder _C_ and a triple valve _V_, placed under each car
with an air pipe _P_, leading to the engine. This is connected to _R_ by
the triple valve _V_. When the pressure in _P_ is reduced by the
engineer or by accident, the triple valve operates so as to admit air
from _R_ into the cylinder _C_ pushing the piston _H_ to the left. _H_
is connected to the brakes by levers which press the brake shoes
strongly against the wheels. When the air pressure in _P_ is restored
the triple valve acts so as to permit the air in _C_ to escape while _R_
is filled again from _P_. The hissing sound heard when a train stops is
caused by air escaping from cylinder _C_. The spring in _C_ keeps the
brakes from the wheels except when the "air is on."
[Illustration: FIG. 51.--Cross-section of a gas meter showing its
construction and action.]
=69. The Gas Meter.=--The gas meter consists of a box divided into two
parts by a vertical partition (Fig. 51). Two bellows are attached to
this partition, one on each side. The valves that regulate the flow of
gas to and from the bellows and the chambers _A_ and _D_ are opened and
closed by levers connected with the bellows. These levers also operate
the hands upon the dials. When the inlet to the bellows _B_ is opened,
the outlet of _A_ is also opened. Gas entering _B_ opens the bellows and
forces the gas in _A_ out into the house-pipe _E_. When _B_ is full its
inlet valve closes and its outlet valve opens. The inlet of _A_ also
opens and its outlet closes. Gas now flows into _A_, compressing the
bellows and _B_, and forcing the gas from it into the house-pipe. At
each filling of the bellows _B_ there will be displaced from _A_ and
forced into the house-pipe as much gas as enters _B_. It is evident that
at each emptying of _B_ an equal amount of gas enters _A_. Thus we have
_A_ and _B_ alternately filling and emptying as long as the gas burner
is open. To have a continuous flow of gas in the house-pipes two pipes
and two chambers are necessary, one being filled while the other is
being emptied.
Fig. 52 represents the dials upon a gas meter showing a reading of
54,600 cu. ft.
[Illustration: FIG. 52.--Dials of a gas meter.]
=70. Centrifugal Pumps.= Fluids, such as water and air, are often put in
motion by devices called _centrifugal pumps_ (see Art. 78). These pumps
contain a revolving part, like a wheel without a rim, whose spokes are
replaced by thin blades. This revolving part resembles the paddle wheel
of some steam boats and is enclosed in a case or cover having one
opening at the rim and another opening on one side about the axle.
[Illustration: FIG. 53.--A vacuum sweeper. (_Courtesy of the Hoover
Suction Sweeper Co._)]
When the wheel is rapidly revolved, the fluid is driven out with
considerable force through the opening at the rim, while a partial
vacuum is produced at the axle causing a rapid flow into the device at
this point.
This is the principle of the action of the _vacuum cleaner_. Fig. 53 is
a section of a vacuum sweeper showing the revolving wheel and the
current of air passing into the wheel at the lower side and out of the
rim of the case at the rear.
_Centrifugal water pumps_ work on the same principle and furnish a
continuous flow of water, often large in volume and at considerable
pressure.
Important Topics
1. Air pump.
2. Condensing pump.
3. Lift and force pumps.
4. Siphon.
5. Cartesian diver.
6. Hydraulic ram.
7. Balloon.
8. Air brake.
9. Gas meter.
10. Vacuum cleaner.
Exercises
1. Explain why smoke settles to the ground before storms.
2. Why does the water rise in the suction pipe of a pump?
3. Why is it easier to float in water when the lungs are filled with air
than when they are not filled?
4. Why is it easier to swim in salt water than in fresh water?
5. How are submarines made to sink? to rise to the surface?
6. How can a fish rise or sink in water?
7. Explain why a life preserver made of cork will enable a person to
float.
8. Hold the open hand out flat with the fingers together. Place
underneath the fingers a piece of paper. Blow between the first and
second fingers against the paper. As long as you blow hard the paper
will not fall but will stick to the hand. Explain.
9. Why does pressing the bulb of an atomizer force out the liquid in a
fine spray?
10. Why is air that contains a large amount of water vapor lighter than
air that only contains a small amount?
11. How are heights above sea-level ascertained by a barometer?
12. Oil floats on water but sinks in alcohol. Explain.
13. In a balloon the lower end is often open to the air. Why does not
the gas escape and prevent the balloon from rising?
14. How long will a balloon continue to rise?
15. If the pressure against the 8-in. piston of an air brake is 70 lbs.
per square inch, how much force does the piston exert?
16. The capacity of a balloon is 40,000 cu. ft. The weight of the
balloon, car, etc., is 600 lbs.; specific gravity of the gas used is
0.46 that of the air. Find how much weight the balloon can carry.
17. The so-called Magdeburg hemispheres were invented by Otto von
Guericke of Magdeburg, Germany. When the hemispheres (see Fig. 54) are
placed in contact and the air exhausted it is found very difficult to
pull them apart. Explain.
18. Von Guericke's hemispheres had an inside diameter of 22 in. What
force would be required to pull them apart if all the air were exhausted
from them? (Find the atmospheric force on a circle, 22 in. in diameter.)
19. Von Guericke made a water barometer whose top extended through the
roof of his house. On the top of the water in the tube was placed a
wooden image. In fair weather the image appeared above the roof, but it
descended before a storm. Explain.
20. The balloon "Goodyear" (Fig. 48), which won the International
championship race at Paris in 1913, has a capacity of 80,000 cu. ft. The
gas bag weighs 653 lbs., the net 240 lbs. and the basket 92 lbs. How
large a load can it carry when filled with hydrogen specific gravity
0.069 (compared with air).
[Illustration: FIG. 54.--Magdeburg hemispheres.]
Review Outline: Liquids and Gases
Liquids: Force, pressure, and density. Floating and immersed bodies.
Laws: Liquid force, _F = A.h.d_, Pascal's, Archimedes. Illustrations and
Applications:
Specific gravity, _W_{a}/(W_{a} - W_{w})_, _(W_{a} - W_{l})/(W_{a}
- W_{w})_, Boyle's, _PV = P´V´_
Devices: Hydraulic press, air cushion, barometer--mercurial and aneroid.
Pumps, lift, force, vacuum, compression, centrifugal, balloon, siphon,
etc. Construction and action of each.
CHAPTER V
FORCE AND MOTION
(1) FORCE, HOW MEASURED AND REPRESENTED
=71. Force.=--We have been studying various forces, such as air
pressure, pressure in liquids, and the force of elasticity in solids,
and have considered them simply as pushes or pulls. A more formal study
of forces in general and of devices for representing and measuring them
will be helpful at this point of the course.
_A force is that which tends to cause a change in the size or shape of a
body or in its state of motion._ In other words a force is a push or a
pull. That is, force tends to produce distortion or change of motion in
a body. Force itself is invisible. We measure it by the effect it
produces. Forces are usually associated with the objects exerting them.
Thus we speak of _muscular force_, _air pressure_, _liquid pressure_,
the force of a spring, the force of the earth's attraction and so on.
Forces are classified in various ways.
I. With respect to the _duration and steadiness_ of the force.
(a) Constant, as the earth's attraction. (b) Impulsive, as the stroke of
a bat on a ball. (c) Variable, as the force of the wind.
II. With respect to the _direction_ of the force.
(a) Attractive, as the earth's attraction. (b) Repulsive, as air
pressure, liquid pressure, etc.
=72. Methods of Measuring Force.=--Since forces are measured by their
effects which are either distortion or change of motion, either of these
effects may be used to measure them. For example, the force exerted by
a locomotive is sometimes computed by the _speed_ it can develop in a
train of cars in a given time, or the force of the blow of a baseball
bat is estimated by the _distance_ the ball goes before it strikes the
ground.
The more common method of measuring force, however, is by _distortion_,
that is, by measuring the change of shape of a body caused by the force.
In doing this, use is made of Hooke's Law (Art. 32), in which it is
stated that "within the limits of perfect elasticity," changes of size
or shape are directly proportional to the forces employed. That is,
twice as great a force will produce twice as great a change of shape and
so on.
[Illustration: FIG. 55.--A spring balance.]
A common contrivance using this principle is the spring balance (Fig.
55), with which all are familiar, as ice scales, meat scales, postal
scales, etc. The object which changes shape in this device is a coiled
spring contained in the case of the instrument. The balance is so
constructed that when the spring is pulled out as far as possible it has
not reached its limit of elasticity, since, if the spring were stretched
so as to exceed its elastic limit, the index would not return to its
first position on removing the load. (See Arts. 30-32.)
=73. Graphic Representation of Forces.=--A force is said to have three
elements. These are (a) _its point_ of _application_, (b) _its
direction_, and (c) _its magnitude_. For example, if there is hung upon
the hook of a spring balance a weight of 5 lbs., then we have: (a) its
point of application on the hook of the balance, (b) its downward
direction and (c) its magnitude, or 5 lbs. These three elements may be
represented by a line. Thus in Fig. 56_a_, a line _AB_ is drawn as
shown, five units long; _A_ represents the point of application; _B_,
the arrow head, shows the direction; and the length of the line (five
units) shows the magnitude of the force.
This is called a _graphic representation_ since it represents by a line
the quantity in question. If another weight of 5 lbs. were hung from the
first one, the graphic representation of both forces would be as in Fig.
56_b_. Here the first force is represented by _AB_ as before, _BC_
representing the second force applied. The whole line represents the
_resultant_ of the two forces or the result of their combination. If the
two weights were hung one at each end of a short stick _AC_ (Fig.
56_c_), and the latter suspended at its center their combined weight or
_resultant_ would of course be applied at the center. The direction
would be the same as that of the two weights. The resultant therefore is
represented by _ON_. In order to exactly balance this resultant _ON_, a
force of equal magnitude but opposite in direction must be applied at
the point of application of _ON_, or _O_. _OM_ then represents a force
that will just balance or hold in equilibrium the resultant of the two
forces _AB_ and _CD_. This line _OM_ therefore represents the
_equilibrant_ of the weights _AB_ and _CD_. The resultant of two forces
at an angle with each other is formed differently, as in Fig. 57 _a_.
Here two forces _AB_ and _AC_ act at an angle with each other. Lay off
at the designated angle the lines _AB_ and _AC_ of such length as will
accurately represent the forces. Lay off _BD_ equal to _AC_ and _CD_
equal to _AB_. The figure _ABCD_ is then a parallelogram. Its diagonal
_AD_ represents the resultant of the forces _AB_ and _AC_ acting at the
angle _BAC_. If _BAC_ equals 90 degrees or is a right angle, _AD_ may be
_computed_ thus: _AB² + BD² = AD²_. Why?
and _AD_ = √_([line]AB² + [line]BD²)._
[Illustration: FIG. 56.--Graphic representation of forces acting along
the same or parallel lines.]
[Illustration: FIG. 57.--Graphic representation of two forces acting
(_a_) at a right angle, (_b_) at an acute angle.]
This method of determining the resultant by _computation_ may be used
when the two forces are at right angles. (In any case, _AD may be
measured_ using the same scale that is laid off upon _AB_ and _AC_, as
shown in Fig. 57 _b_.) The three cases of combining forces just given
may be classified as follows: The _first_ is that of _two forces acting
along the same line_ in the same or opposite direction, as when two
horses are hitched tandem, or in a tug of war. The _second_ is that of
_two forces acting along parallel lines_, in the same direction, as when
two horses are hitched side by side or abreast. The _third_ is that of
_two forces acting at the same point at an angle_. It may be represented
by the device shown in Fig. 58, consisting of two spring balances
suspended from nails at the top of the blackboard at _A_ and _B_. A cord
is attached to both hooks and is passed through a small ring at _O_ from
which is suspended a known weight, _W_. Lines are drawn on the
blackboard under the stretched cords, from _O_ toward _OA_, _OB_, and
_OW_ and distances measured on each from _O_ to correspond to the three
forces as read on balance _A_ and _B_ and the weight _W_. Let a
parallelogram be constructed on the lines measured off on _OA_ and _OB_.
Its diagonal drawn from _O_ will be found to be vertical and of the same
length as the line measured on _OW_. The diagonal is the _resultant_ of
the two forces and _OW_ is the equilibrant which is equal and opposite
to the resultant.
[Illustration: FIG. 58.--Experimental proof of parallelogram of forces.]
Again, the _first_ case may be represented by a boat moving up or down a
stream; the resultant motion being the combined effect of the boat's
motion and that of the stream. The _second_, may be represented by two
horses attached side by side to the same evener. The resultant force
equals the sum of the two component forces. The _third_, may be
represented by a boat going across a stream, the resultant motion being
represented by the diagonal of the parallelogram formed by using the
lines that represent the motion of the stream and of the boat.
=74. Units for Measuring Force.=--Force is commonly measured in units of
weight: in pounds, kilograms, and grams. For example, we speak of 15
lbs. pressure per square inch and 1033.6 g. pressure per square
centimeter as representing the air pressure. It should be noted here
that the words pound, kilogram, and gram are used not only to represent
_weight_ or _force_ but also the masses of the objects considered. Thus,
one may speak of a pound-mass meaning the amount of material in the
object.
It will help to avoid confusion if we reserve the simple terms "gram"
and "pound" to denote exclusively an amount of matter, that is, a mass,
and to use the full expression "gram of force" or "pound of force"
whenever we have in mind the pull of the earth upon these masses. Or,
one may speak of a _pound-weight_ meaning the amount of attraction
exerted by the earth upon the object. The same is true of _gram-mass_
and _gram-weight_. The mass of a body does not change when the body is
transferred to another place. The weight, however, may vary, for on
moving a body from the equator toward the poles of the earth the weight
is known to increase.
Important Topics
1. Definition of force.
2. Classification of forces. (a) Duration: constant, impulsive,
variable. (b) Direction: attractive, repulsive.
3. Methods of measuring force. (a) By distortion. (b) By change of
motion.
4. Graphic representation of forces: component, resultant, equilibrant.
5. Three cases of combining forces. (1) Two forces acting on the same
line. (2) Two forces acting in parallel lines. (3) Two forces acting at
the same point at an angle.
6. Units for measuring force, pound, gram.
Exercises
1. Name five natural forces. Which produce a tension? Which a pressure?
2. How much can you lift? Express in pounds and kilograms.
3. Show graphically the resultant of two forces at right angles, one of
12 lbs., the other of 16 lbs. What is the magnitude of this resultant?
Then determine the answer, first by measurement and then by computation.
Which answer is more accurate? Why?
4. Represent by a parallelogram the two forces that support a person
sitting in a hammock and draw the line representing the resultant.
5. Find graphically the resultant of the pull of two forces, one of 500
lbs. east and one of 600 lbs. northwest.
6. Determine the equilibrant of two forces, one of 800 lbs. south and
one of 600 lbs. west.
7. Would the fact that weight varies on going from the equator to either
pole be shown by a spring balance or a beam balance? Explain.
(2) MOTION. NEWTON'S LAWS OF MOTION
=75. Motion a Change of Position.=--Motion is defined as a continuous
_change in the position_ of a body. The _position_ of a body is usually
described as its _distance_ and _direction_ from some fixed point. Thus
a man on a boat may be at rest with respect to the boat and moving with
respect to the earth. Or, if he walks toward the stern as fast as the
boat moves forward, he may keep directly over a rock on the bottom of
the lake and hence not be moving with reference to the rock and yet be
in motion with respect to the boat. Motion and rest, therefore, are
_relative_ terms. The earth itself is in motion in turning on its axis,
in moving along its orbit, and in following the sun in its motion
through space. Motions are classified in several ways:
(A) MODES OF MOTION
1. _Translation._--A body is said to have motion of _translation_ when
every line in it keeps the same direction.
2. _Rotation._--A body has motion of _rotation_ when it turns upon a
fixed axis within the body, as a wheel upon its axle or the earth upon
its axis.
3. _Vibration_ or _Oscillation_.--A body is said to have _vibratory_ or
_oscillatory_ motion when it returns to the same point at regular
intervals by reversals of motion along a given path, _e.g._, a pendulum.
(B) DIRECTION OF MOTION
1. _Rectilinear._--A body has rectilinear motion when its path is a
straight line. Absolute rectilinear motion does not exist, although the
motion of a train on a straight stretch of track is nearly rectilinear.
2. _Curvilinear._--A body has _curvilinear_ motion when its path is a
curved line, _e.g._, the path of a thrown ball.
(C) UNIFORMITY OF MOTION
1. _Uniform._--A body has uniform motion when its speed and direction of
motion do not change. Uniform motion for extended periods is rarely
observed. A train may cover, on an average, 40 miles per hour but during
each hour its speed may rise and fall.
2. _Variable._--A body has variable motion when its speed or direction
of motion is continually changing. Most bodies have variable motion.
3. _Accelerated._--A body has accelerated motion when its speed or
direction of motion continually changes. If the speed changes by the
same amount each second, _and the direction of motion does not change_
the motion is said to be _uniformly_ accelerated, _e.g._, a falling
body.
Uniformly accelerated motion will be studied further under the topic of
falling bodies.
_Velocity_ is _the rate of motion_ of a body in a given direction. For
example, a bullet may have a velocity of 1300 ft. a second upwards.
_Acceleration_ is _the rate of change of velocity_ in a given direction,
or the change of velocity in a unit of time. A train starting from a
station gradually increases its speed. The gain in velocity during one
second is its acceleration. When the velocity is decreasing, as when a
train is slowing down, the acceleration is opposite in direction to the
velocity. A falling body falls faster and faster. It has _downward
acceleration_. A ball thrown upward goes more and more slowly. It also
has _downward acceleration_.
=76. Momentum.=--It is a matter of common observation that a heavy body
is set in motion with more difficulty than a light one, or if the same
force is used for the same length of time upon a light and a heavy
body,[E] the light body will be given a greater velocity. This
observation has led to the _calculation_ of what is called the "quantity
of motion" of a body, or its _momentum_. It is computed by multiplying
the mass by the velocity. If the C.G.S. system is used we shall have as
the momentum of a 12 g. body moving 25 cm. a second a momentum of 12 ×
25 or 300 C.G.S. units of momentum. This unit has no name and is
therefore expressed as indicated above. The formula for computing
momentum is: _M = mv_.
[E] By a light body is meant one of small mass, a heavy body
possessing much greater mass.
Newton's Laws of Motion
=77. Inertia, First Law of Motion.=--One often observes when riding in a
train that if the train moves forward suddenly the passengers do not get
into motion as soon as the train, and apparently are jerked backward.
While if the train is stopped suddenly, the passengers tend to keep in
motion. This tendency of matter to keep moving when in motion and to
remain at rest when at rest is often referred to as the property of
_inertia_. _Newton's first law of motion_, often called the _law of
inertia_, describes this property of matter as follows:
_Every body continues in a state of rest or of uniform motion in a
straight line unless it is compelled to change that state by some
external force._ This means that if an object like a book is lying on a
table it will remain there until removed by some outside force. No
inanimate object can move itself or stop itself. If a ball is thrown
into the air it would move on forever if it were not for the _force_ of
attraction of the earth and the resistance of the air.
It takes time to put a mass into motion, a heavy object requiring more
time for a change than a light object. As an example of this, note the
movements of passengers in a street car when it starts or stops
suddenly. Another illustration of the law of inertia is the so-called
"penny and card" experiment. Balance a card on the end of a finger.
Place on it a coin directly over the finger, snap the card quickly so as
to drive the card from beneath the coin. The coin will remain on the
finger. (See Fig. 59.)
[Illustration: FIG. 59.--The ball remains when the card is driven away.]
According to Newton's first law of motion a moving body which could be
entirely freed from the action of all external forces would have uniform
motion, and would describe a perfectly straight course. The curved path
taken by a baseball when thrown shows that it is acted upon by an
outside force. This force, the attraction of the earth, is called
_gravity_.
[Illustration: SIR ISAAC NEWTON "By Permission of the Berlin
Photographic Co., New York."
Sir Isaac Newton (1642-1727) Professor of mathematics at Cambridge
university; discovered gravitation; invented calculus; announced the
laws of motion; wrote the Principia; made many discoveries in light.]
[Illustration: GALILEO GALILEI "By Permission of the Berlin Photographic
Co., New York."
Galileo Galilei (1564-1642). Italian. "Founder of experimental science";
"Originator of modern physics"; made the first thermometer; discovered
the laws of falling bodies and the laws of the pendulum; invented
Galilean telescope.]
[Illustration: FIG. 60.--Cross-section of the DeLaval cream separator.]
=78. Curvilinear Motion.=--Curvilinear motion occurs when a moving body
is pulled or pushed away from a straight path. The pull or push is
called _centripetal_ (center-seeking) force. A moving stone on the end
of a string when pulled toward the hand moves in a curve. If the string
is released the stone moves in a tangent to the curve. The string pulls
the hand. This phase of the pull is called _centrifugal_ force. The
_centripetal_ force is the pull on the stone. Centripetal and
centrifugal force together cause a tension in the string. Examples of
curvilinear motion are very common. The rider and horse in a circus ring
lean inward in order to move in a curve. The curve on a running track in
a gymnasium is "banked" for the same reason. Mud flying from the wheel
of a carriage, the skidding of an automobile when passing rapidly around
a corner, and sparks flying from an emery wheel, are illustrations of
the First Law of Motion.
Cream is separated from milk by placing the whole milk in a rapidly
revolving bowl, the cream being lighter collects in the center and is
thrown off at the top. (See Fig. 60.) Clothes in steam laundries are
dried by a centrifugal drier. In amusement parks many devices use this
principle. (See centrifugal pumps, Art. 70.)
[Illustration: FIG. 61.--The two balls reach the floor at the same
time.]
=79. The Second Law of Motion,= sometimes called the _law of momentum_,
leads to the _measurement of force_, by the momentum or the quantity of
motion, produced by it. The law is stated as follows:
_Change of motion, or momentum, is proportional to the acting force and
takes place in the direction in which the force acts._ In other words,
if two or more forces act at the same instant upon a body each produces
the same effect that it would if acting alone. If a card be supported on
two nails driven horizontally close together into an upright board (see
Fig. 61), and two marbles be so placed on the ends as to balance each
other, when one marble is snapped horizontally by a blow, the other will
fall. Both reach the floor at the same time. The two balls are equally
pulled down by the earth's attraction and strike the ground at the same
time, though one is shot sidewise, and the other is dropped vertically.
As gravity is a constant force, while the blow was only a momentary
force, the actual path or resultant motion will be a curved line.
The constant relation, between the acting force and the change of
momentum it produces in a body, has led to the adoption of a convenient
C.G.S. unit of force called the _dyne_. _The dyne is that force which
can impart to a mass of one gram a change of velocity at the rate of one
centimeter per second every second._ This definition assumes that the
body acted upon is free to move without hindrance of any kind, so that
the acting force has to overcome only the _inertia_ of the body.
_However_, the _law_ applies in every case of application of force, so
that each force produces its full effect independently of other forces
that may be acting at the same time upon the body.
=80. Newton's Third Law.=--This law has been experienced by everyone who
has jumped from a rowboat near the shore. The muscular action that
pushes the body forward from the boat also pushes the boat backward,
often with awkward results. The law is stated: _To every action, there
is always an opposite and equal reaction, or the mutual actions of any
two bodies are always equal and opposite in direction_. Many
illustrations of this law are in every one's mind: a stretched rope
pulls with the same force in one direction as it does in the opposite
direction. If a bat hits a ball, the ball hits the bat with an equal and
opposite force. The third law is therefore sometimes called the law of
_reaction_. When a weight is hung upon a spring balance the action of
the weight pulls down the spring until it has stretched sufficiently
(Hooke's Law) to produce an elastic _reaction_ that equals and hence
supports the weight. When a man stands at the center of a plank
supported at its ends, the action of the man's weight bends the plank
until the elastic force developed in the plank equals the weight
applied. Further, when a train or a wagon is on a bridge the bridge
yields until it has developed an elastic reaction equal to the weight
applied. If a person stands in the center of a room, the floor beams
yield until the third law is satisfied. In fact, whenever a force acts,
a contrary equal force always acts.
=81. Stress and Strain.=--A pair of forces that constitute an action and
a reaction is called a _stress_. The two forces are two parts of one
_stress_. If the two forces act away from each other, as in the breaking
of a string, the stress is called a _tension_, but if they act toward
each other as in crushing anything, the stress is called a _pressure_.
In order for a body to exert force it must meet with resistance. The
force exerted is never greater than the resistance encountered. Thus one
can exert but little force upon a feather floating in the air or upon
other light objects. A fast moving shot exerts no force unless it
encounters some resistance.
Forces, then, are always found in pairs. Thus to break a string, to
stretch an elastic band, to squeeze a lemon, one must exert two equal
and opposite forces. Such a thing as a single force acting alone is
unknown. Usually, however, we give our attention mainly to one of the
forces and ignore the other. When a force acts upon a body the change of
shape or size resulting is called a _strain_. Hooke's law (Art. 32) is
often expressed as follows: "The strain is proportional to the stress,"
_e.g._, the stretch of the spring of a spring balance is proportional to
the load placed upon it.
Important Topics
1. Motion a change of position. Kinds of motion.
2. Newton's laws of motion.
3. Momentum.
4. Inertia. First law of motion. Curvilinear motion.
5. Second law of motion.
6. Third law of motion. Action and reaction, stress and strain.
Exercises
1. Mention three illustrations of the third law, different from those
given.
2. A rifle bullet thrown against a board standing upon edge will knock
it down; the same bullet fired at the board will pass through it without
disturbing its position. Explain.
3. A hammer is often driven on to its handle by striking the end of the
latter. Explain.
4. Consider a train moving 60 miles an hour, with a gun on the rear
platform pointing straight backward. If a ball is fired from the gun
with a speed of 60 miles an hour, what will happen to the ball?
5. Could one play ball on the deck of an ocean steamer going 25 miles an
hour without making allowance for the motion of the ship? Explain.
6. On a railroad curve, one rail is always higher. Which? Why?
7. Why can a small boy when chased by a big boy often escape by dodging?
8. Will a stone dropped from a moving train fall in a straight line?
Explain.
9. A blast of fine sand driven against a sheet of glass soon gives it a
rough surface. Explain.
10. Explain the use of fly-wheels in steadying the motion of machinery
(for example, the sewing machine).
11. Is it easier to walk to the front or rear of a passenger train when
it is stopping? Why?
12. Why does lowering the handles of a wheel-barrow on the instant of
striking make it easier to go over a bump?
13. Why should a strong side wind interfere with a game of tennis? How
can it be allowed for?
14. On which side of a railroad track at a curve is it the safer to walk
while a train is passing? Why?
15. Why does a bullet when fired through a window make a clean round
hole in the glass, while a small stone thrown against the window
shatters the glass?
16. A tallow candle can be fired through a pine board. Why?
17. In cyclones, straws are frequently found driven a little distance
into trees; why are the straws not broken and crushed instead of being
driven into the tree unbroken?
18. A bullet weighing one-half oz. is fired from a gun weighing 8 lb.
The bullet has a velocity of 1800 ft. per second. Find the velocity of
the "kick" or recoil of the gun.
18. When football players run into each other which one is thrown the
harder? Why?
20. A railroad train weighing 400 tons has a velocity of 60 miles per
hour. An ocean steamer weighing 20,000 tons has a velocity of one half
mile per hour. How do their momenta compare?
21. Why is a heavy boy preferable to a lighter weight boy for a football
team?
22. Why does a blacksmith when he desires to strike a heavy blow, select
a heavy sledge hammer and swing it over his head?
23. Why does the catcher on a baseball team wear a padded glove?
(3) RESOLUTION OF FORCES
=82. Resolution of Forces.=--We have been studying the effect of forces
in producing motion and the results of combining forces in _many_ ways;
in the _same line_, in _parallel lines_, and in _diverging lines_.
Another case of much interest and importance is _the determination of
the effectiveness of a force in a direction different from the one in
which it acts_. This case which is called _resolution of forces_ is
frequently used. To illustrate: one needs but to recall that a sailor
uses this principle in a practical way whenever he sails his boat in any
other direction than the one in which the wind is blowing, _e.g._, when
the wind is blowing, say from the north, the boat may be driven east,
west, or to any point south between the east and west and it is even
possible to beat back against the wind toward the northeast or
northwest. Take a sled drawn by a short rope with the force applied
along the line _AB_ (see Fig. 62); part of this force tends to lift the
front of the sled as _AC_ and a part to draw it forward as _AD_. Hence
not all of the force applied along _AB_ is used in drawing the sled
forward. Its effectiveness is indicated by the relative size of the
component _AD_ compared to _AB_.
[Illustration: FIG. 62.--_AD_ is the effective component.]
The force of gravity acting upon a sphere that is resting on an
_inclined plane_ may be readily resolved into two components, one, the
_effective_ component, as _OR_, and the other, the _non-effective_ as
_OS_. (See Fig. 63.) If the angle _ACB_ is 30 degrees, _AB_ equals 1/2
of _AC_ and _OR_ equals 1/2 of _OG_, so that the speed of the sphere
down the plane developed in 1 second is less than (about one-half of)
the speed of a freely falling body developed in the same time. Why is
_OS_ non-effective?
[Illustration: FIG. 63.--The effective component is _OR_.]
[Illustration: FIG. 64.--Resolution of the forces acting on an
aeroplane.]
=83. The Aeroplane.=--The aeroplane consists of one or two frames _ABCD_
(see Fig. 64), over which is stretched cloth or thin sheet metal. It is
driven through the air by a propeller turned by a powerful gasoline
motor. This has the effect of creating a strong breeze coming toward the
front of the aeroplane. As in the case of the sailboat a pressure is
created at right angles to the plane along _GF_ and this may be resolved
into two components as _GC_ and _GE_, _GC_ acting to lift the aeroplane
vertically and _GE_ opposing the action of the propeller. Fig. 65
represents the Curtis Flying Boat passing over the Detroit river.
[Illustration: FIG. 65.--The Curtis hydroplane.]
Exercises.
1. If a wagon weighing 4000 lbs. is upon a hill which rises 1 ft. in 6,
what force parallel to the hill will just support the load? (Find the
effective component of the weight down the hill.)
2. If a barrel is being rolled up a 16-ft. ladder into a wagon box 3 ft.
from the ground, what force will hold the barrel in place on the ladder,
if the barrel weighs 240 lbs. Show by diagram.
3. Show graphically the components into which a man's push upon the
handle of a lawn mower is resolved.
4. Does a man shooting a flying duck aim at the bird? Explain.
5. What are the three forces that act on a kite when it is "standing" in
the air?
6. What relation does the resultant of any two of the forces in problem
five have to the third?
7. Into what two forces is the weight of a wagon descending a hill
resolved? Explain by use of a diagram.
8. A wind strikes the sail of a boat at an angle of 60 degrees to the
perpendicular with a pressure of 3 lbs. per square foot. What is the
effective pressure, perpendicular to the sail? What would be the
effective pressure when it strikes at 30 degrees?
9. How is the vertical component of the force acting on an aeroplane
affected when the front edge of the plane is elevated? Show by diagram.
(4) MOMENT OF FORCE AND PARALLEL FORCES
=84. Moment of Force.=--In the study of motion we found that the
quantity of motion is called _momentum_ and is measured by the product
of the _mass times the velocity_. In the study of _parallel forces_,
especially such as tend to produce _rotation_, we consider a similar
quantity. It is called a _moment of force_, which is the term applied to
the _effectiveness_ of a force in producing change of rotation. It also
measured by the product of two quantities; _One, the magnitude of the
force itself_, and the other, _the perpendicular distance from the axis
about which the rotation takes place to the line representing the
direction of the force_.
[Illustration: FIG. 66.--The moments about _S_ are equal.]
_To illustrate:_ Take a rod, as a meter stick, drill a hole at _S_ and
place through it a screw fastened at the top of the blackboard. Attach
by cords two spring balances and draw to the right and left, _A_ and _B_
as in Fig. 66. Draw out the balance _B_ about half way, hold it
steadily, or fasten the cord at the side of the blackboard, and read
both balances. Note also the distance _AS_ and _BS_. Since the rod is at
rest, the tendency to rotate to the right and left must be equal. That
is, the moments of the forces at _A_ and _B_ about _S_ are equal. Since
these are computed by the product of the _force times the force_ arm,
multiply _B_ by _BS_ and _A_ by _AS_ and see if the computed moments are
equal. _Hence a force that tends to turn or rotate a body to the right
can be balanced by another of equal moment that acts toward the left._
[Illustration: FIG. 67.--Law of parallel forces illustrated.]
=85. Parallel Forces.=--Objects are frequently supported by two or more
upward forces acting at different points and forming in this way a
system of parallel forces; as when two boys carry a string of fish on a
rod between them or when a bridge is supported at its ends. The
principle of moments just described aids in determining the magnitude of
such forces and of their resultant. To illustrate this take a wooden
board 4 in. wide and 4 ft. long of uniform dimensions. (See Fig. 67.)
Place several screw hooks on one edge with one set at _O_ where the
board will hang horizontally when the board is suspended there. Weigh
the board by a spring balance hung at _O_. This will be the resultant in
the following tests. Now hang the board from two spring balances at _M_
and _N_ and read both _balances_. Call readings _f_ and _f´_. To test
the forces consider _M_ as a fixed point (see Fig. 67) and the weight of
the board to act at _O_. Then the moment of the weight of the board
should be equal the moment of the force at _N_ since the board does not
move, or _w_ times _OM_ equals _f´_ times _NM_. If _N_ is considered the
fixed point then the moment of the weight of the board and of _f with
reference to the point N_ should be equal, or _w_ times _ON_ = _f_ times
_NM_. Keeping this illustration in mind, the law of parallel forces may
be stated at follows: 1. _The resultant of two parallel forces acting in
the same direction at different points in a body is equal to their sum
and has the same direction as the components._
_The moment of one of the components about the point of application of
the other is equal and opposite to the moment of the supported weight
about the other._
=Problem.=--If two boys carry a string of fish weighing 40 lbs. on
a rod 8 ft. long between them, what force must each boy exert if
the string is 5 ft. from the rear boy?
=Solution.=--The moment of the force _F_ exerted about the opposite
end by the rear boy is _F_ × 8. The moment of the weight about the
same point is 40 × (8 - 5) = 120. Therefore _F_ × 8 = 120, or _F_ =
15, the force exerted by the rear boy. The front boy exerts a force
of _F_ whose moment about the other end of the rod is _F_ × 8. The
moment of the weight about the same point is 40 × 5 = 200. Since
the moment of _F_ equals this, 200 = _F_ × 8, or _F_ = 25. Hence
the front boy exerts 25 lbs. and the rear boy 15 lbs.
[Illustration: FIG. 68.--A couple.]
=86. The Couple.=--If two equal parallel forces act upon a body along
different lines in opposite directions, as in Fig. 68, they have no
single resultant or there is no one force that will have the same effect
as the two components acting together. A combination of forces of this
kind is called a _couple_. Its tendency is to produce change of rotation
in a body. An example is the action upon a compass needle which is
rotated by a force which urges one end toward the north and by an equal
force which urges the other end toward the south.
Important Topics
1. Moment of force, how measured.
2. Parallel forces.
3. The two laws of parallel forces.
4. The couple.
Exercises
1. Show by diagram how to arrange a three-horse evener so that each
horse must take one-third of the load.
2. Two boys support a 10-ft. pole on their shoulders with a 40-lb.
string of fish supported from it 4 ft. from the front boy. What load
does each boy carry? Work by principle of moments.
3. If two horses draw a load exerting a combined pull of 300 lbs., what
force must each exert if one is 28 in. and the other is 32 in. from the
point of attachment of the evener to the load?
[Illustration: FIG. 69.--Forces acting upon a stretched rope.]
[Illustration: FIG. 70.--A crane with horizontal tie.]
4. A weight of 100 lbs. is suspended at the middle of a rope _ACB_ 20
ft. long. (See Fig. 69.) The ends of the rope are fastened at points _A_
and _B_ at the same height. Consider _D_ as the center of the line _AB_.
What is the tension of the rope when _CD_ is 3 ft.? When _CD_ is 1 ft.?
When _CD_ is 1 in.?
5. A crane is set up with the tie horizontal. (See Fig. 70.) If 1000
lbs. is to be lifted, find the tie stress and the boom stress if the
boom angle is 30 degrees? If 45 degrees? 60 degrees?
6. A ball is placed on a plane inclined at an angle of 30 degrees to the
horizontal. What fraction of its weight tends to cause motion down the
plane? What effect does the other component of the weight have? Why?
7. A person weighing 150 lbs. is lying in a hammock. The distance
between the supports is 15 ft. The hammock sags 4 ft. What is the
tension in the supports at each end? What is the tension when the sag is
only 1 ft.?
8. A ladder 30 ft. long and weighing 80 lbs. leans against the side of a
building so that it makes an angle of 30 degrees with the building. Find
the direction and magnitude of the component forces on the ground and at
the building.
9. A traveling crane 50 ft. long weighing 10 tons moves from one end of
a shop to the other, at the same time a load of 4000 lbs. moves from end
to end of the crane. Find the pressure of the trucks of the crane on the
track when the load is at a distance of 5, 10, 15, and 25 ft. from
either end.
[Illustration: FIG. 71--A truss.]
10. Resolve a force of 500 lbs. into two components at right angles to
each other, one of which shall be four times the other.
11. A truss (see Fig. 71), carries a load of 1000 lbs. at _C_. Find the
forces acting along _AC_, _BC_, and _AB_. If _AC_ and _BC_ are each 12
ft. and _AB_ 20 ft., which of these forces are tensions and which are
pressures?
(5) GRAVITATION AND GRAVITY
=87. Gravitation.=--Gravitation is the force of attraction that exists
between all bodies of matter at all distances. This attraction exists
not only between the heavenly bodies, the stars and planets, etc., but
is also found between bodies on the earth. A book attracts all objects
in a room and outside of a room as well, since its weight shows that it
is attracted by the earth itself. The gravitational attraction between
ordinary bodies is so slight that it requires careful experiments to
detect it. In fact, it is only when one of the attracting bodies is
large, as for example the earth, that the force becomes considerable.
Careful studies of the motions of the heavenly bodies, especially of
that of the moon in its orbit about the earth, led Sir Isaac Newton to
the statement of the _law of gravitation_ which is well expressed in the
following statement:
=88. Law of Gravitation.=--_Every particle of matter in the universe
attracts every other particle with a force that is directly proportional
to the product of their masses and inversely proportional to the square
of the distance between them._
The law may be separated into two parts, one referring to the masses of
the bodies concerned, the other to the effect of the distance between
them. The first part is easily understood since we all know that two
quarts of milk will weigh just twice as much as one quart. To illustrate
the second part of the law, suppose that the moon were removed to
_twice_ its present distance from the earth, then the attraction between
the earth and the moon would be _one-fourth_ its present attraction. If
removed to _three_ times its present distance, the attraction would be
_one-ninth_, etc.
The attraction of the earth for other bodies on or near it is called
_gravity_. The _weight_ of a body is the measure of the earth's
attraction for it; or it is the force of gravity acting upon it.
Newton's third law of motion states that every action is accompanied by
an equal and opposite reaction (Art. 80). Hence, the attraction of the
earth for a book or any other object is accompanied by an equal
attraction of the book for the earth.
=89. Weight.=--In advanced physics it is proved that a sphere attracts
as if it were concentrated at its center. Thus if the earth's radius be
considered as 4000 miles, then a body 4000 miles above the earth's
surface would be 8000 miles above the earth's center, or twice as far
from the center of the earth as is a body upon the earth's surface. A
body then 4000 miles above the earth's surface will weigh then but
one-fourth as much as it will at the surface of the earth.
Since the earth is flattened at the poles, the surface at the equator
is farther from the center of the earth than at points north or south.
Thus a body weighing 1 lb. at the equator weighs 1.002 lb. at Chicago,
or about 1/500 more. The rotation of the earth also affects the weight
of a body upon it so that at the equator the weight of a body is 1/289
less than at the pole. Both effects, that of flattening and of rotation,
tend to diminish the weight of bodies at the equator, so that a body at
the latter place weighs about 1/192 less than at the poles.
In studying the effect of the earth's gravity, the following
illustration will be helpful: Imagine an open shaft a mile square
extending through the earth. What would happen to a stone thrown
into the shaft? At first it would have the attraction of the whole
earth drawing it and continually increasing its speed downward. As
it descends from the surface, the pull toward the center grows less
and less. Halfway to the center the body has lost half its weight.
When the stone reaches the center, the pull in all directions is
the same, or in other words, _it has no weight_. It would, however,
continue moving rapidly on account of its inertia, and as it
continues on from the center, the greater part of the earth being
left behind, the attraction pulling toward the center will
gradually stop it. It will then fall again toward the center and be
stopped again after passing it, and after repeatedly moving up and
down will finally come to rest at the center of the earth. At this
point it will be found to be a body without weight since it is
pulled equally in all directions by the material of the earth. What
force brings the body to rest?
=90. Center of Gravity.=--A body is composed of a great many particles
each of which is pulled toward the center of the earth by the force of
gravity. A single force that would exactly equal the combined effect of
the pull of the earth for all the particles of a body would be their
resultant. The _magnitude_ of this resultant is the weight of the body.
The _direction_ of this resultant is in a line passing toward the
earth's center, while the _point of application_ of this resultant is
called the _center of gravity_ of the body. The center of gravity of a
body may also be briefly defined as _the point about which it may be
balanced_. As the location of this point depends upon the distribution
of matter in the body, the center of gravity is also sometimes called
the _center of mass_ of the body.
The earth's attraction for a body is considered for the sake of
simplicity, not as a multitude of little forces, but as a single force
applied at its center of gravity. To find the center of gravity of a
body find two intersecting lines along which it balances, see Fig. 72,
and the center of gravity will be at the intersection. A vertical line
through this point is sometimes called the _line of direction of the
weight_.
[Illustration: FIG. 72.--The center of gravity is at the intersection of
the lines of direction.]
=91. Equilibrium of Bodies.=--Equilibrium means equally balanced. A body
at rest or in uniform motion is then in equilibrium. An object is in
equilibrium under gravity when a vertical line through its center of
gravity passes through the point of support. A trunk is an example of a
body in equilibrium since a vertical line from its center of gravity
falls within the base formed by the area upon which it rests. Work will
be necessary to tip the trunk from its position. The amount of work
required will depend upon the weight of the body and the location of the
center of gravity.
=92. Kinds of Equilibrium.--(a) Stable.=--A body is in stable
equilibrium under gravity if its center of gravity is raised whenever
the body is displaced. It will return to its first position if allowed
to fall after being slightly displaced. In Fig. 73, _a_ and _b_ if
slightly tipped will return to their first position. They are in stable
equilibrium. Other examples are a rocking chair, and the combination
shown in Fig. 74.
[Illustration: FIG. 73.--Stable equilibrium.]
=(b) Unstable.=--A body is in unstable equilibrium under gravity if its
center of gravity is lowered whenever the body is slightly displaced. It
will fall farther from its first position. A pencil balanced on its
point or a broom balanced on the end of the handle are in unstable
equilibrium. The slightest disturbance will make the line of direction
of the weight fall outside of (away from) the point of support (Fig. 75
_a_).
[Illustration: FIG. 74--An example of stable equilibrium. Why?]
[Illustration: FIG. 75.--Unstable equilibrium _a_, neutral equilibrium
_b_.]
=(c) Neutral.=--A body is in neutral equilibrium if its center of
gravity is neither raised nor lowered whenever the body is moved.
Familiar examples are a ball lying on a table (Fig. 75 _b_) and a wagon
moving on a level street (referring to its forward motion).
[Illustration: FIG. 76.--_B_ is more stable than _A_.]
=93. Stability.=--When a body is in stable equilibrium, effort must be
exerted to overturn it, and the degree of stability is measured by the
effort required to overturn it. To overturn a body, it must be moved so
that the vertical line through its center of gravity will pass outside
of its supporting base. This movement in stable bodies necessitates a
raising of the center of gravity. The higher this center of gravity must
be raised in overturning the body, the more stable it is, _e.g._, see
Fig. 76. Thus a wagon on a hillside will not overturn until its weight
falls outside of its base, as in Fig. 77 _B_. The stability of a body
depends upon the position of its center of gravity and the area of its
base. _The lower the center of gravity and the larger the base_, the
more stable the body. What means are employed to give stability to
bodies, in every-day use (such as clocks, ink-stands, pitchers, vases,
chairs, lamps, etc.)?
[Illustration: FIG. 77.--_B_ will overturn; _A_ will not.]
Important Topics
1. Gravitation; law of gravitation, gravity, weight.
2. Center of gravity.
3. The three states of equilibrium. Stability.
Exercises
1. Why is a plumb-line useful in building houses?
2. What is the center of gravity of a body?
3. Explain the action of a rocking chair that has been tipped forward.
4. Is the stability of a box greater when empty or when filled with
sand? Explain.
5. How can you start yourself swinging, in a swing, without touching the
ground?
6. Is the center of gravity of the beam of a balance above, below, or at
the point of a support? How did you find it out?
7. Why are some ink bottles cone shaped with thick bottoms?
8. Would an electric fan in motion on the rear of a light boat move it?
Would it move the boat if revolving under water? Explain.
9. What turns a rotary lawn sprinkler?
10. Why, when you are standing erect against a wall and a coin is placed
between your feet, can you not stoop and pick it up unless you shift
your feet or fall over?
11. What would become of a ball dropped into a large hole bored through
the center of the earth?
12. When an apple falls to the ground, does the earth rise to meet it?
13. How far from the earth does the force of gravity extend?
14. Why in walking up a flight of stairs does the body bend forward?
15. In walking down a steep hill why do people frequently bend backward?
16. Why is it so difficult for a child to learn to walk, while a kitten
or a puppy has no such difficulty?
17. Explain why the use of a cane by old people makes it easier for them
to walk?
(6) FALLING BODIES
=94. Falling Bodies.=--One of the earliest physical facts learned by a
child is that a body unsupported falls toward the earth. When a child
lets go of a toy, he soon learns to look for it on the floor. It is also
of common observation that light objects, as feathers and paper, fall
much slower than a stone. The information, therefore, that all bodies
actually fall at the same rate in a vacuum or when removed from the
retarding influence of the air is received with surprise.
This fact may be shown by using what is called a coin and feather tube.
On exhausting the air from this tube, the feather and coin within are
seen to fall at the same rate. (See Fig. 78.) when air is again
admitted, the feather flutters along behind.
[Illustration: FIG. 78.--Bodies fall alike in a vacuum.]
=95. Galileo's Experiment.=--The fact that bodies of different weight
tend to fall at the same rate was first experimentally shown by Galileo
by dropping a 1-lb. and a 100-lb. ball from the top of the leaning tower
of Pisa in Italy (represented in Fig. 79). Both starting at the same
time struck the ground together. Galileo inferred from this that
feathers and other light objects would fall at the same rate as iron or
lead were it not for the resistance of the air. After the invention of
the air pump this supposition was verified as just explained.
[Illustration: FIG. 79.--Leaning tower of Pisa.]
=96. Acceleration Due to Gravity.=--If a body falls freely, that is
without meeting a resistance or a retarding influence, its motion will
continually increase. The _increase_ in motion is found to be constant
or uniform during each second. This uniform increase in motion or in
velocity of a falling body gives one of the best illustrations that we
have of uniformly accelerated motion. (Art. 75.) On the other hand, a
body thrown upward has uniformly retarded motion, that is, its
acceleration is downward. The velocity acquired by a falling body in
unit time is called its _acceleration_, or the _acceleration due to
gravity_, and is equal to 32.16 ft. (980 cm.) per second, downward, each
second of time. In one second, therefore, a falling body gains a
velocity of 32.16 ft. (980 cm.) per second, downward. In two seconds it
gains twice this, and so on.
In formulas, the acceleration of gravity is represented by "_g_" and the
number of seconds by _t_, therefore the formula for finding the
velocity, _V_,[F] of a falling body starting from rest is _V_ = _gt_. In
studying gravity (Art. 89) we learned that its force varies as one moves
toward or away from the equator. (How?) In latitude 38° the acceleration
of gravity is 980 cm. per second each second of time.
[F] _V_ represents the velocity of a falling body at the end of _t_
seconds.
=97. Experimental Study of Falling Bodies.=--To study falling bodies
experimentally by observing the fall of unobstructed bodies is a
difficult matter. Many devices have been used to reduce the motion so
that the action of a falling body may be observed within the limits of a
laboratory or lecture room. The simplest of these, and in some respects
the most satisfactory, was used by Galileo. It consists of an inclined
plane which reduces the effective component of the force of gravity so
that the motion of a body rolling down the plane may be observed for
several seconds. For illustrating this principle a steel piano wire has
been selected as being the simplest and the most easily understood. This
wire is stretched taut across a room by a turn-buckle so that its slope
is about one in sixteen. (See Fig. 80.) Down this wire a weighted pulley
is allowed to run and the distance it travels in 1, 2, 3, and 4 seconds
is observed. From these observations we can compute the distance covered
each second and the velocity at the end of each second.
[Illustration: FIG. 80.--Apparatus to illustrate uniformly accelerated
motion.]
In Fig. 63, if _OG_ represents the weight of the body or the pull of
gravity, then the line _OR_ will represent the effective component along
the wire, and _OS_ the non-effective component against the wire. Since
the ratio of the height of the plane to its length is as one to sixteen,
then the motion along the wire in Fig. 80 will be one-sixteenth that of
a falling body.
=98. Summary of Results.=--The following table gives the results that
have been obtained with an apparatus arranged as shown above.
In this table, column 2 is the one which contains the results directly
observed by the use of the apparatus. Columns, 3, 4, and 5 are computed
from preceding columns.
(1) (2) (3) (4) (5)
No. of Total Distance Velocity at Acceleration
seconds distance each second end of second each second
moved
Per second Per second
1 30 cm. 30 cm. 60 cm. 60 cm.
2 120 cm. 90 cm. 120 cm. 60 cm.
3 270 cm. 150 cm. 180 cm. 60 cm.
4 480 cm. 210 cm. 240 cm. 60 cm.
Column 5 shows that the acceleration is uniform, or the same each
second. Column 4 shows that the velocity increases with the number of
seconds or that _V_ = _at_. Column 3 shows that the increase in motion
from 1 second to the next is just equal to the acceleration or 60 cm.
This is represented by the following formula: _s_ = 1/2 _a_(2_t_ - 1).
The results of the second column, it may be seen, increase as 1:4:9:16,
while the number of seconds vary as 1:2:3:4. That is, _the total
distance covered is proportional to the square of the number of
seconds_.
This fact expressed as a formula gives: _S_ = 1/2_at_².
Substituting _g_, the symbol for the acceleration of gravity, for _a_ in
the above formulas, we have: (1) _V_ = _gt_, (2) _S_ = 1/2_gt_², (3) _s_
= 1/2_g_(2_t_ - 1).
=99. Laws of Falling Bodies.=--These formulas may be stated as follows
for a body which falls from rest:
1. The velocity of a freely falling body at the end of any second is
equal to 32.16 ft. per sec. or 980 cm. per second multiplied by the
number of the second.
2. The distance passed through by a freely falling body during any
number of seconds is equal to the square of the number of seconds
multiplied by 16.08 ft. or 490 cm.
3. The distance passed through by a freely falling body during any
second is equal to 16.08 feet or 490 cm. multiplied by one less than
twice the number of the second.
Important Topics
1. Falling bodies.
2. Galileo's experiment.
3. Acceleration due to gravity.
4. Laws of falling bodies.
Exercises
1. How far does a body fall during the first second? Account for the
fact that this distance is numerically equal to half the acceleration.
2. (a) What is the velocity of a falling body at the end of the first
second? (b) How far does it fall during the second second? (c) Account
for the difference between these numbers.
3. What is the velocity of a falling body at the end of the fifth
second?
4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) during
the sixth second?
5. (a) What is the difference between the average velocity during the
sixth second and the velocity at the beginning of that second?
(b) Is this difference equal to that found in the second problem? Why?
6. A stone dropped from a cliff strikes the foot of it in 5 seconds.
What is the height of the cliff?
7. Why is it that the increased weight of a body when taken to higher
latitudes causes it to fall faster, while at the same place a heavy body
falls no faster than a light one?
8. When a train is leaving a station its acceleration gradually
decreases to zero, although the engine continues to pull. Explain.
9. Would you expect the motion of equally smooth and perfect spheres of
different weight and material to be equally accelerated on the same
inclined plane? Give reason for your answer. Try the experiment.
10. A body is thrown upward with the velocity of 64.32 ft. per sec. How
many seconds will it rise? How far will it rise? How many seconds will
it stay in the air before striking the ground?
11. 32.16 feet = how many centimeters?
12. The acceleration of a freely falling body is constant at any one
place. What does this show about the pull which the earth exerts on the
body?
(7) THE PENDULUM
=100. The Simple Pendulum.=--Any body suspended so as to swing freely to
and fro is a pendulum, as in Fig. 81. A simple pendulum is defined as a
single particle of matter suspended by a cord without weight. It is of
course impossible to construct such a pendulum. A small metal ball
suspended by a thread is approximately a simple pendulum. When allowed
to swing its vibrations are made in equal times. This feature of the
motion of a pendulum was first noticed by Galileo while watching the
slow oscillations of a bronze chandelier suspended in the Cathedral in
Pisa.
[Illustration: FIG. 81--A simple pendulum.]
=101. Definition of Terms.= _The center of suspension_ is the point
about which the pendulum swings. A _single vibration_ is one swing
across the arc. A _complete_ or _double_ vibration is the swing across
the arc and back again. The time required for a double vibration is
called the _period_. The _length_ of a simple pendulum is approximately
the distance from the point of support to the center of the bob.
A _seconds pendulum_ is one making a single vibration per second. Its
length at sea-level, at New York is 99.31 cm. or 39.1 in., at the
equator 39.01 in., at the poles 39.22 in.
A _compound pendulum_ is one having an appreciable portion of its mass
elsewhere than in the small compact body or sphere called a bob. The
ordinary clock pendulum or a meter stick suspended by one end are
examples of compound pendulums.
The _amplitude_ of a vibration is one-half the arc through which it
swings, for example, the arc _DC_ or the angle _DAC_ in Fig. 81.
=102. Laws of the Pendulum.=--The following laws may be stated:
1. The period of a pendulum is not affected by its mass or the material
of which the pendulum is made.
2. For small amplitudes, the period is not affected by the length of the
arc through which it swings.
3. The period is directly proportional to the square root of the length.
Expressed mathematically, _t_/_t´_ = √_l_/√_l´_.
=103. Uses of the Pendulum.=--The chief use of the pendulum is to
regulate motion in clocks. The wheels are kept in motion by a spring or
a weight and the regulation is effected by an escapement (Fig. 82). At
each vibration of the pendulum one tooth of the wheel _D_ slips past the
prong at one end of the escapement _C_, at the same time giving a slight
push to the escapement. This push transmitted to the pendulum keeps it
in motion. In this way, the motion of the wheel work and the hands is
controlled. Another use of the pendulum is in finding the acceleration
of gravity, by using the formula, _t_ = π√(_l_/_g_), in which _t_ is the
time in seconds of a single vibration and _l_ the length of the
pendulum. If, for example, the length of the seconds pendulum is 99.31
cm., then 1 = π√(99.31/_g_); squaring both sides of the equation, we
have 1² = π²(99.31/_g_), or _g_ = π² × 99.31/1² = 980.1 cm. per sec.,
per sec. From this it follows that, since the force of gravity depends
upon the distance from the center of the earth, the pendulum may be used
to determine the elevation of a place above sea level and also the shape
of the earth.
Important Topics
1. Simple pendulum.
2. Definitions of terms used.
3. Laws of the pendulum.
4. Uses of the pendulum.
Exercises
1. What is the usual shape of the bob of a clock pendulum? Why is this
shape used instead of a sphere?
2. Removing the bob from a clock pendulum has what effect on its motion?
Also on the motion of the hands?
3. How does the expansion of the rod of a pendulum in summer and its
contraction in winter affect the keeping of time by a clock? How can
this be corrected?
4. Master clocks that control the time of a railway system have a cup of
mercury for a bob. This automatically keeps the same rate of vibration
through any changes of temperature. How?
5. How will the length of a seconds pendulum at Denver, 1 mile above
sea-level, compare with one at New York? Why?
[Illustration: FIG. 82--Escapement and pendulum of a clock.]
6. What is the period of a pendulum 9 in. long? _Note._ In problems
involving the use of the third law, use the length of a seconds pendulum
for _l_, and call its period 1.
7. A swing is 20 ft. high, find the time required for one swing across
the arc.
8. A pendulum is 60 cm. long. What is its period?
9. If in a gymnasium a pupil takes 3 sec. to swing once across while
hanging from a ring, how long a pendulum is formed?
10. A clock pendulum makes four vibrations a second, what is its
length?
Review Outline: Force and Motion
Force; definition, elements, how measured, units, dyne.
Graphic Representation; typical examples of finding a component, a
resultant, or an equilibrant.
Motion; Laws of motion (3), inertia, curvilinear motion, centrifugal
force, momentum, (_M = mv_), reaction, stress and strain.
Moment of Force; parallel forces, couple, effective and non-effective
component.
Gravitation; law; gravity, center of; weight. Equilibrium 3 forms;
stability, how increased.
Falling Bodies; velocity, acceleration, "g," Laws; _V_ = _gt_, _S_ =
(1/2)_gt_² - _s_ = (1/2)_g_(2_t_ - 1).
Pendulum; simple, seconds, laws (3), _t_ = π√(_l_/_g_).
CHAPTER VI
WORK AND ENERGY
_104. Work._--"Whenever a force moves a body upon which it acts, it is
said to do work upon that body." For example, if a man pushes a
wheelbarrow along a path, he is doing work on it as long as the
wheelbarrow moves, but if the wheelbarrow strikes a stone and the man
continues to push and no motion results, from a scientific point of view
he is then doing no work on it.
"Work signifies the overcoming of resistance," and unless the resistance
is overcome no work is done. Lifting a weight is doing work on it,
supporting a weight is not, although the latter may be nearly as
tiresome as the former. Work as used in science is a technical term. Do
not attach to it meanings which it has in every-day speech.
=105. Measurement of Work.=--Work is measured by the product of the
force by the displacement caused in the direction of the force, that is
_W_ = _fs_. Therefore if a unit of force acts through a unit of space, a
unit of work will be done. There are naturally several units of work
depending upon the units of force and space employed.
_English Work Unit._--If the force of one _pound_ acts through the
distance of one _foot_, a _foot-pound_ of work is done. A foot-pound is
defined as the work done when 1 lb. is lifted 1 ft. against the force of
gravity.
_Metric Work Unit._--If the force is one _kilogram_ and the distance one
_meter_, _one kilogram-meter_ of work is done.
_Absolute Work Unit._--If the force of one _dyne_ acts through the
distance of one _centimeter_ a _dyne-centimeter_ of work is done. This
usually is called an i. Other work units are sometimes used depending
upon the force and distance units employed. One, the i, is equal to
10,000,000 ergs or 10⁷ ergs.
=Problem.=--If a load is drawn 2 miles by a team exerting 500 lbs.
force, how much work is done?
=Solution.=--Since the force employed is 500 lbs., and the distance
is 2 × 5280 ft., the work done is 500 × 2 × 5280 or 5,280,000
ft.-lbs.
=106. Energy.=--In the various cases suggested in the paragraphs upon
work, an agent, a man, an animal or a machine, was mentioned as putting
forth an effort in order to do the work. It is also true that in order
to perform work an agent must employ _energy, or the energy of a body is
its capacity for doing work_. Where an agent does work upon a body, as
in winding up a spring or in lifting a weight, the body upon which the
work has been done may acquire energy by having work done upon it. That
is, it may become able to do work itself upon some other body. For
instance, a lifted weight in falling back to its first position may turn
wheels, or drive a post into the ground against resistance; a coiled
spring may run clock work, strike a blow, or close a door. Hence the
energy, or the capacity for doing work, is often acquired by a body
because work has first been done upon that body.
=107. Potential Energy.=--The wound up spring may do work because work
has first been done upon it. The lifted weight may also do work because
work has first been done in raising it to its elevated position since in
falling it may grind an object to powder, lift another weight or do some
other kind of work. _The energy that a body possesses on account of its
position or shape and a stress to which it is subjected is called
potential energy._ The potential energy of a body is measured by the
work done in lifting it, changing its shape, or by bringing about the
conditions by which it can do work. Thus if a block of iron weighing
2000 lbs. is lifted 20 ft., it possesses 40,000 ft.-lbs. of potential
energy. It is therefore able to do 40,000 ft.-lbs. of work in falling
back to its first position. If the block just mentioned should fall from
its elevated position upon a post, it could drive the post into the
ground because its motion at the instant of striking enables it to do
work. To compute potential energy you compute the work done upon the
body. That is, _P.E._ = _w_ × _h_ or _f_ × _s_.
=108. Kinetic Energy.=--_The energy due to the motion of a body is
called kinetic energy_. The amount of kinetic energy in a body may be
measured by the amount of work done to put it in motion. It is usually
computed, however, by using its mass and velocity on striking. To
illustrate, a 100-lb. ball is lifted 16 ft. The work done upon it, and
hence its potential energy, is 1600 ft.-lbs. On falling to the ground
again, this will be changed into kinetic energy, or there will be 1600
ft.-lbs. of kinetic energy on striking. It will be noted that since
energy is measured by the work it can do, work units are always used in
measuring energy. To compute the kinetic energy of a falling body by
simply using its mass and velocity one proceeds as follows, in solving
the above problem:
First, find the velocity of the falling body which has fallen 16
ft. A body falls 16 ft. in _one_ second. In this time it gains a
velocity of 32 ft. per second. Now using the formula for kinetic
energy _K.E._ = _wv_²/(2_g_), we have _K.E._ = 100 × 32 × 32/(2 ×
32) = 1600 ft.-lbs. as before. The formula, _K.E._ = _wv_²/(2_g_),
may be derived in the following manner:
The kinetic energy of a falling body equals the work done in giving
it its motion, that is, _K.E._ = _w_ × _S_, in which, _w_ = the
weight of the body and _S_ = the distance the body must fall freely
in order to acquire its velocity. The distance fallen by a freely
falling body, _S_, = 1/2_gt_² = _g_²_t_²/(2_g_) (Art. 98, p. 111).
Now, _v_ = _gt_ and _v_² = _g_²_t_².
Substituting for _g_²_t_², its equal _v_², we have _S_ =
_v_²/(2_g_). Substituting this value of S in the equation _K.E._ =
_w_ × _S_, we have _K.E._ = _wv_²/(2_g_).
Since the kinetic energy of a moving body depends upon its mass and
velocity and not upon the _direction_ of motion, this formula may
be used to find the kinetic energy of any moving body. Mass and
weight in such problems may be considered numerically equal.
=Important Topics=
1. Work defined.
2. Work units, foot-pound, kilogram-meter, erg.
3. Energy defined.
4. Kinds of energy, potential and kinetic.
=Problems=
1. How much work will a 120-lb. boy do climbing a mountain 3000 ft.
high? Should the vertical or slant height be used? Why?
2. In a mine 4000 kg. of coal are lifted 223 meters: how much work
is done upon the coal? What is the kind and amount of energy
possessed by the coal?
3. A pile driver weighs 450 lbs. It is lifted 16 ft. How much work
has been done upon it? What kind and amount of energy will it have
after falling 16 ft. to the pile?
4. A train weighing 400 tons is moving 30 miles per hour. Compute
its kinetic energy. (Change its weight to pounds and velocity to
feet per second.)
5. What would be the kinetic energy of the train in problem 4 if it
were going 60 miles per hour? If it were going 90 miles per hour?
How does doubling or trebling the speed of an object affect its
kinetic energy? How does it affect its momentum?
6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000
ft. per second?
7. Mention as many kinds of mechanical work as you can and show how
each satisfies the definition of work.
8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work
is done upon it?
9. If the pile driver in problem 8 is dropped upon the head of a
pile which meets an average resistance of 30,000 lbs., how far will
one blow drive it?
10. A 40 kg. stone is placed upon the top of a chimney 50 meters
high. Compute the work done in kilogram-meters and foot-pounds.
(2) POWER AND ENERGY
=109. Horse-power.=--In computing work, no account is taken of the time
required to accomplish it. But since the time needed to perform an
undertaking is of much importance, the rate of work, or the _power or
activity_ of an agent is an important factor. Thus if one machine can do
a piece of work in one-fifth the time required by another machine, it is
said to have five times the power of the other. Therefore the power of a
machine is _the rate at which it can do work_. James Watt (1736-1819),
the inventor of the steam-engine, in _expressing_ the power of his
engine, used as a unit a _horse-power_. He considered that a horse could
do 33,000 ft.-lbs. of work a minute. This is equal to 550 ft.-lbs. per
second or 76.05 kg.-m. per second. This is too high a value but it has
been used ever since his time. Steam engines usually have their power
rated in horse-power. That is, locomotives produce from 500 to 1500
horse-power. Some stationary and marine engines develop as high as
25,000 horse-power. The power of an average horse is about 3/4
horse-power and of a man about 1/7 horse-power when working continuously
for several hours.
=110. The Watt.=--In the metric system, the erg as a unit of work would
give as a unit of power 1 erg per second. This amount is so small,
however, that a larger unit is usually employed, the practical unit
being 10,000,000 ergs a second, that is, one joule per second. (See Art.
105.) This practical unit is called a _Watt_ after James Watt. The
power of dynamos is usually expressed in kilowatts, a kilowatt
representing 1000 watts. Steam-engines in modern practice are often
rated in kilowatts instead of horse-power. A horse-power is equivalent
to 746 watts, or is nearly 3/4 of a kilowatt.
=111. Energy. Its Transference and Transformation.= We have considered
energy as the capacity for doing work, and noted the two kinds,
potential and kinetic, and the facility with which one may change into
another. In fact, the transference of energy from one body to another,
and its transformation from one form to another is one of the most
common processes in nature. Take a pendulum in motion, at the _end_ of a
swing, its energy being entirely due to its elevated position is all
_potential_; at the _lowest_ point in its path its energy being entirely
due to its motion is all _kinetic_. The change goes on automatically as
long as the pendulum swings. A motor attached by a belt to a washing
machine is started running. The energy of the motor is transferred by
the belt to the washer where it is used in rubbing and moving the
clothes.
The heat used in warming a house is usually obtained by burning coal or
wood. Coal is believed to be formed from the remains of plants that grew
in former geologic times. These plants grew through the help of the
radiant energy of the sun. The following are transformations of energy
that have occurred: The radiant energy of sunlight was transformed into
the _chemical_ energy of the plants. This remained as chemical energy
while the plants were being converted into coal, was mined, brought to
the stove or furnace and burned. The burning transformed the chemical
energy into heat energy in which form we use it for warming rooms. Take
the energy used in running a street car whose electrical energy comes
from a waterfall. The energy of the car itself is mechanical. Its
motor, however, receives electrical energy and transforms it into
mechanical. This electrical energy comes along a wire from a dynamo at
the waterfall, where water-wheels and generators transform into
electrical energy the mechanical energy of the falling water. The water
obtained its energy of position by being evaporated by the heat of the
radiant energy of the sun. The vapor rising into the air is condensed
into clouds and rain, and falling on the mountain side, has, from its
elevated position, potential energy. The order of transformation,
therefore, is in this case, radiant, heat, mechanical, electrical, and
mechanical. Can you trace the energy from the sun step by step to the
energy you are using in reading this page?
=112. Forms of Energy.=--A steam-engine attached to a train of cars
employs its energy in setting the cars in motion, _i.e._, in giving them
kinetic energy and in overcoming resistance to motion. But what is the
source of the energy of the engine? It is found in the coal which it
carries in its tender. But of what kind? Surely not kinetic, as no
motion is seen. It is therefore potential. What is the source of the
energy of the coal? This question leads us back to the time of the
formation of coal beds, when plants grew in the sunlight and stored up
the energy of the sun's heat and light as _chemical_ energy. The sun's
light brings to the earth the energy of the sun, that central storehouse
of energy, which has supplied nearly all the available energy upon the
earth. Five _forms_ of energy are known, viz., mechanical, heat,
electrical, radiant, and chemical.
=113. Energy Recognized by its Effects.=--Like force, energy is
invisible and we are aware of the forms only by the effects produced by
it.
We recognize _heat_ by _warming_, by expansion, by pressure.
We recognize _light_ by _warming_, by its affecting vision.
We recognize _electrical_ energy by its heat, light, motion, or magnetic
effect. We recognize _mechanical_ energy by the _motion_ that it
produces. We recognize _chemical_ energy by knowing that the source of
energy does not belong to any of the foregoing.
A boy or girl is able to do considerable work. They therefore possess
energy. In what form does the energy of the body mainly occur? One can
determine this for himself by applying questions to each form of energy
in turn as in Art. 114.
_114. Source of the Energy of the Human Body._--Is the energy of the
human body mostly heat? No, since we are not very warm. Is it light or
electrical? Evidently not since we are neither luminous nor electrical.
Is it mechanical? No, since we have our energy even when at rest. Is it
chemical? It must be since it is none of the others. Chemical energy is
contained within the molecule.
It is a form of potential energy and it is believed to be due to the
position of the atoms within the molecule. As a tightly coiled watch
spring may have much energy within it, which is set free on allowing the
spring to uncoil, so the chemical energy is released on starting the
chemical _reaction_. Gunpowder and dynamite are examples of substances
containing chemical energy. On exploding these, heat, light, and motion
are produced. Gasoline, kerosene, and illuminating gas are purchased
because of the potential energy they contain. This energy is set free by
burning or exploding them.
The source of the energy of our bodies is of course the food we eat. The
energy contained in the food is also chemical. Vegetables obtain their
energy from the sunlight (radiant energy). This is why plants will not
grow in the dark. The available energy is mostly contained in the form
of starch, sugar and oil. Digestion is employed principally to dissolve
these substances so that the blood may absorb them and carry them to the
tissues of the body where they are needed. The energy is set free by
oxidation (burning), the oxygen needed for this being supplied by
breathing. Breathing also removes the carbon dioxide, which results from
the combustion. It is for its energy that our food is mostly required.
=115. Conservation of Energy.=--In the study of matter we learned that
it is indestructible. Energy is also believed to be indestructible. This
principle stated concisely teaches that _despite the innumerable changes
which energy undergoes the amount in the universe is unchangeable_, and
while energy may leave the earth and be lost as far as we are concerned,
that it exists somewhere in some form. The principle which teaches this
is called the "Conservation of Energy." The form into which energy is
finally transformed is believed to be heat.
Important Topics
1. Power defined. Units. Horse-power. Watt.
2. Transference and transformations of energy.
3. Forms of energy; heat, electrical, mechanical, radiant, chemical.
4. Effects of the several forms of energy.
5. Energy of the human body.
6. Conservation of energy.
Exercises
1. A boy weighing 110 lbs. ran up a stairs 10 ft. high, in 4 seconds.
How much work was done? What was his _rate_ of work (foot-pounds per
second)? Express also in horse-power.
2. A locomotive drawing a train exerts a draw bar pull of 11,000 lbs.
How much work does it do in moving 3 miles? What is its _rate_ of work
if it moves 3 miles in 5 minutes? Express in horse-power.[G]
[G] The following formula is of assistance in computing
_horse-power_ in problems: H. p. = (lbs. × ft.)/(550 × sec.).
3. If 400 kg. are lifted 35 meters in 5 seconds what work is done? What
is the rate of work? Express in horse-power, watts and kilowatts.
4. Trace the energy of a moving railway train back to its source in the
sun.
5. Why does turning the propeller of a motor boat cause the boat to
move?
6. Does it require more power to go up a flight of stairs in 5 seconds
than in 10 seconds? Explain. Is more work done in one case than in the
other? Why?
7. Can 1 man carrying bricks up to a certain elevation for 120 days do
as much work as 120 men carrying up bricks for 1 day?
8. If the 1 man and 120 men of problem 7 do the same amount of work have
they the same power? Explain.
9. If 160 cu. ft. of water flow each second over a dam 15ft. high what
is the available power?
10. What power must an engine have to fill a tank 11 × 8 × 5 ft. with
water 120 ft. above the supply, in 5 minutes?
11. A hod carrier weighing 150 lbs. carries a load of bricks weighing
100 lbs. up a ladder 30 ft. high. How much work does he do?
12. How much work can a 4-horse-power engine do in 5 minutes?
13. Find the horse-power of a windmill that pumps 6 tons of water from a
well 90 ft. deep in 30 minutes.
14. How many horse-power are there in a waterfall 20 ft. high over which
500 cu. ft. of water pass in a minute?
15. The Chicago drainage canal has a flow of about 6000 cu. ft. a
second. If at the controlling works there is an available fall of 34 ft.
how many horse-power can be developed?
16. How long will it take a 10-horse-power pump to fill a tank of 4000
gallons capacity, standing 300 ft. above the pump?
17. A boy weighing 162 lbs. climbs a stairway a vertical height of 14
ft. in 14.6 seconds. How much power does he exert?
18. The same boy does the same work a second time in 4.2 seconds. How
much power does he exert this time? What causes the difference?
19. What is a horse-power-hour? a kilowatt-hour?
(3) SIMPLE MACHINES AND THE LEVER
=116. Machines and Their Uses.=--A man, while standing on the ground,
can draw a flag to the top of a pole, by using a rope passing over a
pulley.
A boy can unscrew a tightly fitting nut that he cannot move with his
fingers, by using a wrench.
A woman can sew a long seam by using a sewing machine in much less time
than by hand.
A girl can button her shoes much quicker and easier with a button-hook
than with her fingers.
These illustrations show some of the reasons why machines are used. In
fact it is almost impossible to do any kind of work efficiently without
using one or more machines.
=117. Advantages of Machines.=--(a) Many machines make possible an
_increased speed_ as in a sewing machine or a bicycle.
(b) Other machines exert an _increased force_. A rope and a set of
pulleys may enable a man to lift a heavy object such as a safe or a
piano. By the use of a bar a man can more easily move a large rock. (See
Fig. 83.)
[Illustration: FIG. 83.--The rock is easily moved.]
(c) The _direction_ of a force may be changed thus enabling work to be
done that could not be readily accomplished otherwise. As, e.g., the use
of a pulley in raising a flag to the top of a flag pole, or in raising a
bucket of ore from a mine by using a horse attached to a rope passing
over two or more pulleys. (See Fig. 84.)
(d) _Other agents_ than man or animals _can be used_ such as
electricity, water power, the wind, steam, etc. Fig. 85 represents a
windmill often used in pumping water.
_A machine is a device for transferring or transforming energy._ It is
usually therefore an instrument for doing work. An electric motor is a
machine since it _transforms_ the energy of the electric current into
motion or mechanical energy, and _transfers_ the energy from the wire to
the driving pulley.
[Illustration: FIG. 84.--The horse lifts the bucket of ore.]
=118. A Machine Cannot Create Energy.=--Whatever does work upon a
machine (a man, moving water, wind, etc.) loses energy which is employed
in doing the work of the machine. A pair of shears is a machine since it
transfers energy from the hand to the edges that do the cutting. Our own
bodies are often considered as machines since they both transfer and
transform energy.
We must keep in mind that _a machine cannot create energy_. The
principle of "Conservation of Energy" is just as explicit on one side as
the other. Just as energy, cannot be destroyed, so energy cannot be
created. A machine can give out no more energy than is given to it. It
acts simply as an agent in transferring energy from one body to
another. Many efforts have been made to construct machines that when
once started will run themselves, giving out more energy than they
receive. Such efforts, called seeking for _perpetual motion_, have never
succeeded. This fact is strong evidence in favor of the principle of the
conservation of energy.
[Illustration: FIG. 85.--A windmill.]
=119. Law of Machines.=--When a body receives energy, work is done upon
it. Therefore work is done upon a machine when it receives energy and
the machine does work upon the body to which it gives the energy. In the
operation of a machine, therefore, two quantities of work are to be
considered and by the principle of the conservation of energy, these two
must be equal. _The work done by a machine equals the work done upon it,
or the energy given out by a machine equals the energy received by it._
These two quantities of work must each be composed of a _force_ factor
and a _space_ factor. Therefore two forces and two spaces are to be
considered in the operation of a machine. The force factor of the work
done on the machine is called the _force_ or _effort_. It is the force
applied to the machine. The force factor of the work done by a machine
is called the _weight or resistance_. It is the force exerted by the
machine in overcoming the resistance and equals the resistance
overcome.
If _f_ represents the force or effort, and _D_{f}_ the space it acts
through, and _w_ represents the weight or resistance, and _D_{w}_ the
space it acts through, then the law of machines may be expressed by an
equation, _f × D_{f} = w × D_{w}_. That is, _the effort times the
distance the effort acts equals the resistance times the distance the
resistance is moved or overcome_. When the product of two numbers equals
the product of two other numbers either pair may be made the means and
the other the extremes of a proportion. The equation given above may
therefore be expressed _w: f = D_{f}: D_{w}_. Or the resistance is to
the effort as the effort distance is to the resistance distance. The law
of machines may therefore be expressed in several ways. One should keep
in mind, however, that the _same_ law of machines is expressed even
though the form be different. What two ways of expressing the law are
given?
=120. The Simple Machines.=--There are but six _simple machines_. All
the varieties of machines known are simply modifications and
combinations of the six simple machines. The six simple machines are
more easily remembered if we separate them into two groups of three
each. The first or _lever_ group consists of those machines in which a
part revolves about a fixed axis. It contains the _lever_, _pulley_ and
_wheel and axle_. The second or _inclined plane group_ includes those
having a sloping surface. It contains the _inclined plane_, the _wedge_,
and the _screw_.
=121. The Lever.=--The _lever_ is one of the simple machines most
frequently used, being seen in scissors, broom, coal shovel, whip,
wheelbarrow, tongs, etc. _The lever consists of a rigid bar capable of
turning about a fixed axis called the fulcrum._ In studying a lever, one
wishes to know what weight or resistance it can overcome when a certain
force is applied to it. Diagrams of levers, therefore, contain the
letters _w_ and _f_. In addition to these, _O_ stands for the fulcrum
on which it turns. By referring to Fig. 86, _a_, _b_, _c_, one may
notice that each of these may occupy the middle position between the
other two. The two forces (other than the one exerted by the fulcrum)
acting on a lever always oppose each other in the matter of changing
rotation. They may be considered as a pair of parallel forces acting on
a body, each tending to produce rotation.
[Illustration: FIG. 86.--The three classes of levers.]
=122. Moment of Force.=--The _effectiveness_ of each force may therefore
be determined by computing its _moment_ about the fixed axis (see Art.
84), that is, by multiplying each force by its distance to the fulcrum
or axis of rotation. Let a meter stick have a small hole bored through
it at the 50 cm. mark near one edge, and let it be mounted on a nail
driven into a vertical support and balanced by sliding a bent wire along
it. Suspend by a fine wire or thread a 100 g. weight, 15 cm. from the
nail and a 50 g. weight 30 cm. from the nail, on the other side of the
support. These two weights will be found to balance. When viewed from
this side _A_ (Fig. 87) tends to turn the lever in a clockwise direction
(down at right), _B_ in the counter-clockwise direction (down at left).
Since the lever balances, the forces have equal and opposite effects in
changing its rotation as may also be computed by determining the moment
of each force by multiplying each by its distance from the fulcrum.
Therefore the _effectiveness_ of a force in changing rotation depends
upon the distance from it to the axis as well as upon the magnitude of
the force.
[Illustration: FIG. 87.--The two moments are equal about _C_. 100 × 15 =
50 × 30.]
From the experiment just described, the moment of the acting force
equals the moment of the weight or _f × D_{f} = w × D_{w}_, or the
effort times the effort arm equals the weight times the weight arm. This
equation is called the law of the lever. It corresponds to the general
law of machines and may also be written _w: f = D_{f}: D_{w}_.
=123. Mechanical Advantage.=--A lever often gives an advantage because
by its use one may lift a stone or weight which the unaided strength of
man could not move. If the lever is used in lifting a stone weighing 500
lbs., the force available being only 100 lbs., then its _mechanical
advantage_ would be 5, the ratio of _w:f_. In a similar way, the
mechanical advantage of any machine is found by finding the ratio of the
resistance or weight to the effort. What must be the relative lengths of
the effort arm and resistance or weight arm in the example just
mentioned? Since the effort times the effort arm equals the weight times
the weight arm, if _f × D_{f} = w × D_{w}_, then _D_{f}_ is five times
_D_{w}_. Hence the mechanical advantage of a lever is easily found by
finding the ratio of the effort arm to the weight arm.
Important Topics
1. Advantage of machines.
2. Machines cannot create energy.
3. Law of machines.
4. Six simple machines.
5. Lever and principle of moments.
6. Mechanical advantage of a machine.
Exercises
1. Give six examples of levers you use.
2. Fig. 88_a_ represents a pair of paper shears, 88_b_ a pair of
tinner's shears. Which has the greater mechanical advantage? Why?
Explain why each has the most effective shape for its particular work.
[Illustration: FIG. 88.--(_a_) Paper shears. (_b_) Tinner's shears.]
3. Find examples of levers in a sewing machine.
4. What would result if, in Art. 122, the 100 g. weight were put 25 cm.
from O and the 50 g. weight 45 cm. from O? Why? Explain using principle
of moments.
5. How is the lever principle applied in rowing a boat?
6. When you cut cardboard with shears, why do you open them wide and cut
near the pivot?
7. In carrying a load on a stick over the shoulder should the pack be
carried near the shoulder or out on the stick? Why?
8. How can two boys on a see-saw start it without touching the ground?
9. In lifting a shovel full of sand do you lift up with one hand as hard
as you push down with the other? Why?
[Illustration: FIG. 89.--The hammer is a bent lever. What is its
mechanical advantage?]
10. Why must the hinges of a gate 3 ft. high and 16 ft. wide be stronger
than the hinges of a gate 16 ft. high and 3 ft. wide?
11. When one sweeps with a broom do the hands do equal amounts of work?
Explain.
12. A bar 6 ft. long is used as a lever to lift a weight of 500 lbs. If
the fulcrum is placed 6 in. from the weight, what will be the effort
required? Note: two arrangements of weight, fulcrum and effort are
possible.
13. The handle of a hammer is 12 in. long and the claw that is used in
drawing a nail is 2.5 in. long. (See Fig. 89.) A force of 25 lbs. is
required to draw the nail. What is the resistance of the nail?
14. The effective length of the head of a hammer is 2 in. The handle is
15 in. long and the nail holds in the wood with a force of 500 lbs. Only
60 lbs. of force is available at the end of the handle. What will be the
result?
15. If an effort of 50 lbs. acting on a machine moves 10 ft., how far
can it lift a weight of 1000 lbs.?
16. A bar 10 ft. long is to be used as a lever. The weight is kept 2 ft.
from the fulcrum. What different levers can it represent?
17. The effort arm of a lever is 6 ft., the weight arm 6 in. How long
will the lever be? Give all possible answers.
18. Two boys carry a weight of 100 lbs. on a pole 5 ft. long between
them. Where should the weight be placed in order that one boy may carry
one and one-fourth times as much as the other?
(4) THE WHEEL AND AXLE AND THE PULLEY
=124. The Wheel and Axle.=--1. One of the simple machines most commonly
applied in compound machines is the _wheel_ and _axle_. It consists of a
wheel _H_ mounted on a cylinder _Y_ so fastened together that both turn
on the same axis. In Fig. 90, ropes are shown attached to the
circumferences of the wheel and axle. Sometimes a hand wheel is used as
on the brake of a freight or street car, or simply a crank and handle is
used, as in Fig. 91. The _capstan_ is used in moving buildings.
Sometimes two or three wheels and axles are geared together as on a
derrick or crane as in Fig. 92.
[Illustration: FIG. 90.--The wheel and axle.]
[Illustration: FIG. 91.--Windlass used in drawing water from a well.]
[Illustration: FIG. 92.--A portable crane.]
[Illustration: FIG. 93.--The wheel and axle considered as a lever.]
[Illustration: FIG. 94.--View of transmission gears in an automobile. 1,
Drive gear; 2, High and intermediate gear; 3, Low and reverse gear; 4,
8, Reverse idler gears; 5, 6, 7, Countershaft gears. (_Courtesy of the
Automobile Journal_.)]
[Illustration: FIG. 95.--Reducing gear of a steam turbine.]
Fig. 93 is a diagram showing that the wheel and axle acts like a lever.
The axis _D_ is the fulcrum, the effort is applied at _F_, at the
extremity of a radius of the wheel and the resisting weight _W_ at the
extremity of a radius of the axle. Hence, if _D_{f}_, the effort
distance, is three times _D_{w}_, the weight distance, the weight that
can be supported is three times the effort. Here as in the lever, _f ×
D_{f} = w × D_{w}_, or _w:f = D_{f}:D_{w}_, or _the ratio of the weight
to the effort equals the ratio of the radius of the wheel to the radius
of the axle_. This is therefore the mechanical advantage of the wheel
and axle. Since the diameters or circumferences are in the same ratio as
the radii these can be used instead of the radii. Sometimes, when
_increased speed_ instead of increased force is desired, the radius of
the wheel or part to which power is applied is less than that of the
axle. This is seen in the bicycle, buzzsaw, and blower. Sometimes geared
wheels using the principle of the wheel and axle are used to reduce
speed, as in the _transmission_ of an automobile (see Fig. 94), or the
reducing gear of a steam turbine. (See Figs. 95 and 293.)
A _bevel gear_ is frequently used to change the direction of the force.
(See Fig. 94.)
[Illustration: FIG. 96.--A single movable pulley.]
[Illustration: FIG. 97.--Block and tackle.]
[Illustration: FIG. 98.--The fixed pulley considered as a lever.]
[Illustration: FIG. 99.--The movable pulley considered as a lever.]
=125. The Pulley.=--The _pulley_ consists of a wheel turning on an axis
in a frame. The wheel is called a sheave and the frame a block. The rim
may be smooth or grooved. The grooved rim is used to hold a cord or
rope. One use of the pulley is to change the _direction_ of the acting
force as in Fig. 84, where pulley _B_ changes a horizontal pull at _H_
to a downward force and pulley _A_ changes this into an upward force
lifting the weight _W_. These pulleys are fixed and simply change the
direction. Without considering the loss by friction, the pull at _W_
will equal that at _F_. Sometimes, a pulley is attached to the weight
and is lifted with it. It is then called a _movable pulley_. In Fig. 96
the _movable pulley_ is at _P_, a fixed pulley is at _F_. When _fixed
pulleys_ are used, a single cord runs through from the weight to the
effort, so that if a force of 100 lbs. is applied by the effort the same
force is received at the weight. But with movable pulleys several
sections of cord may extend upward from the weight each with the force
of the effort upon it. By this arrangement, a weight several times
larger than the effort can be lifted. Fig. 97 represents what is called
a _block and tackle_. If a force of 50 lbs. is exerted at _F_, each
section of the rope will have the same tension and hence the six
sections of the rope will support 300 lbs. weight. The _mechanical
advantage of the pulley_ or the _ratio of the weight_ to the effort,
therefore, _equals the number of sections of cord supporting the
weight_. The fixed pulley represents a lever, see Fig. 98, where the
effort and weight are equal. In the movable pulley, the fulcrum (see
Fig. 99) is at _D_; the weight, _W_, is applied at the center of the
pulley and the effort at _F_. The weight distance, _D_{w}_, is the
radius, and the effort distance, _D_{f}_, is the diameter of the
pulley. Since _W/F = D_{f} / D_{w} = 2_ in a movable pulley, the weight
is twice the effort, or its mechanical advantage is 2.
Important Topics
1. Wheel and Axle, Law of Wheel and Axle.
2. Pulley, Fixed and Movable, Block and Tackle, Law of Pulley.
Exercises
1. Why do door knobs make it easier to unlatch doors? What simple
machine do they represent? Explain.
2. What combination of pulleys will enable a 160-lb. man to raise a
900-lb. piano?
3. When you pull a nail with an ordinary claw hammer, what is the effort
arm? the resistance arm?
4. How much work is done by the machine in problem 2 in lifting the
piano 20 ft.? How much work must be done upon the machine to do this
work?
5. The pilot wheel of a boat has a diameter of 60 in.; the diameter of
the axle is 6 in. If the resistance is 175 lbs., what force must be
applied to the wheel?
6. Four men raise an anchor weighing {1 1/2} tons, with a capstan (see
Fig. 110) having a barrel 9 in. in diameter. The circle described by the
hand-spikes is {13 1/2} ft. in diameter. How much force must each man
exert?
[Illustration: FIG. 100.--The Capstan.]
7. A bicycle has a 28-in. wheel. The rear sprocket is 3 in. in
diameter,[H] the radius of the pedal crank is 7 in.; 24 lbs. applied to
the pedal gives what force on the rim of the wheel? What will be the
speed of the rim when the pedal makes one revolution a second?
[H] Consider the diameter of the front sprocket as 6 inches.
8. Measure the diameters of the large and small pulleys on the
sewing-machine at your home. What mechanical advantage in number of
revolutions does it give? Verify your computation by turning the wheel
and counting the revolutions.
9. What force is required with a single fixed pulley to raise a weight
of 200 lbs.? How far will the effort move in raising the weight 10 ft.?
What is the mechanical advantage?
10. In the above problem substitute a single movable pulley for the
fixed pulley and answer the same questions.
11. What is the smallest number of pulleys required to lift a weight of
600 lbs. with a force of 120 lbs.? How should they be arranged?
12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys
employing 3 sections of rope. What is the force required?
13. Name three instances where pulleys are used to do work that
otherwise would be difficult to do.
14. Draw a diagram for a set of pulleys by means of which 100 lbs. can
lift 400 lbs.
(5) THE INCLINED PLANE. EFFICIENCY
=126. Efficiency.=--The general law of machines which states that the
work done by a machine equals the work put into it requires a
modification, when we apply the law in a practical way, for the reason
that in using any machine there is developed more or less friction due
to parts of the machine rubbing on each other and to the resistance of
the air as the parts move through it. Hence the statement of the law
that accords with actual working conditions runs somewhat as follows:
_The work put into a machine equals the useful work done by the machine
plus the wasted work done by it._ The _efficiency_ of a machine is the
ratio of the _useful_ work done by it to the _total_ work done on the
machine. If there were no friction or wasted work, the efficiency would
be perfect, or, as it is usually expressed, would be 100 per cent.
Consider a system of pulleys into which are put 600 ft.-lbs. of work.
With 450 ft.-lbs. of useful work resulting, the efficiency would be 450
÷ 600 = {3/4}, or 75 per cent. In this case 25 per cent. of the work
done on the machine is wasted. In a simple lever the friction is slight
so that nearly 100 per cent. efficiency is often secured.
Some forms of the wheel and axle have high efficiencies as in bicycles
with gear wheels. Other forms in which ropes are employed have more
friction. Pulleys have sometimes efficiencies as low as 40 per cent.
when heavy ropes are used.
=127. Inclined Plane.=--We now come to a type of _simple machine of
lower efficiency_ than those previously mentioned. These belong to the
inclined plane group, which includes the inclined plane (see Fig. 101),
the wedge and the screw. They are extensively used, however,
notwithstanding their low efficiency, on account of often giving a high
mechanical advantage. The _relation between these machines may be easily
shown_, as the _wedge_ is obviously _a double inclined plane_. In Art.
82 it is shown that the effort required to hold a weight upon an
inclined plane is to the _weight_ supported as the _height_ of the plane
is to its _length_.
[Illustration: FIG. 101.--An inclined plane.]
Or while the weight is being lifted the vertical height _BC_, the effort
has to move the length of the plane _AC_. Since by the law of machines
the effort times its distance equals the weight times its distance, or
the weight is to the effort as the effort distance is to the weight
distance, therefore the mechanical advantage of the inclined plane is
the ratio of the length to the height of the inclined plane.
_Inclined planes_ are used to raise heavy objects short distances, as
barrels into a wagon, and iron safes into a building. Stairways are
inclined planes with steps cut into them.
=128. The Wedge.=--Wedges are used to separate objects, as in splitting
wood (see Fig. 102), cutting wood, and where great force is to be
exerted for short distances. An axe is a wedge, so is a knife. A fork
consists of several round wedges set in a handle. The edge of any
cutting tool is either an inclined plane or a wedge. Our front teeth are
wedges. Numerous examples of inclined planes may be seen about us.
No definite statement as to the mechanical advantage of the wedge can be
given as the work done depends largely on friction. The force used is
generally applied by blows on the thick end. In general, the longer the
wedge for a given thickness the greater the mechanical advantage.
[Illustration: FIG. 102.--One use of the wedge.]
=129. The Screw.=--The screw is a cylinder around whose circumference
winds a spiral groove. (See Fig. 103.) The raised part between the two
adjacent grooves is the =thread= of the screw. The screw turns in a
block called a =nut=, within which is a spiral groove and thread exactly
corresponding to those of the screw. The distance between two
consecutive threads measured parallel to the axis is called the =pitch=
of the screw. (See Fig. 104.) If the thread winds around the cylinder
ten times in the space of 1 in., the screw is said to have ten threads
to the inch, the pitch being {1/10} in. The screw usually is turned by
a lever or wheel with the effort applied at the end of the lever, or at
the circumference of the wheel. While the effort moves once about the
circumference of the wheel the weight is pushed forward a distance equal
to the distance between two threads (the pitch of the screw). The work
done by the effort therefore equals _F × 2πr_, _r_ being the radius of
the wheel, and the work done on the weight equals _W × s_, _s_ being the
pitch of the screw. By the law of machines _F × 2πr = W × s_ or _W / F =
(2πr) / s_. Therefore the mechanical advantage of the screw equals
_(2πr) / s_. Since the distance the weight moves is small compared to
that the power travels, there is a great gain in force. The screw is
usually employed where _great force_ is to be exerted through small
distances as in the vise (Fig. 105) the jack screw (Fig. 106), screw
clamps, to accurately measure small distances as in the micrometer (Fig.
107) and spherometer, and to lessen the motion in speed-reducing
devices. The worm gear (Fig. 108) is a modification of the screw that is
sometimes used where a considerable amount of speed reduction is
required.
[Illustration: FIG. 103.--The screw is a spiral inclined plane.]
[Illustration: FIG. 104.--The pitch is _S_.]
[Illustration: FIG. 105.--A vise.]
[Illustration: FIG. 106.--A jack screw.]
[Illustration: FIG. 107.--A micrometer screw.]
[Illustration: FIG. 108.--This large worm-wheel is a part of the
hoisting mechanism employed for the lock gates of the Sault Ste. Marie
Canal.]
Important Topics
1. Efficiency of machines.
2. The inclined plane, wedge and screw. Applications.
Exercises
1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into a
wagon 3 ft. high. Find the force required parallel to the incline.
2. How long a plank will be needed to roll an iron safe weighing 1-1/2
tons into a wagon 3 ft. high using a pull of 600 lbs. parallel to the
incline.
3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb.
barrel from rolling down an inclined plane. What is the ratio of the
length to the height of the plane?
4. A man can push with a force of 150 lbs. and wishes to raise a box
weighing 1200 lbs. into a cart 3 ft. high. How long a plank must he use?
5. The radius of the wheel of a letter press is 6 in., the pitch of its
screw is 1/4 in. What pressure is produced by a force of 40 lbs.?
6. The pitch of a screw of a vice is 1/4 in., the handle is 1 ft. long.
what pressure can be expected if the force used is 100 lbs.?
7. A jackscrew is used to raise a weight of 2 tons. The bar of the
jackscrew extends 2 ft. from the center of the screw. There are two
threads to the inch. Find the force required.
(6) FRICTION, ITS USES AND LAWS
=130. Friction.=--Although often inconvenient and expensive, requiring
persistent and elaborate efforts to reduce it to a minimum, friction has
its uses, and advantages. Were it not for friction between our shoes and
the floor or sidewalk, we could not keep our footing. _Friction is the
resistance that must be overcome when one body moves over another._ It
is of two kinds, _sliding_ and _rolling_. If one draws a block and then
a car of equal weight along a board, the force employed in each case
being measured by a spring balance, a large difference in the force
required will be noticed, showing how much less rolling friction is than
sliding friction.
=131. Ways of Reducing Friction.=--(a) Friction is often caused by the
minute projections of one surface sinking into the depressions of the
other surface as one moves over the other. It follows, therefore, that
if these projections could be made as small as possible that friction
would be lessened. Consequently _polishing_ is one of the best means for
reducing friction. In machines all moving surfaces are made as smooth as
possible. In different kinds of materials these little ridges and
depressions are differently arranged. (b) In Fig. 109 the friction
between _R_ and _S_ would be greater than between _R_ and _T_. In _R_
and _S_ the surfaces will fit closer together than in _R_ and _T_. The
_use of different materials will reduce friction_. The iron axles of car
wheels revolve in bearings of brass. Jewels are used in watches for the
same reason. (c) Another very common method of reducing friction is by
the use of _lubricants_. The oil or grease used fills up the
irregularities of the bearing surfaces and separates them. _Rolling
friction_ is frequently substituted for sliding friction by the use of
ball and roller bearings. These are used in many machines as in
bicycles, automobiles, sewing machines, etc. (See Fig. 110.)
[Illustration: FIG. 109.--The friction between _R_ and _S_ is greater
than between _R_ and _T_.]
=132. Value of Friction.=--_Friction always hinders motion_ and whenever
one body moves over or through another the energy used in overcoming the
friction is transformed into heat which is taken up by surrounding
bodies and usually lost. Friction is therefore the great obstacle to
perfect efficiency in machines. Friction, however, like most afflictions
_has its uses_. We would find it hard to get along without it. Without
friction we could neither walk nor run; no machines could be run by
belts; railroad trains, street cars, in fact all ordinary means of
travel would be impossible, since these depend upon friction between the
moving power and the road for propulsion.
[Illustration: FIG. 110.--Timken roller bearings. As used in the front
wheel of an automobile.]
=133. Coefficient of Friction.=--The ratio between the friction when
motion is just starting and the force pushing the surfaces together is
called the _coefficient of friction_.
If the block in Fig. 111 is drawn along the board with uniform motion,
the reading of the spring balances indicates the amount of friction.
Suppose the friction is found to be 500 g., and the weight of the block
to be 2000 g. Then the coefficient of friction for these two substances
will be {500/2000} = {1/4}, or 25 per cent.
=134. Laws of Friction, Law I.=--_The friction when motion is occurring
between two surfaces is proportional to the force holding them
together._ Thus if one measures the friction when a brick is drawn along
a board, he will find that it is doubled if a second brick is placed on
the first. On brakes greater pressure causes greater friction. If a rope
is drawn through the hands more pressure makes more friction.
[Illustration: FIG. 111.--A method for testing the friction between
surfaces.]
=Law II.=--_Friction is independent of the extent of surface in
contact._ Thus a brick has the same friction drawn on its side as on its
edge, since, although the surface is increased, the weight is unchanged.
=Law III.=--Friction is greatest at starting, but after starting is
practically the same for all speeds.
=135. Fluid Friction.=--When a solid moves through a fluid, as when a
ship moves through the water or railroad trains through the air, the
resistance encountered is not the same as with solids but increases with
the square of the velocity for slow speeds and for high speeds at a
higher rate. This is the reason why it costs so much to increase the
speed of a fast train, since the resistance of the air becomes the
prominent factor at high speeds. The resistance to the motion of a ship
at high speed is usually considered to increase as the cube of the
velocity so that to double the speed of a boat its driving force must be
eight times as great.
Important Topics
1. Friction: two kinds; sliding and rolling.
2. Four ways of reducing friction.
3. Uses of friction.
4. Coefficient of friction. Three laws of friction.
5. Fluid friction.
Exercises
1. How long must an inclined plane be which is 10 meters high to enable
a car weighing 2000 kg. to be pushed up its length by a force of 100 kg.
parallel to the incline?
2. State how and where friction is of use in the operation of the
inclined plane, the wedge, the screw, the wheel and axle.
3. A wheelbarrow has handles 6 ft. long. If a load of 300 lbs. is placed
18 in. from the axis of the wheel, what force placed at the end of the
handles will be required to lift it?
4. A jackscrew has 3 threads to the inch, and the lever used to turn it
is 4 ft. long. If the efficiency of the screw is 60 per cent., what
force must be applied to raise a load of 5 tons?
5. In problem 4 how far must the force move in raising the weight 3 in.
Compute the work done upon the weight, the work done by the power and
the efficiency of the machine from these two amounts of work.
6. What simple machines are represented in a jackknife, a
sewing-machine, a screw-driver, a plane, a saw, a table fork?
7. A laborer carries 1500 lbs. of brick to a platform 40 ft. high. How
much useful work does he do?
8. If he weighs 150 lbs. and his hod weighs 10 lbs., how much useless
work does he do in taking 30 trips to carry up the bricks of problem 7?
What is his efficiency?
9. If the laborer hoists the brick of problem 7 in a bucket weighing 50
lbs., using a fixed pulley and rope, what is the useless work done if it
takes 12 trips to carry up the brick? What is the efficiency of the
device?
10. The efficiency of a set of pulleys is 70 per cent. How much force
should be applied if acting through 100 ft. it is to raise a load of 400
lbs. 20 ft.?
11. The spokes of the pilot wheel of a motor-boat are 1 ft. long, the
axle around which the rudder ropes are wound is 3 in. in diameter. What
effort must be applied if the tension in the ropes is 50 lbs.?
12. Why are the elevated railway stations frequently placed at the top
of an incline, the tracks sloping gently away in both directions?
13. The screw of a press has 4 threads to the inch and is worked by a
lever of such length that an effort of 25 lbs. produces a force of 2
tons. What is the length of the lever?
14. It takes a horizontal force of 10 lbs. to draw a sled weighing 50
lbs. along a horizontal surface. What is the coefficient of friction?
15. The coefficient of rolling friction of a railroad train on a track
is 0.009. What pull would an engine have to exert to haul a train
weighing 1000 tons along a level track?
16. How heavy a cake of ice can be dragged over a floor by a horizontal
force of 20 lbs., if the coefficient of friction is 0.06?
17. The coefficient of friction of iron on iron is 0.2. What force can a
switch engine weighing 20 tons exert before slipping?
18. Using a system of pulleys with a double movable block a man weighing
200 lbs. is just able to lift 600 lbs. What is the efficiency of the
system?
19. What is the horse-power of a pump that can pump out a cellar full of
water 40 ft. × 20 ft. by 10 ft. deep, in 30 minutes?
20. How many tons of coal can a 5 horse-power hoisting engine raise in
30 minutes from a barge to the coal pockets, a height of 50 ft.?
(7) WATER POWER
=136. Energy of Falling Water.=--The energy of falling and running water
has been used from the earliest times for developing power and running
machinery. The energy is derived from the action of the moving water in
striking and turning some form of _water-wheel_, several varieties of
which are described below.
=The Overshot Wheel.=--The overshot wheel (Fig. 112) is turned by the
weight of the water in the buckets. It was formerly much used in the
hilly and mountainous sections of this country for running sawmills and
grist mills as it is very easily made and requires only a small amount
of water. Its efficiency is high, being from 80 to 90 per cent., the
loss being due to friction and spilling of water from the buckets. To
secure this high efficiency the overshot wheel must have a diameter
equal to the height of the fall which may be as much as 80 or 90 ft.
[Illustration: FIG. 112.--Overshot water wheel.]
[Illustration: FIG. 113.--Undershot water wheel.]
[Illustration: FIG. 114.--Diagram illustrating the principle of the
Pelton wheel.]
=The Undershot Wheel.=--The old style undershot wheel (Fig. 113) is used
in level countries, where there is little fall, often to raise water for
irrigation. Its efficiency is very low, seldom rising more than 25 per
cent. The principle of the undershot wheel, however, is extensively used
in the water motor and the Pelton wheel (Fig. 114). In these the water
is delivered from a nozzle in a jet against the lower buckets of the
wheel. They have an efficiency of about 80 per cent. and are much used
in cities for running small machines, washing machines, pipe organ
blowers, etc., and in mountainous districts where the head is great.
[Illustration: FIG. 115.--Diagram of a hydro-electric power house
showing a vertical turbine _A_ with penstock _B_ and tail race _C_.]
[Illustration: FIG. 116.--The outer case of a turbine showing the
mechanism for controlling the gates.]
[Illustration: FIG. 117.--Inner case of a turbine showing the gates and
the lower end of the runner within.]
[Illustration: FIG. 118.--The runner of a turbine.]
[Illustration: FIG. 119.--Turbine and generator of the Tacoma
hydro-electric power plant.]
=137. The Turbine.=--The turbine is now used more than any other form of
water-wheel. It was invented in 1827 by De Fourneyron in France. It can
be used with a small or large amount of water, the power depending on
the head (the height of the water, in the reservoir above the wheel). It
is the most efficient type of water-wheel, efficiencies of 90 per cent.
often being obtained. The wheel is entirely under water (Fig. 115). It
is enclosed in an outer case (Fig. 116) which is connected with the
reservoir by a penstock or pipe and is always kept full of water. The
wheel itself is made in two parts, a rotating part called the runner
(see Fig. 118) and an inner case (Fig. 117) with gates that regulate
the amount of water entering the wheel. This case has blades curved so
that the water can strike the curved blades of the rotating part (Fig.
118) at the angle that is best adapted to use the energy of the water.
The water then drops through the central opening into the tail race
below (see Fig. 115). The energy available is the product of the weight
of the water and the head. The turbine is extensively used to furnish
power for generating electricity at places where there is a sufficient
fall of water. The electrical energy thus developed is transmitted from
50 to 200 miles to cities where it is used in running street cars,
electric lighting, etc. Turbines can be made to revolve about either
vertical or horizontal axes. Fig. 119 represents a _horizontal_ water
turbine connected to a dynamo. Compare this with the _vertical_ turbine
in Fig. 115.
Exercises
1. Does a person do more work when he goes up a flight of stairs in 5
seconds than when he goes up in 15 seconds? Explain.
2. A motorcycle has a 4 horse-power motor and can go at a rate of 50
miles per hour. Why cannot 4 horses draw it as fast?
3. What is the efficiency of a motor that is running fast but doing no
useful work?
4. What horse-power can be had from a waterfall, 12 ft. high, if 20 cu.
ft. of water pass over it each second?
5. What is the horse-power of a fire engine if it can throw 600 gallons
of water a minute to a height of 100 ft.?
6. Why are undershot wheels less efficient than the overshot wheel or
turbine?
7. A revolving electric fan is placed on the stern of a boat. Does the
boat move? Why? Place the fan under water. Does the boat now move? Why?
8. Why does an electric fan produce a breeze?
9. Explain the action of the bellows in an organ.
10. At Niagara Falls the turbines are 136 ft. below the surface of the
river. Their average horse-power is 5000 each. 430 cu. ft. of water each
second pass through each turbine. Find the efficiency.
11. At Laxey on the Isle of Man is the largest overshot wheel now in
use. It has a horse-power of 150, a diameter of 72.5 ft., a width of 10
ft., and an efficiency of 85 per cent. How many cubic feet of water pass
over it each second?
12. The power plant at the Pikes Peak Hydro-electric Company utilizes a
head of 2150 ft., which is equal to a pressure of 935 lbs. per square
inch, to run a Pelton wheel. If the area of the nozzle is 1 sq. in. and
the jet has a velocity of 22,300 ft. per minute, what is the horse-power
developed if the efficiency is 80 per cent.?
13. A test made in 1909 of the turbines at the Centerville power house
of the California Gas and Electric Corporation showed a maximum
horse-power of 9700, speed 400 r.p.m. under a head of 550 ft. The
efficiency was 86.25 per cent. How many cubic feet of water passed
through the turbines each second?
14. The turbine in the City of Tacoma Power Plant (see Fig. 120) uses a
head of 415 ft. 145 cu. ft. a second pass through the turbine. Calculate
the horse-power.
15. In problem 14, what is the water pressure per square inch at the
turbine?
16. The power plant mentioned in problem 13 develops 6000 kw. What is
the efficiency?
Review Outline: Work and Energy
Work; how measured, units, foot-pound, kilogram meter, erg.
Energy; how measured, units, potential, _P.E._ = _w × h_, or _f × s_.
Kinetic = _(wv²)/(2g)_.
Power; how measured, units, horse power, watt, 5 forms of energy,
conservation. H.p. = (lbs. × ft.)/(550 × sec.).
Machines; 6 simple forms, 2 groups, advantages, uses, Law: _W × D_{w}_ =
_F × D_{f}_.
Lever; moments, mechanical advantage, uses and applications.
Wheel and Axle and Pulley; common applications, mechanical advantage.
Inclined Plane, Wedge, and Screw; mechanical advantage and efficiency.
Friction; uses, how reduced, coefficient of, laws (3).
Water Wheels; types, efficiency, uses.
CHAPTER VII
HEAT, ITS PRODUCTION AND TRANSMISSION
(1) SOURCES AND EFFECTS OF HEAT
=138. Importance of the Study of Heat.=--Heat is brought to our
attention through the sensations of heat and cold. In winter, we warm
our houses and prevent the escape of heat from them as much as possible.
In summer we endeavor to keep our living rooms cool and our bodies from
being overheated.
A clear understanding of the several _sources_, _effects_, and _modes of
transferring_ heat is of importance to everyone living in our complex
civilization, especially when we consider the multitudes of objects that
have as their principal use the _production, transfer or utilization_ of
heat.
=139. Principal Sources of Heat.=--_First_ and most important is the
_Sun_, which is continually sending to us _radiant energy_ in the form
of light and heat waves. These warm the earth, make plants grow,
evaporate water, besides producing many other important effects.
_Second_, _chemical energy_ is often transformed into heat. One has but
to think of the heat produced by burning coal, wood, oil, and gas, to
recognize the importance of this source. Chemical energy is also the
source of the heat produced within our bodies. The action of quicklime
and water upon each other produces much heat. This action is sometimes
employed during balloon trips as a means of warming things.
_Third_, _Electrical Energy_.--In many cities electric cars are heated
by the electric current. We have all heard of electric toasters and
other devices for heating by electricity. _Electric_ light is produced
by the heating of some material to incandescence by an electric current.
The _electric furnace_ has a wide application in the preparation and
refining of metals.
[Illustration: FIG. 120.--Boy-scout method of making fire by friction.]
_Fourth_, heat is also produced whenever _mechanical energy_ of motion
is overcome, whether it be by _friction_, _concussion_, or
_compression_. Friction _always_ results in the production of heat, as
when we warm our hands by rubbing them together. When friction is
excessive, such as in the case of a heavy bearing not properly oiled,
the bearing may get very hot. This is the cause of the "hot box" on a
railway car. Friction may produce heat enough to set wood on fire. Some
fires in mills are believed to be due to this cause. Every _boy scout_
must learn how to produce fire by friction. (See Fig. 120.) _Concussion_
may be illustrated by the heating of a piece of metal by hammering it,
while the compression of a gas always makes it warmer, as those who have
used a bicycle pump have observed. The production of heat by compressing
a gas is illustrated by the "fire syringe" (Fig. 121). This consists of
a glass tube with a tightly fitted piston. A sudden compression of the
air contained may ignite a trace of carbon bisulfid vapor.
[Illustration: FIG. 121.--A fire syringe.]
The _interior of the earth_ is hot, but its heat seldom gets to the
surface except at _hot springs_ and _volcanoes_.
=140. The Effects of Heat.=--There are five important changes produced
by heat: (a) change of _size_, (b) change of _temperature_, (c) change
of _state_, as the melting of ice or evaporating of water, (d)
_chemical_ change, as the charring of sugar when it is overheated, and
(e) _electrical_ change. This is illustrated by the production of an
electric current, by the heating of the junction of two different
metals. A thermo-electric generator (see Fig. 122) has been constructed
upon this principle and works successfully.
[Illustration: FIG. 122.--A thermo-electric generator.]
Important Topics
1. Importance of a study of heat.
2. Four sources of heat.
3. Five effects of heat.
4. Examples of each.
5. Illustrations of transformation of energy which involve heat.
Exercises
1. Write a list of the _sources_ of heat in the order of their
importance to you. State why each is important to you.
2. Which _three_ of the _effects_ of heat do _you_ make most use of?
Explain what use you make of each of these effects.
3. Which of the forms of energy can be transformed into heat? How in
each case?
4. Into what other forms of energy may heat be transformed? Name the
device or process used in each case.
5. What five different commodities are purchased by people in your
neighborhood for the production of heat? Which of these costs least for
the amount of heat furnished? Which is most expensive? How do you
determine these answers?
6. Why do many people buy heat in an expensive form, as in using an
electric toaster, when they can obtain it in a cheaper form by burning
gas or coal?
7. How many of the five effects of heat have you observed outside of
school?
(2) TEMPERATURE AND EXPANSION
=141. Heat and Temperature.=--We should now clearly distinguish between
the terms, _heat_ and _temperature_. Heat is _a form of energy
consisting of molecular motion_. The temperature of a body is its
_degree of hotness_. The _amount of heat_ present in a body and its
_temperature_ are very different things. The temperature refers to the
intensity of the heat in the body. A quart of water and a red hot iron
ball may contain _equal amounts_ of heat, although the ball has a _much
higher temperature_ than the water. A cup of boiling water will have the
same temperature as a tank full of boiling water, but the tank will
contain more heat. Every one knows that it will take longer to boil a
kettle full of water than a cupful. A hot-water bag, holding 2 quarts of
water will give off heat longer than a 1-quart bag, both being filled
with water at the same temperature. To put it in another way, more work
is done in heating a large amount of water, than a small amount through
the same change of temperature.
=142. Units of Heat and Temperature.=--There are two common units for
measuring heat: the _Calorie_ and the _British thermal unit_. The
_calorie is the amount of heat required to raise the temperature of a
gram of water one centigrade degree_. The British thermal unit is _the
amount of heat required to raise the temperature of one pound of water
one Fahrenheit degree_. One of the units plainly belongs to the metric
system, the other to the English.
An instrument for measuring temperature is called a _thermometer_.
Various scales are placed upon thermometers. The two thermometer scales
most commonly used in this country are the _Centigrade_ and the
_Fahrenheit_. The _Fahrenheit thermometer scale_ has the temperature of
melting ice marked 32°. The boiling point or steam temperature of pure
water under standard conditions of atmospheric pressure is marked 212°
and the space between these two fixed points is divided into 180 parts.
The centigrade thermometer scale has the same fixed points marked 0 and
100 and the space between divided into 100 parts. (See Fig. 123.) The
centigrade scale is the one used by scientists everywhere.
[Illustration: FIG. 123.--Comparison of centigrade and Fahrenheit
scales.]
=143. Comparison of Thermometer Scales.=--It is often necessary to
express in centigrade degrees a temperature for which the Fahrenheit
reading is given or _vice versa_. Since there are 180 Fahrenheit degrees
between the "fixed points" and 100 centigrade degrees, the Fahrenheit
degrees are smaller than the centigrade, or 1°F. = 5/9°C. and 1°C. =
9/5°F. One must also take into account the fact that the melting point
of ice on the Fahrenheit scale is marked 32°. Hence the following rule:
To change a Fahrenheit reading to centigrade subtract 32 and take 5/9
of the remainder, while to change centigrade to Fahrenheit multiply the
centigrade by 9/5 and add 32 to the product. These two rules are
expressed by the following formulas.
(F.° - 32)5/9 = C.°, 9C.°/5 + 32° = F.°
Another method of changing from one thermometric scale to another is as
follows:
A temperature of -40°F. is also _represented_ by -40°C., therefore to
change a Fahrenheit reading into centigrade, we add 40 to the given
reading, then divide by 1.8 after which subtract 40. To change from a
centigrade to Fahrenheit reading the only difference in this method is
to multiply by 1.8 or
C. = (F. + 40)/1.8 - 40 and F. = 1.8(C. + 40) - 40.
[Illustration: FIG. 124--Comparison of absolute, centigrade and
Fahrenheit scales.]
=144. The Absolute Scale of Temperature.=--One often hears the statement
"as cold as ice." This expresses the incorrect idea that ice cannot
become colder than its freezing temperature. The fact is that ice _may
be cooled_ below freezing down to the temperature of its surroundings.
If a piece of ice is placed where the temperature is below the melting
point, the ice, like any other solid, cools to the temperature of the
surrounding space. For example, a piece of ice out of doors is at 10°F.
when the air is at this temperature. It follows then, that when ice has
been cooled below the freezing temperature that heat is required to
warm the ice up to its melting point; or in other words that ice at its
melting temperature possesses some heat. The temperature at which
absolutely no heat exists is called _absolute zero_. There has been
devised an _absolute scale of_ temperature. This scale is based upon the
centigrade scale, _i.e._, with 100° between the two fixed points; the
scale, however, extends down, below the centigrade zero, 273°, to what
is called _absolute zero_. It follows therefore that upon the absolute
scale, the melting point of ice, and the boiling point of water are 273°
and 373° respectively. (See Fig. 124.)
The means employed to find the location of absolute zero are of much
interest. It has been observed that when heated a gas tends to expand.
If a measured volume of air at 0°C. is cooled or heated 1°C., it changes
its volume 1/273, the pressure remaining the same. If it is cooled 10°
it loses 10/273, if cooled 100° it loses 100/273 and so on. No matter
how far it is cooled the same rate of reduction continues as long as it
remains in the gaseous state. From these facts it is concluded that if
the cooling could be carried down 273° that the volume would be reduced
273/273 or that the volume of the gas would be reduced to nothing. This
is believed to mean that the molecular motion constituting heat would
cease rather than that the matter composing the gas would disappear.
Scientists have been able to obtain temperatures of extreme cold far
down on the absolute scale. Liquid air has a temperature of -292°F., or
-180°C. or 93°A. The lowest temperature thus far reported is 1.7°A. or
-271.3°C., obtained in 1911, by evaporating liquid helium.
=145. The Law of Charles.=--The facts given in the last paragraph mean
that if 273 ccm. of a gas at 0°C. or 273° A. are cooled 100°, or to
-100°C., or 173°A., then it will lose 100/273 of its volume or have a
volume of 173 ccm. If warmed 100°, or up to 100°C., or 373°A., it will
have a volume of 373 ccm. It follows then that in every case the volume
will correspond to its absolute temperature, providing the pressure
remains unchanged. The expression of this fact in scientific language is
called the law of _Charles_. _At a constant pressure the volume of a
given mass of gas is proportional to its absolute temperature._
Expressed mathematically, we have _V_{1}/V_{2} = T_{1}/T_{2}_. Compare
the statement and mathematical expression of the laws of Charles and
Boyle.
The formulas for the laws of Boyle and Charles are sometimes combined
into one expression as follows:
_PV/T = P´V´/T´_
or the product of the volume and pressure of a constant mass of gas is
proportional to its absolute temperature.
Important Topics
1. Heat units; calorie, British thermal unit.
2. Three thermometer scales, fixed points on each.
3. Absolute zero, how determined. Its value on each scale.
4. Law of Charles, its meaning. Combination of laws of Boyle and
Charles.
Exercises
1. Does ice melt at the same temperature at which water freezes? Express
the temperature of freezing water on the three thermometer scales.
2. A comfortable room temperature is 68°F. What is this temperature on
the centigrade and absolute scales?
3. Change a temperature of 15°C. to F.; 15°F. to C.; -4°C. to F.; -20°F.
to C.
4. The temperature of the human body is 98.6°F. What is this temperature
on the absolute and centigrade scales?
5. The temperature of liquid air is -180°C. What is it on the Fahrenheit
scale?
6. Mercury is a solid at -40°F. What is this on the centigrade scale?
7. How much heat will be required to raise the temperature of 8 lbs. of
water 32°F.; 5 lbs. 10°F.?
[Illustration: FIG. 125.--A clinical thermometer used to take the
temperature of the body.]
8. How much heat will be required to raise the temperature of 30 g. of
water 43°C.; 20 g., 50°C.?
9. Compute the temperature of absolute zero on the Fahrenheit scale.
10. Take three basins of water, one hot, one cold, and one lukewarm. If
one hand be placed in the hot water while the other is placed in the
cold and after a few minutes both are placed in the lukewarm water, this
water will feel cool to one hand and warm to the other. Explain.
11. If 200 ccm. of air at 200° absolute is heated to 300°A. under
constant pressure, what volume will the air occupy at the latter
temperature?
12. How does one change a reading on the centigrade scale to a
corresponding reading on the absolute scale?
(3) EXPANSION OF LIQUIDS AND SOLIDS
=146. Expansion of Gases.=--The law of Charles is found to apply to all
gases. That is, all gases change in volume in proportion to the change
of temperature provided the pressure remains constant. It is for this
reason that we have the _gas thermometer_ (see Fig. 126) which gives in
skillful hands more accurate temperature readings than the best
mercurial thermometer. Galileo devised and used the first _air
thermometer_ which consisted of a hollow bulb blown on a glass tube and
inverted in a dish of water. (See Fig. 1.) The _water thermometer_
consists of a glass bulb filled with water which rises into a tube
attached to the bulb. One disadvantage of the water thermometer is its
limited range since it cannot be used below 0° or above 100°. Why?
=147. Expansion of Liquids.=--The expansion of liquids differs from that
of gases in several important respects:
(a) Liquids have a smaller rate of expansion than gases. The _rate_ of
expansion per degree is called the _Coefficient of Expansion_. For
example, the coefficient of expansion of a gas under constant pressure
at 0°C. is {1/273} of its volume per degree centigrade.
(b) Different liquids expand at wholly different rates, that is, their
coefficients of expansion differ widely. For example, the coefficient of
expansion of mercury is 0.00018 per degree centigrade, of glycerine
0.0005 per degree centigrade, of petroleum 0.0009 per degree centigrade.
[Illustration: FIG. 126.--Gas thermometer.]
(c) The same liquid often has different coefficients of expansion at
different temperatures. Water between 5°C. and 6°C. has a coefficient
expansion of 0.00002 per degree centigrade, between 8° and 50° of
0.0006, between 99° and 100° of 0.00076. The coefficient of expansion of
mercury, however, is constant for a wide range of temperature and,
therefore, it is well adapted for use in thermometers.
=148. Peculiarity in the Expansion of Water.=--Water has a peculiar rate
of expansion. This is illustrated by the following experiment:
A test-tube filled with cold water is closed by a stopper
containing a small glass tube, the water extending up into the
small tube. (See Fig. 127.) The test-tube is placed in a freezing
mixture of salt and ice contained in a tumbler. As the water cools,
the level of the water in the small tube at first _sinks_. But
before the water freezes it _rises_ again, showing that after the
water cools to a certain temperature that _expansion of the water
occurs with further cooling_.
Careful tests show that the water on cooling contracts until it reaches
4°C. On cooling below this temperature it expands. For this reason, when
the water of a lake or river freezes, the coldest water is at the
surface. On account of this the ice forms at the top instead of at the
bottom. If water contracted as it cooled to the freezing temperature the
coldest water would be at the bottom. Freezing would begin at the bottom
instead of at the surface. Lakes and rivers would freeze solid. In the
summer only in shallow waters would all the ice melt. The result would
be that fish and other aquatic life would be killed. Climate would be so
changed that the earth might become uninhabitable. Since water is
densest at 4°C. all the water in a lake or river, when it is covered
with ice, is at 4°C. except that near the surface.
[Illustration: FIG. 127.--Apparatus used in testing the expansion of
water.]
=149. The Expansion Of Solids.=--Most solids when heated expand less
than liquids and gases. Careful experiments show that expansion is:
(a) Proportional to the change in temperature.
(b) Different in different solids.
Here are a few coefficients of linear (length) expansion.
Brass 0.000018 per degree C.
Glass 0.000009 per degree C.
Ice 0.000052 per degree C.
Iron 0.000012 per degree C.
Platinum 0.000009 per degree C.
Zinc 0.000027 per degree C.
_The coefficient of linear expansion is the fraction of its length that
a body expands when heated one degree._
_The coefficient of cubical expansion is the fraction of its volume that
a body expands when heated one degree._
The expansion of solids is used or allowed for in many cases:
a. Joints between the rails on a railroad allow for the expansion of the
rails in summer.
b. One end of a steel truss bridge is usually supported on rollers so
that it can expand and contract with changing temperatures. (See Fig.
128.)
[Illustration: FIG. 128.--Truss bridge showing roller support at one
end.]
c. Suspension bridges have expansion joints where the ends of the iron
girders can move in or out of an expansion joint thus making the bridge
longer or shorter according to the temperature.
d. Iron tires are heated, slipped on to wagon wheels and then cooled,
the contraction on cooling setting them tightly in place.
e. Metallic thermometers depend upon the movement due to the expansion
of a coiled strip of metal which turns a pointer on the dial of the
instrument. (See Fig. 129.)
f. The wires that are fused into glass in incandescent light bulbs must
have the same coefficient of expansion as the glass. Platinum has
therefore been used for this purpose. (See table above.)
[Illustration: FIG. 129.--Metallic thermometer.]
Important Topics
1. Expansion of Liquids; peculiarities. Anomalous expansion of water and
its results.
2. Expansion of solids; peculiarities, applications.
3. Coefficient of linear expansion.
4. Coefficient of cubical expansion.
Exercises
1. The gas within a partly inflated balloon has a volume of 1000 cu. ft.
at a pressure of 74 cm., and a temperature of 15°C. What will be the
volume of the gas when its pressure is 37 cm. and the temperature is
-17°C.?
2. A man taking a full breath on the top of a mountain fourteen thousand
feet high inhales 4 liters of air, the pressure being 40 cm. What volume
would this same mass of air have in a place 600 ft. above sea-level when
the barometer reads 75 cm. and the temperature is the same as on the
mountain top?
3. If the coefficient of linear expansion of iron is 0.000012 per
degree C., how much will an iron bridge 1000 ft. long change in length
in warming from -20°C. on a winter day to 30°C. upon a summer day.
4. What are some of the results that would follow in freezing weather if
water continually contracted on being cooled to zero instead of
beginning to expand when cooled below 4°C.?
5. Mention two instances that you have noticed of expansion occurring
when a body is heated?
6. Compare the density of air at 30°C. with that at 10°C. at the same
pressure. If both are present in a room, where will each be found? Why?
7. Compare the density of water at 40°C. with that at 10°C. If water at
the two temperatures are in a tank, where will each be found? Why?
8. If water at 0°C. and at 4°C. are both in a tank, where will each be
found? Why?
9. How much heat will be required to raise the temperature of a cubic
foot of water 10°F.?
10. How much heat will be required to raise the temperature of 4 liters
of water 25°C.?
11. How much longer would the cables of the Brooklyn suspension bridge
be on a summer's day when the temperature is 30°C. than in winter at
-20°C., the length of cable between the supports being about 1600 ft.
12. If 25 liters of air at -23°C. is warmed to 77°C. under constant
pressure, what will be the resulting volume of air? Explain.
13. White pig iron melts at about 2000°F. Express this temperature upon
the centigrade and absolute scales.
14. If 200 ccm. of air at 76 cm. pressure and 27°C. temperature be
heated to 127°C. at a pressure of 38 cm. what will be the resulting
volume?
15. A balloon contains 10,000 cu. ft. of gas at 75.2 cm. pressure and
24°C. It ascends until the pressure is 18 cm. and the temperature is
-10°C. What is the volume of gas it then contains.
16. A gas holder contains 50 "cu. ft." of gas at a pressure of one
atmosphere and 62°F. How much gas will it hold at 10 atmospheres and
32°F.
17. One thousand "cubic feet" of illuminating gas has what volume with
75 lbs. pressure and temperature of 10°C.
18. Define a "cubic foot" of illuminating gas.
=150. Methods of Transmitting Heat.=--One of the most practical benefits
of the study of heat is clearer understanding of the different methods
by which heat is transferred from one place to another and an
intelligent idea of the means employed to prevent the transfer of heat.
It should be definitely understood at the beginning that _cold signifies
the absence of heat_, just as darkness implies the absence of light, so
when one speaks of cold getting into a house what is really meant is
either the entrance of cold air by some opening or else the escape of
the heat.
There are three distinct methods by which heat energy is transferred
from one place to another, depending upon the medium or substance that
transfers the heat.
a. A solid transmits heat by the method called _conduction_.
b. A fluid, either a liquid or a gas, transmits heat mainly by the
method called _convection_.
c. Space transmits the energy of hot objects by the method called
_radiation_.
[Illustration: FIG. 130.--Solids conduct heat.]
=151. Conduction.=--To illustrate conduction, place in a gas flame the
ends of same metal wires supported as in Fig. 130. In a short time the
other ends of the wires become hot enough to burn one's hand. This may
be explained as follows: The hot gas flame contains molecules in violent
vibration and those striking the wire set its molecules rapidly
vibrating. Since, in a solid, the molecules are held in the same
relative positions, when one end of a wire is heated the rapidly
vibrating molecules at the hot end set their neighbors vibrating and
these the next in turn and so on until the whole wire is hot. It is a
fortunate circumstance that different substances have different rates of
conductivity for heat. To realize this, suppose that our clothing were
as good a conductor as iron, clothing would then be very uncomfortable
both in hot and in cold weather. The best conductors for heat are
metals. It is interesting to note that, as a rule good conductors of
heat are also good conductors of electricity, while poor conductors of
heat are also poor electric conductors. Careful experiments in testing
the rate that heat will be conducted through different substances show
the following rates of conductivity.
[Illustration: FIG. 131.--Water is a poor conductor of heat.]
These figures are averages taken mainly from the Smithsonian Physical
Tables:
Silver 100
Copper 74
Aluminum 35
Brass 27
Zinc 26
Iron 15
Tin 14.7
German silver 8.4
Mercury 1.7
Granite 0.53
Limestone 0.52
Ice 0.5
Glass 0.2
Water 0.124
Pine, with grain 0.03
Pine, across grain 0.01
Felt 0.008
Air 0.005
To test the conductivity of _liquids_, take a test-tube nearly full of
cold water, hold the lower end in the hand while the tube is inclined so
that the upper end is heated by a gas flame until the water boils. The
lower end will be found to remain cold. (See Fig. 131.) Careful
measurements of the conductivity of water show that heat is transmitted
through it only {1/800} as rapidly as in silver, while air conducts but
{1/25} as rapidly as water.
[Illustration: FIG. 132.--Wall construction of a refrigerator. 1,
Porcelain enamel lining lock joint; 2, inside wood lining; 3, 3-ply red
rope waterproof paper; 4, wool felt deafening paper; 5, flaxlinum
insulation; 6, dead air space; 7, flaxlinum insulation; 8, wool felt
deafening paper; 9, 3-ply red rope waterproof paper; 10, outside wood
case.]
[Illustration: FIG. 133.--Sectional view of a Thermos bottle.]
=152. Non-conductors and Their Uses.=--Many solids, however, are poor
conductors, as leather, fur, felt, and woolen cloth. These substances
owe their non-conductivity mainly to the fact that they are porous. The
air which fills the minute spaces of these substances is one of the
poorest conductors known and hinders the transfer of heat through these
solids. For the same reason loosely packed snow is a protection to
vegetation covered by it during a period of severe cold in winter. The
efficiency of storm sash or double windows, and of the double and
triple walls of ice-houses and refrigerators (see Fig. 132) in
preventing the conduction of heat is also largely due to the poor
conductivity of the air confined in the spaces between the walls. To
prevent the circulation of the air, sawdust, charcoal, and other porous
material is often loosely packed into the space between the walls of
such structure.
Other illustrations of effective non-conductors will occur to every one;
such as _woolen_ clothing, _wooden_ handles for hot objects, and the
_packing_ used in fireless cookers. A _Thermos_ bottle is effective as a
non-conductor of heat because the space between the double walls has the
air exhausted from it (Figs. 133 and 134).
Of several objects in a cold room, some feel much colder to the touch
than others, thus iron, marble, oil cloth, and earthenware will feel
colder than woolen cloth, carpet, feathers, or paper. The first four
objects feel cold because they are conductors, and conduct the heat away
from the hand rapidly. The other substances named are non-conductors and
hence remove heat from the hand less rapidly, and therefore do not feel
so cold. In a similar way, if several hot objects are touched by the
hand, the good conductors are the ones which will burn one most quickly
by conducting heat rapidly to the hand. The non-conductors, however,
will rarely burn one. Why are the handles of hot utensils often made of
non-conducting materials such as wood, cloth, asbestos, etc.?
[Illustration: FIG. 134.--Cross-section of the vacuum flask in a Thermos
bottle.]
=153. Radiation= is the method by which heat comes to us from the sun
across space containing no tangible matter. It is also the method by
which heat gets to us when we stand near a fire. Everyone has noticed
that this heat is cut off by holding an object between the person and
the fire. This fact indicates that radiant heat travels in _straight_
lines.
_The radiation of heat_ is believed to be accomplished by means of waves
in a medium called _ether_, which is invisible and yet pervades
everything. Three of the most important characteristics of radiation are
_first, heat is transferred by radiation with the speed of light_, or
186,000 miles per second. This fact is shown by the cutting off of both
the sun's heat and light at the same instant during an eclipse of the
sun. _Second, radiant heat[I] travels in straight lines_, while other
modes of transferring heat may follow irregular paths. The straight line
motion of radiant heat is shown by its being cut off where a screen is
placed between the source of heat and the object sheltered. _Third,
radiant heat may pass through an object without heating it._ This is
shown by the coldness of the upper layers of the atmosphere and also by
the fact that a pane of glass may not be heated appreciably by the heat
and light from the sun which passes through it.
[I] Radiant heat is really _radiant energy_ and becomes heat when
it is absorbed by a body.
When radiant energy falls upon any object it may be (a) _reflected_ at
the surface of the object, (b) _transmitted_ through the substance, (c),
absorbed. All three of these effects occur in different degrees with
different portions of the radiation. _Well-polished surfaces are good
reflectors._ Rough and blackened surfaces are _good absorbers_.
Transparent objects are those which transmit light well, but even they
absorb some of the energy.
=154. The Radiometer.=--Radiant heat may be detected by means of the
radiometer (Fig. 135). This consists of a glass bulb from which the air
has been nearly exhausted. Within it is a wheel with four vanes of mica
or of aluminum mounted on a vertical axis. One side of each vane is
covered with lampblack, the other being highly polished. when exposed to
radiant heat from any source the vanes revolve with the bright side in
advance.
The bulb is so nearly exhausted of air that a single molecule remaining
may travel from the walls of the bulb to the vanes without coming in
contact with another molecule.
The blackened sides absorb more heat than the highly polished sides. The
air molecules striking these blackened sides receive more heat and so
rebound with greater velocity than from the other side, thus exerting
greater pressure. The blackened sides therefore are driven backward. If
the air were not so rarified the air molecules would hit each other so
frequently as to equalize the pressure and there would be no motion.
[Illustration: FIG. 135.--A radiometer.]
_Sun's Radiation._--Accurate tests of the amount of the sun's radiation
received upon a square centimeter of the earth's surface perpendicular
to the sun's rays were made at Mt. Wilson in 1913. The average of 690
observations gave a value of 1.933 calories per minute. These results
indicate that the sun's radiation per square centimeter is sufficient to
warm 1 g. of water 1.933°C. each minute. Although the _nature_ of
_radiation_ is not discussed until Art. 408-411 in light, it should be
said here that all bodies are radiating heat waves at all temperatures,
the heat waves from cool bodies being much longer than those from hot
bodies. Glass allows the short luminous waves to pass through freely but
the longer heat waves from objects at the room temperature pass through
with difficulty. This is the reason why glass is used in the covering of
greenhouses and hot beds. Water also absorbs many of the longer heat
waves. It is therefore used in stereopticons to prevent delicate lantern
slides from being injured by overheating.
Important Topics
1. Conduction in solids, liquids, gases.
2. Non-conductors; uses, best non-conductors.
3. Radiation, three characteristics.
4. The sun's radiation, amount. The radiometer.
Exercises
1. Does clothing ever afford us heat in winter? How then does it keep us
warm?
2. Why are plants often covered with paper on a night when frost is
expected?
3. Will frost form in the fall of the year sooner on a wooden or a
cement sidewalk? Why? On which does ice remain longer? Why?
4. Why in freezing ice-cream do we put the ice in a wooden pail and the
cream in a tin one?
5. Is iron better than brick or porcelain as a material for stoves?
Explain.
6. Which is better, a good or a poor conductor for keeping a body warm?
for keeping a body cool?
7. Should the bottom of a teakettle be polished? Explain.
8. How are safes made fireproof?
9. Explain the principle of the Thermos bottle.
10. Explain why the coiled wire handles of some objects as stove-lid
lifters, oven doors, etc., do not get hot.
(5) TRANSMISSION OF HEAT IN FLUIDS. HEATING AND VENTILATION
=155. Convection.=--While fluids are poor conductors, they may transmit
heat more effectively than solids by the mode called _convection_. To
illustrate: if heat is applied at the _top_ of a test-tube of water,
the hot water being lighter is found at the top, while at the bottom the
water remains cold. On the other hand, if heat is applied at the
_bottom_ of the vessel, as soon as the water at the bottom is warmed
(above 4°C.) it expands, becomes lighter and is pushed up to the top by
the colder, denser water about it. This circulation of water continues
as long as heat is applied below, until all of the water is brought to
the boiling temperature. (See Fig. 136.)
When a liquid or a gas is heated in the manner just described, the heat
is said to be transferred by _convection_. Thus the air in the lower
part of a room may receive heat by conduction from a stove or radiator.
As it expands on being warmed, it is pushed up by the colder denser air
about it, which takes its place, thus creating a circulation of the air
in the room. (See Fig. 137.) The heated currents of air give up their
heat to the objects in the room as the circulation continues. These air
currents may be observed readily by using the smoke from burning "touch
paper" (unglazed paper that has been dipped into a solution of potassium
nitrate ["saltpeter"] and dried).
[Illustration: FIG. 136.--Convection in a liquid.]
=156. Draft of a Chimney.=--When a fire is started in a stove or a
furnace the air above the fire becomes heated, expands, and therefore is
less dense than it was before. This warm air and the heated gases which
are the products of the combustion of the fuel weigh less than an equal
volume of the colder air outside. Therefore they are pushed upward by a
force equal to the difference between their weight and the weight of an
equal volume of the colder air.
The chimney soon becomes filled with these heated gases. (See Fig. 138.)
These are pushed upward by the pressure of the colder, denser air,
because this colder air is pulled downward more strongly by the force of
gravity than are the heated gases in the chimney.
Other things being equal, the taller the chimney, the greater the draft,
because there is a greater difference between the weight of the gases
inside and the weight of an equal volume of outside air.
[Illustration: FIG. 137.--Convection currents in a room.]
[Illustration: FIG. 138.--Fire place showing draft of a chimney.]
=157. Convection Currents in Nature.=--Winds are produced by differences
in the _pressure_ or _density_ of the air, the movement being from
places of high toward places of low pressure. One of the causes of a
difference in density of the air is a difference in temperature. This
is illustrated by what are called the _land_ and _sea breezes_ along the
sea shore or large lakes. During the day, the temperature of the land
becomes higher than that of the sea. The air over the land expands and
being lighter is moved back and upward by the colder, denser air from
the sea or lake. This constitutes the _sea breezes_ (Fig. 139). At night
the land becomes cooler much sooner than the sea and the current is
reversed causing the _land breeze_. (See Fig. 140.)
[Illustration: FIG. 139.--Sea breeze.]
[Illustration: FIG. 140.--Land breeze.]
The _trade winds_ are convection currents moving toward the hot
equatorial belt from both the north and the south. In the hot belt the
air rises and the upper air flows back to the north and the south. This
region of ascending currents of air is a region of heavy rainfall, since
the saturated air rises to cool altitudes where its moisture is
condensed. The _ocean currents_ are also convection currents. Their
motion is due to prevailing winds, differences in density due to
evaporation and freezing, and to the rotation of the earth, as well as
to changes in temperature.
=158. The heating and ventilation of buildings= and the problems
connected therewith are matters of serious concern to all who live in
winter in the temperate zone. Not only should the air in living rooms be
comfortably heated, but it should be continually changed especially in
the crowded rooms of public buildings, as those of schools, churches,
and assembly halls, so that each person may be supplied with 30 or more
cubic feet of fresh air per minute. In the colonial days, the _open fire
place_ afforded the ordinary means for heating rooms. This heated the
room mainly by _radiation_. It was wasteful as most of the heat passed
up the chimney. This mode of heating secured ample _ventilation_. Fire
places are sometimes built in modern homes as an aid to ventilation.
Benjamin Franklin seeing the waste of heat in the open fire places
devised an iron box to contain the fire. This was placed in the room and
provided heat by conduction, convection, and radiation. It was called
_Franklin's stove_ and in many forms is still commonly used. It saves a
large part of the heat produced by burning the fuel and some ventilation
is provided by its draft.
[Illustration: FIG. 141.--Heating and ventilating by means of a hot-air
furnace.]
=159. Heating by Hot Air.=--The presence of stoves in living rooms of
homes is accompanied by the annoyance of scattered fuel, dust, ashes,
smoke, etc. One attempt to remove this inconvenience led to placing a
large stove or fire box in the basement or cellar, surrounding this with
a jacket to provide a space for heating air which is then conducted by
pipes to the rooms above. This device is called the hot-air furnace.
(See Fig. 141.) The heated air rises because it is pushed up by colder,
denser air which enters through the cold-air pipes. The _hot-air
furnace_ provides a good circulation of warm air and also ventilation,
provided some cold air is admitted to the furnace from the outside. One
objection to its use is that it may not heat a building evenly, one part
being very hot while another may be cool. To provide even and sufficient
heat throughout a large building, use is made of _hot water_ or _steam
heating_.
[Illustration: FIG. 142.--A hot-water system of heating.]
[Illustration: FIG. 143.--One-pipe system of steam heating.]
=160. Hot-water Heating.=--In hot-water heating a furnace arranged for
heating water is placed in the basement. (See Fig. 142.) Attached to the
top of the heater are pipes leading to the radiators in the various
rooms; other pipes connect the radiators to the bottom of the boiler.
The heater, pipes, and radiators are all filled with water before the
fire is started. When the water is warmed, it expands and is pushed up
through the pipes by the colder water in the return pipe. The
circulation continuing brings hot water to the radiator while the cooled
water returns to the heater, the hot radiators heating the several
rooms.
=161. Steam Heating.=--In _steam heating_ a steam boiler is connected to
radiators by pipes. (See Fig. 143.) The steam drives the air out of the
pipes and radiators and serves as an efficient source of heat. Heating
by steam is _quicker_ than heating with hot water. It is therefore
preferred where quick, efficient heating is required. Hot water is less
intense and more economical in mild weather and is often used in private
homes.
[Illustration: FIG. 144.--Heating by an indirect radiator with side-wall
register.]
=162. Direct and Indirect Heating.=--In heating by _direct radiation_
(Figs. 142, 143), the steam or hot-water radiators are placed in the
rooms to be heated. With direct radiation, ventilation must be provided
by special means, such as opening windows, doors, and ventilators.
Sometimes radiators are placed in a box or room in the basement. Air
from out of doors is then driven by a fan over and about the hot
radiators. The air thus heated is conducted by pipes to the several
rooms. This arrangement is called _indirect heating_. (See Fig. 144.)
The latter method, it may be observed, provides both heat and
ventilation, and hence is often used in schools, churches, court houses,
and stores. Since heated air, especially in cold weather, has a low
_relative humidity_ some means of moistening the air of living rooms
should be provided. Air when too dry is injurious to the health and also
to furniture and wood work. The excessive drying of wood and glue in a
piece of furniture often causes it to fall apart.
[Illustration: FIG. 145.--An automatic air valve.]
[Illustration: FIG. 146.--An automatic vacuum valve.]
=163. Vacuum Steam Heating.=--In steam heating, air valves (Fig. 145)
are placed on the radiators to allow the air they contain to escape when
the steam is turned on. When all the air is driven out the valve closes.
Automatic vacuum valves (Fig. 146) are sometimes used. When the fire is
low and there is no steam pressure in the radiators the pressure of the
air closes the valve, making a partial vacuum inside. The boiling point
of water falls as the pressure upon it is reduced. As water will not
boil under ordinary atmospheric pressure until its temperature is 100°C.
(212°F.), it follows that by the use of vacuum systems, often called
vapor systems, of steam heating, water will be giving off hot vapor even
after the fire has been banked for hours. This results in a considerable
saving of fuel.
[Illustration: FIG. 147.--Plenum hot-blast system with temperature
regulation.]
=164. The Plenum System of Heating.=--In the plenum system of heating
(see Fig. 147) fresh air is drawn through a window from outdoors and
goes first through tempering coils where the temperature is raised to
about 70°. The fan then forces some of the air through heating coils,
where it is reheated and raised to a much higher temperature, depending
upon the weather conditions. Both the hot and tempered air are kept
under pressure by the fan in the plenum room and are forced from this
room through galvanized iron ducts to the various rooms to be heated.
The foul air is forced out of the room through vent ducts which lead to
the attic where it escapes through ventilators in the roof.
[Illustration: FIG. 148.--A thermostat. (Johnson System.)]
A thermostat is placed in the tempered-air part of the plenum room to
maintain the proper temperature of the tempered air. This thermostat
operates the by-pass damper under the tempering coils, and sometimes the
valves on the coils. The mixing dampers at the base of the
galvanized-iron ducts are controlled by their respective room
thermostats. Attic-vent, fresh-air, and return-air dampers are under
pneumatic switch control. A humidifier can be provided readily for this
system. This system of heating is designed particularly for school
houses where adequate ventilation is a necessity.
=165. The Thermostat.=--One of the many examples of the expansion of
metals is shown in one form of the thermostat (Fig. 148) in which two
pieces of different metals and of unequal rates of expansion, as brass
and iron, are securely fastened together.
The thermostatic strip _T_ moving inward and outward, as affected by the
room temperature, varies the amount of air which can escape through the
small port _C_. When the port _C_ is completely closed (Fig. 148_a_) the
full air pressure collects on the diaphragm _B_ which forces down the
main valve, letting the compressed air from the main pass through the
chamber _D_ into chamber _E_ as the valve is forced off its seat. The
air from chamber _E_ then passes into the branch to operate the damper.
When port _C_ is fully open (Fig. 148_b_) the air pressure on diaphragm
_B_ is relieved, the back pressure in _E_ lifts up the diaphragm and the
air from the branch escapes out through the hollow stem of the main
valve, operating the damper in the opposite direction from that when _C_
is closed.
Important Topics
1. Transmission of heat in fluids.
2. Convection. Drafts of a chimney. Land and sea breezes.
3. Heating and ventilation of buildings.
(a) By hot air.
(b) Hot-water heating.
(c) Steam heating.
(d) Direct and indirect heating.
(e) Vacuum steam heating.
(f) The plenum system.
(g) The thermostat.
Exercises
1. Is a room heated mainly by conduction, convection, or radiation, from
(a) a stove, (b) a hot-air furnace, (c) a steam radiator?
2. Name three natural convection currents.
3. Explain the _draft_ of a chimney. _What_ is it? _Why_ does it occur?
4. Make a _cross-section_ sketch of your living room and indicate the
convection currents by which the room is heated. _Explain_ the heating
of the room.
5. Make a sketch showing how the water in the hot-water tank in the
kitchen or laundry is heated. Explain your sketch, indicating convection
currents.
6. Is it economical to keep stoves and radiators highly polished?
Explain.
7. If you open the door between a warm and a cool room what will be the
direction of the air currents at the top and at the bottom of the door?
Explain.
8. If a hot-water heating system contains 100 cu. ft. of water how much
heat will be required to raise its temperature 150°F.?
9. Why does a tall chimney give a better draft than a short one?
10. Explain how your school room is heated and ventilated.
11. Should a steam or hot-water radiator be placed near the floor or
near the ceiling of a room? Why?
12. In a hot-water heating system an open tank connected with the pipes
is placed in the attic or above the highest radiator. Explain its use.
(6) THE MOISTURE IN THE ATMOSPHERE, HYGROMETRY
=166. Water Vapor in the Air.=--The amount of water vapor present in the
air has a marked effect upon the weather and the climate of a locality.
The study of the moisture conditions of the atmosphere, or hygrometry,
is therefore a matter of general interest and importance. The water
vapor in the atmosphere is entirely due to evaporation from bodies of
water, or snow, or ice. In the discussion of evaporation, it is
described as due to the gradual escape of molecules into the air from
the surface of a liquid. This description fits exactly the conditions
found by all careful observers. Since the air molecules are continually
striking the surface of the liquid, many of them penetrate it and become
absorbed. In the same manner many vapor molecules reenter the liquid,
and if enough vapor molecules are present in the air so that as many
vapor molecules reenter the liquid each second as leave it, the space
above the liquid is said to be _saturated_ as previously described. (See
Art. 18.)
=167. Conditions for Saturation.=--If a liquid is evaporating into a
vacuum, the molecules on leaving find no opposition until they reach the
limits of the vessel containing the vacuum. Evaporation under these
conditions goes on with great rapidity and the space becomes saturated
almost instantly. If, however, air be present at ordinary pressure, many
of the ordinary water vapor molecules on leaving are struck and returned
to the water by the air molecules directly above. Those escaping
gradually work their way upward through the air. This explains why it is
that our atmosphere is not often saturated even near large bodies of
water, the retarding effect of the air upon the evaporation preventing
more than the layers of air near the water surface becoming saturated.
Just as the amount of salt that can be held in solution in a liquid is
lessened by cooling the solution (Art. 26), so the amount of water vapor
that can be held in the air is lessened by lowering its temperature. If
air not moist enough to be saturated with water vapor is cooled, it
will, as the cooling continues, finally reach a temperature at which it
will be saturated or will contain all the water vapor it can hold at
this temperature. If the air be still further cooled some of the water
vapor will condense and may form fog, dew, rain, snow, etc., the form it
takes depending upon where and how the cooling takes place.
=168. The Formation of Dew.=--If the cooling of the atmosphere is at the
surface of some cold object which lowers the temperature of the air
below its saturation point, some of its moisture condenses and collects
upon the cold surface as _dew_. This may be noticed upon the surface of
a pitcher of ice-water in summer. At night, the temperature of grass and
other objects near or on the ground may fall much faster than that of
the atmosphere owing to the radiation of heat from these objects. If the
temperature falls below the saturation point, dew will be formed. This
natural radiation is hindered when it is cloudy, therefore little dew
forms on cloudy nights. Clear nights help radiation, therefore we have
the most dew on nights when the sky is clear. If the temperature is
below freezing, _frost_ forms instead of dew.
=169. Formation of Fog.=--If the cooling at night is great enough to
cool the body of air near the earth below the saturation temperature,
then not only may dew be formed, but some moisture is condensed in the
air itself, usually upon fine dust particles suspended in it. This
constitutes a _fog_. If the cooling of the body of air takes place above
the earth's surface as when a warm moist current of air enters a colder
region, _e.g._, moves over the top of a cold mountain, or into the upper
air, then as this air is cooled below its saturation point, condensation
upon fine suspended dust particles takes place, and a _cloud_ is formed.
If much moisture is present in the cloud, the drops of water grow in
size until they begin to fall and _rain_ results; or if it is cold
enough, instead of rain, snowflakes will be formed and fall. Sometimes
whirling winds in severe thunderstorms carry the raindrops into colder
and then warmer regions, alternately freezing and moistening the drops
or bits of ice. It is in this way that _hail_ is said to be formed.
=170. The Dew Point.=--The temperature to which air must be cooled to
saturate it or the temperature at which condensation begins is called
the _dew point_. This is often determined in the laboratory by partly
filling a polished metal vessel with water and cooling the water by
adding ice until a thin film of moisture is formed upon the outer
surface. The temperature of the surface when the moisture first forms is
the dew point.
=171. The Humidity of the Atmosphere.=--After the dew point has been
obtained, one may compute the _relative humidity_ or _degree of
saturation of the atmosphere_, from the table given below. This is
defined as the _ratio of the amount of water vapor present in the air to
the amount that would be present if the air were saturated at the same
temperature_.
For example, if the dew point is 5°C. and the temperature of the
air is 22°C., we find the densities of the water vapor at the two
temperatures, and find their ratio: 6.8/19.3 = 35 per cent. nearly.
Determinations of humidity may give indication of rain or frost and
are regularly made at weather bureau stations. They are also made
in buildings such as greenhouses, hospitals, and schoolhouses to
see if the air is moist enough. For the most healthful conditions
the relative humidity should be from 40 per cent. to 50 per cent.
WEIGHT OF WATER (_w_) IN GRAMS CONTAINED IN 1 CUBIC METER OF SATURATED
AIR AT VARIOUS TEMPERATURES (_t_°)C.
--------+------
_t_°C. | _w_
--------+------
-10 | 2.1
- 9 | 2.4
- 8 | 2.7
- 7 | 3.0
- 6 | 3.2
- 5 | 3.5
- 4 | 3.8
- 3 | 4.1
- 2 | 4.4
- 1 | 4.6
0 | 4.9
1 | 5.2
2 | 5.6
3 | 6.0
4 | 6.4
5 | 6.8
6 | 7.3
7 | 7.7
8 | 8.1
9 | 8.8
10 | 9.4
11 | 10.0
12 | 10.6
13 | 11.3
14 | 12.0
15 | 12.8
16 | 13.6
17 | 14.5
18 | 15.1
19 | 16.2
20 | 17.2
21 | 18.2
22 | 19.3
23 | 20.4
24 | 21.5
25 | 22.9
26 | 24.2
27 | 25.6
28 | 27.0
29 | 28.6
30 | 30.1
--------+------
=172. Wet and Dry Bulb Hygrometer.=--A device for indicating the
relative humidity of the air is called an _hygrometer_. There are
various forms. The _wet_ and _dry bulb hygrometer_ is shown in Fig. 149.
This device consists of two thermometers, one with its bulb dry and
exposed to the air, the other bulb being kept continually moist by a
wick dipping into a vessel of water. An application of the principle of
cooling by evaporation is made in this instrument. Unless the air is
saturated so that evaporation is prevented, the wet-bulb thermometer
shows a lower temperature, the difference depending upon the amount of
moisture in the air, or upon the relative humidity. Most determinations
of relative humidity are made with this kind of instrument. It is
necessary in order to make an accurate determination, to fan or set the
air in motion about the thermometers for some time before reading them.
The relative humidity is then found by using tables giving the relative
humidity that corresponds to any reading of the thermometers.
[Illustration: FIG. 149.--Wet and dry bulb hygrometer.]
[Illustration: FIG. 150.--A dial hygrometer.]
A form of hygrometer in common use is shown in Fig. 150. In this
device, a thin strip of hygroscopic material (as a piece of goose
quill) is formed into a spiral coil. One end of this is fastened to
a post. The other end carried a hand or pointer. The latter moves
over a printed scale and indicates directly the relative humidity.
Its indications should be tested by comparing its readings with the
results of dew-point determinations. The position of the pointer
may be adjusted by turning the post.
Important Topics
1. Water vapor in the air. Cause and effect.
2. Formation of dew, fog, rain, and snow.
3. Dew point, relative humidity.
4. Use of the dry- and wet-bulb hygrometer. Goose-quill hygrometer.
Exercises
1. How is the relative humidity of the air affected by warming it?
Explain.
2. How does the white cloud of steam seen about a locomotive in cold
weather differ from fog? Explain.
3. In cold weather is the relative humidity of air out of doors and
indoors the same? Explain.
4. Compare the relative humidity of air in a desert and near the ocean.
5. Look up the derivation of the term "hygrometer." Give the use of the
instrument.
6. Find the relative humidity of air at 20°C. if its dew point is at
10°C.
7. How may the relative humidity of the air in a home be increased?
8. What is the effect of high humidity in the summer upon human beings?
How do you explain this?
9. Does dew fall? Explain how dew is formed?
10. In what respects is a cloud similar to a fog? In what respects
different?
11. Why are icebergs frequently enveloped in fog?
12. Does dew form in the day time? Explain.
(7) EVAPORATION
=173. Effects of Evaporation.=--In Art. 19 the cooling effect of
evaporation is mentioned and some explanation is made of the cooling
effect observed. Since evaporation is employed in so many ways, and
since its action is simply explained by the study we have made of
molecular motions and molecular forces, it may be well to consider this
subject further.
Take three shallow dishes, and place in one a little water, in
another some alcohol, and some ether in the third, the liquids
being taken from bottles that have stood several hours in the room
so that all are at the same temperature. After a short time take
the temperature of the three liquids. Each will be at a lower
temperature than at first, but of the three the ether will be found
to be the coolest, alcohol next, and the water nearest its first
temperature. It will be noticed also that the ether has evaporated
most in the same time. Similar effects may be observed by placing a
few drops of each of these three liquids upon the back of one's
hand, or by placing a few drops in turn upon the bulb of a simple
air thermometer.
=174. Cooling Effect of Evaporation.=--The molecules that leave an
evaporating liquid are naturally the swiftest moving ones, that is, the
ones having the highest temperature, so their escape leaves the liquids
cooler than before, and the one whose molecules leave fastest is
naturally the one that becomes coldest, that is, the ether, in the
experiment of Art. 173. If no air pressure were exerted upon the surface
of the liquid, the escape of the molecules would be much increased and
the temperature of the liquid would be lowered rapidly.
To test this, fill a thin watch glass with ether and place it over
a thin slip of glass with a drop of cold water between the two. Now
place this apparatus under the receiver of an air pump and exhaust
the air. The rapid evaporation of the ether so lowers its
temperature, that often the drop of water is frozen. The lowest
temperatures are obtained by evaporating liquids at reduced
pressure.
Onnes by evaporating liquid helium at a pressure of about 1.2 mm.
reached the lowest temperature yet attained, -456°F., or -271.3°C.
If four thermometers are taken, the bulbs of three being wetted
respectively with ether, alcohol, and water the fourth being dry,
on vigorously fanning these, the moistened thermometers show that
they have been cooled while the dry one is unaffected.
This indicates that fanning a dry body at the temperature of the air
does not change its temperature. Fanning does increase evaporation by
removing the air containing the evaporated molecules near the surface of
the liquid so that unsaturated air is continually over the liquid. If a
pint of water is placed in a bottle and another pint in a wide pan the
latter will become dry much sooner because of the greater surface over
which evaporation can take place. Application of this is made at salt
works where the brine is spread out in shallow pans.
=175. Rate of Evaporation.=--The rate of evaporation is affected by
several factors. These have been illustrated in the preceding
paragraphs. To briefly summarize:
The rate of evaporation of a liquid is affected by--
(a) The nature of the liquid.
(b) The temperature of the liquid.
(c) The pressure upon its evaporating surface.
(d) The degree of saturation of the space into which the liquid is
evaporating.
(e) The rate of circulation of air over its surface.
(f) The extent of surface exposed to evaporation.
=176. Molecular Motion in Solids.=--Evidence of molecular motion in
liquids is given by expansion on heating, evaporation, and diffusion. Do
any of these lines of evidence apply to solids? It is a fact of common
experience that solids do become larger on heating. Spaces are left
between the ends of rails on railroads so that when they expand in
summer they will not distort the track. Iron tires are placed on wheels
by heating them until they slip on easily. Then on cooling, the iron
shrinks and presses the wheel tightly. Many common demonstrations of
expansion are found in lecture rooms. The fact of the evaporation of a
solid is often detected by noticing the odor of a substance. The odor of
moth balls is one example. Camphor also evaporates. Heated tin has a
characteristic odor noted by many. Ice and snow disappear in winter even
though the temperature is below freezing. Wet clothes, "freeze dry,"
that is, dry after freezing, by evaporation. A few crystals of iodine
placed in a test-tube and gently heated form a vapor easily seen, even
though none of the iodine melts. Where the vapor strikes the side of the
tube, it condenses back to dark gray crystals of iodine. This change
from solid directly to gas and back again without becoming liquid is
called _sublimation_. A number of solids are purified by this process.
Important Topics
1. Cooling effect of evaporation, rate of evaporation affected by six
conditions.
2. Effects of molecular motion in solids: (a) Expansion, (b)
Evaporation, (c) Sublimation.
Exercises
1. Does sprinkling the streets or sidewalks cool the air? Why?
2. Give an illustration for each of the factors affecting evaporation.
3. Give an illustration for each of the three evidences of molecular
motions in solids.
4. Since three-quarters of the earth's surface is covered with water,
why is not the air constantly saturated?
5. If the air has the temperature of the body, will fanning the
perfectly dry face cool one? Explain. Will the effect be the same if the
face is moist? Explain.
6. What is the cause of "Cloud Capped" mountains?
7. Why does the exhaust steam from an engine appear to have so much
greater volume on a cold day in winter than on a warm one in summer?
8. What causes an unfrozen pond or lake to "steam" on a very cold day in
winter, or on a very cool morning in summer?
9. As the air on a mountain top settles down the sides to places of
greater pressure, how will its temperature be affected? its relative
humidity? Explain.
10. On our Pacific coast, moist winds blow from the west over the
mountains. Where will it rain? Where be dry? Explain.
CHAPTER VIII
HEAT AND WORK
(1) HEAT MEASUREMENT AND SPECIFIC HEAT
=177. Specific Heat.=--In the study of density and specific gravity it
is made clear that different substances differ widely in the amount of
matter contained in equal volumes, _e.g._, lead is much denser than
water. The study of the relative densities of substance is usually
considered under the subject of _specific gravity_.
_Specific heat_ as distinguished from specific gravity is concerned with
the _capacity_ for heat possessed by different substances. The
definition for specific heat is: _The ratio of the amount of heat
required to change the temperature of a given mass of a substance 1 C.
degree to the amount of heat required to change the temperature of the
same mass of water 1 C. degree._ By definition, it requires 1 calorie to
raise the temperature of the gram of water 1°C. The _specific heat_
therefore of water is taken as one. The specific heat of most substances
except hydrogen, is _less_ than that of water, and as a rule, the denser
the body the less its specific heat, as may be observed in the following
table:
---------+----------+----------
| Specific | Specific
| gravity | heat
---------+----------+----------
Gold | 19.3 | 0.032
Mercury | 13.6 | 0.033
Copper | 8.9 | 0.093
Brass | 8.4-8.9 | 0.094
Nickel | 8.57 | 0.11
Iron | 7.5+ | 0.1125
Aluminum | 2.67 | 0.218
Glass | 2.5-3.6 | 0.19
Ice | 0.918 | 0.504
Air | 0.00129 | 0.237
Steam | 0.00061 | 0.480
Hydrogen | 0.00009 | 3.409
---------+----------+----------
=178. Method of Determining Specific Heat.=--The specific heat of a body
is usually determined by what is called the _method of mixtures_.
For example, a definite weight of a substance, say a 200-g. iron
ball, is placed in boiling water until it has the temperature of
the hot water, 100°C. Suppose that 300 g. of water at 18°C. be
placed in a calorimeter, and that the hot iron ball on being placed
in the water raises its temperature to 23.5°C. The heat received by
the water equals 5.5 × 300 = 1650 calories. This must have come
from the heated iron ball. 200 g. of iron then in cooling 76.5°C.
(100°-23.5°) gave out 1650 calories. Then 1 g. of iron in cooling
76.5°C. Would give out 8.25 calories or 1 g. of iron cooling 1°C.
would yield about 0.11 calorie. The specific heat of the iron is
then 0.11. For accurate determination the heat received by the
calorimeter must be considered.
=179. Heat Capacity of Water.=--The large capacity for heat shown by
water is useful in regulating the temperature of the air near lakes and
the ocean. In hot weather the water rises slowly in temperature
absorbing heat from the warm winds blowing over it. In winter the large
amount of heat stored in the water is slowly given out to the air above.
Thus the climate near the ocean is made more moderate both in winter and
summer by the large capacity of water for heat. This large heat capacity
of water may seem to be a disadvantage when one is warming it for
domestic purposes since it requires so much heat to warm water to
boiling. However, it is this capacity that makes hot-water bottles and
hot-water heating effective.
If one takes a pound of ice at 0°C. in one dish and a pound of
water at 0°C. in another, and warms the dish of ice by a Bunsen
flame until the ice is just melted, and then warms the water in the
other dish for the same time, the water will be found to be _hot_
and at a temperature 80°C., or 176°F.
=180. The Heat of Fusion of Ice.=--This experiment indicates the large
amount of heat required to change the ice to water without changing its
temperature. As indicated by the experiment, it requires 80 calories to
melt 1 g. of ice without changing its temperature or, in other words, if
one placed 1 g. of ice at 0°C. in 1 g. of water at 80°C., the ice would
be melted and the water would be cooled to 0°C.
=181. Heat Given out by Freezing water.=--Just as 80 calories of heat
are required to melt 1 g. of ice, so in freezing 1 g. of water, 80
calories of heat are given out.
The fact that heat is set free or given out when a liquid
solidifies may be strikingly shown by making a strong solution of
sodium acetate. On allowing this to cool quietly it will come to
the room temperature and remain liquid. If now a small crystal of
sodium acetate is dropped into the liquid the latter quickly
becomes a solid mass of crystals, at the same time rising markedly
in temperature. The amount of heat now liberated must enter the
sodium acetate when the mass of crystals is melted again.
The large amount of heat that must be liberated before water freezes
accounts for the slowness of the formation of ice. It is also the reason
why the temperature never falls so low in the vicinity of large lakes as
it does far inland, the heat given out by the freezing water warming the
surrounding air.
The heat that disappears on melting and reappears on solidifying is
called the _heat of fusion_. It is sometimes called _latent heat_ since
the heat seems to become hidden or latent. It is now believed that the
heat energy that disappears when a body melts has been transformed into
the _potential energy_ of partially separated molecules. The heat of
fusion therefore represents the work done in changing a solid to a
liquid without a change of temperature.
=182. Melting of Crystalline and Amorphous Substances.=--If a piece of
ice is placed in boiling hot water and then removed, the temperature of
the unmelted ice is still 0°C. There is no known means of warming ice
under atmospheric pressure above its melting point and maintaining its
solid state. Ice being composed of ice crystals is called a crystalline
body. All crystalline substances have fixed melting points. For example,
ice always melts at 0°C. The melting points of some common crystalline
substances are given below:
_Melting Points of Some Crystalline Substances_
1. Aluminum 658 C.
2. Cast iron 1200 C.
3. Copper 1083 C.
4. Ice 0 C.
5. Lead 327 C.
6. Mercury -39 C.
7. Phenol (carbolic acid) 43 C.
8. Platinum 1755 C.
9. Salt (sodium chloride) 795 C.
10. Saltpeter (potassium nitrate) 340 C.
11. Silver 961 C.
12. Sodium hyposulphite (hypo) 47 C.
13. Zinc 419 C.
_Non-crystalline or amorphous substances_ such as glass, tar, glue,
etc., do not have well defined melting points as do crystalline bodies.
When heated they gradually soften and become fluid. For this reason
glass can be pressed and molded.
=183. Change of Volume During Solidification.=--The fact that ice floats
and that it breaks bottles and pipes in which it freezes shows that
water expands on freezing. How a substance may occupy more space when
solid than when liquid may be understood when we learn that ice consists
of masses of star-shaped crystals. (See Fig. 151.) The formation of
these crystals must leave unoccupied spaces between them in the ice.
When liquefied, however, no spaces are left and the substance occupies
less volume. Most substances contract upon solidifying. Antimony and
bismuth, however, expand on solidifying while iron changes little in
volume. Only those bodies that expand, or else show little change of
volume on solidifying, can make sharp castings, for if they contract
they will not completely fill the mold. For this reason gold and silver
coins must be stamped and not cast. Type metal, an alloy of antimony and
lead, expands on solidifying to form the sharp outlines of good type.
Several important effects of the expansion of water when freezing should
be noted. (a) Ice floats, (b) if it sank as soon as formed, lakes and
rivers would freeze solid, (c) freezing water is one of the active
agents in the disintegration of rocks.
[Illustration: FIG. 151.--Ice crystals.]
[Illustration: FIG. 152.--Melting ice by pressure.]
Since water expands on freezing, pressure would on compressing ice at
0°C., tend to turn it into water. Pressure does lower the melting point
of ice, so that a little ice may melt when it is subjected to pressure.
On removing the pressure the water freezes. This may be shown by placing
a loop of fine piano wire (see Fig. 152) over a piece of ice supported
so that a weight may be hung upon the wire. The wire will be found to
gradually cut through the ice, the melted ice refreezing above the wire.
Important Topics
1. Specific heat.
2. Heat of fusion of ice.
3. Crystalline substances have fixed melting points.
4. Expansion on freezing, importance.
Exercises
1. What are two advantages in the high heat of fusion of ice?
2. What are two advantages in the expansion of water while freezing?
3. How much heat will be required to melt 1000 g. of ice and warm the
water to 20°C.?
4. How many grams of ice at 0°C. can be melted by 400 g. of water at
55°C.?
5. What are two advantages of the high specific heat of water? Two
disadvantages?
6. If the specific heat of iron is 0.1125, how much ice at 0°C. can be
melted by a 200-g. ball of iron heated to 300°C?
7. What is the temperature of a hot ball of iron weighing 80 g., if when
placed on a piece of ice at 0°C. it melts 90 g. of ice?
8. If 500 g. of copper at 400°C. are placed into 3000 g. of water at
10°C. what will be the resulting temperature?
9. What weight of water at 90°C. will just melt 10 kg. of ice at 0°C.?
10. If the smooth dry surface of two pieces of ice are pressed together
for a short time the two pieces will be frozen into one piece. Explain.
11. Tubs of hot water are sometimes placed in vegetable cellars to
prevent the vegetables from freezing. Explain.
12. How many B.t.u. are given out when 2 lbs. of water freeze?
(2) HEAT AND CHANGE OF STATE
[Illustration: FIG. 153.--The black cube in the upper corner represents
one cubic inch of water. The entire cube represents the space occupied
by the cubic inch of water in the form of steam. The reduced spaces at
the bottom and sides show how much short the cube is of being one cubic
foot. (American Radiator Co.)]
=184. Heat of Vaporization.=--In our study of evaporation in Art. 174 we
considered the more rapidly moving or vibrating molecules in the liquid
escaping to the air above and the slower moving molecules being left
behind in the liquid; this means that a loss of heat will result upon
evaporation, the liquid remaining becoming cooler as the process
continues. Now just as a ball thrown up in the air loses its kinetic
energy as it rises, and acquires energy of position or potential energy,
so molecules escaping from a liquid lose a certain amount of kinetic
energy or heat and acquire a corresponding amount of _energy of
position_ or potential energy. _Conversely_, as the ball returns to the
ground its potential energy is changed to kinetic energy. Similarly when
vapor molecules return to the liquid condition they lose their energy of
position and acquire kinetic energy. In other words, when a liquid
evaporates a certain amount of heat disappears, or becomes _latent_ and
when the vapor condenses the heat reappears, or becomes _sensible_ heat.
_The amount of heat that disappears when 1 g. of a substance is
vaporized is called the heat of vaporization._ In the case of water at
its boiling point, 536 calories of heat disappear when 1 g. of water
turns to vapor, and this same amount of heat reappears when the vapor
condenses.
The change of volume of water on turning to steam is shown in Fig. 153.
[Illustration: FIG. 154.--Effect of pressure on the boiling point.]
=185. The Boiling Point.=--The boiling temperature depends upon the
pressure. The boiling point may be defined as _the temperature at which
bubbles of vapor are formed within the liquid_. These bubbles increase
the surface at which evaporation can take place in the liquid, and the
principal reason why rapid application of heat to a liquid does not
raise its temperature above the boiling point is that as more heat is
applied more bubbles form so that the increase of evaporating surface
supplies a correspondingly greater surface for cooling. The variation of
the boiling temperature with changing pressure may be shown by partly
filling a strong 7/8-in. test-tube with water. Close the neck with a
one-hole rubber stopper through which passes a glass tube to which is
attached a soft rubber tube. (See Fig. 154.) Support the tube by a
holder, heat the water and boil until all the air is driven from the
tube, then close the soft rubber tube with a pinch cock and hold the
tube in an inverted position. On cooling the end of the tube above the
water with cold water or snow, the vapor within is condensed and the
pressure upon the water is reduced. Vigorous boiling begins at once. By
condensing the vapor repeatedly the water may be made to boil at the
room temperature. At the top of Mt. Blanc water boils at 84°C. While in
steam boilers at 225 lbs. pressure to the square inch the boiling point
is nearly 200°C.
=186. Laws of Boiling.=--The following statements have been found by
experiments to be true.
1. Every liquid has its own _boiling_ point which under the same
conditions of _pressure_ is always the same.
2. The temperature of the boiling liquid remains at the boiling point
until all the liquid is changed into vapor.
3. The boiling point rises with increased pressure and falls if the
pressure is diminished.
4. A boiling liquid and the vapor formed from it have the same
temperature. On cooling, a vapor will liquefy at the boiling point.
[Illustration: FIG. 155.--Distilling apparatus.]
5. The solution of solid substances in a liquid raises its boiling
point, additional energy being needed to overcome the adhesion involved
in the solution. The boiling point is also affected by the character of
the vessel containing the liquid. In glass the boiling point is 101°.
[Illustration: FIG. 156.--A vacuum pan.]
=187. Distillation of Water.=--Usually when solids are dissolved in
liquids the vapor coming from the liquid contains none of the dissolved
solid. Thus by evaporating salt sea water, and collecting and condensing
the vapor, pure water is obtained. _Distillation_ is the process of
boiling a liquid and condensing the vapor formed back again into a
liquid. (See Fig. 155.) The liquid to be distilled is placed in vessel
_F_ and boiled. The vapor is conducted into the tube _J_ which is
surrounded by a larger tube containing cold water. The vapor is
condensed on the cold walls of the tube. The resulting liquid is
collected in the vessel _R_. Distillation is employed for two purposes:
(a) To remove impurities from a liquid (water is purified in this way).
(b) Mixtures of different liquids having different boiling points may be
separated by distillation. The one having the lower boiling point will
be vaporized first. Thus a mixture of alcohol and water, on distillation
yields a distillate having a much larger percentage of alcohol than at
first. Repeating this process which is called _fractional distillation_
yields alcohol of increasing strength of purity. Distilled liquor such
as alcohol, brandy, and whisky are made by distilling fermented liquor,
alcohol being made from fermented grains. Gasoline and kerosene are
distilled from crude petroleum. Sometimes as in the production of sugar
or evaporated milk the object is to remove the water by evaporation in
order to obtain the solid material. Since the two substances named are
injured by heating, the syrup, or milk is evaporated under reduced
pressure in a _vacuum pan_, that is in a boiler from which air and vapor
are removed by an air pump. (See Fig. 156.)
=188. Artificial Cooling.=--The fact has been brought out that when a
solid is melted, a certain amount of heat, called the heat of fusion, is
absorbed or disappears. This absorption of heat is also noticed when a
solid is liquefied by dissolving it in a liquid as well as when it is
liquefied by simply applying heat. Thus if some table salt is placed in
a tumbler of water the temperature of the solution is lowered several
degrees below that of the salt and water used. The liquefaction or
solution of the salt has been accompanied by an absorption or
disappearance of heat. This heat has been taken from the salt and from
the water, resulting in a lowered temperature. Sal ammoniac or ammonium
nitrate when dissolved in water produce a much more marked cooling
effect than does table salt. The dissolving of a crystal in a liquid is
something like evaporation, except that the molecules of the liquid
attract the molecules of the solid and thus assist the change of state.
=189. Freezing Mixtures.=--If one attempts to freeze a solution of salt
and water, ice will not form at 0°C. but several degrees lower. The ice
formed however is pure. Evidently the attraction of the molecules of
salt for the water molecules prevented the formation of ice until the
motions of the water molecules had been reduced more than is necessary
in pure water. As the temperature of freezing water is that of melting
ice, ice in a salt solution melts at lower temperature than in pure
water. In a saturated salt solution this temperature is -22°C. It is
for this reason that the mixture of ice and salt used in freezing cream
is so effective, the salt water in melting the ice, being cooled to a
temperature many degrees below the freezing point of the cream. The best
proportion for a freezing mixture of salt and ice is one part salt to
three parts of finely powdered or shaved ice.
=190. Refrigeration by Evaporation.=--Intense cold is also produced by
permitting the rapid evaporation of liquids under pressure. Carbon
dioxide under high pressure is a liquid, but when allowed to escape into
the air evaporates so rapidly that a portion of the liquid is frozen
into solid carbon dioxide which has a temperature of -80° C. The
evaporation of liquid ammonia by permitting it to escape into a pipe,
under reduced pressure, is used on a large scale as a means of producing
cold in cold storage and refrigeration plants. (See Fig. 157.)
[Illustration: FIG. 157.--Diagram of a refrigerating system.]
The essential parts of the refrigerating system employing ammonia is
represented in Fig. 157. The _compressor_ exhausts ammonia gas from the
coiled pipe in "_E_" and compresses the gas in "_C_," where under 150
pounds pressure and the cooling effect of water it condenses to liquid
ammonia. This is allowed to pass slowly through the regulating valve,
whereupon it evaporates and expands in the long coiled pipe in "_E_" on
its way back to the compressor. This evaporation and expansion causes a
large amount of heat to be absorbed from the brine, cooling the latter
below the freezing point of pure water and thus permitting the freezing
of cans of water suspended in the brine. The chilled brine may also be
sent through pipes in order to cool storage rooms containing meat or
other food products. The ammonia absorbs heat when it vaporizes and
gives up heat when it is compressed and liquified.
Important Topics
1. Heat of vaporization, of water 536 calories per gram.
2. Boiling point, effect of pressure upon boiling point, laws of
boiling.
3. Distillation, artificial cooling, freezing mixtures, refrigeration by
evaporation.
Exercises
1. How much heat is required (a) to melt 1 g. of ice at 0°C., (b) to
raise the temperature of the water resulting to 100°C., (c) to change
this water to steam?
2. If the water leaving a steam radiator is as hot as the steam how is
the room warmed?
3. What is the effect of placing salt upon icy sidewalks in cold
weather?
4. Is rain water distilled water? Is it perfectly pure?
5. What are two advantages of the high heat of vaporization of water?
6. If the heat from 1 g. of steam at 100°C. in changing to water and
cooling to 0°C. could be used in melting ice at 0°C. how much ice would
be melted?
(3) HEAT AND WORK
=191. Necessity for Heat Energy.=--From early times man has been able to
transform motion into heat, and has used this ability in many directions
as in starting fires and warming himself by friction. It took man many
centuries, however, to devise an effective machine for transforming heat
into mechanical energy or to use it in doing work.
The _power_ of a man is small and as long as the work of the world had
to be done by man power, progress was retarded. When man began the use
of beasts of burden, he took a long step in advance since one man could
then employ and direct the power of many men in the animals he
controlled. Man also built water-wheels and windmills thus gaining power
directly from the forces of nature and these added much to his working
ability. But he took the greatest step in gaining control over his
surroundings when he learned to use heat energy and to make it drive his
machines.
=192. Heat Engines.=--At the present time there is a great variety of
_heat engines_ in use such as _steam_, _hot air_, _gas_, and _gasoline_
engines, all using _heat energy_ to produce motion. The expansive power
of steam when confined has been observed for hundreds of years and many
different machines have been invented to use it in doing work.
[Illustration: FIG. 158.--Cross-section view of cylinder and steam chest
of a steam engine.]
[Illustration: FIG. 159.--The steam drives the piston to the left.]
[Illustration: FIG. 160.--External view of steam engine.]
=193. The Steam-engine.=--The man who perfected the steam-engine, and
devised its modern form was _James Watt_ (1736-1819). The essential
parts and the action of the steam engine may be readily understood by
studying a diagram. In Fig. 158, _S_ stands for _steam chest_, _C_ for
_cylinder_, _P_ for _piston_ and _v_ for _slide valve_. The first two
are hollow iron boxes, the latter are parts that slide back and forth
within them. The action of the steam engine is as follows: Steam under
pressure enters the steam chest, passes into the cylinder and pushes the
piston to the other end. The slide valve is moved to its position in
Fig. 159. Steam now enters the right end of the cylinder, driving the
piston to the left, the "dead" steam in the left end of the cylinder
escaping at _E_ to the air. The slide valve is now shifted to its first
position and the process is repeated. It will assist the student to
understand this action if he makes a cardboard model of these parts, the
piston and slide valve being movable. In practical steam-engines, the
piston rod is attached to a _crank rod_ fastened to a crank which turns
a wheel. (See Fig. 160.) The back and forth, or _reciprocating_ motion
of the piston is by this means transformed into _rotary_ motion, just as
in the sewing-machine the back-and-forth motion of the treadle produces
rotary motion of the large wheel. Upon the shaft of the steam engine is
fastened an _eccentric_ (see Fig. 163) which moves the slide valve. The
steam engine acts continuously as long as steam is supplied to it. Since
it shifts the position of the slide valve automatically, it is called an
automatic steam engine. And because the team drives the piston both
ways, it is called a _double-acting_ steam engine. See Fig. 161 for a
length-section of a modern locomotive.
[Illustration: FIG. 161.--Length-section of modern, fast-passenger
locomotive. _A_, cylinder valve--piston type valve; _B_,
cylinder--piston at out end of stroke; _C_, boiler tubes--flues from
fire-box; _D_, fire-tube type superheater; _E_, draught screen; _F-A_,
fire-brick arch to protect tubes from direct heat; _F-B_, firebox; _G_,
grate; _H_, exhaust nozzle; _I_, safety valve nest; _T_, throttle lever;
_R_, throttle rod; _Y_, throttle valve.]
=194. The Mechanical Equivalent of Heat.=--While watching workmen bore
holes in cannon, Count Rumford, 1753-1814, noticed with much interest
the large amount of heat produced in the process. He observed that the
heat developed seemed to have some relation to the work done upon the
drill in boring the holes. Later experiments performed by many men
indicated that a definite relation exists between the heat produced by
friction and the amount of work done in overcoming the friction. This
discovery indicates that in some way heat is related to energy and that
heat is probably a form of energy. Later experiments have confirmed this
idea, and it is now considered well established that _heat is a form of
energy_. Many attempts have been made to discover the relation between
the units of heat energy and the units of mechanical energy. To
illustrate one method employed, suppose one measures a given _length_ in
inches and in centimeters; on dividing one result by the other, it will
be found that a certain relation exists between the two sets of
measurements, and that in every case that 1 in. equals 2.54 cm.
Similarly, when the same amount of _energy_ is measured both in heat
units and in work units a constant relation is always found between the
units employed. _One B.T.U. is found equivalent to 778 ft.-lbs. 1
calorie being equivalent to 42,700 g. cm. (427 g. m.)._ This relation is
called the _mechanical equivalent of heat_, or in other words it
represents the number of work units equivalent to one heat unit.
[Illustration: FIG. 162.--Apparatus for determining the mechanical
equivalent of heat.]
[Illustration: William Gilbert (1540-1603), "Father of magnetic
philosophy." Especially noted for his experiments and discoveries in
magnetism; first to use the word "electricity." First man to practically
emphasize experimental science.
DR. WILLIAM GILBERT
(Popular Science Monthly)]
[Illustration: James Prescott Joule (1818-1889), England, determined the
mechanical equivalent of heat; discovered the relation between an
electric current and the heat produced; first proved experimentally the
identity of various forms of energy.
JAMES PRESCOTT JOULE
(Popular Science Monthly)]
One of the first successful experiments in determining the relation
between work units and heat units was devised by Joule in England. (See
portrait p. 217.) The experiment consisted in taking a can of metal
containing water (Fig. 162) in which was placed a thermometer, and a rod
carrying paddles. The rod was turned by a cord connected through
suitable apparatus to heavy weights, _W_ and _W_. The energy represented
by the downward motion of the weights through a given distance was
compared with the heat energy developed in the water as shown by its
rise in temperature. Careful experiments showed that when 778 ft.-lbs.
of work had been done by the moving weights the heat produced at the
same time would warm one pound of water 1 Fahrenheit degree. If the
experiment was performed using metric units, it was found that the
expenditure of 42,700 gram centimeters (427 gram meters) would result in
producing enough heat to warm one gram of water one centigrade degree.
The facts just given may be summarized as follows: _778 foot-pounds of
energy are equivalent to 1 British thermal unit and 42,700 gram
centimeters, or 427 gram meters, of energy are equivalent to 1 calorie_.
This relation of work units to heat units is called the _mechanical
equivalent of heat_.
=195. The Heat Equivalent of Fuels and Efficiency Tests of Engines.=--To
determine the efficiency of a steam engine it is necessary to know not
only the mechanical equivalent of heat but also the heat produced by
burning coal or gas; 1 lb. of average soft coal should produce about
12,600 B.t.u. Now since 778 ft.-lbs. are equivalent to one B.t.u. the
energy produced when 2 lbs. of average soft coal is burned is 778 ×
12,600 × 2 = 19,605,600 ft.-lbs. In actual practice 2 lbs. of average
soft coal burned will develop about 1 horse-power for 1 hour. 1
horse-power-hour = 33,000 ft.-lbs. × 60 = 1,980,000 ft.-lbs. Now
efficiency equals (work out)/(work in) 1,980,000/19,605,600 = 1/10 or 10
per cent.. This is the efficiency of a good steam engine. Ordinary ones
require 3 lbs. of coal burned to each horse-power-hour produced or they
are but 2/3 as efficient or have but about 7 per cent. efficiency.
HEAT OF COMBUSTION OF VARIOUS FUELS
Data in this table are taken from U. S. Geological Survey, Bulletin
No. 332, and U. S. Bureau of Mines, Bulletin No. 23.
--------------------------+---------+----------
| B.T.U. | Calories
| per lb. | per gram
--------------------------+---------+----------
Alcohol, denatured | 11,600 | 6,450
Coal, anthracite, average | 12,600 | 7,500
Coal, bituminous, average | 19,000 | 7,000
Gasoline | 19,000 | 10,550
Illuminating gas | 18,000 | 10,000
Kerosene | 19,990 | 11,050
--------------------------+---------+----------
CONSTANTS FOR HEAT TRANSMISSION
Data from "Ideal Fitter," American Radiator Co.
B.t.u. transmitted per square foot per hour per degree (Fahrenheit)
difference in temperature between inside and outside air.
_Brick work_
4 in. thick = 0.68 { concrete }
8 in. thick = 0.46 { cement } 50 per cent. more than brick.
12 in. thick = 0.33 {
stone 33-1/3 per cent. more than brick.
Window = 1.090 {
Wood as wall = 0.220 { concrete } 20 per cent. more than
Double window = 0.560 { reinforced } brick.
Important Topics
1. Heat a manifestation of energy.
2. Steam-engine and its action.
3. Mechanical equivalent of heat and heat equivalent of fuels and
efficiency of engines.
Exercises
1. Construct a working model of the cylinder and steam chest of a steam
engine and be prepared to explain its action.
2. At $5.00 per ton how many B.T.U.'s should be produced from 1 cent's
worth of bituminous coal?
3. Try the following experiment: Place a quart of water in a teakettle
and place it over the fire for 5 minutes, and note the rise in
temperature and compute the number of B.T.U.'s entering the water. Place
another quart of water at the same temperature in an aluminum or tin
dish and heat for 5 minutes, note the rise in temperature and compute
the heat used before. Which of the dishes shows the greater efficiency?
How do the efficiencies of the two dishes compare? How do you account
for any differences in the efficiencies found?
4. How high would 8 cu. ft. of water be lifted if all of the energy
produced by burning 1 lb. of coal were used in raising it?
5. What is the mechanical equivalent of a pound of coal expressed in
horse-power hours?
6. If a furnace burns 100 lbs. of coal a day and its efficiency is 50
per cent. how many B.T.U.'s are used in warming the house?
7. How many B.T.U.'s can be obtained by burning 1/2 ton of bituminous
coal?
8. when a pound of water is heated from 40°F. to 212°F., how many
foot-pounds of energy are absorbed by the water?
9. How many loads of coal each weighing 2 tons, could be lifted 12 ft.
by the energy put into the water in problem 8?
[Illustration: FIG. 163.--An eccentric.]
10. When 3 cu. ft. of water are used for a hot bath and the water has
been heated from 50°F. to 112°F., how many B.T.U.'s have been absorbed
by the water?
11. If the average temperature of water at the surface of Lake Michigan
is 50°F., how many B.T.U.'s would be given off by each cubic foot of
water at the surface, if the temperature of the water should drop 5°F.?
12. In a cold storage plant carbon dioxide gas is used. The pipe
leading from the compression pump to the expansion valve passes through
a condensing tank of cold water. Why?
13. When the gas is compressed in a cold storage plant, what becomes of
the energy used by the compression pump?
14. An eccentric (Fig. 163), is a round disc mounted a little to one
side of its center, _A_, on the engine shaft _B_. A band, _C_, on the
circumference of the disc is connected by a rod, _D_, with the slide
valve in the steam chest. How is the rotary motion of the shaft changed
into a backward and forward motion of the slide valve?
(4) HEAT ENGINES
=196. The Gas Engine.=--One of the heat engines in common use to-day is
the gasoline engine. It is used to propel automobiles and motor boats,
to drive machinery, etc. The construction and action of a gasoline
engine may be understood by studying a working model, or by proper
diagrams.
[Illustration: FIG. 164.--Cut away view of a modern automobile engine,
with parts requiring attention most frequently, indicated. (Courtesy of
the "Automobile Journal")]
The common gasoline or gas engine is called a four-cycle (better
four-part cycle) engine (see Fig. 164), since it requires four
movements of the piston to complete one cycle or series of changes. This
is illustrated in Fig. 165 =1=, which represents a cross-section of the
_cylinder_ of the gasoline engine with the _piston_ moving downward. At
the upper end of the cylinder are two _ports_ or openings. One, the
_exhaust_ port, is closed, the _inlet_ port is open and a mixture of gas
and air is entering. Fig. 165 =2= shows the piston returning; both ports
are closed and the "charge" of air and gas is being compressed. As the
piston reaches the end of its stroke in compressing the charge, an
electric spark explodes or "fires" the charge of gas and air. The hot
burning gas expands suddenly driving the piston downward with great
force (Fig. 165 =3=). The piston rod is attached to the crank of a heavy
fly-wheel and this is given sufficient energy or momentum to keep it
going through the next three strokes. Fig. 165 =4= represents the
returning piston pushing out the burnt "charge" through the open exhaust
valve _e_. On the next downward motion of the piston the valve _e_
closes. It opens, and new charges of gas and air enter and the "cycle"
is repeated.
[Illustration: FIG. 165.--The four strokes of a gas engine cycle.]
In order to make the motion more even and continuous and also to secure
more power, more than one cylinder is attached to the same shaft and
fly-wheel. Two, three, four, six, eight and even more cylinders have
been attached to one shaft. Four or six cylinders are commonly used in
automobile gasoline motors. To lessen the sound of the "exhaust," the
latter is sent through a "muffler" which often reduces the noise to a
low throbbing. (See Fig. 166.) The gasoline engine is more efficient
than the steam-engine, since the fuel, gas, is burned in the cylinder
and not in a separate furnace. The combustion of the fuel in the
cylinders makes some special cooling device necessary to prevent their
overheating. This usually consists of a casing about the cylinders.
Between the cylinder and this casing is water which on being heated
passes to a tank or radiator. In the radiator the water cools and then
returns to the space between the cylinders and casing thus keeping up
the circulation.
[Illustration: FIG. 166.--An efficient automobile muffler. (_Courtesy
Popular Science Monthly._)]
=197. Efficiency of Gas Engines.=--One may test the _efficiency_ of a
gas engine by determining the amount of power developed and comparing it
with the mechanical equivalent of the fuel burned. Illuminating gas is
sometimes employed to drive gas engines. One cubic foot of illuminating
gas should produce 600 B.T.U. when burned. The efficiency of the gas or
gasoline engines is sometimes as high as 25 per cent. This engine is
free from smoke and is also compact and quickly started. While the fuel,
gas or gasoline, is somewhat expensive it is light and easily carried.
Suppose a gas engine produces 1 horse-power and uses 20 cu. ft. of gas
an hour, what is its efficiency? 1 horse-power-hour = 550 × 60 × 60 =
1,980,000 ft.-lbs. 20 cu. ft. of gas = 20 × 600 × 778 = 9,336,000
ft.-lbs.
Efficiency = work out/work in = 1,980,000/9,336,000 = 21.2 per cent.
[Illustration: FIG. 167.--The principle of the steam turbine.]
[Illustration: FIG. 168.--Path of steam in DeLaval steam turbine. (_a_)
and (_c_) movable blades, (_b_) stationary.]
=198. The Steam Turbine.= One form of the steam-engine that is coming
into general use is the turbine. (See Fig. 167.) This consists of a
shaft to which are attached blades, the shaft and blades being contained
in a closed case. Steam is admitted by nozzles and strikes the blades so
as to set them and the shaft in motion. There are also stationary blades
(see Fig. 168), which assist in directing the steam effectively against
the rotating parts. The steam turbine is used for large power plants.
(See Fig. 293.) It is very efficient, makes very little vibration, and
occupies about one-tenth the floor space that a reciprocating engine of
equal power uses. Some large ocean steamers are now driven by steam
turbines.
Important Topics
1. The gas engine, its construction, action and efficiency.
2. The steam turbine.
Exercises
1. If coal costs $4.00 a ton, and gas, $0.80 per 1000 cu. ft. what
amounts of heat can be secured from 1 cent's worth of each?
2. What will it cost to heat 30 gallons of water (1 gal. of water weighs
about 8-1/3 lbs.) from 40°F. to 190°F. with coal costing $4.00 per ton
and yielding 12,000 B.T.U. per lb. if the heater has an efficiency of 50
per cent.
3. What will it cost to heat 30 gallons of water from 40°F. to 190°F.
with gas at $0.80 per 1000 cu. ft. if the heating device has an
efficiency of 75 per cent.
4. Construct a cardboard working-model showing the action of the gas
engine and be prepared to explain the action of the various parts.
5. If 500 lbs. of iron should fall 2000 ft. and all of the resulting
mechanical kinetic energy should be transformed into heat, what would be
the amount of heat produced?
6. What are the special advantages of (a) the gasoline engine? (b) the
turbine? (c) the reciprocating steam engine?
7. Do you burn coal or gas in your kitchen stove at home? Which is for
you the more economical? Why?
8. What are the advantages of using a fireless cooker?
9. What is the efficiency of a locomotive that burns 3.2 lbs. of coal
per horse-power-hour?
10. A gas engine developed in a test 0.34 horse-power for 1 minute. and
50 seconds, 0.5 cu. ft. of gas being used. The heat of combustion of the
gas was 600 B.T.U. per cu. ft. Find the efficiency of the engine.
11. Find the horse-power of an engine, the diameter of the piston being
19 in., stroke 26 in.; it uses steam at an average pressure of 200 lbs.
per square. inch and makes 100 strokes a minute.
12. What is the efficiency of an engine and boiler that develops 200
horse-power, while burning 390 lbs. of soft coal per hour?
13. If a locomotive has an efficiency of 6 per cent. and develops 1700
horse-power how much coal is burned in an hour?
14. If an automobile engine burns 1 gallon of gasoline in an hour and
develops 10 horse-power, what is its efficiency?
15. The A.L.A.M.[J] formula for horse-power is (_N_ _B_²)/2.5 when the
piston speed is 1000 ft. per minute, _N_ being the number of cylinders
and _B_, their diameter. Find the horse-power of a 4-cylinder engine,
the cylinders having a diameter of 4 in.
[J] American League of Automobile Manufacturers.
16. Find the horse-power of a 6-cylinder automobile engine, if the
cylinder diameter is 4.5 in.
17. A 4-cylinder automobile having 4-in. cylinders, uses 1 gallon of
gasoline in 1 hour. Find its efficiency, if its average horse-power
developed is 6.
18. The motor boat Disturber III, has 24 cylinders each with diameter
3.5 in. If the piston speed is 1000 ft. per minute, what is the
horse-power? (See problem 15.)
Review Outline: Heat
Heat; sources (4), effects (5), units (2).
Temperature; thermometer scales (3), absolute temperature, 9C°/5 + 32° =
F°.
Expansion; gases, Law of Charles (V_{1}/V_{2} = T_{1}/T_{2}), liquids,
peculiarity of water, solids, coefficient of expansion, uses, results.
Heat Transference; conduction, uses of good and poor conductors,
convection, in nature, heating and ventilating systems, radiation, 3
peculiarities, value of sun's radiation.
Heat and Moisture; relative humidity, dew point, formation of dew, fog,
rain, snow, etc., evaporation, effects, conditions.
Heat Measurement; specific heat, heat of fusion, of vaporization,
combustion.
Vaporization; Boiling point, laws of boiling, distillation, artificial
cooling.
Heat Engines; steam, gas.--construction, action, efficiency, mechanical
equivalent of heat. Heat equivalent of fuels.
CHAPTER IX
MAGNETISM
(1) GENERAL PROPERTIES OF MAGNETS
=199. Magnets.=--Since the times of the early Greek philosophers men
have known of certain stones that have the property of attracting to
themselves objects of iron and steel. Such stones are called _natural
magnets_. It is thought by many that the name magnet is derived from
Magnesia in Asia Minor, where these stones are abundant, though this is
but tradition.
It was also learned long ago that iron and steel objects when rubbed
with natural magnets become magnetized, that is, acquire the properties
of magnets. These are said to be _artificial magnets_.
[Illustration: FIG. 169.--A bar magnet.]
[Illustration: FIG. 170.--A horseshoe magnet.]
Some 800 years ago it was discovered that magnets, natural or
artificial, when suspended so as to turn freely, always come to rest in
a definite position pointing approximately north or south. This is
especially noticeable when the magnet is long and narrow. Because of
this property of indicating direction, natural magnets were given the
name of _lodestone_ (lode-leading).
Artificial magnets are made by rubbing steel bars with a magnet or by
placing the steel bar in a coil of wire through which a current of
electricity is flowing. The magnetized steel bars may have any form,
usually they are either straight or bent into a "U" shape. These forms
are known as _bar_ and _horseshoe_ magnets. (See Figs. 169 and 170.)
Magnets retain their strength best when provided with soft-iron
"_keepers_," as in Fig. 171.
[Illustration: FIG. 171.--Bar magnets with keepers.]
=200. Magnetic Poles.=--If a magnet is placed in iron filings and
removed, the filings will be found to cling strongly at places near the
ends of the magnet, but for a portion of its length near the middle no
attraction is found. (See Fig. 172.) These places of greatest attraction
on a magnet are called _poles_. If a bar magnet is suspended so as to
swing freely about a vertical axis the magnetic pole at the end pointing
north is called the _north-seeking_ pole; at the other end, is the
_south-seeking_ pole. In most places the needle does not point to the
true north, but somewhat to the east or west of north. The direction
taken by a magnetic needle is parallel to the _magnetic meridian_.
[Illustration: FIG. 172.--Iron filings attracted to the poles of a
magnet.]
=201. Law of Magnetic Action.=--The north pole of a magnet is usually
marked. If a marked bar magnet be held in the hand and its north-seeking
pole be brought near the north-seeking pole of a freely suspended bar
magnet, the two poles will be found to repel each other, as will also
two south-seeking poles, while a north-seeking and a south-seeking pole
attract each other. (See Fig. 173.) This action leads to the statement
of the _Law of Magnetic Action_: _Like poles repel, while unlike poles
attract each other._ The force of attraction or repulsion lessens as the
distance increases. _The force of the action between magnetic poles is
inversely proportional to the square of the distance between them._
Compare this with the law of gravitation (Art. 88).
[Illustration: FIG. 173.--Like poles of two magnets repel.]
[Illustration: FIG. 174.--A magnetoscope.]
=202. Magnetic Substances and Properties.=--It is found that if an iron
or steel magnet is heated _red hot_ that its magnetic properties
disappear. Accordingly one method of _demagnetizing_ a magnet is to
raise it to a red heat. If a magnet that has been heated red hot and
then cooled is brought near a suspended bar magnet, it is found to
_attract either_ end, showing that it has regained _magnetic properties_
even though it has lost its _magnetic polarity_. A suspended bar magnet
used to test the magnetic properties of a body is called a
_magnetoscope_. (See Fig. 174.) The needle of a _magnetic compass_
serves very well as a magnetoscope. Magnetic properties are most
strongly exhibited by iron and steel, though nickel and cobalt show some
magnetic effects. There is a peculiar alloy of copper, aluminum, and
manganese, known as _Heusler's Alloy_, that is also magnetic. However,
of all substances, iron and steel show the strongest magnetic effects.
=203. Magnetic Induction.=--Let the north-seeking pole of a bar magnet
support an iron nail by its head. (See Fig. 175.) Test the point of the
nail for polarity. See whether a second nail can be attached by its head
to the point of the first. Test the polarity of the point of this nail.
Find by trial how many nails can be suspended in succession from the
magnet. Test in each case for polarity. Withdraw carefully the magnet
from the first nail--the string of nails will fall apart. Repeat the
test with a thickness of paper between the magnet and the first nail.
Results similar to those secured at first will be found, though probably
fewer nails will be supported. The presence of paper between the magnet
and nails simply weakens the action. Test the action of the magnet upon
the nail when there is between them a piece of glass, one's thumb, thin
pieces of wood, copper, zinc, etc. _The magnetizing of a piece of iron
or steel by a magnet near or touching it is called magnetic induction._
This action takes place through all substances except large bodies of
iron or steel hence these substances are often used as _magnetic
screens_. The pole of the new _induced magnet_ adjacent to the bar
magnet is just opposite to the pole used. Thus the N.-pole of the magnet
used will produce a S.-pole at the near end of the nail and a N.-pole at
the end farther away. (See Fig. 175.) On removing the magnet, the nails
are found to retain a part of their induced magnetism.
[Illustration: FIG. 175.--Nails magnetized by induction.]
=204. Retentivity.=--In several of the foregoing paragraphs it has been
seen that a piece of iron or steel when once magnetized does not
entirely lose its magnetism when the magnetizing force is removed.
Different pieces of iron and steel vary greatly in this respect, some
remaining strongly magnetized, others losing much of their magnetism.
_This property of retaining magnetism is called retentivity._ Hardened
steel has a high degree of retentivity, while soft iron retains but
little magnetism.
Important Topics
1. Magnet; natural, artificial, bar, horseshoe.
2. Magnetic poles; north seeking, south seeking.
3. Law of action, magnetoscope, retentivity, induced magnet.
Exercises
1. Make a summary of the facts of magnetism presented in this lesson.
2. Is magnetism matter, force, or energy? How do you decide? To what
other phenomenon that we have studied is it similar? How?
3. Make a simple magnetoscope for yourself by suspending a thin steel
needle or rod 5 to 10 cm. long, with a light thread or silk fiber at its
center, so that it will hang level. Then magnetize the needle, and keep
the magnetoscope in your book.
4. Name three uses for magnets or magnetism.
5. Mention three uses for a magnetoscope.
6. Are all magnets produced by induction? Explain.
7. In what magnetic devices is a high retentivity desirable?
(2) THE THEORY OF MAGNETISM AND MAGNETIC FIELDS
=205. The Theory of Magnetism.=--If a magnetized watch spring is broken
in two, _each part_ is found to be a magnet. If one of these parts be
broken and this process of breaking be continued as far as possible, the
smallest part obtained has two poles and is in fact a complete magnet.
(See Fig. 176.) It is supposed that if the division could be continued
far enough that each of the _molecules of the steel spring_ would be
found to have _two poles_ and to be a magnet. In other words, magnetism
is believed to be _molecular_. Other evidence supporting this idea is
found in the fact that when a magnet is heated red hot, to a temperature
of violent molecular motion, its magnetism disappears. Also if a long,
fine soft iron wire be strongly magnetized, a light jar causes its
magnetism to disappear. This would lead us to believe that magnetism is
not a property of the surface of the body, but that it depends upon
molecular structure or the arrangement of the molecules.
[Illustration: FIG. 176.--Effect of breaking a magnet.]
[Illustration: FIG. 177.--Possible arrangement of molecules in an
unmagnetized iron bar.]
It is believed also that the _molecules_ of a magnetic substance are
magnets at all times; that before the body is magnetized the molecules
are arranged haphazard (see Fig. 177) but that when a magnet is brought
near, the molecules tend to arrange themselves in line, with their
north-seeking poles pointing in the same direction. (See Fig. 178.) If
the magnet is jarred some of the molecules tend to get out of line,
perhaps to form little closed chains of molecules. (See Fig. 177.)
[Illustration: FIG. 178.--Arrangement of molecules in a saturated
magnet.]
=206. Magnetic Fields and Lines of Force.=--The behavior of magnets is
better understood after observing and studying the _lines of force_ of
a magnet. The earliest descriptions of these are by William Gilbert, the
first Englishman to appreciate fully the value of making experimental
observations. He wrote a book in 1600 called _De Magnete_ in which he
published his experiments and discoveries in magnetism. (See p. 217.)
Magnetic lines of force may be observed by placing a magnet upon the
table, then laying upon it a sheet of paper and sprinkling over the
latter fine iron filings. On gently tapping the paper, the filings
arrange themselves along curved lines extending from one end of the
magnet to the other. These are called the _magnetic lines of force_.
(See Fig. 179.) The space about a magnet in which the magnetic lines are
found is called the _magnetic field_. (See Fig. 180.)
[Illustration: FIG. 179.--Iron filings on paper over a bar magnet.]
Many interesting things have been discovered concerning the lines of
force. Some of the facts of magnetic action are given a simple
explanation if we think of them as due to the magnetic lines of force. A
summary of several discoveries concerning magnetic fields follows:
(A) Magnetic lines of force run side by side and do not cross one
another. (See magnetic fields.)
(B) Magnetic lines of force are believed to form "_closed curves_" or to
be continuous. The part outside of the magnet is a continuation of the
part within the magnet. (See Fig. 180.)
[Illustration: FIG. 180.--Diagram of the field of a bar magnet.]
(C) The attraction of a magnet is strongest where the magnetic lines are
thickest, hence they are believed to be the means by which a magnet
attracts.
(D) Since like poles repel and unlike poles attract, it is known that
the action along a line of force is not the same in both directions. It
has therefore been agreed by physicists to indicate by an arrow head
(Fig. 180), the direction that a north-seeking pole tends to move along
a line of force. The lines of force are considered as leaving the
north-seeking pole of a magnet and entering the south-seeking pole. (See
Figs. 181 and 182.)
[Illustration: FIG. 181.--Magnetic field between like poles showing
repulsion.]
(E) A freely suspended small magnet in a magnetic field places itself
parallel to the lines of force. (Test this by holding a magnetic compass
in different portions of a magnetic field). Note the position of the
needle and the lines of force. This fact indicates that the compass
needle points north on account of its tendency to turn so as to be
parallel to the earth's magnetic held.
[Illustration: FIG. 182.--Magnetic field between unlike poles showing
attraction.]
(F) Each magnet is accompanied by its own magnetic field. When a piece
of iron is brought within the field of a magnet the lines of force
passing through the iron tend to arrange the iron molecules in line or
to magnetize the iron.
=207. Magnetic Induction.=--The action of magnetic lines of force in
magnetizing iron when they pass through it, is called _Magnetic
Induction_. This may now be defined as _the production of magnetism in a
body by placing it within a magnetic field_. Freely suspended magnets
place themselves parallel to the lines of force in a magnetic field,
therefore when an iron rod is placed in a weak field, or one with few
lines of force, the iron is but slightly magnetized; that is, but few
molecules are brought into line. Increasing the strength of the
magnetizing field, gives stronger magnetization to the iron up to a
certain point. After this, stronger fields give no increase in
magnetizing effect. When iron exhibits its greatest magnetization it is
said to be _saturated_.
[Illustration: FIG. 183.--Effect of a piece of iron in a magnetic
field.]
=208. Permeability.=--If a piece of iron is placed between the poles of
a horseshoe magnet, the "field" obtained by sprinkling iron filings upon
a sheet of paper over the magnet resembles that shown in Fig. 183. The
lines in the space between the poles of the magnet seem to crowd in to
the piece of iron. The _property_ of the iron by which it tends to
concentrate and increase the number of lines of force of a magnetic
field is called _permeability_. Soft iron shows high permeability.
Marked differences in behavior are shown by different kinds of iron and
steel when placed in a magnetic field. Very pure iron, or _soft_ iron,
is strongly magnetized by a magnetic field of medium strength. Its
magnetism, however, is quickly lost when the magnetizing field is
removed. This indicates that soft-iron molecules are easily swung into
line, but also disarrange themselves as easily when removed from a
magnetizing force. Soft-iron magnets having high permeability quickly
lose their magnetism. They are therefore called temporary magnets. On
the other hand a hardened steel bar is difficult to magnetize, but when
once magnetized retains its magnetism permanently, unless some action
weakens the magnet. Such magnets are called _permanent_ magnets.
NOTE.--The term "line of force" as used in this text means the same
as "line of induction" as used in more advanced texts.
Important Topics
1. Molecular theory of magnetism, saturation, permeability.
2. Magnetic fields and lines of force.
3. Six facts concerning magnetic fields.
Exercises
1. Name an object whose usefulness depends upon its retentivity.
Explain.
2. How do you explain the retentivity of hard steel?
3. Are the molecules of a piece of iron magnetized at all times?
Explain.
4. When a piece of iron is magnetized by induction does any magnetism
enter the iron from the magnet? Does the magnet lose as the iron gains
magnetism? Explain.
5. Have all magnets been produced by induction? Explain.
6. Why will tapping a piece of iron when in a magnetic field increase
the amount it will be magnetized?
7. Express in your own words the theory of magnetism.
8. Place two bar magnets in a line 5 cm. apart, _unlike_ poles adjacent;
obtain the magnetic field with iron filings. Sketch it.
9. Repeat Exercise No. 8 using _like_ poles. Describe the appearance of
a field that gives attraction; of a field that gives repulsion.
(3) THE EARTH'S MAGNETISM
=209. The Earth's Magnetic Field.=--Dr. William Gilbert's famous book,
_De Magnete_, contains many helpful and suggestive ideas, none perhaps
more important than his explanation of the behavior of the compass
needle. He assumed that the earth is a magnet, with a _south-seeking_
pole near the geographical north pole, and with a _north-seeking_ pole
near the geographical south pole. This idea has since been shown to be
correct. The north magnetic (or south-seeking) pole was found in 1831,
by Sir James Ross in Boothia Felix, Canada. Its approximate present
location as determined by Captain Amundsen in 1905 is latitude 70° 5´
N. and longitude 96° 46´ W. The south magnetic pole is in latitude 72°
S., longitude 155° 16´ E. The north magnetic pole is continually
changing its position. At present it is moving slowly westward.
[Illustration: FIG. 184.--Magnetic map of the earth for 1910. Isogonic
lines ------ Isoclinic lines - - - -]
=210. Direction of the Earth's Magnetic Field.=--Reference has been made
to the fact that the compass does not always point exactly north. This
indicates that the earth's magnetic field varies in its direction.
Columbus discovered this fact upon his first voyage. The discovery
alarmed the sailors since they feared they might come to a place where
the compass would be unreliable. This variation is called _declination_.
It is defined as the _angle between the direction of the needle and the
geographical meridian_. Declination is due to the fact that the
geographical and magnetic poles do not coincide. What is meant by a
declination of 90°? Lines drawn upon a map so as to pass through places
of the same declination are called _isogonic_ lines. The line passing
through points where the needle points north, without declination, is
the _agonic_ line. The agonic line is slowly moving westward. It now
passes near Lansing, Michigan; Cincinnati, Ohio; and Charleston, S.
Carolina. (See Fig. 184.) At all points in the United States and Canada
east of the agonic line the declination is _west_, at points west of the
agonic line the declination is _east_.
=211. The Dipping Needle.=--Mount an unmagnetized steel needle on a
_horizontal_ axis so as to be in neutral equilibrium, that is, so as to
remain balanced in any position in which it is left. Upon being
magnetized and placed so that it can swing in a north and south plane,
the north-seeking pole will now be found to be depressed, the needle
forming an angle of nearly 70° with the horizontal. (See Fig. 185.) The
position assumed by the needle indicates that the earth's magnetic field
instead of being horizontal in the United States _dips_ down at an
angle of about 70°. Over the magnetic pole, the _dipping needle_ as it
is called, is vertical. At the earth's equator it is nearly horizontal.
_The angle between a horizontal plane and the earth's magnetic lines of
force is called the inclination or dip._
[Illustration: FIG. 185.--A dipping needle.]
=212. Inductive Effect of the Earth's Magnetic Field.=--The earth's
magnetic lines of force are to be considered as filling the space above
the earth, passing through all objects on the surface and into and
through the earth's interior. The _direction_ of the earth's field is
shown by the compass and the dipping needle. Magnetic lines of force
tend to crowd into and follow iron and steel objects on account of their
permeability. Therefore, iron or steel objects, such as posts, columns,
etc., are permeated by the earth's lines of force, which in the United
States enter at the top of these objects and leave at the bottom. The
lines of force passing through these bodies arrange their molecules in
line or magnetize the bodies. The _inductive effect_ of the earth's
magnetism indicates how lodestones or natural magnets acquire their
magnetized condition. So far as is known, magnetism produces no effect
upon the human body. It can therefore be studied only by observing its
effects upon magnets or bodies affected by it.
Important Topics
The earth's magnetic field, dip, declination, agonic line, induction by
the earth's field.
Exercises
1. How would a dipping needle be of assistance in locating the magnetic
poles of the earth?
2. Will a dipping needle weigh more before or after it is magnetized?
Explain.
3. It is said that _induction precedes attraction_. Using this idea,
explain how a magnet attracts a piece of soft iron.
4. Devise an experiment to show that a piece of iron attracts a magnet
just as a magnet attracts a piece of iron.
5. Give two methods for determining the poles of a magnet.
6. State three of the most important points in the theory of magnetism.
What evidence supports each?
7. Why is a permanent magnet injured when it is dropped?
8. Name two important uses of the earth's magnetic field.
9. What magnetic pole would you find at the top of an iron post that has
stood for some time in the ground? What pole at the bottom? How would
you test this?
CHAPTER X
STATIC ELECTRICITY
(1) ELECTRIFICATION AND ELECTRICAL CHARGES
=213. Electrical Charges.=--The ideas gained in the study of magnetism
are of assistance in the study of electricity in giving some fundamental
ideas and principles that will often be referred to as a basis for
comparing the actions of magnetized and electrified bodies. The process
of electrifying a body is very different from that of magnetizing it.
Thus if a rubber comb or rod be rubbed with a woolen cloth the object
rubbed is able to attract to itself light bits of paper, thread, etc.
This peculiar attraction was noticed and recorded by the ancient Greeks,
600 B.C., when it was found that amber when rubbed would attract light
objects to itself. For a long time it was supposed that amber was the
only substance showing this property. Dr. William Gilbert, however,
discovered that the electrified condition could be produced by rubbing a
great variety of substances. He named the _result_ produced,
_electrification_, after the Greek name for amber (_elektron_). A body
like hard rubber or amber which will attract light objects when rubbed
is said to be _electrified_, or to have been given a _charge_ of
electricity.
=214. Law of Electric Action.=--Let a vulcanite rod be electrified by
rubbing with a woolen cloth until it will attract light objects; then
place it in a wire stirrup suspended by a silk thread. If a second
vulcanite rod is similarly electrified and brought near the first, the
two will be found to repel. (See Fig. 186.) If now a glass rod be
rubbed with silk and brought near the suspended rod, the two will
_attract_. This difference in behavior indicates a difference in the
electrification or charge upon the rods. The two charged vulcanite rods
repelling and the charged glass and vulcanite attracting indicate _the
law of electric action_. _Like charges repel each other and unlike
charges attract each other._ Extensive experiments with all kinds of
substances indicate that there are but two kinds of electrical charges.
The electrical charge upon glass when rubbed with silk or wool is called
_positive_, and that upon hard rubber or vulcanite when rubbed with wool
is called _negative_.
[Illustration: FIG. 186.--Repulsion of like charges.]
[Illustration: FIG. 187.--An aluminum foil electroscope.]
[Illustration: FIG. 188.--A proof plane.]
=215. The Electroscope and its Uses.=--An electroscope is a device
employed to test the presence of an electrical charge. The _aluminum
foil electroscope_ consists of a flask closed by a rubber stopper
through which passes a rod which ends at the top in a ball or plate and
below is attached two narrow leaves of thin aluminum-foil. Ordinarily
the two leaves hang close together and parallel but if a charged body is
brought near the electroscope the leaves spread apart at the bottom.
(See Fig. 187.) The _kind of charge_ upon a body may be determined with
an electroscope as follows: Make a _proof-plane_ by sealing a small
metal disc on the end of a hard rubber rod. (See Fig. 188.) Touch the
disc of the proof-plane first to a charged rubber rod and then to the
top of the electroscope. The leaves of the latter will separate showing
that the electroscope is charged. This charge remains after the
proof-plane is removed. If the charged vulcanite rod is brought near the
electroscope, the leaves separate further That is, a charge _like_ that
on the electroscope makes the leaves separate further. But if an
_unlike_ charge, as that on a positively charged glass rod, is
cautiously brought near, the leaves will be seen to move together.
[Illustration: FIG. 189.--Rod with woolen cap.]
=216. Two Charges are Produced at the Same Time.=--A closely fitting
woolen cover or cap some 3 in. long is made for the end of a vulcanite
rod. A silk thread attached to the cap enables one to hold the latter
while the rod is turned within it. (See Fig. 189.) If the rod bearing
the cap is held near a charged electroscope little or no effect is
noticed. If now the cap is removed by the silk thread and held near the
electroscope, it will be found to be positively charged while the rod is
negatively charged. The fact that no result is seen when the cap and rod
are together, indicates that one charge neutralizes the other. In other
words, _the charges_ must _be equal_. This illustrates the truth that
_when electrification is produced by friction, the two objects rubbed
together acquire equal and opposite charges_.
=217. Charging by Contact and Conduction.=--If a small pith ball is
suspended by a silk thread, a charged rod brought near is at first
attracted, but after contact is repelled (see Fig. 190) showing that the
ball has become charged with the same kind of electrification that is
upon the rod. That is, a charge given to an object by _contact_ with a
charged body is of the _same kind_ as that upon the charged one. The
proof-plane in Art. 215 carries the same kind of charge that is upon the
rod it is charged from. Some substances have the ability to transfer
charges of electrification. These are called _conductors_, those that do
not conduct electrification are _insulators_. The conducting power of a
body is readily tested by placing one end of a rod of the material upon
the top of an electroscope and the other end upon an insulated support,
as in Fig. 191. If now a charge be put in contact with the body of _a_,
the electroscope will show by its leaves whether the rod tested conducts
or not. The leaves separate instantly when conducting substances are
tested, while no action results with insulators. In testing some
materials for conductivity the leaves are found to diverge gradually.
Such bodies are said to be _poor_ conductors. All degrees of
conductivity are found. The metals are the best conductors. The best
insulators are rubber, mica, shellac, glass, silk, porcelain, paraffin,
and oils.
[Illustration: FIG. 190.--The pith ball charged by contact is repelled.]
[Illustration: FIG. 191.--Testing for conductivity.]
Important Topics
1. Positive and negative changes. Law of electric action.
2. Electroscope and its uses.
3. Conductors and insulators.
Exercises
1. Is air a conductor? Give reasons for your answer.
2. Mention two points of likeness and two points of difference between
magnetism and electrification.
3. If you were testing the electrification of a body with a charged pith
ball suspended by a silk thread, would attraction or repulsion be the
better test? Give reasons.
4. Have you ever produced electrification by friction outside of a
laboratory? Explain.
5. Are the rods upon which we produce electrification by friction,
conductors or insulators? How do you explain this?
6. Are conductors or insulators of the greater importance in practical
electricity? Explain.
(2) ELECTRIC FIELDS AND ELECTROSTATIC INDUCTION
[Illustration: FIG. 192.--An electric field about a positively charged
shell.]
[Illustration: FIG. 193.--A "detector."]
=218. Electrical Fields.=--In our study of magnetism we learned that a
magnet affects objects about it by its magnetic lines of force. In a
similar way it is assumed that a charged body produces electrical
effects upon its surroundings by _electric lines of force_. For example,
the attraction that a charged body exerts upon light objects through
short distances or the influence of a charge upon an electroscope
several feet away, is said to be due to the _electric field_ about the
charged body. (See Fig. 192.) The presence of the electric lines of
force may be shown by placing a perforated, slender, diamond-shaped
piece of tissue paper upon a light glass pointer (Fig. 193). When
placed in an electric field the tissue paper "detector" places itself
parallel to the lines of force. Electric lines of force are said to
extend from a positive to a negative charge. (See Fig. 194.) The
direction shown by the arrow upon the lines is that along which a small
positive charge tends to move. Electric lines of force unlike those from
magnets are _not_ continuous. They extend from a positive charge to a
negative charge. Therefore each positive charge is connected by lines of
force to a negative charge somewhere. These ideas of electric fields are
of much assistance in explaining many electrical effects. Electrical
fields between _oppositely_ charged shells will be found similar to Fig.
194, while between shells with like charges, fields are found as in Fig.
195.
[Illustration: FIG. 194.--Electric field between unlike charges.]
[Illustration: FIG. 195.--Electric field between like charges.]
=219. Electrostatic Induction.=--If a charged body is brought near an
aluminum-foil electroscope, the leaves separate. (See Fig. 198.) The
nearer the charge is brought the wider the leaves spread, but when the
charge is removed, the leaves collapse showing that nothing was given to
the electroscope. It was simply affected by the charge in its vicinity.
_This production of an electrified condition in a body by the influence
of a charge near it is called electrostatic induction._ Placing
insulators, such as a sheet of glass, between the charge and the
electroscope does not affect the result, which is apparently brought
about by the action of the electric lines of force. These lines of force
extend without difficulty _through uncharged insulators_ and terminate
often at the surface of a conductor, where their influence causes a
charge to accumulate. _Charged insulators_, however, do affect inductive
action. This may be noticed by using a sensitive electroscope.
[Illustration: FIG. 196.--Production of two charges by the influence of
a third charge.]
[Illustration: FIG. 197.--The two charges separated.]
=220. Electrical Separation by Induction.=--The action just described
may be illustrated further by taking two insulated, uncharged brass
shells, _A_ and _B_. (See Fig. 196.) Bring a charged vulcanite rod near
shell "_A_" while the shells are touching each other. Then remove shell
_B_ (Fig. 197) while the rod remains near _A_. On testing the shells for
electrification, _A_ is found to possess a positive charge. This action
is in some respects similar to magnetic induction, for if one places a
north-seeking pole near a piece of iron, the iron develops by induction
a south-seeking pole at the end nearest the magnet and a north-seeking
at the other end. There is, however, one striking difference. If the
magnetized iron be separated into two parts, each part is a complete
magnet possessing two unlike poles; while if the object affected by
electrostatic induction is separated into two parts _one part_ has a
_positive_ charge and the other a _negative_ charge.
[Illustration: FIG. 198.--Effect of a charged rod near an electroscope.]
[Illustration: FIG. 199.--When a finger is touched to the top of the
electroscope, the repelled negative charge escapes.]
[Illustration: FIG. 200.--The electroscope is now positively charged.]
=221. Charging a body by induction= is easily accomplished. To charge an
aluminum-foil electroscope by induction bring _near_ (say 10 cm.) from
the top of the electroscope a charged rubber rod. (See Fig. 198.) The
separated leaves show the presence of the repelled or _negative_ charge,
the _positive_ charge being on the disc at the top. If while the charged
rod is held near, the metal top of the electroscope is touched by the
finger the leaves at once fall together showing that the repelled
negative charge has escaped from the electroscope (Fig. 199). On
removing _first_ the _finger_ and next the charged rod, the positive
charge spreads over the metal parts of the electroscope, as is shown by
the separation of the leaves (Fig. 200). The electroscope is now
_charged positively_ by induction. If the charged rubber rod is brought
to about 30 cm. from the electroscope, its leaves tend to move
together. If a body charged similarly to the electroscope or
_positively_, is moved toward the electroscope the leaves separate
further. This behavior of the electroscope enables one to determine the
_kind_ of charge upon a body.
Two principles of _electrostatic_ induction may now be stated: (1) Two
_equal_, _unlike_ charges are always produced by _electrostatic_
induction.
(2) If the body affected by induction is connected to the earth by a
conductor, the repelled or "_free_" charge is conducted away from the
body while the "_bound_" charge is held by the inducing charge.
These principles apply in every case of induction.
Important Topics
1. Electric lines of force. Characteristics (3).
2. Electrostatic induction. Principles (2).
3. Charging by induction. Explanation.
Exercises
1. What are electric lines of force? Where are they found? What does the
arrow mean upon the lines?
2. Name three effects produced by electric fields.
3. Does electrostatic induction occur outside of laboratories? Where?
When?
4. Given a charged rubber rod, how may one charge from it by induction,
insulated brass shells, giving some a positive and some a negative
charge?
5. How may the charges upon the shells be tested?
6. In charging an electroscope by induction, why must the finger be
removed before the glass rod?
7. Why is it best to have the rubber and glass rods, used in
electrification, warmer than the air of the room in which the
experiments are being performed?
8. When a sharp metallic point is held near the knob of a charged
electroscope the leaves quickly come together. Explain.
9. Might one of the members of your class in physics be charged with
electricity, if he should stand on a board supported by dry glass
insulators? Explain.
10. If a metal can is charged strongly while standing on an insulator,
tests made by means of the proof-plane and electroscope show no charge
on the inside. Explain.
(3) ELECTRICAL THEORIES AND DISTRIBUTION OF CHARGES
=222. Franklin's Theory of Electricity.=--We have studied the production
of electrification by friction and induction. It will be helpful now to
consider some of the theories of electricity. From the ease with which
electrification moves, along a conductor, many have imagined that
electricity is a fluid. Benjamin Franklin's _One Fluid Theory_ held that
a _positive_ charge consisted in an accumulation or an excess of
electricity while a _negative_ charge implies a deficiency or less than
the usual amount. This theory led to representing positive
electrification by a plus (+) sign and _negative_, by a minus (-) sign.
These signs are in general use to-day. The use and significance of these
signs should be clearly fixed in mind.
=223. The Electron Theory.=--Various discoveries and experiments made in
recent years indicate, however, that _negative_ electricity consists of
little _corpuscles_ or _electrons_ which may pass readily from one
molecule of a conductor to another while their movement through an
insulator is much retarded if not entirely prevented. This theory,
sometimes called the _Electron Theory_, holds that each atom of a
substance has as a nucleus a corpuscle of _positive_ electricity, and
surrounding it, minute negative corpuscles or electrons. It is thought
that the electrons in the atom are very much smaller than the positive
charges and are revolving about the latter with great rapidity.
Ordinarily, the positive and negative charges are equal so that the atom
is in a neutral or uncharged condition. By the action of various forces
some of the _negative_ corpuscles within a conductor may be moved from
molecule to molecule. Thus if a negatively charged rod is brought near a
conductor, many electrons stream away to the far end charging it
_negatively_, while the nearer end of the conductor is left with fewer
electrons than usual along with the fixed positive corpuscles. Hence the
near end is positively charged. (See Fig. 198.) On the other hand, if a
positive charge is used, it attracts the electrons from the far end,
leaving the immovable positive corpuscles there, and that end becomes
positively electrified, while the nearer end with its surplus of
electrons is, of course, negatively electrified.
The Electron Theory is considered well founded since the electrons have
(a) had their _mass_ determined, (b) their _speed_ measured, (c) their
_electric charge_ determined, (d) and their _behavior_ while _passing
through magnetic_ and _electric fields_ observed. These facts and other
experimental evidence have demonstrated the existence of electrons. The
positive corpuscle has not been directly observed but is assumed to
exist to account for the effects observed in induction, charging by
friction, etc.
=224. Distribution of an Electric Charge upon a Conductor.=--We have
applied the electron theory in explaining the phenomenon of
electrostatic induction. Let us now use it in studying the distribution
of an electric charge upon a conductor. Let a cylindrical metal vessel
open at the top and insulated by being placed upon pieces of sealing wax
have a charge of negative electricity given it. (See Fig. 201.) On now
taking a proof plane and attempting to obtain a charge from the
_interior_ of the vessel no result is found, while a charge is readily
obtained from the _outside_ of the dish. This result is explained by
considering that the electrons are mutually self-repellent and in their
attempt to separate as widely as possible pass to the outer surface of
the vessel. This same condition is also true of a dish made of woven
wire. If the charged conductor is not spherical in outline, an uneven
distribution of the charge is observed. Thus if an _egg-shaped_
conductor is insulated and charged (see Fig. 202), a proof plane touched
to the broad end of the body and then to an electroscope causes a
certain divergence of the leaves of the latter. If now a charge be taken
from the _pointed_ end by the proof plane to the uncharged electroscope,
a greater spreading of the leaves than before will be noticed. This
indicates that the electricity may be unevenly distributed over the
surface of a body. It is found that the _electric density_, as it is
called, is greatest where the surface curves most sharply. At a very
sharp curve, as at a point, the electric density may be so great that a
part of the charge escapes into the air. (See Fig. 203.) For this reason
electric conductors on which it is desired to _keep_ an electric charge
have round surfaces and all sharp points and corners are avoided. While
conductors, such as lightning rods, which are designed to facilitate the
escape of electric charges, are provided with a number of sharp points
at the end or elsewhere. At such points, air particles are drawn
forcibly against the point and after being charged are driven away
strongly, creating the so-called _electrical wind_ which carries away
the charge at a rapid rate. (See Fig. 203.)
[Illustration: FIG. 201.--No charge is found inside a hollow vessel.]
[Illustration: FIG. 202.--More charge at the pointed end.]
=225. Lightning and Electricity.=--The fact that lightning is an
electrical discharge was first shown in 1752 by Benjamin Franklin, who
drew electric charges from a cloud by flying a kite in a thunderstorm.
With the electricity which passed down the kite string he performed a
number of electrical experiments. This discovery made Franklin famous
among scientific men everywhere. Franklin then suggested the use of
lightning rods to protect buildings from lightning. These rods act as
conductors for the electric discharge and thus prevent it from passing
through the building, with the risk of overheating some part and setting
the latter on fire. The points provided at the top of lightning rods are
believed to aid in preventing strokes of lightning by the _silent
discharge_ of the so-called electric wind which tends to quietly unite
the charges in the clouds and on the earth beneath.
[Illustration: FIG. 203.--Electrical wind produced by a pointed
conductor.]
[Illustration: FIG. 204.--Electrical whirl. The reaction from the
electrical wind causes it to revolve.]
[Illustration: FIG 205. The wire screen protects the electroscope.]
The charge in an electrified cloud acts inductively upon the earth
beneath, attracting an opposite charge to the objects below. The
discharge from the cloud often passes to the objects beneath, such as
trees or buildings. _Thunder_ is believed to be due to the sudden
expansion of the air when intensely heated by the electric discharge
and its sudden contraction, like a _slap_, as the track instantly cools.
Thunder at a distance is usually followed by rumblings due to changes in
the intensity of the sound mainly due to reflections of sound waves from
clouds and other reflecting surfaces.
=226. An electric screen= is a device for cutting off the influence of
an electric charge. Faraday found that if a sensitive electroscope is
surrounded by a wire mesh screen (see Fig. 205), no evidence of
electrification could be found inside. In other words, a network of
conductors on a building makes the best protection against lightning,
provided it is connected to the earth by good conductors at several
places.
Important Topics
1. Electrical theories. Evidences for electron theory.
2. How is the theory used in explaining induction?
3. Charges, and distribution on conductors (effect of shape).
4. Lightning: cause, effects, lightning rods.
Exercises
1. In what respects is Franklin's one-fluid theory like the electron
theory? In what respects different?
2. Consider two shells charged by induction from an electrified rubber
rod, one positively and one negatively. Explain the process, using the
ideas of the electron theory.
3. Should the metal top of an electroscope have sharp corners? Explain.
4. Would a tall steel tower have the same need of a lightning rod as a
brick chimney of the same height? Explain.
5. Will a solid sphere hold a greater charge of electricity than a
hollow one of the same diameter? Explain.
6. If a positively charged cloud floats over a tree which is a good
conductor of electricity will the tree be charged? Show diagram.
Explain.
(4) POTENTIAL, CAPACITY AND THE ELECTRIC CONDENSER
=227. Conditions Causing a Movement of Electricity.=--In the study of
conductors and insulators it was observed that an electric charge moved
along the conducting rod to the electroscope. This _movement_ of
_electricity_ along a conductor is a result of great practical
importance. We will now consider the conditions that produce the "flow"
or "current" of electricity. Let two electroscopes stand near each
other. Charge one, _C´_ (Fig. 206), strongly and charge the other
slightly. If now a light stiff wire attached to a stick of sealing wax
be placed so as to connect the tops of the electroscopes, the leaves of
_C_ will partly close while those of _D_ will open slightly, thus
indicating a movement of electricity from _C_ to _D_ along the wire. The
movement was from a place of greater degree of electrification to one of
less.
[Illustration: FIG. 206.--Electricity flows from high to low potential.]
=228. Potential.=--The _potential_ of an electrified body is its
_degree_ of _electrification_. Therefore, it is said that electroscope
_C_ mentioned above has a greater potential than electroscope _D_. The
movement of electricity is from a place of greater or _high_ potential
to one of lesser or _low_ potential. If two bodies are at the _same_
potential there will be found no movement of electricity between them. A
_difference_ of _potential_ between two points connected by a conductor
is therefore the _necessary condition_ for an electric current. Just as
heat is transmitted along a conductor from a place of high to one of
lower temperature, so electricity is transmitted along a conductor from
a place of high to one of low potential. Thus potential in electricity
corresponds to temperature in heat. One is the "degree of
electrification," the other, "the degree of hotness."
[Illustration: FIG. 207.--Air pressure apparatus to illustrate
electrical pressure.]
=229. Electrical pressure= is a term sometimes used for difference of
potential. To better understand electrical pressure consider three round
tanks (Fig. 207) containing air. _A_ is a tank holding air at 10 lbs.
pressure per square inch, above atmospheric pressure, _B_ is open to the
air and hence is at atmospheric pressure while _C_ has a partial vacuum,
with 10 lbs. less pressure than that of the atmosphere. If the valve at
_D_ or _E_ is opened a flow of air sets up until the pressures are
equalized. While if the pump at _P_ is working a difference in pressure
is easily maintained. Tank _A_ corresponds to an insulated body charged
to a high _positive_ potential; tank _B_, open to the air, a body
connected to the earth; while tank _C_ represents a body having a
_negative_ potential. The earth is said to have _zero potential_.
Now just as compressed air will be pushed into the atmosphere (as from
_A_ to _B_) while air at atmospheric pressure will if possible be forced
itself into a partial vacuum (as from _B_ to _C_), so electricity at a
positive potential will tend to move to a place at zero potential, while
that at zero potential tends to move to a place of negative potential.
Bodies at the _same_ potential as the earth, or at zero potential, are
also said to be _neutral_. Those positively electrified have a positive
potential, those negatively electrified have a negative potential. As in
gases, movement always tends from higher pressure (potential) to lower
pressure (potential).
[Illustration: FIG. 208.--The metal plate gives the electroscope a
greater surface and hence greater capacity.]
=230. Capacity.=--If we have a 100-gallon tank and a 10-gallon tank
connected by a pipe both filled with compressed air, the larger tank
will contain ten times as much air as the smaller at the _same pressure_
since it has ten times the capacity, or, if the two tanks are separated
and the same amount of air is contained in each, the pressure of the air
contained in the small tank will be ten times that in the large one.
The _electrical capacity_ of a conductor is in some respects similar to
the capacity of a tank for air. Since, however, electrical charges are
upon the surface of a body, its capacity depends in part upon the extent
of surface. For example, if a charge is taken from a charged rubber rod
by a proof plane to an electroscope a certain divergence of the leaves
will be noticed. If a circular metal plate several times the diameter of
the top of the electroscope is laid upon the latter (see Fig. 208), and
a charge equal to that used before is brought to the electroscope, the
leaves show less divergence than before, showing that the _same charge
gives a lower potential when placed upon a body of greater capacity_.
[Illustration: FIG. 209.--A plate condenser.]
[Illustration: FIG. 210.--A condenser of several plates.]
=231. The electric condenser= is a device having a large electrical
capacity consisting of parallel conductors separated by good insulators.
It has been devised to enable one to obtain a large electrical charge
upon a body of convenient size. Such an apparatus is of great practical
value in many experiments and operations. Its construction involves the
principle of electrostatic induction in which a charge of one kind
attracts and "holds" strongly a charge of opposite kind near it. In its
simplest form it consists of two parallel conductors separated from each
other (Fig. 209). The upper plate has been charged negatively. This has
given the lower plate a positive charge by induction, since the latter
is connected to the earth. These positive and negative charges hold or
"bind" each other so that a large quantity may be accumulated. To
increase the capacity of a condenser, several plates are used connected
as in Fig. 210.
It is a curious fact that the kind of insulator between the charged
conductors of a condenser affects its capacity. Thus if glass,
paraffine, or beeswax is between the plates instead of air, the plates
will "hold" more electricity at the same potential. For this reason
condenser plates are often separated by sheets of glass, paraffined
paper, or mica.
[Illustration: FIG. 211.--A Leyden jar and a discharger.]
=232. The Leyden Jar.=--A convenient form of condenser, used as long ago
as 1745, is the Leyden jar. It consists of a glass jar (Fig. 211) coated
part way up, inside and out, with tinfoil. The inner coating is
connected by a chain to a knob at the top. The Leyden jar is charged by
connecting the outer coating to the earth while to the inner coating is
given a charge of either kind of electricity. The other kind of charge
is developed by induction upon the outer coating, and each charge binds
the other. To discharge a jar, a conductor, as a wire, is connected
first to the outer coating and held there while the other end is brought
to the knob at the top. A bright spark is produced when the two charges
combine. It is best not to let the discharge from the jar pass through
the body unless one is certain that only a very small charge is present.
=233. Oscillatory Discharge.=--The discharge from a Leyden jar is an
interesting phenomenon. The rush of electricity from one coat to the
other does not stop when the two coats are exactly neutralized but
continues until the two plates are charged just oppositely to their
condition at first, then a rush of electricity in the opposite direction
occurs. This alternation continues several times and constitutes what is
called the _oscillatory discharge_. (See Fig. 414.) This oscillatory
discharge sets up waves in the ether. These are called _Hertzian_ waves
in honor of their discoverer, Heinrich Hertz. They are the ether waves
used in wireless telegraphy. A _lightning flash_ has been shown by
photographs and by other means to be oscillatory. This fact supports the
idea that the electrical conditions just preceding the stroke of
lightning reproduce a condenser on a large scale. The charged cloud is
the upper charged plate, the earth beneath, charged by induction from
the cloud, is the lower charged plate, while the air between is the
insulator or _dielectric_ as it is sometimes called.
Important Topics
1. Potential: high, low, zero, positive, negative, similar to
temperature and air pressure.
2. _Capacity_ affected by (1) area, (2) induction.
3. Condensers, Leyden jar, parallel plate.
4. Oscillatory discharge, conditions, results.
Exercises
1. Is the air a conductor? Explain.
2. Can the Leyden jar be strongly charged if the outer coat is
insulated? Explain.
3. Upon what two conditions does the capacity of a body depend? How in
each case?
4. Would a lightning discharge produce wireless waves? Explain.
5. If a sharp tack be dropped point up on the plate of an electroscope
the latter is quickly discharged. Explain.
(5) ELECTROSTATIC GENERATORS
=234. Static Electric Machines.=--Many machines have been invented to
produce larger quantities of static electricity than we have used in the
experiments previously described. One of the earlier of these was the
_plate friction machine_ in which a large circular glass plate was
rotated while a pad of some material was held against it. This machine
was capable of producing powerful effects, but it took much work to
turn it, and it has been abandoned for a more efficient device, the
_static induction machine_.
=235. The electrophorus= is the simplest static induction generator,
consisting simply of a flat circular plate of some insulating material,
as paraffine, shellac, or rosin contained in a metal pan, and a flat
circular metal _disc_ having an insulating handle.
[Illustration: FIG. 212.--An electrophorus.]
_The electrophorus is used as follows_: The plate is first electrified
by rubbing or beating with fur or a woolen cloth. The plate will be
found to be charged negatively. The metal disc is placed upon the plate
by holding the insulating handle. The upper surface of the charged body
is slightly uneven so that the disc touches but a few high points. The
greater part of the charged surface is separated from the metal disc by
air, a good insulator. The charge therefore acts inductively upon the
disc _repelling negative_ electricity to the upper surface of the disc,
leaving the lower surface charged positively (Fig. 212). If now the
finger is touched to the disc the repelled negative charge escapes and
the whole disc is left positively charged. The disc is now removed (Fig.
213) and the charge upon it may be tested or used in any desired manner.
The disc may be recharged many times without rubbing the plate again.
[Illustration: FIG. 213.--Electrophorus charged.]
These electrical charges possess _energy_. What is the source of this
energy? The answer may be determined by the following experiment. Place
the disc upon the charged plate. Touch the disc with the finger to
remove the repelled charge. Connect an electroscope to the disc by a
fine wire. Nothing appears on the electroscope, since the disc has been
connected to the earth, and is therefore at zero potential. If now the
disc is lifted slowly, the leaves of the electroscope gradually
separate, showing that a charge of electricity appears when the disc is
being lifted against the force of attraction between the two charges.
Just as potential energy is developed in a weight when it is lifted
against the earth's attraction so electrical energy appears in the disc
while it is being separated from the plate. The electrical energy of the
charge is therefore due to the work done in separating the two charges.
This electrical energy appears as heat and light, when the disc is
discharged. It may be employed to ignite gas, gunpowder, etc.
=236. The Toepler-Holtz Induction Machine.=--This is a type of induction
or influence machine that is often used for producing a continuous
supply of electricity as in the operation of "X" ray machines, in
lecture demonstrations, etc. This machine (Fig. 214) consists of two
discs: one fixed, the other mounted so as to revolve. Upon the back of
the fixed plate are two sectors of tinfoil which become charged
oppositely. Upon the revolving plate are six metallic discs. These discs
act like the discs of the electrophorus. They become charged by
induction from the charges upon the sectors fastened to the fixed plate.
The brushes held by a rod touch the discs at just the right time to take
off the repelled charge. The charges induced upon the discs are taken
off by two metal combs whose points are held close to the revolving
disc. The Leyden jars assist in accumulating a good strong charge
before a spark passes between the terminal knobs. Some machines are
built up of several pairs of plates and give correspondingly large
amounts of electricity.
[Illustration: FIG. 214.--The Toepler-Holtz induction machine.]
Important Topics
_Static Electric Generators._--(a) plate friction machine, (b)
electrophorus, (c) induction or influence machine.
Exercises
1. Potential is similar to what other terms that we have studied?
2. What three electrical phenomena are better understood from a study of
the lines of force?
3. How many charges may be produced by an electrophorus before the plate
needs to be electrified again? Explain.
4. The static induction machine is often called a "continuous
electrophorous." Why?
5. The Leyden jars used with the induction machine cause much brighter
sparks to be produced than without them. Explain.
6. With the Leyden jars removed, would the frequency with which the
sparks pass between the knobs be increased or decreased? Explain.
7. Mention three likenesses and three differences between magnetism and
static electricity.
8. Will you receive a greater shock by touching a knob of a charged
Leyden jar when it is held in the hand or when it is standing on a sheet
of glass? Explain.
9. In what way may an electric charge be divided into three equal
parts?
Review Outline: Magnetism and Static Electricity
Comparison between Magnetism and Static Electricity.
Substances are: { magnetic, { conductors,
{ non-magnetic. { insulators.
Produced by: induction. friction, or induction.
Theory: molecular. electron. (fluid)
{ attraction, { attraction,
Fields of Force { repulsion, { repulsion,
Explain: { induction, { induction.
{ action of compass.
{ magnetoscope, dip, { electroscope, electron,
{ declination, pole, { positive, negative,
{ retentivity, { potential, capacity,
Terms: { permeability, { condenser, electrophorus,
{ lodestone, { oscillatory discharge,
{ magnetic meridian. { lightning.
Likeness: { _a_--produced by induction, _b_--attract
both are: { and repel, _c_--have fields of force.
{ _a_--electricity can be _conducted_,
{ magnetism cannot.
{
Differences: { _b_--electricity in _all substances_,
{ magnetism in few.
{
{ _c_--magnetism with the compass indicates
{ direction.
CHAPTER XI
CURRENT ELECTRICITY
(1) ELECTRICAL CURRENTS AND CIRCUITS
=237. Sources of Electric Currents.=--In studying the production and
distribution of static electricity it was seen that if two bodies at
_different potentials_ are connected by a copper wire a _movement of
electricity to the body_ having the _lower potential_ occurred along the
conducting wire. This movement of electricity is called an _electric
current_ (Art. 227). _A difference of potential_ is therefore often
called an _electromotive force_ (E.M.F.), since it produces the movement
of electricity in a conductor. The current between two _oppositely
charged_ bodies lasts for so short a time as to be of little or no
practical value unless some means are found for continually recharging
the bodies. That is, some device must be used to restore the difference
in potential as fast as the conducting wire equalizes it. The continual
charging of the bodies takes work. In other words, it requires a
continual expenditure of some form of energy (which is converted into
electrical energy) to produce the electric current. Two forms of energy
are commonly used for this purpose.
(A) _Chemical energy_ is employed in _voltaic cells_ for producing
electric currents. (B) _Mechanical energy_ is used for the same purpose
in the _dynamo_ and similar devices.
=238. The voltaic cell= is named after Volta, an Italian physicist, who
in 1800 invented it. In its simplest form it consists of a strip of
copper and a strip of zinc placed in dilute sulphuric acid (one part
acid to fifteen or twenty of water) (Fig. 215). By the use of sensitive
apparatus, it can be shown that the copper plate of the voltaic cell has
a positive charge and the zinc plate a negative charge. For example, let
a flat plate 10 cm. in diameter be placed upon the knob of an
electroscope and a similar plate, coated with shellac and provided with
an insulating handle, be set upon it to form a condenser. (See Fig.
216.) If now wires from the two plates of a simple voltaic cell be
respectively connected to the plates of the condenser, charges from the
copper and zinc plates will accumulate upon the two condenser plates.
Now remove the wires and lift the upper plate. The "bound" charge upon
the lower plate will spread over the leaves and cause them to separate.
Upon testing, the charge from the zinc plate will be found to be
_negative_ and that from the copper plate, _positive_. Since a positive
charge is found upon the copper plate it is called the _positive
electrode_; the zinc plate is called the _negative electrode_.
[Illustration: FIG. 215.--Cross-section of a simple voltaic cell.]
[Illustration: FIG. 216.--Testing the charges upon the plates of a
simple voltaic cell.]
=239. Test for an Electric Current.=--If the copper and zinc plates of a
voltaic cell are connected by a wire, a current of electricity is set
up in the conductor. Evidence of the current may be obtained by holding
the conducting wire over and parallel to the needle of a magnetoscope.
The needle is deflected by the action of the current parallel to it
(Fig. 217). This _magnetic effect_ of a current is the means usually
employed for the _detection_ and _measurement_ of an electric current.
Such a device which detects an electric current by its _magnetic effect
is called a galvanoscope_, in honor of Galvani, who in 1786 was the
first to discover how to produce an electric current.
[Illustration: FIG. 217.--The magnetic needle is deflected by the
current.]
[Illustration: FIG. 218.--Diagram of an electric bell circuit.]
=240. The Electric Circuit.=--_The entire conducting path along which a
current of electricity flows is called an electric circuit._ In the case
of a voltaic cell, the circuit includes not only the wires connecting
the plates but also the plates themselves and the liquid between them.
When some device or apparatus is to receive current from the cell, it is
attached to the plates and wires so that the device is a part of the
electric circuit. Separating the circuit at any point is called
_breaking_ or _opening_ the circuit, while connecting the ends of an
open circuit is called _making_ or _closing_ the circuit. A device for
opening and closing a circuit is called a _key_ or _switch_. The
electric circuit used in ringing a door bell is familiar to most boys
and girls. This circuit is _open_ most of the time. It is closed by
pressing the _push-button_ at the door, and the flow of current through
the _electric bell_ causes the latter to ring. Such a circuit is
represented in Fig. 218. Here _C_ is the voltaic cell, the two lines
representing the plates of the cell. A cross-section view of the
push-button (_P_), shows how the circuit is closed, (_B_) is the bell.
Wherever current electricity is used the device in which it is employed
forms a part of an electric circuit extending back to some electric
generator. This generator must be able to continually produce an E.M.F.,
or a difference of potential between its terminals, in order that the
movement of electricity may be continuous.
Important Topics
(a) Electric generators: (1) voltaic cell uses chemical energy; (2)
dynamo uses mechanical energy.
(b) Electric circuits: (1) open, (2) closed, (3) key and switch.
(c) Voltaic and galvanic electricity (names).
(d) Galvanoscope, uses.
Exercises
1. In what _two_ ways are static and current electricity alike? In what
two different?
2. Draw a diagram of an electric bell circuit at your home. Give the
location of the electric bell, the electric generator and the
push-button. Show the connecting wires, and explain briefly how the
circuit is operated.
3. Represent some other electric circuit, naming the generator and other
devices in the circuit.
4. Look up the work of Volta and Galvani and write a statement of the
electrical discoveries and inventions made by them.
(2) THE VOLTAIC CELL AND ITS ACTION
=241. The simple voltaic cell= consists of a strip of copper and a strip
of zinc placed in dilute sulphuric acid. (See Fig. 219.) A short time
after placing the plates in the acid, bubbles of a gas (hydrogen) appear
on the surface of the zinc. These bubbles increase in size and some rise
to the surface of the liquid. Nothing appears upon the copper plate. If
the tops of the plates are connected by a wire, an electric current is
set up through the wire and the cell, and bubbles of gas also appear
upon the _copper_ as well as on the zinc. In a short time the surface of
the copper becomes coated with bubbles and the current becomes much
_weaker_. If the plates are left in the acid for some time the zinc is
found to be eaten away, having been dissolved in the acid through
chemical action. The copper, however, remains practically unaffected.
[Illustration: FIG. 219.--A simple voltaic cell.]
=242. How the Current is Produced.=--To maintain the electric current a
continual supply of energy is required. This is furnished by the
_chemical action_ of the acid upon the zinc. The chemical action is in
several respects like _combustion_ or _burning_, by means of which
chemical energy is transformed into heat energy. In the voltaic cell the
chemical action of the acid upon the zinc _transforms_ chemical energy
into electrical energy. The E.M.F. or _difference of potential_ may be
considered as originating at the surface of the zinc where the chemical
action takes place. At this point the zinc has the lower and the liquid
in contact with it the higher potential. The molecules of the acid are
believed to be separated or broken up into two parts called _ions_; one
ion, the SO_{4} or _sulphion_, combines with the zinc forming zinc
sulphate, the other, or hydrogen (H) ion, passes over to the copper
plate, and accumulates on the surface of this plate giving it a positive
charge. It is therefore called the _positive ion_. The sulphion ion, or
SO_{4} ion, carries a negative charge to the zinc. It is therefore
called the _negative ion_.
=243. The Direction of the Current.=[K]--Beginning at the surface of the
zinc the _direction_ of the movement of _positive_ electricity may be
traced through the liquid to the copper plate, to the wire, to the zinc
plate, to the starting point, thus completing the electric circuit. When
the circuit is closed it is found that the movement of electricity
starts in _all_ parts of the circuit at practically _the same instant_.
[K] Many scientists consider that current in a conductor consists
of _negative electrons_ flowing in a direction _opposite_ to that
described in Art. 243. This is called the _electron current_, as
distinguished from the _electric current_ described above.
[Illustration: FIG. 220.--A comparison of a voltaic cell and circuit to
a water pump and connecting pipes.]
=244. The production of the current= may be illustrated by describing a
device for producing a continuous circulation of water. Thus let _Cu_
and _Zn_ represent two pipes connected by two horizontal tubes, one at
_V_ provided with a valve and one at _P_ with a rotary _Pump_. (See Fig.
220.) Suppose the pipes filled to the level of _V_ and the pump started.
The pump will force water from _Zn_ to _Cu_, through _P_, the level
falling in _Zn_ and rising in _Cu_. If the valve _V_ is open the water
will flow back through _V_ as long as the pump is working. If _V_ is
closed, the level in _Cu_ will rise as high as the driving force of the
pump can send it. If now _V_ is opened, the pump will maintain the water
in circulation from _Cu_ to _Zn_ through _V_. In the illustration, the
tubes _Cu_ and _Zn_ correspond to the conducting plates of _copper_ and
_zinc_ of a voltaic cell. The pump _P_ represents the chemical action
which produces the electrical pressure. The upper pipe represents the
part of the circuit outside of the cell, the valve _V_ corresponds to an
electric key or switch which is used to open and close the electric
circuit.
=245. Polarization.=--In the simple voltaic cell, after the circuit is
closed, bubbles of hydrogen collect upon the copper plate. This
accumulation of hydrogen gas is called _polarization_. It acts as a
non-conducting layer upon the surface of the plate and seriously
interferes with the movement of electricity from the liquid to the
copper plate not only in the simple voltaic cell but in many others as
well. Some voltaic cells are made entirely free from this defect, either
(a) _by the removal of the hydrogen as fast as it is formed_, or (b) _by
the use of such chemicals that no hydrogen is produced_.
=246. Local Action.=--It is noticed that when a strip of zinc is placed
in dilute acid that bubbles appear upon the surface of the zinc. The
appearance of these bubbles indicates that some of the hydrogen ions
carrying positive electricity have moved to the zinc plate. Careful
examination of the plate after it has been in acid shows numerous black
spots upon it. These are bits of carbon. They are always found in
ordinary zinc. Small electric currents are set up which run from
molecules of pure zinc into the liquid and back to the carbon particles,
thus forming small closed circuits. (See Fig. 221.) The formation of
these circuits from and to the zinc is called _local_ action. This
action is a defect in voltaic cells since a part of the current is thus
kept from passing through the main outside circuit, and the zinc may be
consumed even when no outside current is flowing.
[Illustration: FIG. 221.--Local action.]
=247. Amalgamation.=--Local action is prevented by coating the zinc with
mercury. This process is called _amalgamation_. The mercury covers the
entire surface of the plate in the acid. Its action is to dissolve pure
zinc and bring it to the outer surface where it is acted upon by the
acid. The carbon particles are kept covered so that no local currents
can be formed as long as the bits of carbon are below the surface.
Amalgamation therefore prevents local action.
Important Topics
_The Simple Voltaic Cell_
1. Two plates: zinc, copper; electrolyte, dilute sulphuric acid.
2. Ions: hydrogen, positive: sulphion, negative.
3. Current, where and how produced, direction, illustration.
4. Polarization: cure, local action, cure.
Exercises
1. Write in your own words an account of the production of an electric
current by the simple voltaic cell. Use sketches.
2. Which plate has the higher potential? How is it produced?
3. Would you expect to get an E.M.F. by forming a cell of two copper
plates? Why?
(3) PRACTICAL VOLTAIC CELLS
=248. Advantages of Voltaic Cells.=--Many forms of voltaic cells have
been devised. Several of the more common of these will be described and
their electro-chemical action explained.
At the present time voltaic cells are employed only where small currents
are needed, such as for electric bells and induction coils. Where more
than a small amount of current is required, the dynamo and the storage
battery have generally taken their place as sources of electric current.
The advantages of voltaic cells as electric generators are: (a) they are
inexpensive, (b) they are easily taken from place to place, (c) they may
be ready for instant use.
The most desirable voltaic cell would be one having the following
qualities: (a) High electromotive force, (b) no polarization or local
action, (c) very low internal resistance, (d) small expense, both as to
first cost and upkeep.
[Illustration: FIG. 222.--The Leclanché cell, "wet" type.]
=249. The Leclanché cell= is the one commonly used for ringing door
bells. It has two plates: one of zinc and the other of _carbon_. These
are placed in a solution of sal ammoniac (Fig. 222). Take up the
desirable qualities mentioned at the end of the preceding paragraph. (a)
It may be shown that this cell has a good E.M.F. about 1.5 volts. (b) It
_polarizes_ easily yet it recovers well when left upon open circuit.
Usually a substance called manganese dioxide is mixed with the carbon.
This acts as a _depolarizer_, that is, it combines with the hydrogen to
form water. (c) Its resistance varies and is often considerable. (d) The
expense for upkeep is small, since a 5-cent rod of zinc, and a 5-cent
charge of sal ammoniac will keep the cell in action on a bell circuit
from six months to a year or more. It is well suited for use on _open
circuits_ that is, where the circuit is open the greater part of the
time and is closed only occasionally; as in ringing door bells,
operating telephones, and other devices whose circuits are usually open.
=250. The Dry Cell.=--Many forms of Leclanché cells are made. One of
these is called the _dry cell_ (See Fig. 223.) In this cell the zinc
plate is made into a jar or can and contains the other materials. At the
center of the cell is a rod of carbon and manganese dioxide. The space
between the carbon and zinc is filled with a porous material such as
sawdust or plaster of Paris. A strong solution of sal ammoniac fills the
porous material. The top of the cell is sealed with pitch or wax to
prevent evaporation. The great advantage of this cell is that it may be
used or carried in any position without danger of spilling its contents.
Dry cells are often used to operate the spark coils of gas and gasoline
engines. The Leclanché cell described in Art. 249 is commonly known as
the "wet cell."
[Illustration: FIG. 223.--The Leclanché cell, "dry" type.]
[Illustration: FIG. 224.--The Daniell cell.]
=251. The Daniell Cell.=--This cell is often used in laboratories, and
on closed circuits such as those connected with fire and burglar alarms
and telegraph lines. It has two plates of zinc and copper placed in two
different liquids which are kept separated by a porous clay cup (Fig.
224). The zinc rod is kept in a solution of zinc sulphate contained in
the porous cup. The copper plate is in a solution of copper sulphate
filling the rest of the glass jar. Unlike the Leclanché cell, this one
must be kept upon a _closed circuit_ to do its best work, as the two
liquids mix when the circuit is open. Taking its qualities in order, (a)
its E.M.F. is about one volt, (b) it has no polarization since copper
instead of hydrogen is deposited upon the copper plate. Therefore a
uniform E.M.F. may be obtained from it, making it especially useful in
laboratory experiments and tests. (c) Its resistance is considerable and
(d) it is more expensive to operate than the Leclanché. It is sometimes
used upon closed circuits outside of laboratories as in burglar and
fire alarms, although in recent years, the storage battery is taking its
place for these purposes.
=252. The Gravity Cell.=--Fig. 225 is like the Daniell cell in most
respects, except that in this cell, the zinc plate is held at the top of
the jar in a solution of zinc sulphate while the copper plate is at the
bottom, surrounded by a solution of copper sulphate. The solutions mix
but slowly as the copper sulphate solution is denser and remains at the
bottom. This cell like the Daniell must also be kept upon closed
circuit. On account of its simplicity and economy it is often used to
operate telegraph instruments. Its qualities are similar to those of the
Daniell cell.
[Illustration: FIG. 225.--The gravity cell.]
=253. Symbol for Voltaic Cells.=--In electrical diagrams, the symbol
employed to represent a voltaic cell is a short thick line near to and
parallel to a longer thin one. As in Fig. 226. If several cells are to
be represented the conventional symbol of the combination is represented
as in Fig. 227. A single cell and a group of cells are each frequently
called a battery.
[Illustration: FIG. 226.--Diagram of a single cell.]
[Illustration: FIG. 227.--Diagram of a group of cells.]
=254. Effects of Electric Currents.=--Having studied some of the devices
for producing an electric current, let us now consider some of the
_effects_ caused by it. These effects will be studied under three heads:
(a) _Magnetic_, (b) _Chemical_, and (c) _Heat_ effects. Devices or
articles showing these effects known to most high school students are
respectively: (a) the _electromagnet_ (b) _electro-plated silver ware_
and (c) _electric heaters_, such as electric flat irons, electric
toasters, etc. The _magnetic_ effect of an electric current was first
detected by Oersted at the University of Copenhagen in 1819. It may be
observed by holding a wire carrying a current from a voltaic cell above
and _parallel_ to the needle of a _magnetoscope_. The needle is at once
deflected (Fig. 228). If the current is reversed in direction the
magnetoscope needle is deflected in the reverse direction. This simple
device is the most common means for detecting an electric current. It
therefore constitutes a _galvanoscope_. (See Art. 239.)
[Illustration: FIG. 228.--A galvanoscope.]
Important Topics
1. Leclanché cells, (a), wet, (b), dry, construction, advantages, uses.
2. Daniell and gravity cells, construction, advantages, uses.
3. Three effects of electric currents, illustrations.
4. The galvanoscope, uses.
Exercises
1. Explain how the direction of current in a wire can be determined by a
compass.
2. Would you expect to obtain a current from a zinc and copper cell
containing a solution of common salt? Perform the experiment.
3. What conditions in a voltaic cell will give a steady electromotive
force.
4. What conditions in a voltaic cell will give a strong electromotive
force.
5. Name three different electric circuits that you know exist. Which are
_open_ and which are _closed_ circuits?
6. Are voltaic cells used in your home? If so, for what purpose are they
used? On open or closed circuits? Have you seen them? what kind are
they?
CHAPTER XII
THE MAGNETIC EFFECT OF ELECTRIC CURRENTS. ELECTRICAL MEASUREMENTS
(1) THE MAGNETIC EFFECT OF ELECTRIC CURRENTS
=255. The Magnetic Effect.=--Of all the effects of electric currents, it
is generally conceded that the _magnetic effect_ is the one of _greatest
practical importance_, and it is also the one most extensively used. An
experiment illustrating this effect has been described in Art. 239. This
experiment shows that an electric current, if _parallel_ to a magnetic
needle, and _near it_ will deflect the north-seeking pole of the needle
to the right or left depending upon the _direction_ of the current flow.
This _deflection_ of the magnetic needle is due to the fact that
surrounding every electric current are magnetic lines of force. It is
this magnetic field of the current that causes the needle to turn. The
position taken by the needle is the resultant of the forces of two
magnetic fields; one, the earth's field, the other, that of the current.
=256. Right-hand Rule for a Conductor.=--To show the presence of the
magnetic field about a current, pass a thick copper wire vertically
through a sheet of paper, and connect the ends of the wire to a source
of current. While the current (this should be as much as 10 amperes if
possible) is flowing, sprinkle iron filings upon the paper and tap
gently. The filings will arrange themselves in circles about the wire
showing the magnetic field. (See Fig. 229.) The needle of a magnetoscope
tends to place itself parallel to the lines of force of this field and
from this action or tendency the _direction_ of the magnetic lines
about a current may be determined. The following rule is helpful and
should be memorized: _Grasp the conductor with the right hand with the
outstretched thumb in the direction that the current is flowing. The
fingers will then encircle the wire in the direction of the lines of
force._ This rule may be reversed, for, if the fingers of the right hand
grasp the wire so as to point with the magnetic field, then the current
flows in the direction in which the thumb points. (See Fig. 230.)
[Illustration: FIG. 229.--Magnetic field about a wire carrying an
electric current.]
[Illustration: FIG. 230.--Right-hand rule for the magnetic field of a
current.]
=257. Magnetic Field of a Helix.=--If a wire be wound about a cylinder
to form a cylindrical coil with parallel turns, it forms a _helix_ or
_solenoid_. The shape of the magnetic field about a current depends upon
the _form_ of the conductor. If the latter is in the form of a _helix_
its magnetic field resembles that of a straight bar magnet. (See Fig.
231). In fact the helix _has the properties of a magnet_ with north- and
south-seeking poles while a _current_ is _flowing_ through it. If such a
coil is suspended so as to turn freely, it tends to turn until the field
within it is parallel to the earth's magnetic field. Such a suspended
helix may therefore be used as a compass. In order to strengthen the
magnetic field of a helix or solenoid, the space within its turns is
filled with iron, often in the form of small soft-iron wires. This
bundle of iron wire is called the _core_ of the helix. The core becomes
strongly magnetized by the field of the helix while the current is
flowing and quickly loses its magnetic force when the current is
stopped. _The direction of the current in a helix_ (Fig. 232) or the
_polarity_ of its core may be determined by another _right-hand rule_.
_If the helix is grasped with the right hand so that the fingers point
in the direction in which the current is flowing, the extended thumb
will point in the direction of the north pole of the helix._ On the
other hand, if the poles of the helix are known, then, when the helix is
grasped with the right hand so that the thumb points to the
north-seeking pole, the current is flowing in the wires in the direction
that the fingers point.
[Illustration: FIG. 231.--The magnetic field of a helix.]
[Illustration: FIG. 232.--Right-hand rule for a helix.]
=258. The Electromagnet.=--These "right-hand" rules are applied in many
different devices. Among these, perhaps the most important is the
electromagnet, which is used in the electric bell, the telegraph, the
telephone, the dynamo, the motor, and many other electric contrivances.
The electromagnet is defined as a _mass of iron around which is placed a
helix for conducting an electric current_. On account of its large
permeability, the iron core of the helix adds greatly to the
effectiveness of the electromagnet, since the magnetism of the iron is
added to that of the current in the helix. The magnetism remaining in
the iron after the current stops is called the _residual_ magnetism. The
residual magnetism is small when the core is made of small wires or thin
plates, but is larger when the iron core is solid. Like artificial steel
magnets, electromagnets are usually of two forms, _bar_ and _horseshoe_.
(See Figs. 233 and 234.) For most purposes the horseshoe form is the
more effective since it permits a complete iron circuit for the magnetic
lines of force. (See Fig. 235.) This is the form used in the electric
bell, in the telegraph sounder, and in lifting magnets. (See Fig. 236.)
[Illustration: FIG. 233.--A bar electromagnet.]
[Illustration: FIG. 234.--A horseshoe electromagnet.]
[Illustration: FIG. 235.--A horseshoe electromagnet may have a complete
iron circuit for its lines of force.]
[Illustration: FIG. 236.--A lifting magnet.]
=259. Effective Electromagnets.=--The _magnetic_ effect of a current in
a helix is small, hence the force usually is increased by inserting a
core of iron. When at first man tried to signal with electromagnets at
a distance it was found that the current would not work the
electromagnet. An American by the name of Joseph Henry discovered the
remedy for this condition. He found that if the copper wire was
insulated by wrapping silk thread about it, and then many layers of the
silk insulated wire were wound upon a spool with an iron core, that the
magnet would work at a great distance from the source of current. If the
current is increased, the magnet is stronger than at first. Thus an
_electromagnet may be made stronger by_ (a) _increasing the number of
turns of wire in its coils_ and by (b) _sending a stronger current
through it_.
[Illustration: FIG. 237.--A simple telegraph circuit.]
=260. The Telegraph.=--The invention of an effective electromagnet by
Henry made possible the _electric telegraph_. In its simplest form it
consists of a battery, _C_, a key, _K_, and a sounder, _S_, with
connecting wires. (See Fig. 237.) The _sounder_ (Fig. 238) contains a
_horseshoe electromagnet_ and a bar of soft iron across its poles called
an armature, _A_, attached to a lever _L_. When the key is closed, the
electromagnet draws down the armature and lever until the latter hits a
stop _O_, making a click. When the key is raised, the magnet releases
the armature which is raised by the action of a spring at _S_ until the
lever hits a stop at _T_ making another click. Closing and opening the
circuit at _K_ will start and stop the current which operates _S_ which
may be 100 miles or more from _K_. One voltaic cell will work a sounder
in the same room. But if many miles of wire are in the circuit, the
E.M.F. of a single cell will not force sufficient current through the
long wire to operate the sounder.
[Illustration: FIG. 238.--A telegraph sounder.]
[Illustration: FIG. 239.--A telegraph relay.]
[Illustration: FIG. 240.--How the relay is used.]
[Illustration: Samuel F. B. Morse (1791-1872). Inventor of the
electromagnetic recording telegraph and of the dot and dash alphabet.
SAMUEL F. B. MORSE
"From Appleton's Cyclopedia of American Biography, Copyright 1888 by D.
Appleton & Co."]
[Illustration: Thomas A. Edison, Orange, New Jersey. Invented the
incandescent lamp; phonograph; moving picture; most noted inventor of
electrical appliances of the present day.
THOMAS A. EDISON
"Copyright, Photographische Gessellschaft," and "By Permission of the
Berlin Photographic Co., New York."]
A battery of several cells is then required. Even a large battery is
insufficient to operate a long line containing many sounders in circuit.
Recourse is therefore usually made to a more sensitive device called a
_relay_. (See Fig. 239.) In the relay a very small current will
magnetize its electromagnet enough to draw toward it the delicately hung
armature thereby closing a second circuit which contains a sounder and a
battery. (See Fig. 240.) when the current in the main circuit is
stopped, the armature of the relay is drawn back by a light spring. This
opens the _local_ circuit. Thus the local circuit is closed and opened
by the relay just in time with the starting and stopping of the current
in the main line. It is thus possible for a small current in the main
line by the use of a relay, to close and open a second local circuit
containing a local battery and sounder. Modern telegraph lines are
operated in this manner.
[Illustration: FIG. 241.--An electric bell and its circuit.]
=261. The electric bell= (see Fig. 241), consists of an electromagnet,
_M_, a soft iron _armature_, _A_, attached to the _tapper_, _T_, and a
post, _R_. When no current is flowing a spring at _S_ holds the armature
against the post _R_. When current flows through the helix, its core
becomes magnetized and attracts the armature, drawing it away from the
post, _R_, and causing the tapper to hit the bell. Drawing _A_ away from
the post, however, breaks the circuit at _R_ and the current stops. The
magnetism in the core disappears releasing the armature, which is then
pulled back by the spring _S_ against the post _R_. This completes the
circuit and the process repeats itself several times a second as long as
the current flows.
[Illustration: FIG. 242.--Magnetizing by the discharge of a Leyden jar.]
=262. Static and Current Electricity Compared.=--The likeness between a
discharge of static electricity and an electric current may be shown by
winding a coil of insulated wire about a glass tube which contains a
steel needle. If a Leyden jar (see Fig. 242) is discharged through the
coil the steel needle is usually found to be magnetized, showing that
the discharge of the static electricity has a magnetic effect similar to
that of an electric current. Sometimes a given end of the needle has a
north pole and at other times a south pole. This is believed to
indicate that the charge of the Leyden jar is _oscillatory_, and that
in different discharges sometimes a surge in one direction and at other
times a surge in the reverse direction has been most effective in
magnetizing the needle. Compare this action with that described in Art.
233.
Important Topics
1. Right-hand rules, for conductor, for helix.
2. The electromagnet, two forms, where used?
3. Likeness between static and current electricity.
4. The electric bell, parts, action.
5. The telegraph, key, sounder, relay.
Exercises
1. What is the difference between an electric charge and a current?
2. How can a magnetic effect be produced from an electric charge?
3. What is a magnetic field? Give two evidences of a magnetic field
about a current in a wire?
4. A current is flowing north in trolley wire, what is the direction of
the magnetic field under the wire? Explain.
5. What would be the result if a hard steel core were placed in the
electromagnet? Explain.
6. If the north-seeking pole of a helix is facing you, does the current
in the coils before you move in a clockwise or in a counter-clockwise
direction? Explain.
7. A helix is placed horizontally with its north-seeking pole toward the
north. Does the current in the wire at the top of the helix move east or
west? Explain.
8. State at least six conditions any one of which will put an electric
bell circuit out of commission.
9. If one desires to insert a battery into a telegraph circuit already
in operation, how will he determine the direction of the current in the
wire?
10. If a boy who had magnetized his knife blade in a physics laboratory,
pointed end south-seeking, should lose his way in the woods on a cloudy
day, how could he determine his way out?
11. At a certain point the earth's field acts north, that of an electric
current, east. The magnetoscope needle points exactly northeast when
placed at that point. How do the two magnetic fields compare?
(2) ELECTRICAL MEASUREMENTS
=263. Galvanometers.=--In using electric currents it is often necessary
or desirable to be able to know not only that a given current is weak or
strong, but precisely what its strength is. We can determine the
relative strengths of two currents by the use of a _galvanometer_.
[Illustration: FIG. 243.--The magnet is at the center of the coil.]
[Illustration: FIG. 244.--A moving-magnet (tangent) galvanometer.]
The older or _moving-magnet_ type of galvanometer is similar to the
galvanoscope mentioned in Art. 239. It consists of a magnetic needle
mounted at the center of a coil of wire. The coil is placed facing east
and west, so that the needle will be held by the earth's magnetic field
parallel to the plane of the coil. When a current is sent through the
coil a magnetic field is produced within it. This deflects the needle,
its north end turning east or west depending upon the direction of the
current. (See Fig. 243.) The _coils_ of a moving-magnet or _tangent_
galvanometer (see Fig. 244) are _large_ and firmly fastened to the base,
while the _magnet_ is _small_.
The _moving-coil_ type of galvanometer (see Fig. 245) consists of a
_large magnet_ fastened to the frame of the device. The magnet usually
has a horseshoe form to produce as strong a field as possible. The
_coil_ is wound on a _light_ rectangular frame and is suspended between
the two poles of the magnet. To concentrate the magnetic field, a
cylinder of soft iron is usually placed within the coil. Fig. 246
represents a common form of moving-coil galvanometer.
[Illustration: FIG. 245.--To illustrate the principle of the moving-coil
galvanometer.]
[Illustration: FIG. 246.--A moving-coil (D'Arsonval) galvanometer.]
=264. Measurement of Electric Currents.=--A galvanometer enables one to
_compare_ electric currents. To _measure_ electric currents it is
necessary to employ a _unit_ of electrical quantity, just as in
measuring the quantity of water delivered by a pipe, a unit of liquid
measure is employed; thus, _e.g._, the current delivered by a given pipe
may be 2 gallons of water per second, so in measuring the flow of an
electric current one may speak of two _coulombs_ per second. The
_coulomb_ is the unit quantity of electricity just as the unit of
quantity of water is the gallon.
For most practical purposes, however, we are more interested in the
_rate_ or _intensity_ of flow of current than in the actual _quantity_
delivered. The unit of rate of flow or current is called the _ampere_.
In determining the exact _quantity_ of an electric current, physicists
make use of a device called a _coulomb meter_. (See Fig. 247.) This
contains a solution of silver nitrate in which are placed two silver
plates. The current to be measured is sent through the solution, in at
one plate and out at the other. The plate where the current goes _in_,
the _anode_, _A_ (Fig. 247), loses in weight since some of the silver is
dissolved. The plate where the current goes _out_, the _cathode_, _C_,
increases in weight since some of the silver is deposited. By an
international agreement, _the intensity of the current which deposits
silver at the rate of 0.001118 g. per second is 1 ampere_. This is equal
to 4.025 g. per hour.
[Illustration: FIG. 247.--A coulomb meter, the anode _A_ is separated
from the cathode _C_ by a porous cup.]
The _coulomb_ is defined as the quantity of electricity delivered by a
current of one ampere during one second.
A 40-watt-incandescent lamp takes about 0.4 ampere of current. An arc
lamp takes from 6 to 15 amperes. A new dry cell may send 20 amperes
through a testing meter. A street car may take from 50 to 100 amperes.
=265. The Ammeter.=--The method described above is not used ordinarily
for measuring current strengths on account of its inconvenience. The
usual device employed is an _ammeter_. This instrument is a _moving-coil
galvanometer_. It contains, wound on a light form, a coil of fine
copper wire. The form is mounted on jewel bearings between the poles of
a strong permanent horseshoe magnet. (See Fig. 248.) As in other
moving-coil galvanometers, a soft iron cylinder within the form
concentrates the field of the magnet. The form and its coil is held in
balance by two spiral springs which also conduct current into and out of
the coil.
Only a small part of the whole current measured, in some cases only
0.0001 passes through the coil, the larger part of the current passing
through a metal wire or strip called a _shunt_[L] (see Fig. 248)
connecting the binding posts of the instrument. A fixed fraction of the
whole current flows through the coil. Its field crossing the field of
the horseshoe magnet, tends to turn until its turning force is balanced
by the spiral springs. As the coil turns it moves a pointer attached to
it across a scale graduated to indicate the number of amperes in the
whole current.
[L] A shunt is a conductor or coil connected in parallel with
another conductor or circuit. It carries a part of the current.
[Illustration: FIG. 248.--Diagram of a commercial ammeter. _S_ is the
shunt.]
It should be noted that while _all_ of the current measured passed
through the ammeter, but a small _part_ goes through the coil.
=266. Resistance of Conductors.=--With an ammeter one may study the
change produced in the amount of current flowing in a wire when a change
is made in the wire conducting the current. For example, if one measures
with an ammeter the current flowing from a dry cell through a long and
then through a short piece of fine copper wire, it will be seen that
less current flows when the long piece is used. That is, the long wire
seems to hinder or to _resist_ the passing of the current more than the
short piece. In other words, the long wire is said to have more
_resistance_.
The resistance of a conducting body is affected by several conditions.
(a) It is _directly_ proportional to the _length_ of the conductor, one
hundred feet of wire having twice the resistance of fifty feet.
(b) It is _inversely_ proportional to the _square of the diameter_; a
wire 0.1 inch in diameter has four times the resistance of a wire 0.2
inch in diameter.
(c) It differs with different substances, iron having about six times as
much as copper.
(d) It varies with the temperature, metals having greater resistance at
a higher temperature.
Since silver is the best conductor known, the resistances of other
substances are compared with it as a standard.
The ratio of the resistance of a wire of any substance as compared to
the resistance of a silver wire of exactly the same diameter and length
is called its _relative_ resistance.
Purified substances arranged in order of increasing resistance for the
same length and sectional area (Ayrton-Mather) are given on p. 294.
Silver annealed 1.00
Copper annealed { from 1.04
{ to 1.09
Aluminum annealed 1.64
Nickel annealed 4.69
Platinum annealed 6.09
Iron annealed 6.56
German Silver { from 12.80
{ to 20.20
Mercury 63.30
Nichrome 67.50
Carbon { from 2700.00
{ to 6700.00
=267. The ohm, the unit of resistance=, is defined by international
agreement as follows: _An ohm is the resistance of a column of pure
mercury, 106.3 cm. long with a cross-section of a square millimeter and
at a temperature of 0°C._
It should be noted that each of the four conditions affecting resistance
is mentioned in the definition, viz., length, cross-section, material,
and temperature. Since it is inconvenient to handle mercury, _standard
resistance coils_, made of an alloy of high resistance are used in
comparing and measuring resistances.
A piece of copper wire No. 22 (diameter 0.644 mm.) 60. 5 ft. long has a
resistance of 1 ohm. See table p. 296.
The resistance of some telephone receivers is 75 ohms, of a telegraph
sounder, 4 ohms, of a relay 200 ohms.
=268. Resistance of Circuits.=--Every part of an electrical circuit
possesses resistance. In an electric-bell circuit, for instance, the
wires, the bell, the push-button, and the cell itself, each offers a
definite resistance to the passage of the current. The resistance
_within the cell_ is termed _internal resistance_, while the resistance
of the parts outside of the electric generator is called _external
resistance_.
=269. Electromotive Force.=--In order to set in motion anything, some
_force_ must be applied. This is as true of electricity as of solids,
liquids, or gases. By analogy that which is exerted by a battery or by a
dynamo in causing current to flow is called an _electromotive force_.
The unit of electromotive force, the _volt_, may be defined as _the
electromotive force that will drive a current of 1 ampere through the
resistance of 1 ohm_. The electromotive force of a dry cell is about 1.5
volts, of a Daniell cell 1.08 volts. Most electric light circuits in
buildings carry current at 110 or 220 volts pressure. Currents for
street cars have an electromotive force of from 550 to 660 volts.
[Illustration: FIG. 249.--Diagram of a commercial voltmeter.]
=270. The Voltmeter.=--An instrument for measuring the electromotive
force of electric currents is called a _voltmeter_ (Fig. 249). It is
usually a moving-coil galvanometer, and is always of _high resistance_.
It is like an ammeter in construction and appearance. In fact, a
voltmeter is an ammeter which has had its shunt removed or disconnected.
In place of a shunt, the voltmeter uses a coil of wire of high
resistance (see _R_, Fig. 249) _in series_ with the galvanometer coil.
The high resistance of the voltmeter permits but a very small current to
flow through it. Hence a voltmeter must be placed _across_ a circuit
and not in it. In other words _a voltmeter is connected in shunt_,
while _an ammeter is in series with the circuit_ as is shown in Fig.
250.
DIMENSIONS AND FUNCTIONS OF COPPER WIRES
Column headings:
B: B. & S. gauge number
MM: Millimeters
SA: Sectional area in square millimeters
WL: Weight and length, Density = 8.9, feet per pound
R: Resistance at 24°C., feet per ohm
C: Capacity in amperes
----+--------------+----------+---------+---------+----------+------
| Diameter | | | | |
B +-------+------+ Circular | SA | WL | R | C
| Mils | MM | mils | | | |
----+-------+------+----------+---------+---------+----------+------
0000|460.000|11.684|211,600.00|107.219 | 1.56|19,929.700|312.0
000|409.640|10.405|167,805.00| 85.028 | 1.97|15,804.900|262.0
00|364.800| 9.266|133,079.40| 67.431 | 2.49|12,534.200|220.0
0|324.950| 8.254|105,592.50| 53.470 | 3.13| 9,945.300|185.0
2|257.630| 6.544| 66,373.00| 33.631 | 4.99| 6,251.400|131.0
4|204.310| 5.189| 41,742.00| 21.151 | 7.93| 3,931.600| 92.3
6|162.020| 4.115| 26,250.50| 13.301 | 12.61| 2,472.400| 65.2
8|128.490| 3.264| 16,509.00| 8.366 | 20.05| 1,555.000| 46.1
10|101.890| 2.588| 10,381.00| 5.260 | 31.38| 977.800| 32.5
12| 80.808| 2.053| 6,529.90| 3.309 | 50.69| 615.020| 23.0
14| 64.084| 1.628| 4,106.80| 2.081 | 80.59| 386.800| 16.2
16| 50.820| 1.291| 2,582.90| 1.309 | 128.14| 243.250| 11.5
18| 40.303| 1.024| 1,624.30| 0.823 | 203.76| 152.990| 8.1
20| 31.961| 0.812| 1,021.50| 0.5176 | 324.00| 96.210| 5.7
22| 25.347| 0.644| 642.70| 0.3255 | 515.15| 60.510| 4.0
24| 20.100| 0.511| 504.01| 0.2047 | 819.21| 38.050| 2.8
26| 15.940| 0.405| 254.01| 0.1288 | 1,302.61| 23.930| 2.0
28| 12.641| 0.321| 159.79| 0.08097| 2,071.22| 15.050| 1.4
30| 10.025| 0.255| 100.50| 0.05092| 3,293.97| 9.466| 1.0
32| 7.950| 0.202| 63.20| 0.03203| 5,236.66| 5.952| 0.70
34| 6.304| 0.160| 39.74| 0.02014| 8,328.30| 3.743| 0.50
36| 5.000| 0.127| 25.00| 0.01267|13,238.83| 2.355| 0.35
38| 3.965| 0.101| 15.72| 0.00797|20,854.65| 1.481| 0.25
40| 3.144| 0.080| 9.89| 0.00501|33,175.94| 0.931| 0.17
----+-------+------+----------+---------+---------+----------+------
Important Topics
(1) _Galvanometers_: (1) moving magnet, fixed coil; (2) moving coil,
fixed magnet, ammeter, voltmeter.
(2) _Unit of quantity, coulomb._
(3) _Unit of current, ampere._
(4) _Unit of resistance, ohm._
(5) _Unit of electromotive force, volt._
Exercises
1. How will the resistance of 20 ft. of No. 22 German silver wire
compare with that of 10 ft. of No. 22 copper wire? Explain.
2. Where in a circuit is copper wire desirable? Where should German
silver wire be used?
3. Explain the action of the ammeter. Why does not the needle or coil
swing the full distance with a small current?
4. Why is a telegraph sounder more apt to work on a short line than upon
a long one?
[Illustration: FIG. 250.--The ammeter is connected in series and the
voltmeter in shunt.]
5. Find the resistance of 15 miles of copper telephone wire No. 12. (See
table p. 296.)
6. What will be the weight and resistance of 1,000 feet of No. 20 copper
wire?
7. A storage battery sends 4 amperes of current through a plating
solution. How much silver will it deposit in 2 hours?
8. (a) Compare the diameters of No. 22 and No. 16 copper wire.
(b) Compare the lengths of the same wires giving 1 ohm resistance.
(c) What relation exists between (a) and (b)?
9. Why is an electric bell circuit usually open while a telegraph line
circuit is usually closed?
10. A copper wire and an iron wire of the same length are found to have
the same resistance. Which is thicker? Why?
11. Why are electric bells usually arranged in parallel instead of in
series?
12. What would happen if a voltmeter were put in series in a line?
(3) OHM'S LAW AND ELECTRICAL CIRCUITS
=271. Conditions Affecting Current Flow.=--Sometimes over a long circuit
one cell will not work a telegraph sounder. In such a case, two, three,
or more cells are connected so that the zinc of one is joined to the
copper plate of the other. When connected in this way the cells are said
to be _in series_ (Fig. 251). In the figure _A_ represents a voltmeter.
It is found that _when cells are in series the E.M.F. of the battery is
the sum of the electromotive forces of the cells_. An ammeter in the
circuit shows increased current as the cells are added. Hence _if the
resistance of the circuit remains unchanged, the greater the E.M.F. the
greater is the current strength_. In this respect, the movement of
electricity in a circuit is similar to the flow of water in a small pipe
under pressure, as in the latter the flow of water increases as the
pressure becomes greater. The current in a circuit may also be increased
by lessening the resistance, since the current through a long wire is
less than that through a short one, just as the flow of water will be
greater through a short pipe than through a long one. To increase the
current flowing in an electric circuit, one may therefore either
increase the E.M.F. or decrease the resistance.
[Illustration: FIG. 251.--Diagram of cells connected in series.]
=272. Ohm's Law.=--The relation between the electromotive force applied
to a circuit, its resistance, and the current produced was discovered in
1827 by George Ohm. Ohm's law, one of the most important laws of
electricity, states that, in any circuit, _the current in amperes equals
the electromotive force in volts divided by the resistance in ohms_.
This principle is usually expressed thus:
Current intensity = electromotive force/resistance or
Amperes = volts/ohms or _I_ = _E_/_R_
[Illustration: FIG. 252.--The street cars are connected in parallel with
each other.]
=273. Resistance of Conductors in Series.=--A study of the _resistance_
of conductors when alone and when grouped in various ways is of
importance _since, the current flow through any circuit is dependent
upon its resistance_. The two most common methods of combining several
conductors in a circuit are in _series_ and in _parallel_. Conductors
are in _series_ when all of the current passes through each of the
conductors in turn (Fig. 218), thus the cell, push-button, wires, and
electric bell in an electric-bell circuit are in series. Conductors are
in _parallel_ when they are so connected that they are side by side and
a part of the whole current goes through each. None of the current that
passes through one conductor can go through the conductors in parallel
with it. Thus the electric street cars are in _parallel_ with each
other. (See Fig. 252.) It is easily seen that none of the current
passing through one car can go through any of the others. When the
conductors are in _series_ the combined resistance is the _sum_ of the
several resistances. Thus in an electric-bell circuit if the battery has
a resistance of 1 ohm, the bell of 2 ohms, and the wire 1 ohm, the total
resistance in the circuit is 4 ohms. When conductors are in _parallel_
the combined resistance is always _less_ than the separate resistances.
Just as a crowd of people meets less resistance in leaving a building
through several exits, so electricity finds less resistance in moving
from one point to another along several parallel lines, than along one
of the lines.
=274. Resistance of Conductors in Parallel.=--If three conductors of
equal resistance are in parallel, the combined resistance is just
one-third the resistance of each separately (Fig. 253). The rule that
states the relation between the combined resistance of conductors in
parallel and the separate resistances is as follows:_The combined
resistance of conductors in parallel is the reciprocal of the sum of the
reciprocals of the several resistances_. For example, find the combined
resistance of three unequal resistances in parallel; the first being 4
ohms, the second, 6 ohms, and third 3 ohms. The reciprocals of the three
resistances are 1/4, 1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 =
18/24. The reciprocal of this is 24/18 which equals 1-1/3 ohms, the
combined resistance.
FIG. 253.--The three conductors are connected in parallel.
This rule may be understood better if we consider the _conductance_
of the conductors in parallel. Since the conductance of a two ohm
wire is just one-half that of a one-ohm wire, we say that the
conductance of a body is inversely as the resistance, or that it is
the _reciprocal of the resistance_. The conductance of the 4-, 6-,
and 3-ohm coils will therefore be respectively 1/4, 1/6, and 1/3,
and since the combined conductance is the sum of the several
conductances, the total conductance is 18/24. Also since this is
the reciprocal of the total resistance, the latter is 24/18 or
1-1/3 ohms.
When two or more conductors are connected in parallel each one is said
to be a _shunt_ of the others. Many circuits are connected in _shunt_ or
in parallel. Fig. 254 represents four lamps in parallel. Incandescent
lamps in buildings are usually connected in parallel, while arc lamps
are usually connected in series. Fig. 255 represents four lamps in
series.
Important Topics
1. Conditions affecting current flow, (a) E.M.F., (b) resistance.
2. Ohm's law, three forms for formula.
3. Resistance of conductors: (a) in series, (b) in parallel; how
computed, illustrations.
[Illustration: FIG. 254.--The four lamps are connected in parallel.]
[Illustration: FIG. 255.--The four lamps are connected in series.]
Exercises
1. What current flows through a circuit if its E.M.F. is 110 volts and
the resistance is 220 ohms?
2. A circuit contains four conductors in series with resistances of 10,
15, 6, and 9 ohms respectively. What current will flow through this
circuit at 110 volts pressure? What will be the resistance of these four
conductors in parallel?
3. What is the combined resistance of 8 conductors in parallel if each
is 220 ohms? What current will flow through these 8 conductors at 110
volts pressure?
4. What is the resistance of a circuit carrying 22 amperes, if the
E.M.F. is 20 volts?
5. What E.M.F. will send 8 amperes of current through a circuit of 75
ohms resistance?
6. How does the voltmeter differ from the ammeter?
7. How can one determine the resistance of a conductor?
8. The resistance of a hot incandescent lamp is 100 ohms. The current
used is 1.1 amperes. Find the E.M.F. applied.
9. What is the resistance of the wires in an electric heater if the
current used is 10 amperes, the voltage being 110?
10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. How
many feet should be used in winding a 200 ohms relay?
11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. What
is the resistance of a line 1 mile long?
12. A wire has a resistance of 20 ohms. It is joined in parallel with
another wire of 6 ohms, find their combined resistance.
13. The separate resistances of two incandescent lamps are 200 ohms and
70 ohms. What is their combined resistance when joined in parallel? When
joined in series?
(4) METHODS OF GROUPING CELLS AND MEASURING RESISTANCE
=275. Internal Resistance of a Voltaic Cell.=--The current produced by a
voltaic cell is affected by the resistance that the current meets in
passing from one plate to another through the liquid of the cell. This
is called the _internal resistance_ of the cell. A Daniell cell has
several (1-5) ohms internal resistance. The resistance of dry cells
varies from less than 0.1 of an ohm when new to several ohms when old.
If cells are joined together their combined internal resistance depends
upon the method of grouping the cells.
[Illustration: FIG. 256.--The four cans exert four times the water
pressure that one can will exert.]
=276. Cells Grouped in Series and in Parallel.=--When in _series_ the
copper or carbon plate of one cell is joined to the zinc of another and
so on. (See Fig. 251.) The effect of connecting, say four cells, in
series may be illustrated by taking four cans of water, placed one above
another. (See Fig. 256.) The combined water pressure of the series is
the sum of the several pressures of the cans of water, while the
opposition offered to the movement of a quantity of water through the
group of cans is the sum of the several resistances of the cans. In
applying this illustration to the voltaic cell, we make use of Ohm's
law. Let _E_ represent the e.m.f. of a single cell, _r_ the internal
resistance of the cell, and _R_ the external resistance or the
resistance of the rest of the circuit. Consider a group of cells in
series. If _n_ represents the _number_ of cells in _series_, then Ohm's
law becomes
_I_ = _nE_/(_nr_ + _R_).
Cells are grouped in _series_ when large E.M.F. is required to force a
current through a large external resistance such as through a long
telegraph line. Cells are connected in _parallel_ when it is desired to
send a large current through a small external resistance. To connect
cells in parallel all the copper plates are joined and also all the zinc
plates. (See Fig. 257.) To illustrate the effect of this mode of
grouping cells, suppose several cans of water are placed side by side
(Fig. 258). It is easily seen that the pressure of the group is the same
as that of a single cell, while the resistance to the flow is less than
that of a single cell. Applying this reasoning to the electric circuit
we have by Ohm's law the formula for the current flow of a group of
_n_ cells arranged in parallel _I_ = _E_/((_r/n_) + _R_).
[Illustration: FIG. 257.--Four cells connected in parallel.]
[Illustration: FIG. 258.--The water pressure of the group in parallel is
the same as that of one.]
=277. Illustrative Problems.=--Suppose that four cells are grouped in
parallel, each with an E.M.F. of 1.5 volts and an internal resistance of
2 ohms. What current will flow in the circuit if the external resistance
is 2.5 ohms? Substitute in the formula for cells in parallel the values
given above, and we have _I_ = 1.5/(0.5 + 2.5) = 1.5/3 = 0.5 ampere.
Suppose again that these four cells were grouped in series with the same
external resistance, substituting the values in the formula for cells in
series we have _I_ = 4(1.5)/(4 × 2 + 2.5) = 6/10.5 = 0.57 ampere.
=278. Volt-ammeter Method for Finding Resistance.=--Measurements of the
resistance of conductors are often made. One of these methods depends
upon an application of Ohm's law. It is called the volt-ammeter method
since it employs both a voltmeter and an ammeter. If the conductor whose
resistance is to be measured is made a part of an electric circuit,
being connected _in series with the ammeter_ and _in shunt with the
voltmeter_, the resistance may easily be determined, since _R_ = _E/I_.
(See Fig. 250.) If, for example, the difference in E.M.F., or as it is
often called, the _fall of potential_ between the ends of the wire as
read on the voltmeter is 2 volts, and the current is 0.5 ampere, then
the resistance of the wire is 4 ohms. This method may be readily applied
to find the resistance of any wire that is a part of an electric
circuit.
=279. The Wheatstone Bridge.=--To find the resistance of a separate wire
or of an electrical device another method devised by an Englishman named
Wheatstone is commonly employed. This method requires that three known
resistances, _a_, _b_, _c_, in addition to the unknown resistance _x_
be taken. These four resistances are arranged in the form of a
parallelogram. (See Fig. 259.) A voltaic cell is joined to the
parallelogram at the extremities of one diagonal while a moving-coil
galvanometer is connected across the extremities of the other diagonal.
The known resistances are changed until when on pressing the keys at _E_
and _K_ no current flows through the galvanometer. when this condition
is reached, the four resistances form a true proportion, thus _a_: _b_ =
_c_: _x_.
Since the values of _a_, _b_, and _c_ are known, _x_ is readily
computed. Thus if _a_ = 10, _b_ = 100, and _c_ = 1.8 ohms, then _x_, the
unknown resistance, equals 18 ohms, since 10: 100 = 1.8: 18. This method
devised by Wheatstone may be employed to find the resistance of a great
variety of objects. It is the one most commonly employed by scientists
and practical electricians.
[Illustration: FIG. 259.--Diagram of a Wheatstone bridge.]
Important Topics
1. The internal resistance of voltaic cells.
2. Ohm's law applied to groups of cells. (a) Cells in series, (b) cells
in parallel.
3. Measurement of resistance: (a) volt-ammeter method, (b) Wheatstone
bridge method.
Exercises
1. What is the resistance of an electric bell circuit where the E.M.F.
is 3 volts and the current is 0.6 ampere?
2. A telegraph wire is broken somewhere, the ends lying upon damp
ground. If an E.M.F. of 30 volts is applied from the ground to the wire
and a current of 0.1 of an ampere flows, what is the resistance of the
part connected to the ammeter. (The earth which completes the circuit
from the end of the wire has very small resistance.) Why?
3. How far away is the break in the wire if the latter has a resistance
of 80 ohms to the mile? Diagram.
4. What current will flow through a bell circuit of 8 ohms resistance if
it contains three cells _in series_ each with an E.M.F. of 1.5 volts and
an internal resistance of 1/3 ohm?
5. If the same three cells are connected in parallel on the same circuit
what current flows? Is the current in problem 4 or 5 the larger? Why?
6. If four cells each with 1.5 volts E.M.F. and an internal resistance
of 0.4 ohm are connected with a circuit having an external resistance of
0.8 ohm, what current will the parallel connection give? The series
connection? Which gives the larger current? Why?
7. Four Daniell cells each having 1 volt E.M.F. and 3 ohms internal
resistance are connected in series with 2 telegraph sounders of 4 ohms
each. The connecting wires have 6 ohms resistance. Find the current
intensity.
8. A battery of 2 cells arranged in series is used to ring a door bell.
The E.M.F. of each cell is 1.5 volts, internal resistance 0.3 ohm, and
the resistance of the bell is 4 ohms. What is the current in amperes?
9. In the above problem find the current if the cells are connected in
parallel.
CHAPTER XIII
THE CHEMICAL AND HEAT EFFECTS OF ELECTRIC CURRENTS
(1) THE CHEMICAL EFFECT OF AN ELECTRIC CURRENT
=280. Electroplating.=--If two carbon rods (electric light carbons
answer very well) are placed in a solution of _copper sulphate_ (Fig.
260) and then connected by wires to the binding posts of an electric
battery, one of the rods soon becomes covered with a coating of
_metallic copper_ while bubbles of gas may be seen upon the other
carbon. If a solution of _lead acetate_ is used in the same way a
deposit of _metallic lead_ is secured, while a solution of _silver
nitrate_ gives silver.
[Illustration: FIG. 260.--Two carbons placed in a solution of copper
sulphate.]
[Illustration: FIG. 261.--An electroplating bath.]
This process of depositing metals upon the surface of solids by an
electric current is called _electroplating_. Everyone has seen
_electroplated_ articles such as silver plated knives, forks, and
spoons, and nickel-plated rods, handles, etc. _Copper electrotype_
plates such as are used in printing school books are made by this
process. In practical electroplating a solution of the metal to be
deposited is placed in a tank; across the top of this tank are placed
copper rods to act as conducting supports. From one of these rods, the
cathode, objects to be plated are hung so as to be immersed in the
liquid. From other rods, the anodes, are hung plates of the metal to be
deposited. These are dissolved as the current deposits a coating upon
the articles, thus keeping the solution up to its proper strength. (See
Fig. 261.)
[Illustration: FIG. 262.--The current is carried through the solution by
ions.]
=281. Electrolysis.=--A solution from which a deposit is made by an
electric current is called an _electrolyte_. The plates or other objects
by which the current enters or leaves the electrolyte are called the
_electrodes_. The electrode by which the current enters is called the
_anode_ (_an_ = in) while the electrode by which it leaves is the
cathode (_cath_ = away). The process by which an electric current
decomposes a solution and deposits a substance upon an electrode is
called _electrolysis_. The _current_ always flows within the cell from
_anode to the cathode_. (See Fig. 262.) The metal goes with the current
and is found deposited upon the cathode.
=282. Theory of Electrolysis.=--The action going on in an _electrolytic_
cell has been carefully studied. The _theory of electrolysis_, which is
supported by much experimental evidence, supposes that many of the
molecules in a _dilute_ solution of a substance "split up" into two
parts called "ions," one ion having a positive, the other a negative
charge. In a dilute solution of sulphuric acid, the _positive_ ion is of
hydrogen, while the _negative_ ion is the (SO_{4}) or sulphion. These
ions bearing electric charges are believed to be the _carriers of the
electric current_ through the electrolyte.
The positive ions move with the current from the anode to the cathode,
while the negative ions apparently are repelled by the cathode and
appear upon the anode. Evidence of the accumulation of the two kinds of
ions at the two electrodes is furnished by the _electrolysis_ of water,
described below.
=283. Electrolysis of Water.=--Two glass tubes (Fig. 263), _H_ and _O_,
are attached at the bottom to a horizontal glass tube. To the latter is
also connected an upright tube _T_. At the lower ends of _H_ and _O_ are
inserted, fused in the glass, platinum wires, _A_ and _C_. The tubes are
filled with a weak solution of sulphuric acid. The tops of _H_ and _O_
are closed with stopcocks, _T_ being open; a current of electricity is
sent in at _A_ and out at _C_. A movement of the ions at once begins,
the positive hydrogen ions appearing at _C_. These accumulate as bubbles
of hydrogen which rise to the top of _H_ and displace the liquid. At the
same time bubbles of oxygen appear at _A_. These rise in _O_ and also
displace the liquid which rises in _T_. After the action has continued
some time it may be noticed that the volume of hydrogen is just twice
that of the oxygen. This was to have been expected since the formula
for water is H_{2}O. The nature of the gas in _H_ or _O_ may be tested
by opening the stopcock and allowing the gas to escape slowly. The
hydrogen gas can be lighted by a flame while the oxygen gas will cause a
spark upon a piece of wood to glow brightly, but does not burn itself.
[Illustration: FIG. 263.-Electrolysis of water; oxygen collects in _O_,
hydrogen in _H_.]
=284. Evidence that ions are necessary to conduct a current in a liquid=
is furnished by the following experiment. A quart jar is carefully
cleaned, and half filled with distilled water. Two pieces of zinc 5 cm.
square are soldered to pieces of rubber-insulated No. 14 copper wire.
The zincs are placed in the distilled water (Fig. 264) and the wires are
connected to a 110 volt circuit with a 16 candle-power incandescent lamp
in _series_ with the cell, as in the figure. If the zincs have been
carefully cleansed and the water is pure, no current flows as is shown
by the lamp remaining dark. If a minute quantity of sulphuric acid or of
common salt is placed in the water the lamp at once begins to glow. Ions
are now present in the liquid and conduct the current. That some
substances in solution do not form ions may be shown by adding to
another jar of pure water some glycerine and some cane sugar, substances
resembling the acid and salt in external appearance but which do not
_ionize_ when dissolved as is shown by the lamp remaining dark after
adding the glycerine and sugar. The acid and salt are of _mineral_
origin while the glycerine and sugar are _vegetable_ products. This
experiment illustrates the principle that the water will conduct only
when it contains ions.
[Illustration: FIG. 264.--The current passes only when ions are present
in the liquid.]
=285. Laws of Electrolysis.=--These were discovered by Faraday in 1833,
and may be stated as follows: _I. The mass of a substance deposited by
an electric current from an electrolyte is proportional to the intensity
of current which passes through it._
_II. The mass of any substance deposited by a current of uniform
intensity is directly proportional to the time the current flows._
These laws have been used as a basis for defining and measuring the unit
of current flow, the _ampere_. (See Art. 264.)
=286. Instances of Electrolysis.=--(a) Medicines, especially those
containing a mineral substance, are sometimes introduced into the human
body by electrolysis. (b) Water and gas pipes are sometimes much
weakened by the effects of electric currents in the earth, especially
return currents from street railways. Such currents use the metal pipes
as a conductor. At the place where the current leaves the metal and
enters the ground, it removes metallic ions from the pipe. This process
continuing, the pipe becomes weakened and at length breaks. (c) _Copper_
is purified by the use of electric currents that remove the copper from
ore or from other metals and deposit it upon electrodes. _Electrolytic_
copper is the purest known. (d) _Aluminum_ is obtained by the use of
large currents of electricity that first heat the material used until it
melts and then deposit the metal from the fluid material by
electrolysis. These results are called chemical effects of the current
since by the use of electric currents substances are changed chemically,
that is, they are separated into different chemical substances.
Important Topics
1. Electrolysis, electroplating, anode, cathode, ion.
2. Theory of electrolysis--evidence: (a) electrolysis of water; (b)
conductivity of acid and water.
3. Laws of electrolysis.
4. Practical use of electrolysis.
Exercises
1. A dynamo has an E.M.F. of 10 volts. What is the resistance in the
circuit when 20 amperes are flowing?
2. How much silver will be deposited in an hour by this current?
3. Name five objects outside of the laboratory that have been acted upon
by electrolysis. How in each case?
4. Why is table ware silver plated? Why are many iron objects nickel
plated?
5. How is the electrolysis of water pipes prevented?
6. Two grams of silver are to be deposited on a spoon by a current of 1
ampere. Find the time required.
7. How long will it take to deposit 20 g. of silver in an electroplating
bath if a current of 20 amperes is used?
8. If 1000 g. of silver are deposited on the cathode of an electrolytic
reduction plant in 10 minutes, what is the current intensity employed?
(2) THE STORAGE BATTERY AND ELECTRIC POWER
=287. Differences Between Voltaic and Storage Cells.= Voltaic cells in
which electric currents are produced by the chemical action between
metal plates and an electrolyte are often called _primary batteries_. In
voltaic cells one or both plates and the electrolyte are used up or lose
their chemical energy in producing the current and after a time need to
be replaced by new material, the _chemical energy_ of the electrolyte
and of one of the plates having been _transformed_ into electrical
energy.
A different proceeding obtains with another type of cell. This is
called a _storage battery_, or an accumulator. In these cells, the same
_plates_ and electrolyte are _used_ without change _for extended
periods_, sometimes for a number of years. For this reason storage
batteries have displaced many other types of cells, and they are now
used (a) to operate many telephone, telegraph, and fire-alarm circuits,
(b) to work the spark coils of gas and gasoline engines, (c) to help
carry the "peak" load upon lighting and power circuits and (d) to
furnish power for electric automobiles. Since a storage battery can
deliver an electric current only after an electric current from an
outside source has first been sent through it, they are often called
_secondary batteries_.
=288. Construction and Action of a Storage Cell.=--The common type of
storage cells consists of a _number of perforated_ plates made of an
alloy of lead and a little antimony. (See Figs. 265, 266, 267.) Into the
perforations is pressed a paste of red lead and litharge mixed with
sulphuric acid. The plates are placed in a strong solution (20 to 25 per
cent.) of sulphuric acid. The plates are now ready to be charged. This
is accomplished by sending a direct current from an electric generator
through the cell. The hydrogen ions are moved by the current to one set
of plates and change the paste to _spongy_ metallic lead. The sulphions
move to the other set of plates and change the paste to lead oxide. This
electrolytic action causes the two plates to become quite different
chemically so that when the cell is fully charged it is like a voltaic
cell, in having plates that are different chemically. It has, when fully
charged, an E.M.F. of about 2.2 volts. The several plates of a cell
being in parallel and close together, the cell has but small internal
resistance. Consequently a large current is available.
[Illustration: FIG. 265.--The positive plate of a storage cell.]
[Illustration: FIG. 266.--The negative plate of a storage cell.]
[Illustration: FIG. 267.--A complete storage cell.]
[Illustration: FIG. 268.]
About 75 per cent. of the energy put into the storage cell in charging
can be obtained upon _discharging_. Therefore the _efficiency_ of a good
storage cell is about 75 per cent. Fig. 268 represents a storage battery
connected to charging and discharging circuits. The lower is the
charging circuit. It contains a dynamo and a resistance (neither of
which are shown in the figure) to control the current sent into the
cell. The charging current enters the positive pole and leaves by the
negative pole. The current produced by the cell, however, flows in the
_opposite_ direction through it, that is, out from the positive and in
at the negative pole. This current may be controlled by a suitable
resistance and measured by an ammeter. Storage cells have several
advantages: (a) They can be charged and discharged a great many times
before the material placed in the perforations in the plates falls out.
(b) The electrical energy used in charging the plates _costs less_ than
the plates and electrolyte of voltaic cells. (c) Charging storage cells
takes much _less labor_ than replacing the electrolyte and plates of
voltaic cells. (d) Storage cells produce _larger currents_ than voltaic
cells. The two principal _disadvantages_ of storage cells are that (a)
they are _very heavy_, and (b) their initial _cost_ is _considerable_.
[Illustration: FIG. 269.--The Edison storage cell.]
[Illustration: FIG. 270.--The plates of the Edison storage cell.]
=289. The Edison storage cell= (Figs. 269 and 270) has plates of iron
and nickel oxide. The electrolyte is a strong solution of potassium
hydroxide. These cells are lighter than lead cells of the same capacity
and they are claimed to have a longer life.
=290. Energy and Power of a Storage Cell.=--In a storage cell, the
electrical energy of the charging current is transformed into _chemical_
energy by the action of electrolysis. It is this chemical energy that is
transformed into the energy of the electric current when the cell is
discharged. The _capacity_ of storage cells is rated in "ampere hours,"
a 40 ampere hour cell being capable of producing a current of 1 ampere
for 40 hours, or 5 amperes for 8 hours, etc. The production and
extensive use of electric currents have made necessary accurate methods
for measuring the _energy_ and _power_ of these currents. To illustrate
how this is accomplished, let us imagine an electric circuit as
represented in Fig. 268. Here four storage cells in series have an
E.M.F. of 8 volts and in accordance with Ohm's law produce a current of
2 amperes through a resistance in the circuit of 4 ohms. Now the work
done or energy expended by the current in passing through the resistance
between the points _M_ and _N depends_ upon three factors (1) the E.M.F.
or _potential difference_; (2) the _current intensity_ and (3) the
_time_. The energy is measured by their product. That is, _electrical
energy_ = _potential difference_ × _current intensity_ × _time_. This
represents the electrical energy in _joules_, or
Joules = volts × amperes × seconds, or
_j_ = _E_ × _I_ × _t_.
In the circuit represented in Fig. 268 the energy expended between the
points _M_ and _N_ in 1 minute (60 seconds) is 8 × 2 × 60 = 960 joules.
=291. Electric Power.=--Since power refers to the _time rate_ at which
work is done or energy expended, it may be computed by dividing the
electrical energy by the time, or the _electrical power_ = _volts_ ×
_amperes_. The power of 1 joule per second is called a _watt_.
Therefore,
Watts = volts × amperes, or
Watts = _E_ × _I_.
Other units of power are the _kilowatt_ = 1000 watts and the
_horse-power_ = 746 watts. In the example given in Art. 290 the power of
the current is 8 × 2 = 16 watts, or if the energy of the current
expended between the joints _M_ and _N_ were converted into mechanical
horse-power it would equal 16/746 of a horse-power. Electrical energy is
usually sold by the _kilowatt-hour_, or the amount of electrical energy
that would exert a power of 1000 watts for one hour, or of 100 watts for
10 hours, or of 50 watts for 20 hours, etc.
Important Topics
1. The storage battery, its construction, electrolyte, action, uses,
advantages, disadvantages.
2. Electric energy, unit value, how computed?
3. Electric power, three units, value, how computed, how sold?
Exercises
1. In what three respects are voltaic and storage cells alike? In what
two ways different?
2. Name the four advantages of storage cells in the order of their
importance. Give your reasons for choosing this order.
3. Why are dry cells more suitable for operating a door-bell circuit,
than a storage battery? Give two reasons.
4. The current for a city telephone system is provided by a storage
battery. Why is this better than dry cells at each telephone?
5. An incandescent lamp takes 0.5 ampere at 110 volts. What power is
required to operate it? How much _energy_ will it transform in 1 minute?
6. How long would it take for this lamp to use a kilowatt hour of
energy?
7. A street car used 100 amperes at 600 volts pressure. What power was
delivered to it? Express also in kilowatts and horse-power.
8. An electric toaster takes 5 amperes at 110 volts. If it toasts a
slice of bread in 2 minutes, what is the cost at 10 cents a kilowatt
hour?
9. An electric flat iron takes 5 amperes at 110 volts. Find the cost of
using it for 2 hours at 12 cents a kilowatt hour.
10. A 1/4 kilowatt motor is used to run a washing-machine for 5 hours.
What is the expense for this power at 10 cents a kilowatt hour?
11. What is the efficiency of a motor that takes 7390 watts and develops
9 horse-power?
12. How many horse-power are there in a water-fall 212 ft. high over
which flows 800 cu. ft. of water per second? Express this power in
kilowatts.
13. What horse-power must be applied to a dynamo having an efficiency of
go per cent. if it is to light 20 arc lamps in series, each taking 10
amperes at 60 volts?
(3) THE HEAT EFFECT OF ELECTRIC CURRENTS
=292. The Production of Heat by an Electric Current.=--When no chemical
or mechanical work is done by an electric current its energy is employed
in overcoming the resistance of the conducting circuit and is
transformed into _heat_. This effect has many practical applications and
some disadvantages. Many devices employ the heating effect of electric
currents, (a) the electric furnace, (b) electric lights, (c) heating
coils for street cars, (d) devices about the home, as flat irons,
toasters, etc. Sometimes the heat produced by an electric current in the
wires of a device such as a transformer is so large in amount that
especial means of cooling are employed. Unusually heavy currents have
been known to melt the conducting wires of circuits and electrical
devices. Hence all circuits for electric power as well as many others
that ordinarily carry small currents are protected by _fuses_. An
_electric fuse_ is a short piece of wire that will melt and break the
circuit if the current exceeds a determined value. The fuse wire is
usually enclosed in an incombustible holder. Fuse wire is frequently
made of lead or of an alloy of lead and other easily fusible metals.
(See Figs. 271 and 272.)
[Illustration: FIG. 271.--A type of enclosed fuse.]
[Illustration: FIG. 272.--A link fuse (above); plug fuses (below).]
=293. Heat Developed in a Conductor.=--A rule for computing the amount
of heat produced in an electric circuit by a given current has been
accurately determined by experiment. It has been found that 1 _calorie_
of heat (Art. 142), is produced by an expenditure of 4.2 joules of
electrical (or other) energy. In other words, 1 joule will produce 1/4.2
or 0.24 calorie. Now the number of joules of electrical energy in an
electric circuit is expressed by the following formula:
Joules = volts × amperes × seconds, or since 1 joule = 0.24 calorie,
Calories = volts × amperes × seconds × 0.24 or
_H_ = _EI_ × _t_ × 0.24 (1)
By Ohm's law, _I_ = _E_/_R_ or _E_ = _I_ × _R_, substituting in equation
(1) _IR_ for its equal _E_ we have
_H_ = _I²R_ × _t_ × 0.24 (2)
Also since _I_ = _E_/_R_ substitute _E_/_R_ for _I_ in equation (1) and
we have
_H_ = _E²_/_R_ _t_ × 0.24 (3)
To illustrate the use of these formulas by a problem suppose that a
current of 10 amperes is flowing in a circuit having a resistance of 11
ohms, for 1 minute. The heat produced will be by formula (2) = (10)² ×
11 × 60 × 0.24 equals 15,840 calories.
[Illustration: FIG. 273.--A carbon filament incandescent lamp.]
[Illustration: FIG. 274.--A tungsten lamp.]
=294. The Incandescent Lamp.=--One of the most common devices employing
the heat effect of an electric current is the _incandescent lamp_. (See
Fig. 273.) In this lamp the current is sent through a carbon filament,
which is heated to incandescence. In order to keep the filament from
burning as well as to prevent loss of heat by convection, it is placed
in a glass bulb from which the air is exhausted. Two platinum wires
fused in the glass connect the carbon filament with the grooved rim and
the end piece of the base. The end piece and rim connect with the socket
so that an electric current may flow through the filament of the lamp.
The carbon incandescent lamp has a low efficiency. It takes 0.5 ampere
of current at 110 volts or in other words it requires 55 watts to cause
a 16-candle-power lamp to glow brightly, hence 1 candle power in this
lamp takes 55/16 = 3.43 watts.
The _efficiency of electric lamps_ is measured by the _number of watts
per candle power_. This is a peculiar use of the term efficiency, as the
larger the number the less efficient is the lamp. More efficient lamps
have been devised with filaments of the metals _tantalum_ and _tungsten_
(Fig. 274). These give a whiter light than do carbon lamps, and consume
but about 1.25 watts per candle power.
COMPARATIVE "EFFICIENCY" OF ELECTRIC LAMPS
------------------+----------+----------------+------------
|Watts per | | Watts per
Name of lamp | candle | Name of lamp | candle
| power | | power
------------------+----------+----------------+------------
Carbon filament | 3 to 4 |Arc lamp | 0.5 to 0.8
Metallized carbon | 2.5 |Mercury arc | 0.6
Tantalum | 2.0 |Flaming arc | 0.4
Tungsten | 1.0 to |Nitrogen-filled | 0.6 to 0.7
| 1.5 | tungsten |
------------------+----------+----------------+------------
Incandescent lamps are connected in parallel (see Fig. 254) to wires
that are kept at a constant difference of potential of 110 or 115 volts.
It is customary to place not more than twelve lamps upon one circuit,
each circuit being protected by a fuse and controlled by one or more
switches.
=295. The Arc Light.=--The electric _arc_ light (see Fig. 275) is
extensively used for lighting large rooms, also in stereopticons and
motion picture machines. The light is intense, varying from 500 to 1700
candle power. The so-called mean spherical candle power of the arc light
is about 510. The candle power in the direction of greatest intensity is
about 1200. It is produced at an expenditure of about 500 watts. It is
therefore more efficient than the incandescent lamp, often taking less
than 0.5 watt per candle power produced. The arc light was first devised
by Sir Humphrey Davy in 1809, who used two pieces of charcoal connected
to 2000 voltaic cells. The arc light requires so much power that its
production by voltaic cells is very expensive. Consequently it did not
come into common use until the dynamo had been perfected. Fig. 276 shows
the appearance of the two carbons in an arc light. If a direct current
is used the positive carbon is heated more intensely, and gives out the
greater part of the light. The positive carbon is consumed about twice
as fast as the negative and its end is concave, the negative remaining
pointed.
[Illustration: FIG. 275.--An electric arc light.]
[Illustration: FIG. 276.--The appearance of a pair of used carbons.]
With alternating currents, the rods are equally consumed and produce
equal amounts of light. In the stereopticon, the carbons are usually
placed at right angles as in Fig. 277. In the stereopticon as well as
in outdoor lighting the direct current is more effective, although the
alternating current is often used, since the latter can be produced and
distributed more cheaply than can direct currents. In arc lamps, placing
an inner glass globe (Fig. 278) about the carbons, decreases the
consumption of the carbons materially. The carbon rods of _enclosed_ arc
lamps often last 60 to 100 hours.
[Illustration: FIG. 277.--A right-angle electric arc lamp for a
stereopticon.]
[Illustration: FIG. 278.--An enclosed arc lamp.]
The reason why an _open_ arc lamp needs to be "retrimmed" oftener
than the _enclosed_ lamp, that is, have new carbons placed in it,
is because the carbons "burn" freely, that is unite with the oxygen
of the air. In the enclosed arc lamp, the supply of oxygen in the
inner globe is limited and is soon consumed, therefore the carbons
last many times longer in such lamps.
Some carbon rods have soft cores containing calcium salts. These
vaporize in the arc producing the _flaming arc light_ of a bright yellow
color, and give more light than the ordinary lamp.
Important Topics
1. Heat effects of electric currents, uses and applications.
2. Computation of the heat developed in a circuit. Three formulas.
3. Electric lamps; incandescent and arc; construction, uses,
efficiency.
Exercises
1. Sketch a circuit containing 10 incandescent lamps in parallel. If
each lamp when hot has a resistance of 220 ohms, and the E.M.F. is 100
volts, what current will flow?
2. What will it cost to use these lights for 3 hours a day for 30 days
at 10 cents a kilowatt hour?
3. How much heat will these lamps produce per minute?
4. How could you connect 110-volt lamps to a street car circuit of 660
volts? Explain this arrangement and draw a diagram.
5. A certain arc lamp required 10 amperes of current at 45 volts
pressure. What would it cost at 10 cents per kilowatt hour if used 3
hours a day for 30 days?
6. Show a diagram of 3 arc lamps in series. If each takes 45 volts and
10 amperes, how much E.M.F. and current will they require?
7. If an electric toaster uses 5 amperes at 115 volts, how much heat
will this develop in half an hour?
9. How much heat is developed in an electric toaster in 2 minutes, if it
uses 5 amperes at 100 volts?
10. How many B.t.u.'s are given off in an electric oven that takes 10
amperes at 110 volts for 1 hour? (1 B.t.u. equals 252 calories.)
11. An electric heater supplies heat at the rate of 700 B.t.u.'s an
hour. How much power does it require?
12. How many watts are required to operate 120 incandescent lamps in
parallel if each takes 0.5 amperes at 110 volts?
13. An electric lamp takes 12 amperes at a P.D. of 110 volts. How many
B.t.u.'s are radiated from it each second? How many calories?
14. If a 110-volt incandescent lamp is submerged for 10 minutes in 400
gr. of cold water while a current of 0.5 amperes is flowing, how many
degrees centigrade will the water be warmed?
15. In an electric furnace a current of 3000 amperes is used at a P.D.
of 10 volts. Find the heat developed in 1 minute.
16. How many candle power should a 20-watt tungsten lamp give if its
efficiency is one watt per candle power?
17. What is the "efficiency" of a 40-watt tungsten lamp if it gives 34
candle power?
Review Outline: Current Electricity
Produced by--Chemical action; voltaic and storage cells.
Three { Magnetic, electromagnet, uses and applications.
Principal { Chemical, electrolysis, applications.
Effects: { Heat, lighting and heating devices.
Theories: (a) of voltaic cells, (b) of electrolysis.
Units: Ampere, ohm, volt, watt, joule, kilowatt, horse power.
Measurement--(a) magnetic effect; galvanometer, ammeter, voltmeter,
wattmeter, Wheatstone bridge, construction
and use.
(b) chemical effect; voltameter.
Laws: (a) Right hand rules, for conductor and helix.
(b) Resistance, Conductors in series and parallel.
(c) Ohm's law, heat law, power law, 3 forms for each.
(d) Cells in parallel and series.
Problems: Upon applications of the laws and formulas studied.
Devices. { Voltaic cells; wet, dry, and Daniell.
and { Electrolysis and the storage battery.
Instruments: { Measuring instruments, electric bell, sounder,
{ heating and lighting devices.
Terms: Anode, cathode, electrolyte, ion, circuit switch, current,
e.m.f., resistance, potential.
CHAPTER XIV
INDUCED CURRENTS
(1) ELECTROMAGNETIC INDUCTION
=296. Current Induced by a Magnet.=--The discovery in 1819 that a
current in a conductor can deflect a magnetic needle or that it has a
magnetic effect, led to many attempts _to produce an electric current by
means of a magnet_. It was not until about 1831, however, that _Joseph
Henry_ in America and _Michael Faraday_ in England, independently
discovered how to accomplish this important result.
At the present time, voltaic cells produce but a very small part of the
current electricity used. Practically all that is employed for _power,
light, heat, and electrolysis is produced by the use of magnetic fields,
or by electromagnetic induction_.
=297. Laws of Induced Currents.=[M]--To illustrate how a current can be
produced by electromagnetic induction:
[M] An induced current is one produced by changing the number of
magnetic lines of force passing through a coil.
Connect a coil of 400 or more turns of No. 22 insulated copper wire
to a sensitive galvanometer. (See Fig. 279.) Now insert a bar
magnet in the coil. A sudden movement of the galvanometer will be
noticed, indicating the _production of a current_. When the magnet
stops moving, however, the current stops, and the coil of the
galvanometer returns to its first position. If now the magnet is
removed, a movement of the galvanometer coil _in the opposite
direction is_ noticed. This action may be repeated as often as
desired with similar results.
Careful experiments have shown that it is the _magnetic field_ of the
magnet that produces the action, and that only when the _number of
lines of force in the coil is changing_ do we find a current produced in
the coil. These facts lead to _Law I_. _Any change in the number of
magnetic lines of force passing through or cut by a coil will produce an
electromotive force in the coil._ In the account of the experiment just
given, _electric currents_ are produced, while in Law I, _electromotive
forces_ are mentioned. This difference is due to the fact that an E.M.F.
is _always_ produced in a coil when the magnetic field within it is
changed, while a current is found only when the coil is part of a
_closed circuit_. The inductive action of the earth's magnetic field
(see Fig. 280), may be shown by means of a coil of 400 to 500 turns a
foot in diameter.
[Illustration: FIG. 279.--The moving magnet induces a current in the
coil.]
[Illustration: FIG. 280.--A current may be induced by turning the coil
in the earth's magnetic field.]
Connect its ends to a sensitive galvanometer and hold it at right
angles to the earth's field. Then quickly revolve the coil through
180 degrees and note the movement of the galvanometer. Reverse the
coil and the galvanometer swings in the opposite direction.
If the magnet in Fig. 279 is moved _in_ and _out_ of the coil at first
_slowly_ and _later swiftly_, _small and large_ deflections of the
galvanometer coil are noticed. The quicker the movement of the magnetic
field the greater are the galvanometer deflections produced. This leads
to _Law II_. _The electromotive forces produced are proportional to the
number of lines of force cut per second._
=298. The magneto= is a device that illustrates the laws of induced
currents stated in Art. 297. The magneto (see Fig. 281), consists of
several permanent, "U"-shaped magnets placed side by side. Between the
poles of these magnets is placed a slotted iron cylinder having a coil
of many turns of fine insulated copper wire wound in the slot as in Fig.
282. The cylinder and coil form what is called an _armature_. The
armature is mounted so as to be revolved between the poles of the
"U"-shaped magnets by means of a handle. As the armature revolves, the
lines of force from the magnets pass through the coil first in one
direction and then in the other. This repeated change in the lines of
force passing through the coil produces an E.M.F. which may be felt by
holding in the hands the two wires leading from the armature coil. On
turning the armature _faster_ the current is felt _much stronger_,
showing that the E.M.F. in the coil increases as the rate of cutting the
magnetic lines of force by the coils increases.
[Illustration: FIG. 281.--A magneto.]
[Illustration: FIG. 282.--A shuttle armature.]
[Illustration: FIG. 283.--The induced current has a field which opposes
the motion of the magnet. The heavy line represents the direction of the
induced current.]
=299. Lenz's Law.=--While one is turning the armature of a magneto if
the two wires leading from its coil are connected, forming what is
called a "short circuit," the difficulty of turning the armature is at
once increased. If now the circuit is broken, the armature turns as
easily as at first. The increased difficulty in turning the armature is
due to the _current_ produced in the coil. This current sets up a
magnetic field of its own that opposes the field from the steel magnets.
This opposition makes it necessary for _work_ to be done to keep up the
motion of the coil when a current is passing through it. This fact is
called _Lenz's Law_. It may be expressed as follows: _Whenever a current
is induced by the relative motion of a magnetic field and a conductor,
the direction of the induced current is always such as to set up a
magnetic field that opposes the motion._ Lenz's Law follows from the
principle of conservation of energy, that energy can be produced only
from an expenditure of other energy. Now since an electric current
possesses energy, such a current can be produced only by doing
mechanical work or by expending some other form of energy. To illustrate
Lenz's Law, suppose that the north-seeking pole of a bar magnet be
inserted in a closed coil of wire. (See Fig. 283.) The current induced
in the coil has a direction such that its lines of force will pass
within the coil so as to _oppose_ the field of the bar magnet, when the
north pole of the magnet is inserted so as to point to the left. That
is, the north pole of the helix is at the right. Applying the right-hand
rule to the coil, its current will then be _counter clockwise_. On
withdrawing the magnet, the current reverses, becoming _clockwise_ with
its field passing to the left within the coil.
A striking illustration of the opposition offered by the field of the
induced current to that of the inducing field is afforded by taking a
strong electromagnet (see Fig. 284) and suspending a sheet of copper so
as to swing freely between the poles. When no current flows through the
magnet the sheet swings easily for some time. When, however, the coils
are magnetized, the copper sheet has induced within it, currents that
set up magnetic fields strongly opposing the motion, the swinging being
stopped almost instantly. The principle is applied in good ammeters and
voltmeters to prevent the swinging of the needle when deflected. The
current induced in the metal form on which is wound the galvanometer
coil is sufficient to make the needle practically "dead beat."
[Illustration: FIG. 284.--The magnetic field stops the swinging of the
sheet of copper.]
=300. The Magneto and the Dynamo.=--Magnetos are used to _develop small_
currents, such as are used for telephone signals, and for operating the
_sparking_ devices of gasoline _engines_. They are therefore found in
automobiles containing gasoline motors. The most important device for
producing electric currents by electromagnetic induction, however, is
the _dynamo_. It is employed whenever large currents are desired. The
principle of this device is similar to that of the magneto except that
it contains an _electromagnet_ for producing the magnetic field.
Since the electromagnet can develop a much stronger field than a
permanent magnet, the dynamo can produce a higher E.M.F. and a much
larger current than the magneto.
[Illustration: LORD KELVIN
"By Permission of the Berlin Photographic Co., New York."
Lord Kelvin (Sir William Thomson), (1824-1907). Professor of Physics,
Glasgow University. Invented the absolute scale of temperature: also
many practical electrical measuring instruments. The foremost physicist
of the latter part of the nineteenth century.]
[Illustration: MICHAEL FARADAY
"By Permission of the Berlin Photographic Co., New York."
Michael Faraday (1791-1867). Famous English Physicist. Made many
discoveries in electricity and magnetism; "Greatest experimentalist of
the nineteenth century."]
=301. The Magnetic Fields of Generators.=--In the magneto, the magnetic
field is produced by _permanent_ steel magnets. In dynamos powerful
_electromagnets_ are used. The latter are sometimes excited by currents
from some other source, but usually current from the armature is sent
around the field coils to produce the magnetic fields. Dynamos are
classified according to the manner in which the current is sent to their
field coils.
[Illustration: FIG. 285.--A series-wound dynamo.]
[Illustration: FIG. 286.--A shunt-wound dynamo.]
[Illustration: FIG. 287.--A compound-wound dynamo.]
_A._ The _series wound dynamo_ (see Fig. 285) is arranged so that _all_
of the current produced by the armature is sent through coils of coarse
wire upon the fields, after flowing through the external circuit.
_B._ The _shunt wound dynamo_ (see Fig. 286) sends a part only of the
current produced through the field coils. The latter are of many turns
of fine wire so as to use as little current as possible. The greater
part of the current goes to the main circuit. If the number of lamps or
motors connected to the main circuit is increased, the voltage is
lessened which weakens the current in the field coils, causing a weaker
field and still lower voltage, producing a fluctuating E.M.F. which is
unsatisfactory for many purposes. This fault is overcome by
_C._ the _compound wound dynamo_. This dynamo has both shunt and series
coils upon its fields. (See Fig. 287.) If more current is drawn into the
main circuit with this dynamo, the series coils produce a stronger field
compensating for the weaker field of the shunt coils, so that uniform
voltage is maintained. The compound wound generator is therefore the one
most commonly employed.
Important Topics
1. Laws of electromagnetic induction (a) conditions, (b) E.M.F., (c)
direction.
2. Devices, (a) magneto, (b) dynamo: series, shunt, compound.
3. Illustrations of the laws.
Exercises
1. Under what conditions may an electric current be produced by a
magnet?
2. Show how Lenz's Law, follows from the principle of conservation of
energy.
3. A bar magnet is fixed upright with its north-seeking pole upward. A
coil is thrust down over the magnet. What is the direction of the
current induced in the coil? Explain.
4. In what two ways may a current be induced in a closed coil?
5. What method is employed in the magneto? In the dynamo?
6. What is the nature of the current produced in the armature coil of a
magneto, that is, is it direct or alternating? Why?
7. What is the resistance of a 20-watt tungsten lamp if the E.M.F. is
115 volts?
8. Find the resistance of a 40-watt tungsten lamp when the voltage is
115? How much heat will it produce per minute?
9. An Edison storage battery cell on a test gave a discharge of 30
amperes. The average voltage was 1.19. What was the resistance of the
cell?
10. Eight storage cells are connected in series. Each has an E.M.F. of
1.2 volts and an internal resistance of 0.03 ohms. What will be the
current flowing through a voltmeter having 500 ohms resistance in
circuit with them?
(2) THE DYNAMO AND THE MOTOR
=302. The Dynamo= may be defined as a machine for transforming
mechanical energy into the energy of electric currents by
electromagnetic induction. Although electromagnetic induction was
discovered in 1821, practical dynamos were not built for about 40 years
or until between 1860 and 1870. The great development in the production
and use of electric currents has come since the latter date. The
principle parts of the dynamo are (a) the _field magnet_, (b) the
_armature_, (c) the _commutator_ or _collecting rings_, (d) the
_brushes_. Fig. 288 shows several common methods of arranging the field
coils and the armature.
[Illustration: FIG. 288.--Several methods of arranging the field coils
and the armature of a dynamo.]
[Illustration: FIG. 289.--A drum armature.]
The field coils vary in number and position. The purpose of their
construction is always to send the largest possible number of lines of
force through the armature. Some dynamos are _bipolar_, or have _two_
poles, others are multipolar or have more than two. In Fig. 288 No. 4
has four poles. The _armature_ of a dynamo differs from a magneto
armature in that it consists of a series of coils of insulated copper
wire wound in numerous slots cut in the surface of a cylindrical piece
of iron. Fig. 289 shows a _side_ view of the iron core of such an
armature. Iron is used to form the body of the armature since the
magnetic lines of force flow easily through the iron. The iron by its
permeability also concentrates and increases the magnetic flux. The best
armatures are made of many thin sheets of soft iron. These are called
_laminated_ armatures. An armature made of a solid piece of iron becomes
hot when revolving in a magnetic field. This is due to electric currents
induced in the iron itself. This heating is largely reduced by
_laminating_ the armature. Why?
[Illustration: FIG. 290.--Armature connected to slip rings producing an
alternating current.]
=303. Methods of Collecting Current from the Armature.=--The electric
currents produced in the armature are conducted away by _special sliding
contacts_. The stationary part of the sliding contact is called a
_brush_. The moving part is a _slip ring_ or a _commutator_. Fig. 290
shows an armature coil connected to slip rings. As the armature
revolves, the coils and slip rings revolve with it. The two ends of the
armature coils are connected to the two rings respectively. Now as the
armature revolves it cuts the lines of force first in one direction and
then in the other. This produces in the coils an E.M.F. first one way
and then the other. This E.M.F. sets up a current which is conducted to
the outside circuits through the slip rings and brushes. Such a current
which repeatedly reverses its direction is called an _alternating
current_. Fig. 291 (1) indicates graphically how the current moves
alternately one way and then the other. Alternating currents are
extensively used for electric _light, heat, and power_. _Direct
currents_ or those going continuously in one direction are however in
much demand especially for _street car service_, _for electrolysis_, and
for _charging storage batteries_.
=304. The Commutator.=--For a dynamo to deliver a _direct current_ it
must carry upon the shaft of the armature a _commutator_. The commutator
is used to _reverse_ the connections of the ends of the armature coils
at the instant that the current changes its direction in the armature.
This reversal of connection when the direction of current changes, keeps
the current in the outside circuit flowing in the same direction. Fig.
291 is a diagram of an armature with a commutator. The commutator is a
_split ring_, having as many parts or _segments_ as there are coils upon
the armature. The brushes touch opposite points upon the commutator as
they slide over the surface of the latter. Suppose that the armature
viewed from the commutator end rotates in a counter-clockwise direction,
also that the currents from the upper part move toward the commutator
and out the top brush.
[Illustration: FIG. 291.--The armature coils are connected to a
commutator producing a direct current.]
As the armature revolves, its coils soon begin to cut the force lines in
the opposite direction. This change in the direction of cutting the
lines of force causes the current to reverse in the coils of the
armature. At the instant the current changes in direction, what was the
upper segment of the commutator slips over into contact with the lower
brush, and the other segment swings over to touch the upper brush. Since
the current has reversed in the coils it continues to flow out of the
upper brush. This change in connection at the brushes takes place at
each half turn of the armature, just as the current changes in direction
in the coils. This is the manner in which the commutator of a dynamo
changes the alternating current produced in the armature coils, into a
direct current in the external circuit. Fig. 292 (1) represents
graphically an alternating current, (2) of the same figure shows current
taken from the brushes of the commutator of a dynamo with one coil on
the armature.
[Illustration: FIG. 292.--Graphic representation of (1) an alternating
current; (2) a pulsating current; (3) a continuous current.]
[Illustration: FIG. 293.--DeLaval multi-stage turbine and gear driving
750-kw., 750-r.p.m., 600-volt direct-current generator.]
A practical dynamo, however, has many coils upon its armature with a
corresponding number of segments upon the commutator. (See Figs. 289 and
293.) As each coil and commutator segment passes a brush, it contributes
an impulse to the current with the result that armatures with many coils
produce currents that flow quite evenly. (See Fig. 292, 3.)
The current represented in Fig. 292 (2) is called a _pulsating_ current.
[Illustration: FIG. 294.--A wire carrying a current across a magnetic
field is pushed sideways by the field.]
=305. The electric motor= is a machine which transforms the energy of an
electric current into mechanical energy or motion. The _direct current
motor_ consists of the same essential parts as a direct current dynamo,
viz., the field magnet, armature, commutator and brushes. Its operation
is readily comprehended after one understands the following experiment:
Set up two bar electromagnets with unlike poles facing each other about
an inch apart. A wire connected to a source of current is hung loosely
between the poles as in Fig. 294. The circuit through the wire should
contain a key or switch. If a current is sent through the electromagnets
and then another is sent through the wire, the latter will be found to
be pushed either up or down, while if the current is reversed through
the wire it is pushed in the opposite direction. These results may be
explained as follows:
Consider the magnetic field about a wire carrying a current (See Fig.
295.) If such a wire is placed in the magnetic field between two
opposite poles of an electromagnet (Fig. 296), the wire will be moved
either up or down. The reason for this is shown by the diagram in Fig.
297. Here a wire carrying a current and therefore surrounded by a
magnetic field passes across another magnetic field. The two fields
affect each other causing a crowding of the force lines either above or
below the wire. The wire at once tends to move sideways across the field
away from the crowded side. In the figure, the wire tends to move
downward.
[Illustration: FIG. 295.--The magnetic field about a wire carrying a
current.]
[Illustration: FIG. 296.--The magnetic field between two unlike poles.]
[Illustration: FIG. 297.--The crowding of the lines of force above the
wire, pushes it downward.]
In a practical motor, the wires upon the armature are so connected that
those upon one side (see Fig. 298), carry currents that pass in, while
on the other side they pass out. To represent the direction of the
current in the wires, the following device is employed; a circle with a
cross (to represent the feather in the tail of an arrow) indicates a
current going away from the observer, while a circle with a dot at its
center (to represent the tip of an arrow) indicates a current coming
toward the observer.
[Illustration: FIG. 298.--The crowding of the lines of force causes the
armature to revolve in a clockwise direction.]
In Fig. 298 the north pole is at the left and the south pole at the
right. The field of the magnets therefore passes from left to right as
indicated in the figure. Now in the armature the currents in the wires
on the left half of the armature are coming toward the observer while
those on the right move away. Applying the right-hand rule, the magnetic
lines will crowd _under_ the wires on the left side of the armature
while they will crowd _over_ the wires on the right side. This will
cause a rotation up on the left side and down on the right, or in a
_clockwise_ direction.
[Illustration: FIG. 299.--View of a one-half horse-power motor.]
If the current in the armature is reversed (in on the left and out on
the right), the lines of force will crowd the armature around in the
opposite direction or _counter clockwise_. The rotation of the armature
will also be reversed if, while the current in the armature is unchanged
in direction, the poles of the magnet are changed thus reversing the
magnetic field.
The motorman of a street car reverses the motion of his car by reversing
the direction of the current in the _armature_ of the motor.
[Illustration: FIG. 300.--The frame and electromagnet (at left), front
bracket and brush holder (at right) of the motor shown in Fig. 299.]
[Illustration: FIG. 301.--The armature of a motor.]
=306. Practical motors= have many coils upon the armature with a
corresponding number of segments upon the commutator. A large number of
coils and commutator segments enables some one of the coils to exert its
greatest efficiency at each instant, hence a steady force is provided
for turning the armature which causes it to run smoothly. Fig. 299
represents a 1/2 horse-power motor ready for use while Fig. 300 shows
the frame and poles and the front bracket and brush holder, and Fig. 301
represents the armature.
Important Topics
1. The dynamo, four essential parts, action (a) for alternating
currents, (b) for direct currents.
2. The electric motor: (a) essential parts, (b) action.
Exercises
1. _Why_ is an alternating current produced in the armature of a dynamo?
2. _How_ is this current produced? Give careful explanations.
3. What is the result of Lenz's law as applied to the dynamo?
4. Apply the first two laws of electromagnetic induction to the dynamo.
5. What is the power of a dynamo if it produces 40 amperes of current at
110 volts?
6. How much power must be applied to this dynamo if its efficiency is 90
per cent.?
7. A motor takes 10 amperes of current at 220 volts; what is the _power_
of the current in _watts_? If this motor has an efficiency of 95 per
cent., how many horse-power of mechanical energy can it develop?
8. Explain why reversing the current in the armature of a motor reverses
the direction of rotation.
9. Find the cost of running a washing machine using a 1/2-horsepower
motor 2 hours if the cost of the electricity is 10 cents a kilowatt
hour.
10. A 1/8-horse-power motor is used to run a sewing machine. If used for
3 hours what will be the cost at 11 cents a kilowatt hour?
(3) THE INDUCTION COIL AND THE TRANSFORMER
=307. The Induction Coil.=--Practically all electric currents are
produced either by voltaic cells or by dynamos. It is frequently found,
however, that it is desirable to change the E.M.F. of the current used,
either for purposes of _effectiveness_, _convenience_, _or economy_. The
_induction coil_ and the _transformer_, devices for changing the E.M.F.
of electric currents, are therefore in common use. _The induction coil_
(see Fig. 302) consists of a _primary_ coil of coarse wire _P_ (Fig.
303) wound upon a core of soft iron wire, and a _secondary_ coil, _S_,
of several thousand turns of fine wire. In circuit with the primary coil
is a battery, _B_, and a current interrupter, _K_, which works like the
interrupter upon an electric bell. The ends of the secondary coil are
brought to binding posts or spark points as at _D_.
[Illustration: FIG. 302.--An induction coil.]
The current from the battery flows through the primary coil magnetizing
the iron core. The magnetism in the core attracts the soft-iron end of
the interrupter, drawing the latter over and breaking the circuit at the
screw contact, _K_. This abruptly stops the current and at once the core
loses its magnetism. The spring support of the interrupter now draws the
latter back to the contact, _T_, again completing the circuit. The whole
operation is repeated, the interrupter vibrating rapidly continually
opening and closing the circuit.
[Illustration: FIG. 303.--Diagram showing the parts of an induction
coil.]
=308. The Production of Induced Currents in the Secondary Coil.=--When
the current flows through the _primary_ it sets up a magnetic field in
the _core_. When the current is interrupted, the field disappears. The
increase and decrease in the field of the core induces an E.M.F. in the
secondary coil, in accordance with the first law of electromagnetic
induction. The E.M.F. produced depends upon (a) the number of turns in
the secondary, (b) the strength of the magnetic field and (c) the rate
of change of the field. The rate of change in the field is more rapid at
the break than at the make. When the circuit is closed it takes perhaps
1/10 of a second for the current to build up to its full strength while
at a break the current stops in perhaps 0.00001 of a second, so that the
induced E.M.F. is perhaps 10,000 times as great at "break" as at make.
To increase the suddenness of the "make" and "break," a condenser is
often connected in the primary circuit, in parallel, with the
interrupter. (See Fig. 303, _C._) This condenser provides a place to
hold the rush of current at the instant that the interrupter breaks the
circuit. This stored up charge reinforces the current at the make
producing a much more sudden change in the magnetic field with a
corresponding increase in the E.M.F. The induced currents from induction
coils are sometimes called _faradic currents_ in honor of Faraday who
discovered electromagnetic induction. They are used to operate sparking
devices upon gas and gasoline engines and in many devices and
experiments in which high-tension electricity is employed.
[Illustration: FIG. 304.--The transformer has a closed core; the
induction coil, an open core.]
[Illustration: FIG. 305.--The laminated iron core of a transformer.]
[Illustration: FIG. 306.--Cross-section of the transformer shown in Fig.
305 showing the magnetic field around the primary and secondary coils.]
=309. The Transformer.=--This is like the induction coil in that it uses
a _primary_ and a _secondary_ coil, and an iron core to carry the
magnetic field. (See Fig. 304.) They differ in that the transformer has
a _closed_ core or one forming a continuous iron circuit, while the
induction coil has an _open_ core, or one in which the magnetic field
must travel in air from the north to the south poles of the core. The
transformer must always be used with an _alternating_ current while the
induction coil may use either a direct or an alternating current.
Further, the _induction_ coil always produces a higher E.M.F. while the
transformer may produce an E.M.F. in its secondary coil that is either
higher or lower than the one in the primary. The former is called
"_step-up_" while the latter is a "_step-down_" transformer. The
alternating current in the primary coil of the transformer produces an
_alternating magnetic flux_ in the iron core. This iron core is
_laminated_ (see Fig. 305) to prevent the heating that would result if a
solid core were used. The alternating magnetic flux induces in the
secondary coil an E.M.F. in accordance with the following rule. The
ratio of the _number_ of _turns_ in the _primary_ to the _number_ of the
_turns_ in the _secondary_ coil equals the ratio of the electromotive
forces in these respective coils. If the secondary coil has 8 turns
while the primary has 4, the E.M.F. of the secondary will be just twice
that of the primary. Or, if in the primary coil of the transformer Fig.
306 is an E.M.F. of 110 volts, in the secondary will be found an E.M.F.
of 220 volts.
[Illustration: FIG. 307.--A commercial transformer.]
=310. Uses of Transformers.=--In electric lighting systems, dynamos
often produce alternating currents at 1000 to 12,000 volts pressure. It
is very dangerous to admit currents at this pressure into dwellings and
business houses, so that transformers are installed just outside of
buildings to "step-down" the high voltage currents to 110 or 220 volts.
The lighting current that enters a house does not come directly from a
dynamo. It is an induced current produced by a transformer placed near
the house. (See Fig. 307.) In a perfect transformer the efficiency would
be 100 per cent. This signifies that the energy that is sent into the
primary coil of the transformer exactly equals the energy in the
secondary coil. The best transformers actually show efficiencies better
than 97 per cent. The lost energy appears as heat in the transformer.
"The transfer of great power in a large transformer from one circuit to
another circuit entirely separate and distinct, without any motion or
noise and almost without loss, is one of the most wonderful phenomena
under the control of man."
=311. The mercury arc rectifier= is a device for changing an alternating
current into a direct current. It is frequently used for charging
storage batteries where only alternating current is supplied by the
electric power company. It consists of an exhausted bulb containing two
carbon or graphite electrodes marked _G_ in Fig. 308 and a mercury
electrode marked _M_. It is found that current will pass through such a
bulb only from the graphite to the mercury but not in the reverse
direction. In operating the device, the secondary terminals of an
alternating current transformer _T_ are connected to the graphite
terminals of the rectifier. A wire connected to the center of the
secondary of the transformer at _C_ is attached to the _negative_
terminal of the storage battery _SB_. The _positive_ terminal of the
battery is connected to the mercury electrode of the rectifier tube
through a reactance or choke coil _R_. This coil serves to sustain the
arc between the alternations. _Sw_ is a starting switch, used only in
striking the arc. It is opened immediately after the tube begins to
glow.
[Illustration: FIG. 308.--Diagram of a mercury arc rectifier.]
Important Topics
Transformer, induction coil, mercury arc rectifier, construction,
action; uses of each.
Exercises
1. Does the spark of an induction coil occur at "make" or at "break?"
Why?
2. What must be the relative number of turns upon the primary and
secondary coils of a transformer if it receives current at 220 volts
and delivers current at 110? Also show by diagram.
3. Would the transformer work upon a direct current? Why?
4. Explain why the interrupter is a necessary part of the induction coil
and not of the transformer.
5. If a building used eighty 110-volt incandescent lamps, what would be
necessary to light them if they were joined in series? Why would this
not be practical?
6. If a 16-candle-power lamp requires 0.5 ampere upon a 110-volt circuit
what current and voltage will be needed to operate 12 such lamps in
parallel?
7. What will it cost to run these lamps 4 hours a night for 30 days at
10 cents per kilowatt hour?
8. If a mercury arc rectifier uses 5 amperes of current at 110 volts
alternating current to produce 5 amperes of direct current at 70 volts,
what is the efficiency of the rectifier?
9. Compute the heat produced in a 40 watt tungsten lamp in 1 minute.
10. Compute the heat produced in a 60 watt carbon incandescent lamp in 1
hour.
(4) THE TELEPHONE
=312. The Electric Telephone.=--This is an instrument for reproducing
the human voice at a distance by an electric current. The modern
electric telephone consists of at least four distinct parts (see Fig.
312); viz., a _transmitter_, an induction coil, an electric battery, and
a _receiver_. The first three of these are concerned in sending, or
_transmitting_ over the connecting wires a fluctuating electric current,
which has been modified by the waves of a human voice. The receiver, is
affected by the fluctuating current and reproduces the voice. It will be
considered first, in our study.
=313. The telephone receiver= was invented in 1876 by Alexander Graham
Bell. It consists of a permanent steel magnet, U shaped, with a coil of
fine insulated copper wire about each pole. (See Fig. 310.) A disc of
thin sheet iron is supported so that its center does not quite touch
the poles of the magnet. A hard rubber cap or ear piece with an opening
at its center is screwed on so as to hold the iron disc firmly in place.
[Illustration: FIG. 309.--The simplest telephone system. It consists of
two telephone receivers connected in series on a circuit. It will work,
but not satisfactorily.]
_The action of the receiver_ may be understood from the following
explanation: The electric current sent to the receiver, comes from the
secondary coil of the induction coil; it is an alternating current,
fluctuating back and forth just in time with the waves of the voice
affecting it at the transmitter. This alternating current flows around
the coils on the poles of the permanent magnet. When this current flows
in one direction, its magnetic field assists the field of the permanent
magnet, strengthening it. This stronger magnetic field draws the thin
iron disc in front of the poles of the magnet a little closer to them.
When the current in the coils flows the other way, its magnetic field
weakens the field of the steel magnet, and the disc is drawn back by the
force of its own elasticity. Thus the disc of the receiver vibrates with
the alternations of the current, and reproduces the same sounds that
were spoken into the transmitter.
[Illustration: FIG. 310.--A telephone receiver. This receiver has a
permanent horseshoe magnet with a coil about each pole.]
=314. The Telephone Transmitter.=--The telephone receiver just described
has great sensitiveness in reproducing sound, but it is not satisfactory
as a transmitter or sending apparatus. The _transmitter_ commonly used
is represented in cross-section in Fig. 311. In this figure, back of the
mouthpiece, is a thin carbon disc, _D_. Back of this disc is a circular
compartment containing granular carbon, _g_. The wires of the circuit
are connected to the carbon disc and to the back of the case containing
granular carbon. The circuit through the transmitter also includes a
voltaic or storage cell and the primary coil of an induction coil. (See
Fig. 312.)
[Illustration: FIG. 311.--A telephone transmitter.]
[Illustration: FIG. 312.--Telephone instruments at one end of a talking
circuit.]
=315. The action of the transmitter= is explained as follows: When the
sound waves of the voice strike upon the carbon disc, the latter
vibrates, alternately increasing and decreasing the pressure upon the
granular carbon. When the pressure _increases_, the electrical
resistance of the granular carbon is _lessened_, and when the pressure
upon it is _decreased_, its resistance _increases_. This changing
resistance causes fluctuations in the electric current _that_ correspond
exactly with the sound waves of the voice affecting it.
=316. A complete telephone system= operating with a local battery is
shown in Fig. 312. A person speaking into the transmitter causes a
fluctuation in the electric current in the transmitter as described in
Art. 315. This fluctuating current passes through the primary coil of
the induction coil _Ic_. This fluctuating current produces a fluctuating
magnetic field in its core. This fluctuating field induces an
_alternating_ current in the secondary coil which alternates just as the
primary current fluctuates, but with a much higher E.M.F. than the
latter. The alternating current passes to the receiver which reproduces
the speech as described in Art. 313. The line circuit includes the
secondary of the induction coil, the receiving instrument and the
receiver of the sending instrument so that the voice is reproduced in
both receivers. An electric bell is placed at each station to call the
attention of parties wanted. The movement of the receiver hook when the
receiver is lifted, disconnects the bell and closes the talking circuit.
The latter is opened and the bell connected when the receiver is hung up
again.
[Illustration: FIG. 313.--Diagram of a telephone system as used in a
large exchange.]
In cities and towns, the telephone system in use differs from the one
described in usually having one large battery placed in the central
exchange, instead of dry cells at each instrument. (See Fig. 313.) Also
the operator at _central_ is called by simply taking the receiver from
the hook instead of being "rung up" by the subscriber. The operations of
the transmitter, induction coil and receiver, however, are the same in
all telephones.
Important Topics
1. Receiver: parts, action.
2. Transmitter: parts, action.
3. Induction coil, bell, line wires, etc.
4. Action of the whole device.
Exercises
1. State three important electrical laws or principles that are employed
in the operation of the telephone. What is the application of each?
2. Connect the binding posts of a telephone receiver with a sensitive
galvanometer and press on the diaphragm of the receiver; a deflection of
the galvanometer will be noticed. Release the diaphragm and a reflection
in the opposite direction is seen. Explain.
3. Is the current passing through the transmitter the one going to the
receiver of the instrument? Explain.
4. Does the receiver at the telephone used by a person repeat the speech
of the person? Explain.
5. How many 0.5 ampere lamps can be used with a 6 ampere fuse?
6. Why is it necessary to have a rheostat connected in series with a
stereopticon or moving picture machine while a rheostat is not used with
arc lights out doors?
7. How many candle power should a 60 watt carbon incandescent lamp give,
if its efficiency is 3.4 watts per candle power?
8. Three incandescent lamps having resistances of 100, 150, and 240
ohms, respectively, are connected in parallel. What is their combined
resistance?
Review Outline: Induced Currents
Induced currents; 3 laws, illustrations.
Construction, action, and uses of--magneto, dynamo, induction coil,
transformer, motor, telephone. Mercury arc rectifier.
Terms--primary, secondary, for coils and currents, armature, commutator,
slip ring, brush, rectifier, open core, series, shunt, and compound
connections for dynamos.
CHAPTER XV
SOUND
(1) SOUND AND WAVE MOTION
=317. What is a Sound?=--This question has two answers, which may be
illustrated as follows: Suppose that an alarm clock is set so that it
will strike in one week and that it is placed upon a barren rock in the
Pacific Ocean by sailors who immediately sail away. If when the tapper
strikes the bell at the end of the week no ear is within a hundred
miles, is any sound produced? The two view-points are now made evident,
for some will answer "no" others "yes." Those answering "no" hold that
sound is a _sensation_ which would not be produced if no ear were at
hand to be affected. Those answering "yes" understand, by the term
sound, _a mode of motion capable of affecting the auditory nerves_, and
that sound exists wherever such motions are present. This latter point
of view is called the _physical_ and is the one we are to use in this
study.
[Illustration: FIG. 314.--The tuning fork is vibrating.]
=318. Source of Sound.=--If we trace any sound to its source, it will be
found to originate in a body in rapid motion usually in what is called a
state of _vibration_. To illustrate, take a tuning fork, strike it to
set it in vibration and place its stem firmly against a thin piece of
wood; the sound will be strengthened materially by the vibration of the
wood. If now the vibrating fork is placed with the tips of the prongs in
water, the vibration is plainly shown by the spattering of the water
(Fig. 314). When one _speaks_, the vibrating body is in the _larynx_ at
the top of the windpipe. Its vibration may be plainly felt by the hand
placed upon the throat while speaking.
=319. Sound Media.=--Usually sounds reach the ear through the air. The
air is then said to be a _medium for sound_. Other substances may serve
as a sound medium, for if the head is under water and two stones, also
under water, are struck together a sharp sound is heard. Also if one end
of a wooden rod is held at the ear and the other end of the rod is
scratched by a pin, the sound is more plainly perceived through the wood
than through the air. Think of some illustration from your own
experience of a solid acting as medium for sound. If an electric bell is
placed in a bell jar attached to an air pump, as in Fig. 315, on
exhausting the air the loudness of the sound is found to diminish,
indicating that in a perfect vacuum no sound would be transmitted. This
effect of a vacuum upon the transmission of sound is very different from
its effect upon radiation of heat and light. Both heat and light are
known to pass through a vacuum since both come to the earth from the sun
through space that so far as we know contains no air or other matter.
Sound differs from this in that it is always transmitted by some
material body and cannot exist in a vacuum.
[Illustration: FIG. 315.--Sound does not travel in a vacuum.]
=320. Speed of Sound.=--Everyone has noticed that it takes time for
sound to travel from one place to another. If we see a gun fired at a
distance, the report is heard a few seconds after the smoke or flash is
seen. The time elapsing between a flash of lightning and the thunder
shows that sound takes time to move from one place to another. Careful
experiments to determine the speed of sound have been made. One method
measures accurately the time required for the sound of a gun to pass
between two stations several miles apart. A gun or cannon is placed at
each station. These are fired alternately, first the one at one station
and then the one at the other so as to avoid an error in computation due
to the motion of wind. This mode of determining the speed of sound is
not accurate. Other methods, more refined than the one just described
have given accurate values for the speed of sound. The results of a
number of experiments show that, at the freezing temperature, 0°C., the
speed of sound in air is 332 meters or 1090 ft. a second. The speed of
sound in air is affected by the temperature, increasing 2 ft. or 0.6
meter per second for each degree that the temperature rises above 0°C.
The speed decreases the same amount for each degree C. that the air is
cooled below the freezing point. The speed of sound in various
substances has been carefully determined. It is greater in most of them
than in air. In water the speed is about 1400 meters a second; in wood,
while its speed varies with different kinds, it averages about 4000
meters a second; in brass the speed is about 3500 meters; while in iron
it is about 5100 meters a second.
=321. The Nature of Sound.=--We have observed that sound originates at a
vibrating body, that it requires a medium in order to be transmitted
from one place to another, and that it travels at a definite speed in a
given substance. Nothing has been said, however, of the _mode_ of
transmission, or of the _nature_ of _sound_. Sounds continue to come
from an alarm clock even though it is placed under a bell jar. It is
certain that nothing material can pass through the glass of the jar.
If, however, we consider that _sound is transmitted by waves through
substances_ the whole matter can be given a simple explanation. In order
to better understand the nature of sound a study of waves and wave
motion will be taken up in the next section.
Important Topics
Sound: two definitions, source, medium, speed, nature.
Exercises
1. Give two illustrations from outside the laboratory of the fact that
sound is transmitted by other materials than air.
2. Name the vibrating part that is the source of the sound in three
different musical instruments.
3. Is sound transmitted more strongly in solids, liquids or gases? How
do you explain this?
4. How far away is a steamboat if the sound of its whistle is heard 10
seconds after the steam is seen, the temperature being 20°C.? Compute in
feet and in meters.
5. How many miles away is lightning if the thunder is heard 12 seconds
after the flash in seen, the temperature being 25°C.?
6. Four seconds after a flash of lightning is seen the thunder clap is
heard. The temperature is 90°F. How far away was the discharge?
7. The report of a gun is heard 3 seconds after the puff of smoke is
seen. How far away is the gun if the temperature is 20°C.?
8. An explosion takes place 10 miles away. How long will it take the
sound to reach you, the temperature being 80°F?. How long at 0°F.?
9. How long after a whistle is sounded will it be heard if the distance
away is 1/4 mile, the temperature being 90°F.?
10. The report of an explosion of dynamite is heard 2 minutes after the
puff of smoke is seen. How far away is the explosion the temperature
being 77°F.?
(2) WAVES[N] AND WAVE MOTION
[N] A wave is a disturbance in a substance or medium that is
transmitted through it.
=322. Visible Waves.=--It is best to begin the study of wave motion by
considering some waves which are familiar to most persons. Take for
example the waves that move over the surface of water (Fig. 316). These
have an onward motion, yet boards or chips upon the surface simply rise
and fall as the waves pass them. They are not carried onward by the
waves. The water surface simply rises and falls as the waves pass by.
Consider also the waves that may be seen to move across a field of tall
grass or grain. Such waves are produced by the bending and rising of the
stalks as the wind passes over them. Again, waves may be produced in a
rope fastened at one end, by suddenly moving the other end up and down.
These waves move to the end of the rope where they are _reflected_ and
return. The three types of waves just mentioned are illustrations of
_transverse_ waves, the ideal case being that in which the particles
move at _right angles_ to the path or course of the wave. Such waves are
therefore called _transverse_ waves.
[Illustration: FIG. 316.--Water waves.]
=323. Longitudinal waves.=--Another kind of wave is found in bodies that
are elastic and compressible and have inertia, such as gases and coiled
wire springs. Such waves may be studied by considering a wire spring as
the medium through which the waves pass. (See Fig. 318.)
[Illustration: FIG. 317.--The compression wave travels through the
spring.]
If the end of the wire spring shown in Fig. 317 is struck the first few
turns of the spring will be compressed. Since the spring possesses
elasticity, the turns will move forward a little and compress those
ahead, these will press the next in turn and so on. Thus a _compression_
wave will move to the end of the spring, where it will be reflected and
return. Consider the turns of the spring as they move toward the end.
On account of their _inertia_ they will continue moving until they have
separated from each other _more_ than at first, before returning to
their usual position. This condition of a greater separation of the
turns of the spring than usual is called a _rarefaction_. It moves along
the spring following the wave of compression. The condensation and
rarefaction are considered as together forming a complete wave. Since
the turns of wire move back and forth in a direction parallel to that in
which the wave is traveling, these waves are called _longitudinal_.
[Illustration: FIG. 318.--Longitudinal waves (1) in a spring, (2) in
air, and (3) graphic representation showing wave length, condensations,
and rarefactions.]
=324. The transmission of a sound by the air= may be understood by
comparing it with the process by which a _wave is transmitted by a wire
spring_. Consider a light spring (Fig. 318, 1) attached at the end of a
vibrating tuning fork, _K_, and also to a diaphragm, _D_. Each vibration
of the fork will first compress and then separate the coils of the
spring. These impulses will be transmitted by the spring as described in
Art. 315, and cause the diaphragm to vibrate _at the same rate_ as the
tuning fork. The diaphragm will then give out a sound similar to that of
the tuning fork. Suppose that the spring is replaced by air, and the
diaphragm, by the ear of a person, _E_, (Fig. 318, 2.) when the prong
of the fork moves toward the ear it starts a compression and when it
moves back a rarefaction. The fork continues vibrating and these
impulses move onward like those in the spring at a speed of about 1120
ft. in a second. They strike the diaphragm of the ear causing it to move
back and forth or to vibrate at the same rate as the tuning fork, just
as in the case of the diaphragm attached to the spring.
=325. Graphic Representation of Sound waves.=--It is frequently
desirable to represent sound waves graphically. The usual method is to
use a curve like that in (Fig. 318, 3). This curve is considered as
representing a train of waves moving in the same direction as those in
Fig. 318 1 and 2, and also having the same length. The part of the wave
_A-B_ represents a condensation of the sound wave and the part _B-C_
represents a rarefaction. A complete wave consisting of a condensation
and a rarefaction is represented by that portion of the curve _A-C_. The
portion of the curve _B-D_ also represents a _full wave length_ as the
latter is defined as _the distance between two corresponding parts of
the adjacent waves_. The curve, Fig. (318, 3) represents not only the
wave length, but also the height of the wave or the amount of movement
of the particles along the wave. This is called the _amplitude_ and is
indicated by the distance _A-b_. Since the _loudness_ or intensity of a
sound is found to depend upon the amount of movement of the particles
along the wave, the _amplitude_ of the curve is used to indicate the
loudness of the sound represented. All of the characteristics of a sound
wave may be graphically represented by curves. Such curves will be used
frequently as an aid in explaining the phenomena of wave motion both in
sound and in light.
=326. Reflections of Sound.=--It is found that a wave moving along a
wire spring is reflected when it reaches the end and returns along the
spring. Similarly a sound wave in air is reflected upon striking the
surface of a body. If the wave strikes perpendicularly it returns along
the line from which it comes, if, however, it strikes at some other
angle it does not return along the same line, but as in other cases of
reflected motion, the _direction_ of the _reflected_ wave is described
by the _Law of Reflected Motion_ as follows: _The angle of reflection is
always equal to the angle of incidence_. This law is illustrated in Fig.
319. Suppose that a series of waves coming from a source of sound move
from _H_ to _O_. After striking the surface _IJ_ the waves are reflected
and move toward _L_ along the line _OL_. Let _PO_ be perpendicular to
the surface _IJ_ at _O_. Then _HOP_ is _the angle_ of incidence and
_LOP_ is the _angle of reflection_. By the law of reflected motion these
angles are equal. In an ordinary room when a person speaks the sound
waves reflected from the smooth walls reinforce the sound waves moving
directly to the hearers. It is for this reason that it is usually easier
to speak in at room than in the open air. Other illustrations of the
reinforcement of sound by reflection are often seen. Thus an _ear
trumpet_ (Fig. 320), uses the principle of reflection and concentration
of sound. So-called _sounding boards_ are sometimes placed back of
speakers in large halls to reflect sound waves to the audience.
[Illustration: FIG. 319.--Law of reflection.]
[Illustration: FIG. 320.--An ear trumpet.]
=327. Echoes.=--_An echo is the repetition of a sound caused by its
reflection from some distant surface_ such as that of a building, cliff,
clouds, trees, etc. The interval of time between the production of a
sound and the perception of its echo is the time that the sound takes to
travel from its source to the reflecting body and back to the listener.
Experiments have shown that the sensation of a sound persists about
one-tenth of a second. Since the velocity of sound at 20°C. is about
1130 ft. per second, during one-tenth of a second the sound wave will
travel some 113 ft. If the reflecting surface is about 56 ft. distant a
_short_ sound will be followed immediately by its echo as it is heard
one-tenth of a second after the original sound. The reflected sound
tends to strengthen the original one if the reflecting surface is less
than 56 ft. away. If the distance of the reflecting surface is much more
than 56 ft. however, the reflected sound does not blend with the
original one but forms a distinct echo. The echoes in large halls
especially those with large smooth walls may very seriously affect the
clear perception of the sound. Such rooms are said to have poor
_acoustic_ properties. Furniture, drapery, and carpets help to deaden
the echo because of diffused reflection. The Mormon Tabernacle at Salt
Lake City, Utah, is a fine example of a building in which the reflecting
surfaces of the walls and ceiling are of such shape and material that
its acoustic properties are remarkable, a pin dropped at one end being
plainly heard at the other end about 200 ft. away.
Important Topics
1. Waves: transverse, longitudinal; wave length, condensation,
rarefaction.
2. Wave motion: in coiled spring, in air, on water.
3. Reflection of waves: law, echoes.
Exercises
1. A hunter hears an echo in 8 seconds after firing his gun. How far is
the reflecting surface if the temperature is 20°C.?
2. How far is the reflecting surface of a building if the echo of one's
footsteps returns in 1 second at 10°C.?
3. Why is it easier to speak or sing in a room than out of doors?
4. Draw a curve that represents wave motion. Make it exactly three full
wave lengths, and state why your curve shows this length. Indicate the
parts of the curve that correspond to a condensation and to a
rarefaction.
5. How long does it take the sound of the "pin drop" to reach a person
at the farther end of the building mentioned at the end of Art. 327?
6. An echo is heard after 6 seconds. How far away is the reflecting
surface, the temperature being 70°F.?
7. Why are outdoor band-stands generally made with the back curving over
the band?
8. A man near a forest calls to a friend. In 4 seconds the echo comes
back. How far away is he from the forest?
9. Would it be possible for us ever to hear a great explosion upon the
moon? Explain.
10. If a sunset gun was fired exactly at 6:00 P.M. at a fort, at what
time was the report heard by a man 25 miles away, if the temperature was
10°C.?
(3) INTENSITY AND PITCH OF SOUNDS
[Illustration: FIG. 321.--Graphic representations of (_a_) a noise,
(_b_) a musical sound.]
=328. Musical Sounds and Noises Distinguished.=--The question is
sometimes raised, what is the difference between a _noise_ and a
_musical sound_? The latter has been found to be produced by an even and
regular vibration such as that of a tuning fork or of a piano string. A
noise on the other hand is characterized by sudden or irregular
vibrations such as those produced by a wagon bumping over a stony
street. These differences may be represented graphically as in Fig. 321,
(a) represents a noise, (b) a musical tone.
[Illustration: FIG. 322.--Curve _b_ represents a tone of greater
intensity.]
=329. Characteristics of Musical Sounds.=--Musical tones differ from one
another in three ways or are said to have _three characteristics_, viz.,
_intensity_, _pitch_, and _quality_. Thus two sounds may differ only in
intensity or _loudness_, that is, be alike in all other respects except
this one, as when a string of a piano is struck at first gently, and
again harder. The second sound is recognized as being louder. The
difference is due to the greater _amplitude_ of vibration caused by more
energy being used. Fig. 322 shows these differences graphically. Curve
_b_ represents the tone of greater intensity or loudness, since its
amplitude of vibration is represented as being greater.
=330. Conditions Affecting the Intensity of Sound.=--The intensity of
sounds is also affected by the _area_ of the vibrating body. This is
shown by setting a tuning fork in vibration. The area of the vibrating
part being small, the sound is heard but a short distance from the fork.
If, however, the stem of the vibrating fork is pressed against the panel
of a door or the top of a box, the sound may be heard throughout a room.
The stem of the fork has communicated its vibrations to the wood. The
vibrating area, being greater, the sound is thereby much increased in
intensity, producing a wave of greater amplitude. The same principle is
employed in the sounding boards of musical instruments as in the piano,
violin, etc. It is a common observation that sounds decrease in
loudness as the distance from the source increases. This is due to the
increase of the surface of the spherical sound waves spreading in all
directions from the source. Careful experiments have shown that in a
uniform medium _the intensity of a sound is inversely proportional to
the square of the distance from its source_. If a sound is confined so
that it cannot spread, such as the sound moving through a speaking tube,
it maintains its intensity for a considerable distance. An _ear trumpet_
(see Fig. 320) also applies this principle. It is constructed so that
sound from a given area is _concentrated_ by reflection to a much
smaller area with a corresponding increase in intensity. The _megaphone_
(Fig. 323), and the _speaking trumpet_ start the sound waves of the
voice in one direction so that they are kept from spreading widely,
consequently by its use the voice may be heard several times the usual
distance. The intensity of a sound is also affected by the _density_ of
the transmitting medium. Thus a sound produced on a mountain top is
fainter and thinner than one produced in a valley. The sound of a bell
in the receiver of an air pump becomes weaker as the air is exhausted
from the latter. _Four_ factors thus influence the intensity of a sound,
the _area_ of the vibrating body, its _amplitude_ of vibration, the
_distance_ of the source and the _density_ of the transmitting medium.
It is well to fix in mind the precise effect of each of these factors.
[Illustration: FIG. 323.--The megaphone.]
=331. Pitch.=--The most characteristic difference between musical sounds
is that of _pitch_. Some sounds have a high pitch, such as those
produced by many insects and birds. Others have a low pitch as the notes
of a bass drum or the sound of thunder. How notes of different pitch
are produced may be shown by the siren (Fig. 324). This is a disc
mounted so as to be rotated on an axis. Several rows of holes are
drilled in it in concentric circles. The number of holes in successive
rows increases from within outward. If when the siren is rapidly rotated
air is blown through a tube against a row of holes a clear musical tone
is heard. The tone is due to the succession of pulses in the air
produced by the row of holes in the rotating disc alternately cutting
off and permitting the air blast to pass through at very short
intervals. If the blast is directed against a row of holes nearer the
circumference the pitch is higher, if against a row nearer the center
the pitch is lower. Or if the blast is sent against the same row of
holes the pitch rises when the speed increases and lowers when the speed
lessens. These facts indicate that the pitch of a tone is due to the
number of pulses or vibrations that strike the ear each second; also
that _the greater the rate of vibration, the higher the pitch_.
[Illustration: FIG. 324.--A siren.]
=332. The Major Scale.=--If a siren is made with eight rows of holes, it
may indicate the relation between the notes of a _major scale_. To
accomplish this, the number of holes in the successive rows should be
24, 27, 30, 32, 36, 40, 45, 48. If a disc so constructed is rapidly
rotated at a uniform rate, a blast of air sent against all of the rows
in succession produces the tones of the scale. These facts indicate that
the relative vibration numbers of the notes of any _major scale_ have
the same relation as the numbers 24, 27, 30, 32, 36, 40, 45, 48.
The note called middle C is considered by physicists as having 256
vibrations a second. This would give the following _actual vibration_
numbers to the remaining notes of the major scale that begins with
"Middle C" D.-288, E.-320, F.-341.3, G.-384, A.-426.6, B.-480, C'.-512.
Musicians, however, usually make use of a scale of slightly higher
pitch. The _international_ standard of pitch in this country and in
Europe is that in which "A" has 435 vibrations per second. This
corresponds to 261 vibrations for middle C.
=333. The Relation between Speed, Wave Length, and Number of Vibrations
per Second.=--Since the notes from the various musical instruments of an
orchestra are noticed to harmonize as well at a distance as at the place
produced, it is evident that notes of all pitches travel at the same
rate, or have the _same speed_. Notes of high pitch, having a high
vibration rate produce more waves in a second than notes of low pitch,
consequently the former are shorter than the latter. The following
formula gives the relation between the speed (_v_), wave length (_l_),
and number of vibrations per sec. (_n_):
_v_ = _l_ × _n_, or _l_ = _v/n_
that is, _the speed of a sound wave is equal to the number of vibrations
per second times the wave length, or the wave length is equal to the
speed divided by the number of vibrations per second_. This formula may
also be employed to find the _number_ of vibrations when the wave length
and speed are given.
Important Topics
1. Difference between noise and music.
2. Factors affecting intensity: area, amplitude, density, distance.
3. Pitch, major scale, relative vibration numbers.
4. Relation between speed, wave length and vibration rate.
Exercises
1. Give an illustration from your own experience of each of the factors
affecting intensity.
2. Write the relative vibration numbers of a major scale in which _do_
has 120 vibrations.
3. What is the wave length of the "A" of international concert pitch at
25°C.? Compute in feet and centimeters.
4. At what temperature will sound waves in air in unison with "Middle C"
be exactly 4 ft. long?
5. Explain the use of a megaphone.
6. What tone has waves 3 ft. long at 25°C.?
7. What is the purpose of the "sounding board" of a piano?
8. Two men are distant 1000 and 3000 ft. respectively from a fog horn.
What is the relative intensity of the sounds heard by the two men?
9. The speaking tone of the average man's voice has 160 vibrations per
second. How long are the waves produced by him at 20°C.?
(4) MUSICAL SCALES AND RESONANCE
=334. A musical interval= _refers to the ratio between the pitches[O] of
two notes_ as indicated by the results of the siren experiment. The
simplest interval, or ratio between two notes is the _octave_, C':C, or
2:1 (48:24). Other important intervals with the corresponding ratios are
the _fifth_, G:C, or 3:2 (36:24); the _sixth_, A:C, or 5:3 (40:24); the
_fourth_, F:C, 4:3 (32:24); the _major third_, E:C, or 5:4 (30:24); and
the _minor third_, G:E, 6:5. The interval between any two notes may be
determined by finding the ratio between the vibration numbers of the two
notes. Thus, if one note is produced by 600 vibrations a second and
another by 400, the interval is 3:2, or a _fifth_, and this would be
recognized by a musician who heard the notes sounded together or one
after the other. Below is a table of musical nomenclatures, showing
various relations between the notes of the major scale.
[O] Pitch as used here, means _vibration rate_.
TABLE OF MUSICAL NOMENCLATURES
---------------------+---+------+------+------+------+------+-------+----
Name of note | C | D | E | F | G | A | B | C´
---------------------+---+----- +----- +------+------+------+-------+----
Frequency in terms of|_n_|9/8_n_|5/4_n_|4/3_n_|3/2_n_|5/3_n_|15/8_n_|2_n_
"do" | | | | | | | |
---------------------+---+--+---+--+---+--+---+--+---+--+---+---+---+----
Intervals | 9/8 | 10/9 | 16/15| 9/8 | 10/9 | 9/8 | 16/15
---------------------+---+--+---+--+---+--+---+--+---+--+---+---+---+----
Name of note in vocal|do | re | mi | fa | sol | la | ti | do
music | | | | | | | |
---------------------+---+------+------+------+------+------+-------+----
Treble clef.
[Music]
Bass clef.
[Music]
---------------------+---+------+------+------+------+------+-------+----
International pitch | | | | | | | |
of treble clef |261| 293.6| 326.3| 348. | 391.5| 435 | 489.4 | 522
---------------------+---+------+------+------+------+------+-------+----
Scientific scale |256| 288 | 320 | 341.3| 384 | 426.6| 480 | 512
---------------------+---+------+------+------+------+------+-------+----
Relative vibration | 24| 27 | 30 | 32 | 36 | 40 | 45 | 48
numbers | | | | | | | |
---------------------+---+------+------+------+------+------+-------+----
=335. Major and Minor Triads.=--The notes C, E, G (_do_, _mi_, _sol_)
form what is called a _major triad_. The _relative vibration numbers_
corresponding are 24, 30, 36. These in simplest terms have ratios of
4:5:6. Any three other tones with vibration ratios of 4:5:6 will also
form a major triad. If the octave of the lower tone is added, the four
make a major chord. Thus: F, A, C´ (_fa_, _la_, _do_), 32:40:48, or
4:5:6, also form a major triad as do G, B, D´ (_sol_, _ti_, _re_),
36:45:54, or 4:5:6. Inspection will show that these three major triads
comprise all of the tones of the major scale D´ being the octave of D.
It is, therefore, said that the major scale is based, or built, upon
these three major triads. The examples just given indicate the
mathematical basis for harmony in music. Three notes having vibration
ratios of 10:12:15 are called _minor triads_. These produce a less
pleasing effect than those having ratios of 4:5:6.
=336. The Need for Sharps and Flats.=--We have considered the key of C.
This is represented upon the piano or organ by white keys only (Fig.
325). Now in order (a) to give variety to instrumental selections, and
(b) to accommodate instruments to the range of the human voice, it has
been necessary to introduce other notes in musical instruments. These
are represented by the _black keys_ upon the piano and organ and are
known as _sharps_ and _flats_. To illustrate the necessity for these
additional notes take the major scale starting with B. This will give
vibration frequencies of 240, 270, 300, 320, 360, 400, 450, and 480. The
only white keys that may be used with this scale are E 320 and B 480
vibrations. Since the second note on this scale requires 270 vibrations
about halfway between C and D the black key C sharp is inserted. Other
notes must be inserted between D and E (D sharp), between F and G (F
sharp), also G and A sharps.
[Illustration: FIG. 325.--Section of a piano keyboard.]
=337. Tempered Scales.=--In musical instruments with fixed notes, such
as the harp, organ, or piano, complications were early recognized when
an attempt was made to adapt these instruments so that they could be
played in all keys. For the vibration numbers that would give a perfect
major scale starting at C are not the same as will give a perfect major
scale beginning with any other key. In using the various notes as the
keynote for a major scale, 72 different notes in the octave would be
required. This would make it more difficult for such instruments as the
piano to be played. To avoid these complications as much as possible, it
has been found necessary to abandon the simple ratios between successive
notes and to substitute another ratio in order that the vibration ratio
between any two successive notes will be equal in every case. The
differences between semitones are abolished so that, for example, C
sharp and D flat become the same tone instead of two different tones.
Such a scale is called a _tempered scale_. The tempered scale has 13
notes to the octave, with 12 equal intervals, the ratio between two
successive notes being the ¹²√2 or 1.059. That is, any vibration rate on
the tempered scale may be computed by multiplying the vibration rate of
the preceding note by 1.059. While this is a necessary arrangement,
there is some loss in perfect harmony. It is for this reason that a
quartette or chorus of voices singing without accompaniment is often
more harmonious and satisfactory than when accompanied with an
instrument of fixed notes as the piano, since the simple harmonious
ratios may be employed when the voices are alone. The imperfection
introduced by _equal temperament tuning_ is illustrated by the following
table:
C D E F G A B C
Perfect Scale of C 256.0 288.0 320.0 341.3 384.0 426.6 480.0 512.0
Tempered Scale 256.0 287.3 322.5 341.7 383.6 430.5 483.3 512.0
=338. Resonance.=--If two tuning forks of the same pitch are placed near
each other, and one is set vibrating, the other will soon be found to be
in vibration. This result is said to be due to _sympathetic vibration_,
and is an example of _resonance_ (Fig. 326). If water is poured into a
glass tube while a vibrating tuning fork is held over its top, when the
air column has a certain length it will start vibrating, reinforcing
strongly the sound of the tuning fork. (See Fig. 327.) This is also an
example of resonance. These and other similar facts indicate that _sound
waves started by a vibrating body will cause another body near it to
start vibrating if the two have the same rate of vibration_. Most
persons will recall illustrations of this effect from their own
experience.
[Illustration: FIG. 326.--One tuning fork will vibrate in sympathy with
the other, if they have exactly equal rates of vibration.]
[Illustration: FIG. 327.--An air column of the proper length reinforces
the sound of the tuning fork.]
=339. Sympathetic vibration= is explained as follows: Sound waves
produce very slight motions in objects affected by them; if the
vibration of a given body is exactly in time with the vibrations of a
given sound each impulse of the sound wave will strike the body so as to
increase the vibratory motion of the latter. This action continuing, the
body soon acquires a motion sufficient to produce audible waves. A good
illustration of sympathetic vibration is furnished by the bell ringer,
who times his pulls upon the bell rope with the vibration rate of the
swing of the bell. In the case of the resonant air column over which is
held a vibrating tuning fork (see Fig. 328), when the prong of the fork
starts downward from 1 to 2, a condensation wave moves down to the water
surface and back just in time to join the condensation wave _above_ the
fork as the prong begins to move from 2 to 1; also when the prong
starts upward from 2 to 1, the rarefaction produced under it moves to
the bottom of the air column and back so as to join the rarefaction
_above_ the fork as the prong returns. While the prong is making a
_single_ movement, up or down, it is plain that the air wave moves twice
the length of the open tube. During a _complete_ vibration of the fork,
therefore, the sound wave moves four times the length of the air column.
In free air, the sound progresses a wave length during a complete
vibration, hence the resonant air column is one-fourth the length of the
sound wave to which it responds. Experiments with tubes cf different
lengths show that the diameter of the air column has some effect upon
the length giving best resonance. About 25 per cent. of the diameter of
the tube must be added to the length of the air column to make it just
one-fourth the wave length. The sound heard in seashells and in other
hollow bodies is due to resonance. Vibrations in the air too feeble to
affect the ear are intensified by sympathetic vibration until they can
be heard. A tuning fork is often mounted upon a box called a
_resonator_, which contains an air column of such dimensions that it
reinforces the sound of the fork's sympathetic vibration.
[Illustration: FIG. 328.--Explanation of resonance.]
Important Topics
1. Musical intervals: octave, sixth, fifth, fourth, third.
2. Major chord, 4:5:6.
3. Use of sharps and flats. Tempered scale.
4. Resonance, sympathetic vibration, explanation, examples.
Exercises
1. What is a major scale? Why is a major scale said to be built upon
three triads?
2. Why are sharps and flats necessary in music?
3. What is the tempered scale and why is it used? What instruments need
not use it? Why?
4. Mention two examples of resonance or sympathetic vibration from your
own experience out of school.
5. An air column 2 ft. long closed at one end is resonant to what wave
length? What number of vibrations will this sound have per second at
25°C.?
6. At 24°C. What length of air column closed at one end will be resonant
to a sound having 27 vibrations a second?
7. A given note has 300 vibrations a second. What will be the number of
vibrations of its (a) octave, (b) fifth, (c) sixth, (d) major third?
8. In the violin or guitar what takes the place of the sounding board of
the piano?
9. Can you explain why the pitch of the bell on a locomotive rises as
you rapidly approach it and falls as you recede from it?
10. Do notes of high or low pitch travel faster? Explain.
11. An "A" tuning fork on the "international" scale makes 435 vibrations
per second. What is the length of the sound waves produced?
(5) WAVE INTERFERENCE, BEATS, VIBRATION OF STRINGS
=340. Interference of waves.=--The possibility of two trains of waves
combining so as to produce a reduced motion or a _complete destruction_
of motion may be shown graphically. Suppose two trains of waves of equal
wave length and amplitude as in Fig. 329 meet in _opposite phases_. That
is, the parts corresponding to the _crests_ of _A_ coincide with the
_troughs_ of _B_, also the troughs of _A_ with the crests of _B_; when
this condition obtains, the result is that shown at _C_, the union of
the two waves resulting in complete destruction of motion. _The more or
less complete destruction of one train of waves by another similar train
is an illustration of_ =interference=. If two sets of water waves so
unite as to entirely destroy each other the result is a level water
surface. If two trains of sound waves combine they may so interfere that
silence results. The conditions for securing interference of sound waves
may readily be secured by using a tuning fork and a resonating air
column. If the tuning fork is set vibrating and placed over the open end
of the resonating air column (see Fig. 328), an increase in the sound
through resonance may be heard. If the fork is rotated about its axis,
in some positions no sound is heard while in other positions the sound
is strongly reinforced. Similar effects may be perceived by holding a
vibrating fork near the ear and slowly rotating as before. In some
positions interference results while in other positions the sound is
plainly heard. The explanation of interference may be made clear by the
use of a diagram. (See Fig. 330.) Let us imagine that we are looking at
the two square ends of a tuning fork. When the fork is vibrating the two
prongs approach each other and then recede. As they approach, a
condensation is produced at 2 and rarefactions at 1 and 3. As they
separate, a rarefaction is produced at 2 and condensations at 1 and 3.
Now along the lines at which the simultaneously produced rarefactions
and condensations meet there is more or less complete interference. (See
Fig. 331.) These positions have been indicated by dotted lines extending
through the ends of the prongs. As indicated above, these positions may
be easily found by rotating a vibrating fork over a resonant air column,
or near the ear.
[Illustration: FIG. 329.--Interference of sound waves.]
[Illustration: FIG. 330.--At 2 is a condensation; at 1 and 3 are
rarefactions.]
[Illustration: FIG. 331.--The condensations and rarefactions meet along
the dotted lines producing silence.]
[Illustration: FIG. 332.--Diagram illustrating the formations of beats.]
=341. Beats.=--If two tuning forks of slightly different pitch are set
vibrating and placed over resonating air columns or with the stem of
each fork upon a sounding board, so that the sounds may be intensified,
a peculiar pulsation of the sound may be noticed. This phenomenon is
known as _beats_. Its production may be easily understood by considering
a diagram (Fig. 332). Let the curve _A_ represent the sound wave sent
out by one tuning fork and _B_, that sent out by the other. _C_
represents the effect produced by the combination of these waves. At _R_
the two sound waves meet in the _same phase_ and reinforce each other.
This results in a louder sound than either produces alone. Now since the
sounds are of slightly different pitch, one fork sends out a few more
vibrations per second than the other. The waves from the first fork are
therefore a little shorter than those from the other. Consequently,
although the two waves are at one time in the _same_ phase, they must
soon be in opposite phases as at _I_. Here interference occurs, and
silence results. Immediately the waves reinforce, producing a louder
sound and so on alternately. The resulting rise and fall of the sound
are known as _beats_. The number of beats per second must, of course, be
the same as the difference between the numbers of vibrations per second
of the two sounds. One effect of beats is _discord_. This is especially
noticeable when the number of beats per second is between 30 and 120.
Strike the two lowest notes on a piano at the same time. The beats are
very noticeable.
[Illustration: FIG. 333.--Turkish cymbals.]
[Illustration: FIG. 334.--The cornet.]
=342. Three Classes of Musical Instruments.=--There are three classes or
groups of musical instruments, if we consider the vibrating body that
produces the sound in each: (A) Those in which the sound is produced by
a vibrating _plate_ or _membrane_, as the drum, cymbals (Fig. 333),
etc.; (B) those with vibrating _air columns_, as the flute, pipe organ,
and cornet (Fig. 334), and (C) with vibrating _wires_ or _strings_, as
the piano, violin, and guitar. It is worth while to consider some of
these carefully. We will begin with a consideration of vibrating wires
and strings, these often producing tones of rich quality.
Let us consider the strings of a piano. (If possible, look at the
strings in some instrument.) The range of the piano is 7-1/3 octaves.
Its lowest note, A_{4}, has about 27 vibrations per second. Its highest,
C⁴, about 4176. This great range in vibration rate is secured by varying
the length, the tension, and the diameter of the strings.
=343. The Laws of Vibrating Strings.=--The relations between the
vibration rate, the length, the tension and the diameter, of vibrating
strings have been carefully studied with an instrument called a
_sonometer_ (Fig. 335). By this device it is found that the pitch of a
vibrating string is raised one octave when its vibrating length is
reduced to one-half. By determining the vibration rate of many lengths,
the following law has been derived: (Law I) _The rate of vibration of a
string is inversely proportional to its length._
[Illustration: FIG. 335.--A sonometer.]
Careful tests upon the change of vibration rate produced by a change of
_tension_ or pull upon the strings show that if the pull is increased
four times its vibrations rate is _doubled_, and if it is increased nine
times its rate is tripled, that is: (Law II) _The vibration rates of
strings are directly proportional to the square roots of their
tensions._
Tests of the effects of diameter are made by taking wires of equal
length and tension and of the same material but of different diameter.
Suppose one is twice as thick as the other. This string has a tone an
octave lower or vibrates one-half as fast as the first. Therefore: (Law
III) _The vibration rates of strings are inversely proportional to the
diameters._ These laws may be expressed by a formula _n_ ∝√(_t_)/_dl_.
The vibration of a string is rarely a simple matter. It usually vibrates
in parts at the same time that it is vibrating as a whole. The tone
produced by a string vibrating as a whole is called its _fundamental_.
The vibrating parts of a string are called _loops_ or _segments_ (see
Fig. 336), while the points of least or no vibration are _nodes_.
Segments are often called _antinodes_.
[Illustration: FIG. 336.--A string yielding its fundamental and its
first overtone.]
=344. Overtones.=--The _quality_ of the tone produced by a vibrating
string is affected by its vibration in parts when it is also vibrating
as a whole. (See Fig. 336.) The tones produced by the vibration in parts
are called _overtones_ or _partial_ tones. The presence of these
overtones may often be detected by the sympathetic vibration of other
wires near-by. What is called the _first_ overtone is produced by a
string vibrating in _two_ parts, the _second_ overtone by a string
vibrating in _three parts_, the _third_ overtone by its vibration in
_four_ parts and so on. In any overtone, the number of the parts or
vibrating segments of the string is one more than the number of the
overtone. For example, gently press down the key of middle C of a piano.
This will leave the string free to vibrate. Now strongly strike the C an
octave lower and then remove the finger from this key. The middle C
string will be heard giving its tone. In like manner try E¹ and G¹,
with C. This experiment shows that the sound of the C string contains
these tones as overtones. It also illustrates sympathetic vibration.
Important Topics
1. Interference, beats, production, effects.
2. Vibration of strings, three laws.
3. Three classes of musical instruments.
4. Fundamental and overtones, nodes, segments, how produced? Results.
Exercises
1. What different means are employed to produce variation of the pitch
of piano strings? For violin strings?
2. How many beats per second will be produced by two tuning forks having
512 and 509 vibrations per second respectively?
3. A wire 180 cm. long produces middle C. Show by a diagram, using
numbers, where a bridge would have to be placed to cause the string to
emit each tone of the major scale.
4. How can a violinist play a tune on a single string?
5. What are the frequencies of the first 5 overtones of a string whose
fundamental gives 256 vibrations per second?
6. One person takes 112 steps a minute and another 116. How many times a
minute will the two walkers be in step? How many times a minute will one
be advancing the left foot just when the other advances the right?
7. Why is it necessary to have a standard pitch?
8. How can the pitch of the sounds given by a phonograph be lowered?
9. How many beats per second will occur when two tuning forks having
frequencies of 512 and 515 respectively, are sounded together?
10. Which wires of a piano give the highest pitch? Why?
(6) TONE QUALITY, VIBRATING AIR COLUMNS, PLATES
=345. Quality.=--The reason for the _differences in tone quality_
between notes of the same pitch and intensity as produced, _e.g._, by a
violin and a piano, was long a matter of conjecture. Helmholtz, a German
physicist (see p. 397) first definitely proved that tone quality is due
to the _various overtones_ present along with the fundamental and _their
relative intensities_. If a tuning fork is first set vibrating by
drawing a bow across it and then by striking it with a hard object, a
difference in the _quality_ of the tones produced is noticeable. It is
thus evident that the manner of setting a body in vibration affects the
overtones produced and thus the quality. Piano strings are struck by
felt hammers at a point about one-seventh of the length of the string
from one end. This point has been selected by experiment, it having been
found to yield the best combination of overtones as shown by the quality
of the tone resulting.
[Illustration: FIG. 337.--Chladni's plate.]
[Illustration: FIG. 338.--Chladni's figures.]
=346. Chladni's Plate.=--The fact that vibrating bodies are capable of
many modes of vibration is well illustrated by what is known as
Chladni's plate. This consists of a circular or square sheet of brass
attached to a stand at its center so as to be held horizontally. (See
Fig. 337.) Fine sand is sprinkled over its surface and the disc is set
vibrating by drawing a violin bow across its edge. The mode of
vibration of the disc is indicated by the sand accumulating along the
lines of least vibration, called _nodal lines_. A variety of nodal lines
each accompanied by its characteristic tone may be obtained by changing
the position of the bow and by touching the fingers at different points
at the edge of the disc. They are known as Chladni's figures. (See Fig.
338.)
[Illustration: FIG. 339.--Manometric flame apparatus.]
=347. Manometric Flames.=--The actual presence of overtones along with
the fundamental may be made _visible_ by the _manometric flame
apparatus_. This consists of a wooden box, _C_, mounted upon a stand.
(See Fig. 339.) The box is divided vertically by a flexible partition or
diaphragm. Two outlets are provided on one side of the partition, one,
_C_, leads to a gas pipe, the other is a glass tube, _D_. On the other
side of the partition a tube, _E_, leads to a mouthpiece. A mirror, _M_,
is mounted so as to be rotated upon a vertical axis in front of _F_ and
near it. Gas is now turned on and lighted at _F_. The sound of the voice
produced at the mouthpiece sends sound waves through the tube and
against the diaphragm which vibrates back and forth as the sound waves
strike it. This action affects the flame which rises and falls. If now
the mirror is rotated, the image of the flame seen in the mirror rises
and falls, showing not only the fundamental or principal vibrations but
also the overtones. If the different vowel sounds are uttered in
succession in the mouthpiece, each is found to be accompanied by its
characteristic wave form (Fig. 340). In some, the fundamental is
strongly prominent, while in others, the overtones produce marked
modifications. Other devices have been invented which make possible the
accurate analysis of sounds into their component vibrations, while still
others unite simple tones to produce any complex tone desired.
=348. The Phonograph.=--The _graphophone_ or _phonograph_ provides a
mechanism for cutting upon a disc or cylinder a groove that reproduces,
in the varying form or depth of the tracing, every peculiarity of the
sound waves affecting it. The reproducer consists of a sensitive
diaphragm to which is attached a needle. The disc or cylinder is rotated
under the reproducing needle. The irregularities of the bottom of the
tracing cause corresponding movements of the needle and the attached
diaphragm, which start waves that reproduce the sounds that previously
affected the recorder. The construction of the phonograph has reached
such perfection that very accurate reproduction of a great variety of
sounds is secured.
[Illustration: FIG. 340.--Characteristic forms of manometric flames.]
=349. Wind Instruments.=--In many musical instruments as the _cornet_,
_pipe-organ_, _flute_, etc., and also in _whistles_, the vibrating body
that serves as a source of sound is _a column of air_, usually enclosed
in a tube. Unlike vibrating strings, this vibrating source of sound
changes but little in tension or density, hence changes in the pitch of
air columns is secured by changing their length. The law being similar
to that with strings, _the vibration rates of air columns are inversely
proportional to their lengths_.
[Illustration: FIG. 341.--(_R_) Cross-section of an organ pipe showing
action of tongue at _C_. (_a_) The fundamental tone in a closed pipe has
a wave length four times the length of the pipe; (_b_) and (_c_) how the
first and second overtones are formed in a closed pipe; (_d_) the
fundamental tone of an open pipe has a wave length equal to twice the
length of the pipe; (_e_) and (_f_) first and second overtones of open
pipe.]
If an _open_ organ pipe be sounded by blowing gently through it, a tone
of definite pitch is heard. Now if one end is closed, on being sounded
again the pitch is found to be an octave lower. Therefore, _the pitch of
a closed pipe is an octave lower than that of an open one of the same
length_.
=350. Nodes in Organ Pipes.=--Fig. 341, _R_ represents a cross-section
of a wooden organ pipe. Air is blown through _A_, and strikes against a
thin tongue of wood _C_. This starts the jet of air vibrating thus
setting the column of air in vibration so that the sound is kept up as
long as air is blown through _A_. To understand the mode of vibration of
the air column a study of the curve that represents wave motion (Fig.
342) is helpful Let _AB_ represent such a curve, in this 2, 4 and 6
represent nodes or points of least vibration, while 1, 3 and 5 are
antinodes or places of greatest motion. A full wave length extends from
1-5, or 2-6. Now in the open organ pipe (Fig. 341_d_), the end of the
air column _d_ is a place of great vibration or is an antinode. At the
other end also occurs another place of great vibration or an antinode;
between these two antinodes must be a place of least vibration or a
node. The open air column therefore extends from antinode to antinode
(or from 1-3) or is _one-half_ a wave length. _The closed air column_
(Fig. 341_a_) extends from a place of _great_ vibration at _a_ to a
place of _no_ vibration at the closed end. The distance from an antinode
to a node is that from 1-2 on the curve and is _one-fourth_ a wave
length.
[Illustration: FIG. 342.--Graphic representation of sound waves.]
[Illustration: FIG. 343.--A clarinet.]
When a pipe is blown strongly it yields overtones. The _bugle_ is a
musical instrument in which notes of different pitch are produced by
differences in blowing. (See Fig. 341.) (_d_), (_e_), (_f_). In playing
the _cornet_ different pitches are produced by differences in blowing,
and by valves which change the length of the vibrating air column. (See
Fig. 334.) The _clarinet_ has a mouthpiece containing a reed similar to
that made by cutting a tongue on a straw or quill. The length of the
vibrating air column in the clarinet is changed by opening holes in the
sides of the tube. (See Fig. 343.)
=351. How we Hear.=--Our hearing apparatus is arranged in three parts.
(See Fig. 344.) _The external ear_ leads to the _tympanum_. _The middle
ear_ contains three bones that convey the vibrations of the tympanum to
the _internal ear_. The latter is filled with a liquid which conveys the
vibrations to a part having a coiled shell-like structure called the
_Cochlea_. Stretched across within the cochlea are some 3000 fibers or
strings. It is believed that each is sensitive to a particular vibration
rate and that each is also attached to a nerve fiber. The sound waves of
the air transmitted by the tympanum, the ear bones and the liquid of the
internal ear start sympathetic vibrations in the strings of the cochlea
which affect the auditory nerve and we hear. The highest tones
perceptible by the human ear are produced by from 24,000 to 40,000
vibrations per second. The average person cannot hear sounds produced by
more than about 28,000 vibrations. The usual range of hearing is about
11 octaves. The tones produced by higher vibrations than about 4100 per
second are shrill and displeasing. In music the range is 7-1/3 octaves,
the lowest tone being produced by 27.5 vibrations, the highest by about
4100 per second.
[Illustration: FIG. 344.--The human ear.]
The tones produced by men are lower than those of women and boys. In men
the vocal cords are about 18 mm. long; in women they are 12 mm. long.
The compass of the human voice is about two octaves, although some
noted singers have a range of two and one-half octaves. In ordinary
conversation the wave length of sounds produced by a man's voice is from
8 to 12 ft. and that of a woman's voice is from 2 to 4 ft.
Important Topics
1. Tone quality. Fundamental and overtones. Chladni's plate.
2. Manometric flame apparatus.
3. Phonograph recorder and reproducer.
4. Air columns and wind instruments.
5. How we hear.
Exercises
1. What determines the pitch of the note of a toy whistle?
2. The lowest note of the organ has a wave length of about 64 ft. What
is the length of a closed pipe giving this note? Of an open pipe?
3. What is the first overtone of C? What are the second and third
overtones? Give vibration numbers and pitch names or letters.
4. Why is the music of a band just as harmonious at a distance of 400
ft. as at 100 ft.?
5. A resonant air column 60 cm. long closed at one end will respond to
what rate of vibration at 10°C.?
6. Can you find out how the valves on a cornet operate to change the
pitch of the tone?
7. How is the trombone operated to produce tones of different pitch?
8. The lowest note on an organ has a wave length of about 64 ft. What
must be the length of a closed pipe giving this note?
9. What is the approximate length of an open organ pipe which sends out
waves 4 ft. long?
Review Outline: Sound
Sound--definition, source, medium, speed, nature.
Waves--longitudinal, transverse, illustrations.
Characteristics of { intensity--area, amplitude, density, distance.
Musical Sounds: { pitch--scales; major, tempered, triads, _N_ =
{ _V_/_L_ quality--fundamental and overtones.
Sympathetic Vibrations--resonance, interference, beats, discord.
Musical Instruments--string, air column, membrane or plate.
Laws of; (a) vibrating strings (3), (b) vibrating air columns (2).
CHAPTER XVI
LIGHT
(1) LIGHT, ITS RECTILINEAR PROPAGATION, SHADOWS
=352. A Comparison of Sound and Light.=--Light from the standpoint of
physics is considered much as is _sound_, as a _mode_ of _motion_; one
affecting the ear, the other producing the result called _vision_. There
are other differences also worth considering. (a) While sound travels as
vibrations of some _material_ medium, light travels only as vibrations
of the _ether_; solids, liquids, and gases act so as to hinder rather
than to assist in its movement. That is, light travels best in a vacuum
or in a space devoid of ordinary matter. (b) The _speed_ of light is so
great that at ordinary distances on the earth its motion is practically
instantaneous. Experiments have shown that its speed is about 186,000
miles to 300,000 kilometers a second.
=353. Luminous and Illuminated Bodies.=--If we consider the objects
within a room, some of them, as books and furniture, would be invisible
if all light from external sources were excluded. On the other hand,
some other objects, such as a lighted lamp, a burning coal, or a red hot
iron, would be seen if no outside light were present. Such bodies are
said to be luminous. Most luminous bodies are hot and become
non-luminous on cooling. There are, however, some bodies that are
luminous at ordinary room temperatures, as the firefly and some
phosphorescent paints. When light emitted by a luminous body strikes an
object, a portion of it is always _reflected_. It is this reflected
light that makes the illuminated object _visible_. If the object is a
sheet of glass, some of the light is _transmitted_. If a substance is so
clear that objects can be seen through it, the substance is
_transparent_, but if objects cannot be seen through it, the substance
is said to be _translucent_. Objects transmitting no light are _opaque_.
Some of the light falling upon a body is neither reflected nor
transmitted, but is _absorbed_ and tends to warm the body. The light
falling upon a body is therefore either _reflected_, _transmitted_, or
_absorbed_. Thus Fig. 345 represents light coming from _S_ to a piece of
glass _GL_. A portion of the light represented by _R_ is reflected.
Another part _A_ is absorbed and disappears, while still another part
_T_ is transmitted and passes on.
[Illustration: FIG. 345.--The light is transmitted (_T_), reflected
(_R_), or absorbed (_A_).]
There is no sharply drawn line between transparent and opaque bodies.
Very thin sheets of gold transmit a greenish light, and experiments have
shown that substances as transparent as clear water absorb enough light
so that at considerable depths in an ocean or lake little or no light is
ever found. All light whether from luminous bodies or reflected from
non-luminous objects shows certain properties which will now be
considered.
=354. The Rectilinear Propagation of Light.=--If a beam of light passes
through a hole in a window shade into a darkened room, it is seen to
follow a perfectly straight course. If a person while coughing holds a
book before the face, the sound passes around the book and is heard at
any point in the room while the face is hidden by the book. In other
words, light ordinarily does not pass around corners as sound does, but
travels in _straight lines_. This fact is made use of when one aims a
gun or merely looks at an object. So well established in our minds is
the idea that an _object_ is in the direction from which we see the
light coming to us from it, that we are sometimes deceived as to the
real position of an object, when the course of the light from it has
been changed by a mirror or some other reflecting surface. Many
_illusions_ are produced in this way, of which the _mirage_ of the
desert is one example. (See Art. 381.)
[Illustration: FIG. 346.--Shadow from a small source of light.]
[Illustration: FIG. 347.--Shadow when source of light is large.]
=355. Shadows.=--_A shadow is the space from which light is cut off by
an opaque body._ Thus if a book (see Fig. 346) is held between a screen,
_N_, and a _small_ source of light, _L_, a shadow is produced which
extends from the book to the screen. Notice that the shadow is a _space_
and not an _area_. If a _large_ gas flame (see Fig. 347) is used as the
source of light, the shadow of the book is no longer clear cut at the
edges as before, but has a darker central part with a lighter fringe of
partial shadow at the edges. The dark portion within the shadow has all
the light excluded from it and is called the _umbra_. The lighter
portion of the shadow at the edges has only a part of the light from the
flame cut off. This portion is called the _penumbra_. when one stands in
sunlight his shadow extends from his body to the ground or object on
which the shadow falls. At night we are in the earth's shadow, which
extends out into space beyond the earth.
[Illustration: FIG. 348.--Character of the earth's shadow.]
=356. Eclipses.=--Since the sun is a very large object the shadow cast
by the earth contains both umbra and penumbra. (See Fig. 348.) When the
moon passes into the shadow of the earth, there is said to be an eclipse
of the moon, while if the moon's shadow falls upon the earth, the
portion of the earth cut off from the sun's light has an eclipse of the
sun.
=357. Images by Small Apertures.=--The straight line movement of light
makes possible the _pin-hole_ camera, by which satisfactory photographs
have been made. The action of this device may be illustrated by placing
a luminous body, a lighted candle, an incandescent lamp, or a gas flame,
in front of a piece of cardboard, _S_, which has a small opening in it.
Light from the object (see Fig. 349) falls upon a screen, _S_{2}_, so as
to produce an _inverted image_. Other applications of this principle
will be given later.
In Fig. 349 let _PQ_ represent a gas flame, then light from point
_P_ at the _top_ of the flame will pass in a straight line through
the opening or aperture of the cardboard and strike at _P_{2}_ at
the _bottom_ of the illuminated spot upon the screen. Light from
_Q_ passing in straight lines through the aperture will strike at
_Q_{2}_ at the top of the lighted space. This spot of light will
have the same outlines as the luminous body _PQ_ and being formed
as just described will be _inverted_.
[Illustration: FIG. 349.--Image formed by a small aperture is inverted.]
This spot of light, resembling in its outlines the flame, is called an
_image_. _An image is defined as an optical counterpart of an object_.
Images are formed in a variety of devices, such as _apertures_,
_mirrors_, and _lenses_. The _pin-hole camera_ is simply a light-tight
box with a small aperture in one side. Light passing through this
aperture forms an image upon the opposite side of the interior of the
box, of whatever object is in front of the camera. Light entering a room
through a _large_ aperture such as a window produces a multitude of
overlapping images which blend to form a somewhat evenly illuminated
surface.
Important Topics
1. Light contrasted with sound (three differences).
2. Bodies: transparent, translucent, opaque.
3. Light: reflected, transmitted, absorbed.
4. Light travels in straight lines, evidence, shadows, umbra, penumbra.
5. Formation of images by small apertures.
Exercises
1. Consider the circumference of the earth as 25,000 miles. How many
times would the speed of light cover this distance in a second?
2. How soon after any great disturbance takes place on the sun,
93,000,000 miles distant, can it be seen upon the earth?
3. Construct a diagram of the moon's shadow. How much of the sun can one
see when in the moon's umbra? When in its penumbra? Have you ever been
in either? When? Have you ever been in the earth's umbra? In its
penumbra?
4. Explain, using a diagram, the formation of an inverted image by a
small aperture.
5. If the sun is 45 degrees above the horizon, what is the height of a
pole casting a shadow 60 ft. long?
6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically
upon a walk, how tall is the tree whose shadow is 42 ft. long, both
measurements being made at the same time?
7. Why are the shadows caused by an electric arc lamp so sharply
defined?
8. Why should schoolroom windows be all on one side and reach to the
ceiling?
9. What is the relation between the size of an image and its distance
from the aperture forming it? Can you prove this by geometry?
10. What are silhouettes and how are they produced?
(2) PHOTOMETRY AND THE LAW OF REFLECTION
=358. Photometry.=--It is desirable at times to compare the intensities
of illumination produced by light from different sources. This is done
to determine the _relative cost or effectiveness_ of various illuminants
such as candles, kerosene and gas lamps, and electric lights The process
of determining the relative intensity of lights or lamps is called
photometry. (_Photos_ = light.)
The unit for measuring the power of light is called a _candle power_. It
is the light produced by a sperm candle burning 120 grains per hour. An
ordinary gas light burns 5 or more cubic feet of gas per hour and yields
from 15 to 25 candle power. A Welsbach gas lamp, consuming 3 cu. ft. per
hour, produces 50 to 100 candle power.
Instead of using candles, for practical photometry, incandescent lamps
standardized by the Bureau of Standards are used for testing or
calibration purposes.
It is necessary to distinguish between the intensity of a _luminous_
body, _i.e._, as a source of light, and the _intensity_ of
_illumination_ upon some surface produced by a light. It is considered
that two sources of light are of _equal intensity_ if they produce equal
illumination at equal distances.
=359. Law of Intensity of Light.=--A device for measuring the candle
power of a light is called a _photometer_. Its use is based upon the
_law of intensity of light_. _The intensity of illumination of a surface
is inversely proportional to the square of its distance from the source
of light._ This relation is similar to that existing between the
intensity of a sound and the distance from its source. The following
device illustrates the truth of this law in a simple manner.
[Illustration: FIG. 350.--The light spreads over four times the area at
twice the distance.]
Cut a hole 1 in. square in a large sheet of cardboard (_K_) and
place the card in an upright position 1 meter from an arc light or
other _point source_ of light (_L_). Now rule inch squares upon
another card (_M_) and place it parallel to the first card and 2
meters from it. (See Fig. 350.) The light that passed through the
hole of 1 sq. in. at a distance of 1 meter is spread over 4 sq.
in. at a distance of 2 meters. Therefore, the intensity of
illumination on each square inch of _M_ is one-fourth that upon the
surface of _K_. If _M_ is placed 3 meters from the light, 9 sq. in.
are illuminated, or the intensity is one-ninth that at 1 meter
distance.
[Illustration: FIG. 351.--The Bunsen photometer.]
These relations show that the intensity of illumination is inversely
proportional to the square of the distance from the source of light. An
application of the law of intensity is made in using a simple (Bunsen)
photometer. This consists of a card containing a spot soaked with oil or
melted wax. (See Fig. 351.) The lights whose intensities are to be
compared are placed upon opposite sides of the card. The card is then
adjusted so that the spot appears the same on both sides. The
illumination is now equal on both sides of the card and the _candle
powers of the two lights are proportional to the squares of their
distances from the card_. The simple device just described will give
approximate results only. For accurate results more elaborate apparatus
is required.
=360. Measurement of the Intensity of Illumination.=--A standard candle
(Art. 358) produces when lighted 1 candle power. The illumination caused
by this upon a surface 1 ft. away and at right angles to the light rays
is called a =foot-candle=. It is the unit of intensity of illumination.
A 4-candle-power lamp, at a distance of 1 ft., produces 4 foot-candles.
A 16-candle-power lamp at a distance of 2 ft. also produces 4
foot-candles--(16 ÷ 2²).
The intensity of illumination required for a good light for seeing
varies with the conditions. Thus, for stage and store lighting about 4
foot-candles are needed, while homes and churches may require but 1
foot-candle.
Too great an intensity of illumination is as harmful as not enough.
Exposed lights having an intensity of more than 5 candle power per
square inch are often a cause of eye trouble. Such lights should be
protected by frosted globes.
A pleasing form of lighting for large halls and public buildings is the
_indirect system_. In this, the lamps are hidden by reflectors which
throw the light upon the ceiling from which it is diffused over the
room. This form of lighting is more expensive than other systems since
but a part of the light is reflected. Its cost therefore is an important
factor when considering its use.
=361. The Reflection of Light.=--The light reflected from the surfaces
of bodies about us gives us information concerning our surroundings. A
knowledge of the behavior of light undergoing reflection is not usually
gained from ordinary observation. The law of reflection of light may be
shown, however, by an experiment.
[Illustration: FIG. 352.--_B´_ is as far back of the mirror as _B_ is in
front of it.]
[Illustration: CHRISTIAN HUYGENS
(Popular Science Monthly)
Christian Huygens (1629-1695). Dutch physicist; invented the pendulum
clock (1656); developed the wave theory of light; discovered
polarization of light (1690).]
[Illustration: H. V. HELMHOLTZ
"By Permission of the Berlin Photographic Co., New York."
Hermann von Helmholtz (1821-1894) Germany. Established the doctrine of
conservation of energy; made many discoveries in sound; invented the
ophthalmoscope; established the physical basis of tone quality.]
A plane mirror, _M_, is held in a vertical position resting upon a
sheet of paper. (See Fig. 352.) Pins are set upright in the paper
at _A_ and _B_. On placing the eye along the line _AC_ and looking
toward the mirror an image of _B_ may be seen in the mirror due to
the light reflected from its surface. Pins _C_ and _D_ are now set
in the paper so that when one looks along the line _BD_ toward the
mirror one may see all four pins apparently in one line. This
indicates that the light from _A_ and _C_ passing along _CA_ toward
_O_ is reflected back along the light _CBD_. By means of a ruler,
draw lines through _BD_ and _AC_ till they intersect at _O_. Also
draw _PO_ perpendicular to the mirror at _O_.
Then the angles _AOP_ and _BOP_ will be found equal. These are called
the angles of _incidence_ and _reflection_ respectively. _The law of
reflection_ is therefore stated: _The angle of reflection is equal to
the angle of incidence._ These angles are in the same plane, that of the
paper. This law applies in all cases of reflection of light. It is
similar to the law of reflection of sound (Art. 326.)
Important Topics
1. Photometry, law of intensity, candle power, foot-candle.
2. Intensity of illumination.
3. Reflected light and law of reflection.
Exercises
1. Both sides of a card are equally illuminated when two lights are on
opposite sides of it and 10 and 30 cm. respectively from it. what are
their relative intensities?
2. What are the relative intensities of illumination from a gas light
upon a book 6 ft. and 2 ft. respectively from the light?
3. Which is more expensive per candle power? How many times as
expensive? A 50-watt 16-candle-power incandescent lamp at 10 cents per
kilowatt-hour or a 100-candle-power Welsbach light burning 5 cu. ft. of
gas per hour at 80 cents per 1000 cu. ft. of gas. (Find cost of each per
hour, and then the cost of 1 candle power hour for each.)
4. Why are not ordinary shadows perfectly dark?
5. At what distance will a 16-candle-power lamp give the same
illumination as a single candle at 10 in.?
6. If the sun is at an elevation of 30 degrees what is the angle of
incidence at which it strikes the surface of water? What is the angle
between the incident and the reflected rays?
7. What is the difference between the phenomena of reflection of light
from a white sheet of writing paper and from a piece of clear window
glass?
8. A horizontal ray of light, traveling due east, strikes a vertical
mirror so that after reflection it is traveling due north. If the mirror
be now turned 10 degrees about a vertical axis, the north edge moving
east, what will be the direction of the reflected ray?
9. The necessary illumination for reading is about 2 foot-candles. How
far away may an 8-candle-power lamp be placed?
10. What is the illumination in foot-candles upon a surface 20 ft. from
an arc lamp having an intensity of 1000 candle power?
11. How far from a 100-candle-power Welsbach light would the
illumination be 2 foot-candles?
(3) MIRRORS AND THE FORMATION OF IMAGES
[Illustration: FIG. 353.--Reflection of light, (_a_) diffused, (_b_)
regular.]
=362. Mirrors.=--The many purposes served by mirrors in our every-day
life has made their use familiar to everyone. Yet without study and
experiment few understand their properties and action. _Any smooth_
surface may serve as a mirror, as that of glass, water, polished wood,
or metal. Most objects, unlike mirrors, have irregular surfaces; these
scatter or diffuse the light that falls upon them. (See Fig. 353_a_.)
This is called _diffused or irregular reflection_. The reflection of
light from the smooth surface of a mirror is _regular_. (See Fig.
353_b_.) In every case of reflected light, however, the angle of
reflection equals the angle of incidence, diffusion being due to the
irregularity of the surface. It is by means of the light "diffused"
from the surface of illuminated bodies, such as plants, animals, food,
and manufactured articles, that we "see" the various objects about us,
and it is this light that enables us to judge of their distance, size,
form, color, etc. The moon is seen by the sunlight reflected from its
surface. Moonlight is therefore sunlight diffused by reflection. The
_new moon_ is that phase or condition of the moon when only a narrow
strip of the moon's illuminated surface is turned toward the earth. At
the time of the _full moon_ the whole illuminated surface is seen.
=363. Images Formed by a Plane Mirror.=--The most common use of mirrors
is in the formation of images. The way in which images are formed by a
plane mirror may be illustrated by diagrams. Thus in Fig. 354, let _L_
represent a luminous body and _E_ and _E´_ two positions of the
observer's eye. Take any line or ray as _LO_ along which the light from
_L_ strikes the mirror _O-O´_. It will be reflected so that angle _LOP_
equals angle _POE_. Similarly with any other ray, as _LO´_, the
reflected ray _O´E´_ has a direction such as that angle _L´O´E´_ equals
angle _P´O´E´_. Any other rays will be reflected in a similar manner,
each of the reflected rays appearing to the eye to come from a point
_L´_ behind the mirror.
[Illustration: FIG. 354.--The virtual image of a fixed object as seen in
a plane mirror, has the same location from every position of the
observer's eye.]
=364. Light Waves and Wave Diagrams.=--Just as a stick continually moved
at the surface of a body of water sets up a series of waves spreading in
all directions, so one may imagine a train of waves sent out by a
luminous body _L_ (as in Fig. 355) to the mirror _MN_. These waves will
be reflected from the mirror as if the source of light were at _L´_. It
is much simpler and more convenient to locate the position of the image
of a point by the use of lines or "rays" (as in Fig. 354) than by the
wave diagram (as in Fig. 355). In all _ray diagrams_, however, it should
be kept in mind that the _so-called_ ray is a symbol used to represent
the direction taken by a part of a light wave. Thus in Fig. 354, the
light from _L_ moving toward _O_ is reflected to _E_ along the line
_OE_, the heavy lines representing rays.
[Illustration: FIG. 355.--Wave diagram of image formed in a plane
mirror.]
=365. To locate the image of an object formed by a plane mirror=
_requires_ simply an application of the law of reflection. Thus in Fig.
356 let _AB_ represent an object and _MN_ a plane mirror. Let _AA´_ be a
ray from _A_ striking the mirror _perpendicularly_. It is therefore
reflected back along the same line toward _A_. Let _AO_ represent any
other ray from _A_. It will be reflected along _OE_ so that angle _r_
equals _i_. The intersection of _AC_ and _OE_ at _A´_ behind the mirror
locates the image of the point _A_, as seen by reflection from the
mirror. The triangles _ACO_ and _A´CO_ may be proved equal by geometry.
Therefore _A´C_ equals _AC_. This indicates that _the image of a point
formed by a plane mirror is the same distance back of the mirror as the
point itself is in front of it_. This principle may be used in locating
the image of point _B_ at _B´_. Locating the position of the _end
points_ of an image determines the position of the whole image as
_A´B´_.
[Illustration: FIG. 356.--The image _A´B´_ is as far back of the mirror
_M N_ as the object _A B_ is in front of the mirror.]
=366. How the Image is Seen.=--Suppose the eye to be placed at _E_. It
will receive light from _A_ by reflection as if it came from _A´_.
Similarly light starting from _B_ reaches the eye from the direction of
_B´_. There is nothing back of the mirror _in reality_ that affects our
sight, the light traveling only in the space in front of the mirror. Yet
the action of the reflected light is such that it produces the same
effect as if it came from behind the mirror. Images such as are seen in
plane mirrors are called _virtual_ to distinguish them from _real_
images, in which light actually comes to the eye from the various parts
of the visible image, as from the real image formed by a projecting
lantern upon a screen, or by an aperture as in the pin-hole camera.
Real images therefore are those that can be obtained upon a screen while
virtual images cannot.
=367. Multiple Reflection.=--If the light from an object is reflected by
two or more mirrors various effects may be produced, as may be
illustrated by the _kaleidoscope_. This consists of three plane mirrors
so arranged that a cross-section of the three forms an equilateral
triangle. The mirrors are placed in a tube across the end of which is a
compartment with a translucent cover containing pieces of colored glass.
On looking through the tube, the reflections from the several surfaces
produce beautiful hexagonal designs.
[Illustration: FIG. 357.--Perspective view of "Pepper's ghost."]
[Illustration: FIG. 358.--Diagram of the "Pepper Ghost" illusion.]
=368. Optical Illusions by a Plane Mirror.=--The _illusion_ called
_Pepper's Ghost_ is typical of many illusions produced by reflection. It
may be illustrated by taking a piece of plate glass, _M-N_, a tumbler of
water, _W_, and a lighted candle, _C_, placed in a box, _B_, having one
side open and arranged as shown in perspective in Fig. 357, and in
section in Fig. 358. If the effect is produced in a darkened room, the
observer at _E_ sees a virtual image of the lighted candle as if it were
in the glass of water, the water being seen by transmitted light
_through_ the plate glass, the latter forming a virtual image of the
candle by reflection. Some of the illusions produced by this means are:
(_a_) the figure suspended in mid air; (_b_) the bust of a person
without a trunk; (_c_) the stage ghost; (_d_) the disappearing bouquet.
[Illustration: FIG. 359.--Action of a concave mirror on parallel rays of
light.]
[Illustration: FIG. 360.--Real image formed by a concave mirror.]
=369. Concave Mirrors.=--Another useful piece of physical apparatus is
the concave spherical mirror. It is frequently made from plano-convex
lenses by silvering the convex surface of the lens, thus making a
concave reflecting surface from the inner surface of the silvered part;
they are also made by polishing the inner surfaces of metallic spherical
shells. The concave mirror is represented in section in Fig. 359 by the
curve _MN_; _C_ is the _center of curvature_ or the center of the
surface of which this mirror _MN_ is a part; the line _VC_ through the
center _V_ of the mirror is called the _principal axis_; while any other
line passing through _C_ is called a _secondary axis_. The point midway
between the vertex _V_ and center of curvature _C_ is called the
_principal focus_, _F_. It is the point through which parallel incident
rays pass after reflection. The angle _MCN_ which the curve of the
mirror subtends at the center is called the aperture of the mirror. We
learned in Art. 361, the angle of reflection of a ray of light is always
equal to the angle of incidence no matter what the nature of the
reflecting surface may be. If the reflecting surface is a regular
concave surface, like the inner surface of a sphere, the rays of light
coming from a point source may after reflection come to a focus, forming
a real image. The two extreme points of an object should be selected for
locating its image; Fig. 360 shows the construction. The real images
formed by concave mirrors are always inverted. The principal focus of a
concave mirror may be observed by holding the mirror in a beam of
sunlight entering a darkened room. The sun's rays after reflection
converge to form a small, round, intense spot of light, which is a real
image of the sun, located at the principal focus of the mirror. The
distance of the principal focus from the mirror is the least distance
that a real image can be formed in front of a concave mirror.
=370. Virtual Images by Concave Mirrors.=--When light comes from a small
point situated between a concave mirror and its principal focus, the
reflected rays are divergent and hence no real image of the object can
be found in front of the mirror. But if the rays are extended behind the
mirror they will meet in a point called the _virtual focus_. This is the
point from which they appear to come. Any image of an object situated
between the principal focus and a concave mirror is therefore a virtual
image, erect and larger than the object. (See Fig. 361.)
[Illustration: FIG. 361.--Virtual image formed by a concave mirror.]
=371. Construction of Real Images.=--There are five positions at which
an object may be situated in front of a concave mirror, namely: (1)
_beyond C_; (2) at _C_; (3) _between C and F_; (4) _at F_ and (5)
_between F_ and _V_. There are two ways by means of which the image
formed at each of these positions may be located, namely; (1)
_experimentally_, by allowing the rays of light from a luminous body to
focus on a screen and (2) _diagrammatically_. By the latter method the
two rays of light are considered the course of each of which may easily
be determined; first, the ray which strikes the mirror parallel to its
principal axis and which after reflection passes through the principal
focus; second, the ray which passing through the center of curvature
strikes the mirror at right angles and therefore after reflection must
pass directly back along its incident path. Where these two reflected
rays intersect is located the real image of the object. Whenever these
two rays of light do actually intersect, as in Fig. 360, a real image
(_ab_) is formed of the object _AB_.
The points _A_ and _a_, _B_ and _b_ and others similarly situated on an
axis extending through the center of curvature _C_ are called _conjugate
foci_, for they are so related that an object being at either one, its
image will be found at the other.
[Illustration: FIG. 362.--Action of a convex mirror upon parallel rays
of light.]
=372. The Convex Mirror.=--There are few practical uses to which convex
mirrors can be put. They are sometimes used to give the chauffeur of an
automobile a view of the road behind him. It is then attached to the
wind shield by a short rod. The reflected rays coming from a Convex
mirror are always divergent (see Fig. 362), hence the image is always
virtual and located behind the reflecting surface. The method of
construction for images formed by a convex mirror is similar to that for
concave mirrors. (See Fig. 363.) The center of curvature and principal
focus are behind the mirror and consequently the reflected rays have to
be produced backward until they meet. The images are always _virtual_,
_erect_ and _smaller_ than the object.
[Illustration: FIG. 363.--Construction of an image by a convex mirror.]
[Illustration: FIG 364.--Illustrations of Spherical Aberration.]
=373. Spherical Aberration.= Sometimes in a concave mirror when the
aperture _MCN_ (Fig. 364) is large the images are blurred or indistinct.
This is due to the fact that the incident rays near the outer edge of
the mirror do not focus after reflection at the same point as those
which pass into the mirror near the vertex, but cross the principal axis
at points between the mirror and principal focus as is shown in Fig.
364; this result is called _spherical aberration_. The larger the
aperture of the mirror the more the image is blurred. Concave mirrors in
practical use do not have an aperture much greater than 10 degrees. This
non-focusing of the rays of light by curved reflecting surfaces may be
noticed in many places, as when light is reflected from the inside of a
cup that contains milk or from the inside of a wide gold ring placed on
top of a piece of white paper. The pupil will note other instances.
This curve of light observed is called the _caustic by reflection_.
=374. Parabolic Mirrors.=--The best possible surface to give to concave
mirrors is parabolic. This is a curve which may be generated by moving a
point so that its distance from a fixed point and a fixed line are
always equal. If a source of light is placed at _F_ the rays after
reflection are rendered parallel. See Fig. 365. This reflector is used
in automobile lamps, headlights of locomotives, search-lights, etc. It
is also used in large reflecting astronomical telescopes to collect as
large an amount of light as possible from distant stars and bring it to
a focus. Such mirrors may be made exceedingly accurate.
[Illustration: FIG. 365.--Parabolic mirror.]
Important Topics
1. Reflection: regular, diffused; plane mirrors; laws of reflection.
2. Formation and location of images by plane mirrors. Wave and ray
diagrams.
3. Multiple reflection, illusions.
4. Curved mirrors, uses; concave, convex, parabolic.
Exercises
1. Distinguish between regular and diffused reflection. By means of
which do we see non-luminous bodies?
2. Could a perfect reflecting surface be seen? Explain.
3. A pencil is stood upright in front of a plane mirror set at an angle
of 45 degrees to the vertical. Shown by a diagram the location and
position of the image.
4. Show by diagrams the position and location of the images of a pencil
(a) when standing erect and in front of a _vertical_ mirror. (b) when
standing upon a horizontal mirror.
5. What is the difference between a real and a virtual image?
6. A standard candle and a lamp give equal illuminations to a screen
that is 1 ft. from the candle and 6 ft. from the lamp. What is the
candle power of the lamp? Explain.
7. Why are walls finished in rough plaster or painted with soft tones
without gloss better for schoolrooms than glossy paints or smooth white
plaster?
8. Try to read a printed page by looking at its image in a mirror. write
your name backward on a sheet of paper, and then look at the image of
the writing in a mirror. What effect is produced by the mirror in each
case?
9. If the point of a pencil is held to the surface of a piece of
plate-glass mirror two or more images may be seen in the mirror.
Explain.
10. Given a small lighted candle, a concave mirror, a meter stick, and a
white screen, how would you prove the statements made in Arts. 369 and
370 concerning the location of images formed by concave mirrors? Make
the diagram in each case.
11. Why do images seen in a quiet pond of water appear inverted? Explain
by a diagram.
(4) REFRACTION OF LIGHT
=375. Common Examples of Refraction.=--Everyone has noticed the apparent
bending of an oar, of a stick, or of a spoon when placed in water (see
Fig. 366), while many have observed that the bottom of a pond or stream
looks nearer to the surface than it really is. These and similar
illusions are due to the _refraction_ or bending of light rays as they
pass from one medium to another. The principles of refraction are among
the most useful found in the study of light since application is made of
them in the construction and use of important optical instruments, such
as the camera, microscope, telescope, and the eye.
[Illustration: FIG. 366.--The stick appears to be bent on account of
refraction.]
=376. Action of Light Undergoing Refraction.=--If a beam of sunlight be
admitted to a darkened room and reflected by a mirror so that it strikes
the surface of water in a glass jar, a part of the beam may be seen to
be reflected while another portion is transmitted through the water
(Fig. 367). The reflected beam follows the law of reflection while the
transmitted beam is seen to be _refracted_, or to have its courses
slightly changed in direction upon entering the water. If the mirror is
turned so that the angle at which the light strikes the water is
changed, the amount of refraction or change of course of the light is
varied. When the light strikes the water perpendicularly there is no
refraction. On the other hand, the greater the angle at which the light
strikes the water the greater the bending.
[Illustration: FIG. 367.--Part of the ray is reflected and part passes
into the water and is refracted.]
[Illustration: FIG. 368.--Illustrating the laws of refraction of light.]
=377. Laws of Refraction.= The action of light on entering, passing
through, and leaving a great variety of substances has been carefully
studied. A summary of the results of these observations is given in the
following _laws of refraction_: I. _When light enters a transparent
body, perpendicularly, it passes on without changing its direction._
II. _When light enters a denser transparent body obliquely, it is bent
toward the perpendicular; when light enters a less dense body obliquely,
it is bent away from the perpendicular._ (See Fig. 368.)
=378. The cause of refraction= may be illustrated by considering a line
of men moving across a field and occupying at equal time intervals the
successive positions 1, 2, 3, etc., indicated in Fig. 369. Suppose that
the upper and lower parts of the field have a smooth hard surface, while
at the center is a strip of newly ploughed ground. The line will move
more slowly over the ploughed field than over the hard field. This will
result in a retardation of the end of the line first striking the soft
ground with a resulting change of direction of the line, _toward_ the
perpendicular to the edge of the field (_on entering the place of more
difficult travel_), and _away_ from the perpendicular on moving into a
place where _increased speed results_.
[Illustration: FIG. 369.--Diagram illustrating the cause of refraction.]
=379. Index of Refraction.=--By studying the change of direction of the
marching men as shown in Fig. 369 it is evident _first_ that it is due
to a difference in speed in the two media. It is not easy to measure the
speed of light in a medium. However, the amount of refraction may be
determined easily and from this the _relative_ speed may be computed.
The _number that expresses the ratio of the speed of light in air to its
speed in another medium is called the index of refraction of that
medium_. The relative speeds of light, or the indices of refraction for
some substances, are: water, 1.33, crown glass, 1.51, flint glass,
1.61, diamond, 2.47, carbon bisulphide, 1.64.
[Illustration: FIG. 370.--The incident ray and the emergent rays are
parallel.]
=380. Plates, Prisms, Lenses.=--The refraction of light is usually
observed when it is passing through a plate, a prism, or a lens. The
important differences between the effects of each in refracting light
are illustrated in Figs. 370, 371 and 372. In Fig. 370 it is seen that
the refraction of the ray on entering the glass is counteracted by the
refraction away from the perpendicular upon leaving it. So that the
entering and emergent rays are _parallel_. In Fig. 371 the refraction at
the two surfaces of the prism results in a change of direction of the
ray, the course being bent toward the _thicker_ part of the _prism_. In
Fig. 372 it may be noticed that the convex lens resembles two prisms
with their bases together. Since all parts of the lens refract light
toward the thicker part, the center, the effect of the convex lens is to
bring the rays of light to a focus, at _F_.
[Illustration: FIG. 371.--Effect of a prism upon a ray of light.]
[Illustration: FIG. 372.--The convex lens brings the rays of light to a
focus.]
=381. Total Reflection.=--It has been shown that when light passes from
a _denser to a lighter_ medium, as from glass or water to air, that the
beam is refracted _away_ from the perpendicular. This is illustrated in
Fig. 373. The diagram represents the change in the course of a ray of
light that passes through water to a surface with air above it. A ray
striking perpendicularly passes through without refraction. Other rays
show increasing refraction with increasing angle of incidence. For one
ray the angle of refraction is so large that the refracted ray is
parallel to the surface. When this condition is reached, the _angle of
incidence_ is called the _critical angle_. Any increase in the angle of
incidence causes all of the light to be reflected as is the beam _E_.
This action is called _total reflection_, the course of the reflected
ray being according to the law of reflection. _A right-angle prism_ (see
Fig. 374) is often used where a mirror would ordinarily be employed, the
total reflection occurring within the prism giving more satisfactory
results than a mirror. See Art. 398 for a description of the Zeiss
binocular field-glass for an example of this use of total reflection.
[Illustration: FIG. 373.--An example of total reflection.]
[Illustration: FIG. 374.--Total reflection in a right-angle prism.]
The mirage (see Fig. 375) is an optical illusion by which distant
objects, below the horizon, are sometimes plainly seen. This
phenomenon is most frequently observed in hot, desert regions, when
the air conditions are such that the lower strata near the ground
are very much hotter than those above. These lower strata, having
expanded the most, are less dense than the cooler ones above. Hence
a ray of light traveling obliquely downward is refracted more and
more until total reflection takes place. The images seen are
inverted giving a representation of trees or other objects
reflected on the surface of still water. The mirage is also
frequently seen at sea, ships being observed, sometimes erect,
sometimes inverted, apparently sailing in the clouds near the
horizon. Over the Great Lakes, trees, boats, and towns on the
opposite shore, sixty or seventy miles away, can sometimes be
plainly seen, apparently but a few miles out. In this case the
images are erect, the total reflection being from warm, still
layers of air over colder layers near the water.
[Illustration: FIG. 375.--Diagram of a mirage.]
Important Topics
(A) Refraction: cause, illustration, two principles.
(B) Index of refraction, meaning.
(C) Plates, prisms, lenses, action of each.
(D) Total reflection, uses.
Exercises
1. Compute the speed of light in water, the index of refraction being
1.33.
2. If one wished to shoot a fish under water, should he aim at the
apparent location of the fish as viewed from the air? Explain, using a
diagram.
3. Define refraction. Mention two illustrations of this action that you
have observed out of school.
4. Why does the moon look larger near the horizon?
5. Is your reflection seen in a pool of water upside down? Why?
6. Why does it whiten molasses candy to pull it?
7. When looking at a building through the ordinary glass of a window why
do straight lines of the building appear to be so distorted? What makes
them appear to move as you move your head slightly?
8. Explain the phenomenon which one observes when looking at an object
through the air arising from a hot stove or radiator.
9. Frequently the horizontal diameter of the setting sun appears to be
greater than the vertical. Explain.
10. Explain why one observes several images of a luminous body like a
lighted candle when the reflected light from a thick glass mirror enters
the eye, the angle of reflection being large.
(5) THE FORMATION OF IMAGES BY LENSES
=382. Uses of Lenses in Optical Instruments.=--The use of instruments
that employ lenses in their operation, such as spectacles, reading and
opera glasses, and the camera, microscope, and telescope, is familiar to
most students of physics. The part played by the lenses, however, is not
generally understood. Consequently the study of the formation of images
by lenses is of general interest and importance.
=383. Forms of Lenses.=--While a lens may be formed from any transparent
solid it is commonly made of glass. It may have two curved surfaces or
one curved and one plane surface. Most lenses are _spherical lenses_,
since their curved surfaces form a part of the surface of a sphere. Fig.
376 represents a spherical lens with a curved surface coinciding with
that of a sphere whose center is at _C_. This center is called the
_center of curvature_, while the radius of the sphere _R_, is the
_radius of curvature_.
[Illustration: FIG. 376.--Formation of a spherical lens.]
There are two classes of lenses: those thick in the middle are called
_convex_, while those thick at the edges are _concave_. The mode of
constructing the six forms of spherical lenses is shown in Fig. 377.
These are named as follows: (1) double convex, (2) plano convex, (3)
concavo-convex, (4) double concave, (5) plano concave, (6)
convexo-concave.
[Illustration: FIG. 377.--Forms of Lenses. 1. double convex; 2. plano
convex; 3. concavo convex; 4. double concave; 5. plano concave; 6.
convexo concave.]
[Illustration: FIG. 378.--The action of a burning glass.]
=384. Effect of Lenses upon Light.=--The most important characteristic
of a lens is its effect upon a beam of light. Most persons have seen a
"burning glass," a double convex lens, used to bring to a point, or
focus, a beam of sunlight. To show the action of a burning glass send a
beam of light into a darkened room, and place in its path a double
convex lens. (See Fig. 378.) If two blackboard erasers are struck
together near the lens, the chalk particles in the path of the light are
strongly illuminated, showing that the light after passing through the
lens it brought to a focus and that it spreads out beyond this point.
This point to which the cone of light rays converges after passing
through the convex lens is called the _principal_ focus of the lens. The
distance from the principal focus to the center of the lens is the
_focal length_ or _principal focal distance_ of the lens. _The focal
length of double convex lenses of crown glass is about the same as the
radius of curvature of either surface._ The action of a convex or
converging lens upon light may be better understood by studying Fig. 379
in which light is passing from _S_ to _F_. The successive positions and
shape of the advancing light waves are indicated by lines drawn across
the beam. The light being retarded more in the thicker part of the lens,
the light waves on leaving the lens have a concave front. Since light
waves tend to move at right angles to the front of the wave, the light
is brought to a focus. After passing the focus the waves have a convex
front, forming a diverging cone.
[Illustration: FIG. 379.--Wave diagram of light passing through a convex
lens.]
=385. Concave Lenses.=--When sunlight passes through a _concave_ lens a
diverging cone of light is formed. (See Fig. 380.) This is caused by the
edges of the wave being retarded more than the center, producing a
convex wave front. This diverging cone of light acts as if it had
proceeded from a luminous point at _F_.
This point is called a _virtual_ focus and is nearly at the center of
the curvature of the nearer surface.
[Illustration: FIG. 380.--Wave diagram of light passing through a
concave lens.]
=386. The Formation of Images by Lenses.=--If a beam composed of
_parallel_ rays of light, as sunlight, is sent in turn through three
convex lenses of the same diameter but of different thickness, it is
found that the _thicker the lens the greater is its converging power, or
the shorter is its focal_ length. (See Fig. 381.) Now if a luminous
body, such as a lighted candle, be placed near the convex lens but
_beyond its focal length_, the light will be brought to a focus upon the
other side of the lens and an image of the candle may be clearly seen
upon the screen placed at this point. (See Fig. 382.) _The two points so
situated on opposite sides of a lens that an object at one will form an
image at the other are called conjugate foci._
[Illustration: FIG. 381.--The thicker the lens, the shorter is its focal
length.]
[Illustration: FIG. 382.--_C_ and _S_ are at conjugate foci.]
It will be helpful to compare the images formed of a candle by an
_aperture_ and by a _convex_ lens. Rays of light from each point of the
luminous body pass through the aperture in straight lines and produce
upon the screen a lighted space of the same shape as the candle. This
image is rather _hazy_ in outline. Each cone of rays from luminous
points of the flame is brought by the lens to a focus on the screen,
producing a _sharp image_. It is the converging power of convex lenses
that enables them to produce clear images.
[Illustration: FIG. 383.--Construction of a real image by a convex
lens.]
=387. The Construction of Diagrams to Represent the Formation of Images
by Lenses.=--Just as the earth has an axis at right angles to its
equator to which are referred positions and distances, so a lens has a
_principal axis_ at right angles to its greatest diameter and along this
axis are certain definite positions as shown in Fig. 383. Let _MN_ be
the _principal axis_ of a convex lens, _P_ and _P´_ are _principal foci_
on either side of the lens, _S_ and _S´_ are _secondary foci_. These are
at points on the principal axis that are twice as far from _O_, the
center of the lens, as are the principal foci. In the formation of
images by a convex lens, several distinct cases may be noticed:
(A) If a luminous body is at a _great distance_ at the left, its light
is brought to a _focus_ at _P_, or its _image is formed at P_. (B) As
the _object approaches_ the lens the _image gradually recedes_ until the
object and image are at _S_ and _S´_, _equally distant from O and of
equal size_ (as in Fig. 383). The object and image are now said to be at
the _secondary foci_ of the lens. (C) As the _object moves from S to P_
the image recedes, rapidly increasing in size until (D) when the object
is at _P_ the rays become parallel and no image is formed. (E) When the
object is between _P_ and the lens, the rays _appear to proceed from
points back of the object_, thus forming an _erect, larger, virtual
image_ of the object. (See Fig. 384.) This last arrangement illustrates
the _simple microscope_.
With a concave lens but one case is possible, that corresponding to the
one last mentioned with convex lenses; since the rays from a body are
divergent after passing through a concave lens they appear to proceed
from points _nearer_ the lens than the object and hence a _virtual,
erect, smaller image_ of the object is formed. This virtual image may be
seen by looking _through_ the lens toward the object. (See Fig. 385.)
[Illustration: FIG. 384.--Construction of a virtual image by a convex
lens.]
[Illustration: FIG. 385.--Construction of a virtual image by a concave
lens.]
=388. The Lens Equation.=--The location of either the object or of the
image upon the principal axis of the lens may be calculated if the
position of one of these and the focal length are known. This is
accomplished by the use of a formula 1/_F_ = 1/_D_{0}_ + 1/_D_{1}_ in
which _F_ represents the focal length and _D_{0}_ and _D_{1}_ the
distance from the lens of the object and the image respectively. Thus if
an object is placed 30 cm. from a lens of 10 cm. focal length, where
will the image be formed? Thus: 1/10 = 1/30 + 1/_D_ and 3_D_{1}_ =
_D_{1}_ + 30, or 2_D_{1}_ = 30 _D_{1}_ = 15. This result indicates that
a real image will be 15 cm. from the lens. A minus value would indicate
a virtual image.
Important Topics
(A) Lenses: convex, concave, six forms, center and radius of curvature.
(B) Principal focus, focal length, virtual focus, conjugate foci.
(C) Principal axis, images formed when object is in various locations.
(D) Computation of location of images.
Exercises
1. Why is an image of a candle formed by an aperture, not sharply
defined?
2. When a photographer takes your picture and moves the camera nearer
you, must he move the ground glass screen toward the lens or away
from it? Explain.
3. How can you find the principal focal length of a lens.
4. How can you test a spectacle lens to see whether it is convex
concave?
5. When will a convex lens produce a virtual image? Have you ever seen
one? Where?
6. When a photographer wishes to obtain a full length view of a person,
where does he place the camera?
7. The focal length of the lens is 24 cm. How far from the lens must an
object be placed in order that a real image may be three times as long
as the object?
8. There is a perfect image of an object on the ground glass of a
camera. The center of the lens is 20 cm. in front of the image and the
object 75 cm. from the lens. What is the focal length of the lens?
9. An object is 60 cm. from the lens, the image 120 cm. from it. Find
the focal length.
10. How can you find experimentally the principal focal length of a
lens?
11. A lens is used to project an enlarged image of a candle upon a
screen. Which is farther from the lens, the candle or the image?
Explain.
(6) OPTICAL INSTRUMENTS
=389. The Eye.=--The most common optical instrument is the _eye_. While
the structure of the eye is complicated, the principle of it is simple,
involving the formation of an image by a double convex lens. (See Fig.
386, in which is shown a front to back, vertical cross-section of the
eye.) The eye appears to be made of portions of two spheres, one of
which, smaller than the other, is placed in front. This projecting part
is transparent, but refracts the light which strikes it obliquely, so as
to turn it into the eye. This enables us to see objects at the side when
looking straight ahead. Test this by looking directly in front of you
and see how far back on each side of the head you can notice a movement
of the forefinger of each hand.
[Illustration: FIG. 386.--Cross-section of the eye.]
=390. Action of the Eye in Vision.=--When we look at an object, a small,
real, inverted image is formed upon the _retina_ at the back of the
interior of the eye. The retina is an expansion of the optic nerve and
covers the inner surface at the back of the eyeball. Seeing is due to
the action of light in forming images upon the retina. Our eyes are so
constructed that when they are relaxed the lens is adjusted to form
clear images of _distant_ objects upon the retina. If we look from
distant to near objects without changing the shape of the eye lens, a
sharp image of the latter cannot be formed and we get a blurred
impression. It is difficult, however, to look at objects without
automatically adjusting the eye lens so that it will make a sharp image.
Test this by looking out of a window at a distant object, then without
moving the head or eyes look at the glass of the window; you will notice
a slight change of some sort _in_ the eye itself as the vision is
adjusted. This adjustment is made by muscles that pull or compress the
eye lens so as to make it thicker for near objects and thinner for
distant ones. The eye ordinarily does not see objects nearer than 10 in.
clearly. This means that the greatest possible thickening of lens will
not form clear images upon the retina if the object is nearer than 10
in. (25 cm.).
[Illustration: FIG. 387.--The visual angle, _AOB_ is greater at _AB_
than at _A´B´_.]
=391. The Visual Angle.=--To examine objects carefully we usually bring
them as close to the eye as possible, for the nearer to the eye the
object is brought, the larger is the visual angle formed by it (see Fig.
387), and the larger is its image upon the retina. _The visual angle of
an object is the angle at the eye lens between the rays that have come
from the ends of the object._ Consequently the more distant the object,
the smaller is its visual angle. Now if we wish to examine small objects
with great care, we frequently find that it is necessary to bring them
close to the eye so that they have a visual angle of adequate size. If
they must be brought closer than 10 in. a double convex lens is placed
in front of the eye. This assists the eye lens in converging the light
so that a clear image may be formed when the object is close, say an
inch or so from the eye. This is the principle of the magnifying glass
used by watch-makers and of the _simple microscope_. The action of the
latter is illustrated by Fig. 388. The convex lens forms a virtual,
enlarged image "_A´-B´_" of the object "_A-B_" which it observed instead
of the object itself.
[Illustration: FIG. 388.--Action of the simple microscope.]
[Illustration: FIG. 389.--"Near sightedness", or myopia. Parallel rays
come to a focus at _F_; emerging rays focus at _A_, the far point.]
=392. Defects of Vision.=--There are several defects of vision that may
be corrected by spectacles or eye-glasses. One of these is
"near-sightedness." It is due either to an eyeball that is elongated, or
to an eye lens that is too convex, or to both conditions. This condition
brings light from distant objects to a focus too soon (as shown in Fig.
389). Only light from near objects will focus upon the retina in such
cases. With _normal_ vision light from _distant_ or _near_ objects may
be focused without unusual effort upon the retina, see Fig. 390. The
remedy for near-sightedness is to use concave lenses which will assist
in properly refracting the light so the focus will be formed on the
retina (Fig. 391). "Far-sightedness" is the reverse of near-sightedness;
the eyeball is either too short, or the lens too flat, or both
conditions obtain, so that the light entering the eye is brought to a
focus behind the eyeball (Fig. 392). The remedy is convex lenses which
will assist in properly converging the light, see Fig. 393. A third
defect is called _astigmatism_. This is caused by some irregularity or
lack of symmetry in the eye. It is corrected by a _cylindrical_ lens
that compensates for this defect of the eye. A diagram similar to Fig.
394 is used as a test for astigmatism. If the lines appear with unequal
distinctness, some irregularity of refraction (astigmatism) is
indicated.
[Illustration: FIG. 390.--The normal eye. The parallel rays _A B_ focus
without accommodative effort at _C_.]
[Illustration: FIG. 391.--Correction of near-sightedness by concave
lens.]
[Illustration: FIG. 392.--Far-sightedness or hyperopia. Parallel rays
focused behind the retina.]
[Illustration: FIG. 393.--Correction of far-sightedness by a convex
lens.]
[Illustration: FIG. 394.--Test card for astigmatism.]
=393. The Photographic Camera.=--This is a light-tight box, provided
with a convex lens in front, covering an aperture and a ground glass
screen at the back. The distance between the lens and the screen is
adjusted until a sharp image is obtained upon the latter, which is then
replaced by a sensitive plate or film. The sensitized surface of the
plate or film contains a salt of silver which is changed by the action
of light. After the plate has been "exposed" to the action of light, it
is "developed" by the use of chemicals producing a _negative_ image.
From "negative," by the use of sensitized paper, "positive" prints may
be secured which resemble the object photographed.
[Illustration: FIG. 395.--Diagram of the projecting lantern.]
=394. The projecting lantern= (see Fig. 395) employs a strong source of
light, as an electric arc lamp _L_, to strongly illuminate a transparent
picture, or _lantern slide_, _S_, a real image (_I_) of which is formed
upon a large screen. Two large plano-convex lenses (_C_), called
condensing lenses, are placed near the lamp to concentrate the light
upon the "slide" _S_. The convex lens forming the image is called the
"objective" (_O_).
=395. The compound microscope= consists of two lenses. One called the
_objective_ is placed near the object to be viewed. This lens has a
short focal length usually less than a centimeter. It forms a _real
image_ of the object. _A´_-_B´_. The other lens, the _eyepiece_ forms a
virtual image of this real image. _A´´_-_B´´_. (See Fig. 396.)
=396. The telescope= consists of two lenses, the eyepiece and the
objective. As in the compound microscope, the objective of the telescope
forms a real image of the distant object, the eyepiece forming an
enlarged virtual image of the real image. It is the virtual image that
is viewed by the observer. (See Fig. 397.) In order to collect
sufficient light from distant stars the objective is made large,
sometimes 50 in. in diameter.
[Illustration: FIG. 396.--Formation of an image by a microscope. _A_-_B_
is the object. _B´_-_A´_ the real image formed by the "objective."
_B´´_-_A´´_ is the virtual image formed by the eyepiece. The eye sees
the virtual image.]
The length of the telescope tube depends upon the focal length of the
objective, since the distance between the two lenses must equal the
_sum_ of their focal lengths.
[Illustration: FIG. 397.--Formation of an image by a telescope. _b_-_a_
is the real image; _d_-_c_ is the virtual image seen by the observer.]
=397. The opera glass= consists of a convex lens as objective and a
_concave_ lens as an eyepiece. The former tends to form a real image but
the latter diverges the rays before a real image can be formed, the
action of the two lenses producing an enlarged virtual image (as in Fig.
398) which is viewed by the one using the glass. The compact size of
the opera glass is due to the fact that the distance between the two
lenses is the _difference_ of the focal lengths.
[Illustration: FIG. 398.--Formation of an image by an opera-glass.
_a_-_b_ is the virtual image.]
[Illustration: FIG. 399.--Diagram of the Zeiss binocular or prism field
glass.]
=398. The Prism Field Glass or Binocular.=--This instrument. has come
into use in recent years. It possesses the wide field of view of the spy
glass but is as compact as the opera glass. This compact form is secured
by causing the light to pass back and forth between two right-angle
prisms (as shown in Fig. 399). This device permits the use of an
objective lens with a focal length three times that of the tube,
securing much greater magnifying power than the short instrument would
otherwise possess. A further advantage is secured by the total
reflection from the two prisms, one of which is placed so as to reverse
the image right for left and the other inverts it, so that when viewed
in the eyepiece it is in its proper position.
Important Topics
1. The eye: parts, formation of image, kind, how, where.
2. Eye defects, how remedied. Visual angle.
3. Simple microscope, camera; images, kind, how formed.
4. Compound microscope, telescope and opera glass; images, action of
each lens.
Exercises
1. Name three instruments in which lenses form virtual images and three
in which _real_ images are formed.
2. In what direction is an oar in water apparently bent? Explain by a
diagram.
3. What optical instruments have you used? Is the _visible_ image formed
by each of these _real_ or _virtual_?
4. The focal length of a copying camera lens is 14 in. Where must a
drawing be placed so that an image of the same size may be formed upon
the ground glass screen? What must be the distance of the screen from
the lens?
5. What are two methods by which you can determine the focal lengths of
the lens of a photographic camera?
6. The critical angle for water is 48-1/2 degrees. Show by a diagram how
much of the sky can be seen by a diver who looks upward through the
water.
7. How is near-sightedness caused? How is it corrected? Illustrate by a
diagram.
8. How is the eye accommodated (focused) as an object gradually
approaches it?
9. Explain why a simple microscope assists in looking at the parts of a
flower or insect.
10. Why do people who have good eyesight when young require glasses as
they grow old?
(7) COLOR AND SPECTRA
[Illustration: GUGLIELMO MARCONI
"Copyright by Underwood & Underwood, N. Y."
Guglielmo Marconi (Italy). Inventor of wireless telegraphy.]
[Illustration: ALEXANDER GRAHAM BELL
"Copyright by Underwood & Underwood, N. Y."
Alexander Graham Bell, Washington, D. C. Inventor of the telephone.]
=399. Color.=--Much of the pleasure experienced in gazing at beautiful
objects is due to the _color_ shown by them. The blue sky, the green
grass, and the varied tints of flowers, and of the rainbow all excite
our admiration The study of color begins naturally with the production
of the _spectrum_, the many-colored image upon a screen produced by
passing a beam of light through a prism. The spectrum is best shown when
the light enters by a narrow slit (Fig. 400). The spectrum was first
produced by Sir Isaac Newton in 1675 by the means just described. The
names usually given to the more prominent colors of the spectrum are
violet, indigo, blue, green, yellow, orange, and red. The initials of
these names, combined, spell _vibgyor_, a word without meaning except to
assist in remembering the order of the colors in a spectrum. If the
light that has passed through a prism is sent through a second prism
placed in reverse position (see Fig. 401), the light passing through
both prisms is found to be white. This experiment _indicates that white
light is composed of light of all colors_.
[Illustration: FIG. 400.--Formation of the spectrum by a prism.]
[Illustration: FIG. 401.--The colors of the spectrum recombine to form
white light.]
=400. Dispersion.=--The separation of the colors by a prism is called
dispersion. In experimenting to find a reason for dispersion, it has
been learned that lights of different colors are of different wave
lengths. Color in light is therefore analogous to pitch in sound. We
hear through many octaves, but we see through about one octave. That is,
the shortest visible waves of violet light are about 0.000038 cm. in
length while the longest visible red rays are 0.000076 cm., or the
longest visible light waves are about twice the length of the shortest
visible ones. It appears from the evidence of experiments upon
dispersion that _light waves of different lengths are refracted
differently_. This causes the images formed by refraction through simple
glass lenses to be fringed with color and to lose some of their
sharpness and definiteness of outline, since the violet light is brought
to a focus sooner than the red. (See Fig. 402.) This seriously affects
the value of such lenses for optical purposes. Fortunately it is found
that _different kinds of glass have a different rate of dispersion for
the same amount of refraction_.
[Illustration: FIG. 402.--Violet light comes to a focus sooner than
red.]
=401. The Achromatic Lens.=--The existence of these different kinds of
glass makes possible a combination of lenses in which dispersion is
entirely overcome with the loss of only about one-half of the
refraction. Such a combination is shown in Fig. 403. It is called an
_achromatic lens_, since images formed by it are not colored but white
(_a_ = without, _chroma_ = color). _The achromatic lens consists of a
double convex lens of crown glass combined with a plano-concave lens of
flint glass._ Achromatic lenses are used in all high-grade optical
instruments such as telescopes and microscopes. The colored images that
are sometimes seen in cheap opera glasses show the result of not using
achromatic lenses.
[Illustration: FIG. 403.--An achromatic lens. _C_ is of crown glass;
_F_, of flint glass.]
=402. The Color of Bodies.=--Project the spectrum of sunlight upon a
white surface in a darkened room.
Now place in different parts of the spectrum objects of various
colors. Red objects will show brilliant red when at the red end of
the spectrum but look black at the blue end, while blue objects
appear blue only at the blue end.
These facts indicate that the color of an object depends upon two
things: (a) _the light that falls upon it and_ (b) _the light which it
sends to the eye_. A _black_ surface absorbs all color while a _white_
one reflects all wave lengths to the eye in the same proportion that
they come to it. A white object will appear red in red light, and blue
in blue light since it reflects both of these. A _colored_ object
reflects light of its own color but absorbs all others. The color then
of a body is due to the light which it does not absorb, but which comes
from it to the eye.
_403. The color of transparent bodies_, such as colored glass, is due to
the presence of a _dye_ or _pigment_ contained in the body. This pigment
absorbs a part of the light, the part transmitted giving the color. This
may be shown by holding a sheet of colored glass in a beam of light
either before or after it has passed through a prism. Some colors, as
red, may be found to be nearly _pure_, only the red passing through,
while green glass often transmits in addition to the green some yellow
and some red light.
=404. Complementary Colors.=--If two prisms are placed in reversed
position near each other (see Fig. 401), a beam of light dispersed by
one is recombined into white light by the other. If now a card is held
between the two prisms so as to cut off some of the colored light, say
the red, the remaining light will be found to form a _greenish blue_. If
the card is removed, the light becomes _white_ again. That is, red and
_peacock blue_ light together form white. Any two colors that together
form white light are called _complementary_. Other complementary colors
are light yellow and blue, green and crimson, orange and greenish blue,
violet and greenish yellow. We must not confuse the combining of colors
(light) and the combining of _pigments_, the latter consisting of bodies
that absorb light. Yellow pigment absorbs all but yellow and some green,
while blue pigment absorbs all but blue and some green. Mixing these two
pigments causes the absorption of all colors but _green_. Blue and
yellow _paint_ mixed produce _green_, while blue and yellow _light_ give
white.
=405. The solar spectrum=, as the spectrum of sunlight is called, may be
observed in the _rainbow_. The latter is produced through the dispersion
of light by spherical raindrops. Its formation may be imitated by
sending a small circular beam of light through a screen against a round
glass flask filled with water. (See Fig. 404.) The light passes through
the water and is dispersed when it enters and when it leaves, producing
a color upon the screen at _R_-_V_. The course of the light within the
drop is indicated in Fig. 405. The violet ray comes to the eye more
nearly horizontal and is therefore below red, as we look at the rainbow.
=406. Fraunhofer Lines.=--Some of the most important features of the
solar spectrum are not seen in the rainbow or in the band of light
usually observed upon a screen. By the use of a narrow slit and a
convex lens to carefully focus the slit upon a white screen it is seen
that the solar spectrum is crossed by many _dark_ lines. These are
called Fraunhofer lines, to honor the German scientist who in 1814 first
accurately determined _their_ position. Two experiments _with a
spectroscope_ will help to make clear the meaning of the Fraunhofer
lines.
[Illustration: FIG. 404.--A rainbow formed by a beam of light striking a
flask of water.]
[Illustration: FIG. 405.--The course of a beam of light within a drop of
water.]
=407. The Spectroscope and Its Uses.=--The spectroscope (Fig. 406) is an
instrument for observing spectra. It consists of a prism, a slit, and a
convex lens _T_ for focusing an image of the slit accurately upon a
screen (Fig. 407) where the spectrum is observed through the eyepiece
_E_.
[Illustration: FIG. 406.--The spectroscope.]
(A) A Bunsen flame is placed in front of the slit and a heated platinum
wire which has been dipped in common salt or some sodium compound placed
in the Bunsen flame; the latter becomes yellow and a vivid yellow line
is observed on the screen in the spectroscope. Other substances, as
barium and strontium salts, when heated to incandescence in the Bunsen
flame, give characteristic bright lines. In fact each _element_ has been
found to have its own characteristic set of colored lines. This fact is
made use of in _spectrum analysis_, by which the presence of certain
elements in a substance can be definitely proved upon the appearance of
its particular lines in the spectrum.
[Illustration: FIG. 407.--Diagram of a spectroscope.]
[Illustration: FIG. 408.--The bright line spectrum of iron and its
coincidences with some of the dark lines of the solar spectrum.]
(B) If light from, for example, an arc light is sent over a gas flame
containing _sodium_ vapor, a _dark line_ appears in the spectrum--in
the exact position in which the yellow sodium line appeared. It seems
that the sodium vapor removes from white light the same wave lengths
that it itself produces. This absorption is supposed to be due to
sympathetic vibration; just as a tuning fork is set in vibration by the
waves of another fork in unison with it, at the same time absorbing the
wave energy, so in the gas flame the sodium particles absorb the wave
motion of the same vibration rate as that emitted by them. The fact that
the spectrum of sunlight contains a great many dark lines is believed to
indicate that the sun is surrounded by clouds formed by the vaporization
of the various substances in the sun itself. By comparing the dark lines
of the solar spectrum with the _bright-line spectra_ of various
substances found in the earth, such an exact correspondence of the lines
is found that the presence of the vapor of these substances about the
sun is considered proved. (See Fig. 408 which shows the exact
correspondence between the bright-line spectrum of iron vapor and the
dark lines appearing in a portion of the sun's spectrum.) The spectra of
the stars also contain certain dark lines. Thus the presence of the
corresponding substances in distant stars is considered as determined.
=408. Theory of Color Vision.=--By combining light of the _three colors_
_red_, _green_ and _blue-violet_ in proper proportions, it has been
found possible to produce any color effect, even white. This leads to
the conclusion that in the retina of the eye are three different kinds
or sets of sensitive nerve endings, sensitive respectively to red, to
green, and to blue light. This idea is given corroboration by some facts
of color blindness. Thus some persons have no sensation of _red_, this
color not being distinguished from green. Others are color blind to
green or blue. It is supposed that in color blind persons one of the
sets of nerve endings sensitive to one of these three colors is lacking.
=409. Three-color Printing.=--Since all colors may be produced by mixing
the three colors, light red, green, and blue-violet, these are called
_the three primary colors_. The so-called primary pigments or paints are
simply the complements of the three primary colors. They are, in order,
peacock blue, crimson, and light yellow. The three pigments when mixed
yield black, since combined they absorb all kinds of visible light. The
process of three-color printing, now so generally employed in printing
colored pictures for books, calendars, etc., consists in combining upon
white paper three colored impressions, using successively the three
primary pigments (yellow, crimson and blue) from plates prepared as
follows:
Three photographs of a given colored object are taken, each through a
different sheet of gelatine called a filter, stained the color of one of
the primary colors. From these photographs half-tone blocks are made in
the usual way. The colored picture is made by carefully superposing
impressions from these blocks, using in each case an ink whose color is
the complement of the "filter" through which the original picture was
taken. An illustration of the process is given upon the plate in the
frontispiece of this book.
Important Topics
1. Color, due to wave length; dispersion by prism, sphere in rainbow,
complementary colors, color of opaque and transparent bodies.
2. Spectra, solar; formation of rainbow; bright-line spectra, how
formed, how used; dark-line, how formed, used.
3. Theory of color vision. Three color printing.
Exercises
1. How does a white flower look when viewed through a blue glass?
Through a red glass? Through a red and blue glass at the same time?
2. Why does a red ribbon appear black when seen by blue light and red
when seen by red light?
3. In what part of the sky must you look to see a rainbow in the
morning? In the afternoon? Explain.
4. How would you arrange two similar prisms so as to produce double the
deviation produced by one?
5. The color of an object depends upon what two things?
6. What kind of a spectrum should moonlight give? Why?
7. A mixture of green and red lights gives a sensation of yellow. Can
you suggest why a mixture of blue and yellow lights gives the sensation
of white?
(8) NATURE OF LIGHT, INTERFERENCE, POLARIZATION
=410. The Corpuscular Theory.=--The theory of the nature of light that
was most generally accepted until about the year 1800, held that light
consists of streams of minute particles, called corpuscles, moving at
enormous velocities. This _corpuscular theory_ was in accord with the
facts of reflection and the _rectilinear_ motion of light, but was
abandoned after the discovery of the _interference of light_, as it
could not account for the latter phenomenon.
=411. The Wave Theory of Light.=--The theory that _light is_ a _form of
wave motion_ was first advanced by Huygens, a Dutch physicist, in the
seventeenth century. This theory was opposed at the start since (A) _no
medium_ was known to exist which would convey wave motion through space,
as from the sun to the earth, and (B) the _rectilinear motion_ of light
was _unlike_ that of any _other_ form of known wave motions, such as
that of water or of sound waves which are able to bend around corners.
In answer to the first objection, Huygens assumed the presence of a
medium which he named _ether_, while the second objection has been
completely overcome during the past century by the discovery that _light
may deviate from a straight line_. It is now known that the _excessive
shortness_ of light waves is the reason for its straight-line motion.
Further, long ether waves, as those of wireless telegraphy, are found to
bend around obstacles in a manner similar to those of water or sound.
[Illustration: FIG. 409.--Two plates pressed together by a screw clamp.]
[Illustration: FIG. 410.--Illustrating the interference of light by a
thin film of air.]
=412. The interference of light= is one of the phenomena for which the
wave theory offers the only satisfactory explanation. Interference of
light may be shown by taking two pieces of plate glass and forcibly
pressing them together by a screw clamp, as shown in Fig. 409. After a
certain pressure has been reached, colored rings will appear about the
compressed spot when viewed by light _reflected_ from the upper surface
of the glass. If light of one color, such as that transmitted by red
glass, falls upon the apparatus, the rings are seen to be alternately
red and dark bands. The explanation of this phenomenon according to the
wave theory is as follows: The two sheets of glass, although tightly
pressed together, are separated in most places by a thin wedge of air
(see Fig. 410), which represents in an exaggerated form the bending of
the plates when pressed by the clamp. Several waves are represented as
coming from the right and entering the glass. Now the wave moving from
_R_ to the plates has some of its light reflected from each glass
surface. Consider the two portions of the wave reflected at each of the
surfaces between the plates, _i.e._, from the two surfaces of the wedge
of air. If the portion of the wave reflected from the second surface of
the air wedge combines with that reflected from the first surface, in
the _same phase_ as at _C_, the two reflected waves strengthen each
other. While if the two reflected portions of the wave meet in opposite
phases as at _A_ and _B_, a decrease or a complete extinction of the
light results. This is called _interference_. If light of one wave
length is used, as red light, the regions of reinforcement and
interference are shown by red and dark rings, while if white light is
used, the ring where red light interferes, yields its complementary
color, greenish blue. Where interference of greenish blue occurs, red is
found, etc. Many phenomena are due to interference, such as (A) the
color of thin films of oil on water, where the portions of light
reflected from the two surfaces of the oil film interfere resulting in
the production of color; (B) the color of soap bubbles. When first
formed, soap-bubble films are not thin enough to show interference well,
but as the bubbles increase in size or become thinner on standing, the
conditions for interference are reached and, as the film becomes
thinner, a regular succession of colors is noticed.
=413. Differences Between Light and Sound.=--Among the important
differences between light and sound that have been considered are the
following: the former are (a) _waves_ in the ether, (b) _of very short
wave length_, and (c) their _motion is in straight lines_. Another
difference (d) is in _the mode of vibration_.
Sound waves are _longitudinal, while light waves are transverse_. Light
waves consist of vibrations of the ether at right angles to the line of
motion. To illustrate the reasoning that has led to this conclusion,
suppose a rope to be passed through two vertical gratings. (See Fig.
411, 1.) If the rope be set in _transverse_ vibration by a hand, the
waves produced will readily pass through to the gratings _P_ and _Q_ and
continue in the part extending beyond _Q_. If, however, _Q_ is at right
angles to _P_, no motion will be found beyond _Q_. Now if a stretched
coiled spring with longitudinal vibrations should take the place of the
rope, it is evident that the crossed position of the two gratings would
offer no obstacles to the movement of the vibration. In other words,
crossed gratings offer no obstruction to longitudinal vibrations, while
they may completely stop transverse vibrations.
[Illustration: FIG. 411.--Transverse waves will pass through both
gratings in (1) where the openings in the two gratings are at right
angles. The waves passing _P_ are stopped by _Q_ (2).]
[Illustration: FIG. 412.--Effect of tourmaline crystals on light.]
=414. Polarization of Light.=--It is found that two crystals of
tourmaline behave toward light just as the two gratings behave with
respect to the transverse waves of the rope. Thus, if a small opening in
a screen is covered with a _tourmaline_ crystal, light comes through but
slightly diminished in intensity. If a second crystal is placed over the
first one so that the two axes are in the same direction as in Fig.
412_P_, light is as freely transmitted through the second crystal as
through the first, but if the crystals are crossed (Fig. 412_S_) no
light passes the second crystal. This experiment shows that the light
which has passed through one tourmaline crystal will pass through
another only when the latter is held in a certain position, hence it is
believed that a tourmaline crystal is capable of transmitting light
that is vibrating in one particular plane. The direct conclusion from
this is that _light waves_ are _transverse rather than longitudinal_.
The experiment just described illustrates what is called _polarization
of light_. The beam that after passing through _a_ (Fig. 412) is unable
to pass through _b_, if the two axes are crossed, is called a _polarized
beam_. The conclusion that light waves are transverse is therefore based
upon the phenomenon of the polarization of light. This was first
discovered by Huygens in 1690.
Important Topics
1. Interference of light: evidence, reasoning involved, illustration.
2. Polarization of light: evidence, reasoning involved.
3. Nature of light, differences between sound and light.
Exercises
1. Make a list of the differences between sound and light and state
briefly the evidence upon which the knowledge of these differences is
based.
2. Why will a thickness of film that will produce interference of red
light be different from that producing interference for green or blue?
3. Using the formula _n_ = _v_/_l_ compute the vibration rate for violet
light if its wave length is considered as 0.00004 cm.
4. Explain how the fact of polarization affects the wave theory of
light.
5. Show how it is possible by comparing the spectrum of the sun with
that of a star to tell whether the star is approaching or receding from
the earth.
Review Outline: Light
Light; speed, source, medium.
Straight Line Motion; shadow, umbra, penumbra, eclipse, image.
Photometry; Law of intensity, candle power, foot-candle.
Mirrors; Law of reflection; image--real, virtual; plane, curved,
parabolic, mirrors.
Refraction; cause and effects; plate, prism, lens; total reflection.
Lenses; six forms, principal focus, center, lens equation, 1/_F_ =
1/_D_{o}_ + 1/_D_{i}_.
Optical instruments; eye, defects and correction, camera, microscope,
etc.
Spectra; 3 kinds, dispersion, production of color effects, spectroscope,
uses.
Nature of Light; wave theory, interference, polarization, significance.
CHAPTER XVII
INVISIBLE RADIATIONS
(1) ELECTRIC WAVES AND RADIO-ACTIVITY
=415. Oscillatory Nature of the Spark from a Leyden Jar.=--In studying
sound (Art. 339), the sympathetic vibration of two tuning forks having
the same rate of vibration was given as an illustration of resonance.
The conditions for obtaining _electrical resonance_ by the use of two
Leyden jars are given in the following experiment.
Join the two coats of a Leyden jar (Fig. 413) to a loop of wire
_L_, the sliding crosspiece _M_ being arranged so that the length
of the loop may be changed as desired. Also place a strip of
tinfoil in contact with the inner coating and bring it over to
within about a millimeter of the outer coating as indicated at _G_.
Now join the outer coating of another exactly similar jar _A_ to a
wire loop of fixed length, the end of the loop being separated from
the knob connected to the inner coating, a short distance at _P_.
Place the jars near each other with the wire loops parallel and
connect coatings of _A_ to the terminals of a static machine or an
induction coil. At each discharge between the knobs at _P_, a spark
will appear in the other jar at _G_, if the crosspiece _M_ is so
adjusted that the areas of the two loops are exactly equal. When
the wire _M_ is moved so as to make the areas of the two loops
quite unequal, the spark at _G_ disappears.
[Illustration: FIG. 413.]
The experiment just described shows that two electrical circuits can be
_tuned_ by adjusting their lengths, just as two tuning forks may be
made sympathetic by adjusting their lengths. This fact indicates that
the discharge of the Leyden jar is _oscillatory_, since resonance can
plainly not be secured except between bodies having natural periods of
vibration. This same fact is also shown by examining the discharge of a
Leyden jar as it appears when viewed in a rapidly revolving mirror. (See
Fig. 414.) The appearance in the mirror shows that the discharge is made
up of a number of sparks, often a dozen or more, vibrating back and
forth until they finally come to rest. The time of one vibration varies
from one millionth to one hundred millionth of a second, depending on
the space between the discharging balls and the size of the jars.
[Illustration: FIG. 414.--Photograph of the oscillatory discharge of a
Leyden jar.]
The discharge of a Leyden jar or of another condenser sets up ether
waves that have the speed of light. Heinrich Hertz in Germany first
proved this in 1888. These waves are now known as Hertzian waves. The
length of these varies from 3 cm. to several miles, depending upon the
size and conditions of the discharging circuit.
[Illustration: FIG. 415.--A coherer.]
=416. The Coherer.=--The coherer is a device for detecting electric
waves. It consists of a glass tube with metal filings loosely packed
between two metal plugs that fit the tube closely. (See Fig. 415.) These
filings offer a _high_ resistance to the passage of an electric current,
but when electric waves pass through the filings these _cohere_ and
allow a weak current to pass through. This current may be strong enough
to operate a relay connected with a sounder or bell that gives audible
signals. If the tube be tapped the filings will be disturbed and the
resistance again made so high that no current can pass through.
=417. Wireless Telegraphy.=--In 1894 Marconi, then a young man of
twenty, while making some experiments with electrical discharges
discovered that the coherer would detect electrical waves at a
considerable distance from their source and that by the use of a
telegraph key the "dots and dashes" of the telegraph code could be
reproduced by a sounder attached to a relay. At present the coherer is
used principally in laboratory apparatus, as much more sensitive
detectors are now available for commercial work. The essential parts of
a modern wireless telegraph apparatus as used in many commercial
stations are shown in Fig. 416.
Alternating current at 110 volts is sent into the primary, _P_, of
a transformer, the secondary, _S_, of which produces a potential of
5000 to 20,000 volts. The secondary charges a condenser until its
potential becomes high enough to produce a discharge across a spark
gap, _SG_. This discharge is oscillatory, the frequency being at
the rate of about one million a second, depending upon the capacity
of the condenser and the induction of the circuit.
These oscillations pass through the primary of the oscillation
transformer, inducing in the secondary, electric oscillations which
surge back and forth through the antennæ, or aerial wires, _A_.
These oscillations set up the "wireless waves." The production of
these waves is explained as follows: An electric current in a wire
sets up a magnetic field spreading out about the conductor; when
the current stops the field returns to the conductor and
disappears. The oscillations in the antennæ, however, have such a
high frequency, of the order of a million a second, that when one
surge of electricity sets up a magnetic field, the reverse surge
immediately following sets up an opposite magnetic field before the
first field can return to the wire. Under these conditions a
succession of oppositely directed magnetic fields are produced
which move out from the antennæ with the speed of light and induce
electric oscillations in any conductors cut by them.
[Illustration: FIG. 416.--Diagram of a commercial wireless telegraph
apparatus.]
While the electric waves are radiated in all directions from the
aerial, the _length_ of the waves set up is approximately four
times the combined length of the aerial wires and the "lead in"
connection to the oscillation transformer.
The electric waves induce effective electrical oscillations in the
aerial of the receiving station, even at distances of hundreds of
miles, provided the receiving transformer, _RT_, is "tuned" in
resonance with the transmitting apparatus by adjustments of the
variable condenser, _VC_, and the loading coil, _L_. The _detector_
of these oscillations in the receiving transformer is simply a
crystal of silicon or carborundum, _D_, in series with two
telephone receivers, _Ph_. The crystal detector permits the
electric oscillations to pass through it in one direction only. If
the crystal did not possess this property, the telephone could not
be used as a receiver as it cannot respond to high frequency
oscillations. While one spark passes at _SG_, an intermittent
current passes through the receiver in one direction. Since some
300 to 1200 sparks pass each second at _SG_ while the key, _K_, is
closed, the operator at _Ph_ hears a musical note of this frequency
as long as _K_ is depressed. Short and long tones then correspond
to the dots and dashes of ordinary telegraphy. In order to maintain
a _uniform tone a rotary spark gap_, as shown, is often used. This
insures a tone of fixed pitch by making uniform the rate of
producing sparks.
The _Continental_ instead of the _Morse_ code of signals is generally
employed in wireless telegraphy, since the former employs only _dots_
and _dashes_. The latter code employs, in addition to dots and dashes,
_spaces_ which have sometimes caused confusion in receiving wireless
messages. The United States government has adopted the regulations of
the _International Radio Congress_ which directs that commercial
companies shall use wave lengths between 300 and 600 or above 1600
meters. Amateurs may use wave lengths less than 200 meters and no
others, while the government reserves the right to wave lengths of 600
to 1600 meters. See p. 459 for Continental telegraph code.
=418. Discharges in Rarefied Air.=--Fig. 417 represents a glass tube 60
or more centimeters long, attached to an air pump. Connect the ends of
the tube to the terminals of a static machine or of an induction coil,
_a-b_. At first no sparks will pass between _a_ and _f_, because of the
high resistance of the air in the tube. Upon exhausting the air in the
tube, however, the discharge begins to pass through it instead of
between _a_ and _b_. This shows that an electrical discharge will pass
more readily through a partial vacuum than through air at ordinary
pressure. As the air becomes more and more exhausted, the character of
the discharge changes. At first it is a faint spark, gradually changing
until it becomes a glow extending from one terminal to the other and
nearly filling the tube.
[Illustration: FIG. 417.--An Aurora tube.]
_Geissler tubes_ are tubes like the above. They are usually made of
different kinds of glass twisted into various shapes to produce
beautiful color effects. The _aurora borealis_ or northern light is
supposed to be electric discharges through rarefied air at the height of
from 60 to 100 miles above the earth's magnetic poles. (See Fig. 418.)
[Illustration: FIG. 418.--Aurora Borealis.]
=419. Cathode Rays.=--When the tube in Art. 420 is exhausted to a
pressure of 0.001 mm., or a little less than one millionth of an
atmosphere, the character of the discharge is entirely changed. The
tube becomes filled with a yellowish green phosphorescent light. This is
produced by what are called cathode rays striking the glass walls of the
tube. These rays are called cathode rays because they come from the
cathode of the tube. They are invisible and that they travel in straight
lines is shown by the shadow obtained by using a tube with a screen
(Fig. 419).
[Illustration: FIG. 419.--A cathode ray tube.]
=420. "X" Rays.=--In 1895, Professor Röntgen of Wurtzburg, Germany,
discovered that when the cathode rays strike the walls of the tube or
any solid within it they excite a form of invisible radiation. This
radiation is called Röntgen rays, or more commonly, "X" rays. Careful
experiments show that they travel in straight lines, and that they can
not be reflected or refracted as light waves are. They pass through
glass and opaque objects such as flesh, cardboard, cloth, leather, etc.,
but not through metallic substances. The tube in Fig. 420 has a screen
covered with crystals which become luminous when struck by the cathode
rays. On bringing a magnet near the tube the luminous line is raised or
lowered showing that the magnetic field affects the stream of cathode
rays, attracting it when in one position but repelling it when in the
reverse direction. The cathode rays which cause the bright line possess
a negative charge of electricity. They are now believed to be electrons
shot off from the surface of the cathode with speeds that may reach
100,000 miles a second. "X" rays possess no electrical charge whatever
and cannot be deflected by a magnet. They produce the same effect on a
photograph plate as light does, only more slowly. Hence, they can be
used in taking "X" ray photographs. Certain crystals, like barium
platinum cyanide, fluoresce when struck by the "X" rays. The
_fluoroscope_ is the name given to a light-tight box closed at one end
by a cardboard covered with these crystals (Fig. 421). On looking into
the fluoroscope with an opaque object such as the hand placed between
the screen and the "X" ray tube, a shadow of the bones of the hand can
be seen upon the screen of the fluoroscope. (See Fig. 422.)
[Illustration: FIG. 420.--The stream of cathode rays is deflected by a
magnet.]
[Illustration: FIG. 421.--A fluoroscope.]
[Illustration: FIG. 422.--A view of the "shadow" of a hand as seen in a
fluoroscope.]
A special form of the tube is used. (See Fig. 423.) In this tube a
platinum disc is placed at the focus of the concave cathode. This
concentrates the "X" rays in one direction. It is now generally believed
that "X" rays are waves in the ether set up by the sudden stoppage of
the cathode rays at the platinum anode.
[Illustration: FIG. 423.--An "X" ray tube.]
=421. The Electromagnetic Theory of Light.=--The study of electric waves
has shown that they are similar to light waves in many respects: (a)
they have the same velocity; (b) they can be reflected and refracted.
The main difference is in their length, light waves being very much
shorter. In 1864 James Clerk Maxwell, an English physicist, proposed the
theory that ether waves could be produced by electrical means and that
light waves are electromagnetic. In 1888 Hertz proved by his experiments
that ether waves having the same velocity as light could be produced in
this way. It is now the general belief that light waves are ether waves
produced by the vibrations of the electrons within the atoms and that
they consist of electromagnetic waves in the ether.
=422. Radio-activity.=--In 1896 Henri Becquerel of Paris discovered that
uranium and its compounds emit a form of radiation that produces an
effect upon a photographic plate that is similar to that resulting from
the action of "X" rays. These rays are often called _Becquerel_ rays in
honor of their discoverer. The property of emitting such rays is called
=radio-activity=, and the substances producing them are called
=radio-active=.
In 1898, Professor and Mme. Curie after an investigation of all the
elements found that _thorium_, one of the chief constituents of
incandescent gas mantles, together with its compounds, was also
radio-active. This may be shown by the following experiment:
Place a flattened gas mantle upon a photographic plate and leave in
a light tight-box for several days. Upon developing the plate in
the usual way a distinct image of the mantle will be found upon the
plate.
=423. Radium.=--Mme. Curie discovered also that pitch-blende possessed
much greater radio-active power than either thorium or uranium. After
prolonged chemical experiments she obtained from several tons of the ore
a few milligrams of a substance more than a million times as active as
thorium or uranium. She called this new substance _radium_. Radium is
continually being decomposed, this decomposition being accompanied by
the production of a great deal of heat. It has been calculated that it
will take about 300 years for a particle of radium to be entirely
decomposed and separated into other substances. It is also believed that
radium itself is the product of the decomposition of uranium, atomic
weight 238, and that the final product of successive decompositions may
be some inert metal, like lead, atomic weight 207.
The radiation given off by radio-active substances consists of three
kinds: (A) Positively charged particles of helium called _alpha_ rays:
(B) negatively charged particles called _beta_ rays: (C) _gamma_ rays.
The alpha rays have little penetrating power, a sheet of paper or a
sheet of aluminum 0.05 mm. stopping them. Upon losing their charges they
become atoms of helium. Their velocity is about 1/10 of that of light or
18,000 miles a second. The _spinthariscope_ is a little instrument
devised by Sir Williams Crookes in 1903 to show direct evidence that
particles are continually being shot off from radium. In this instrument
(Fig. 424), a speck of radium _R_ is placed on the under side of a wire
placed a few millimeters above a screen _S_ covered with crystals of
zinc sulphide. Looking in the dark at this screen through the lens _L_,
a continuous succession of sparks is seen like a swarm of fireflies on a
warm summer night. Each flash is due to an alpha particle striking the
screen. The beta rays are supposed to be cathode rays or electrons with
velocities of from 40,000 to 170,000 miles a second. The gamma rays are
supposed to be "X" rays produced by the beta rays striking solid
objects.
[Illustration: FIG. 424.--A spinthariscope.]
=424. The discovery of radio-activity= has revolutionized the ideas of
the constitution of matter. Further, the results of experiments upon
radio-active materials reveals the presence of immense quantities of
sub-atomic energy. If man ever discovers a means of utilizing this, he
will enter a storehouse of energy of far greater extent and value than
any of which he has as yet made use. A consideration of this unexplored
region gives zest to the work of those who day by day are striving to
understand and control forces of nature.
Important Topics
1. Oscillatory nature of discharge of Leyden jar. Proofs.
2. Wireless telegraphy and telephony.
3. Electrical discharges in rarefied gases.
4. Cathode and "X" rays.
5. Electromagnetic theory of light.
6. Radio activity and radium.
[Illustration: CONTINENTAL TELEGRAPH CODE
A . - J . - - - S . . .
B - . . . K - . - T -
C - . - . L . - . . U . . -
D - . . M - - V . . . -
E . N - . W . - -
F . . - . O - - - X - . . -
G - - . P .- - . Y - . - -
H . . . . Q - - . - Z - - . .
I . . R . - .
PERIOD INTERROGATION EXCLAMATION
. . . . . . . . - - . . - - . . - -
1 . - - - - 2 . . - - - 3 . . . - -
4 . . . . - 5 . . . . . 6 - . . . . 7 - - . . .
8 - - - . . 9 - - - - . 0 - - - - -]
CHAPTER XVIII
WIRELESS TELEPHONY AND ALTERNATING CURRENTS
The developments in wireless communication have been so rapid
during recent years that a more extended account, than that given
in Art. 417 of the apparatus and methods used at the present time,
seems desirable. The study of Alternating Currents is also included
with the idea that it will make the text more complete and of wider
usefulness.
WIRELESS TELEPHONY
=425. The Wireless Telephone.=--One of the most important developments
in wireless communication in recent years has been in wireless
telephony. We realize its possibilities, when we hear of the
achievements of talking across an ocean or between airplanes and the
ground.
The wireless telephone can be best understood by comparing it with the
common telephone. When the latter is in use, a direct current flows
continually through the instrument. (See Arts. 312-316.) When a person
speaks into the transmitter, the sound waves of the voice cause the
diaphragm to vibrate, this action causes rapid changes in the
_resistance_ of the transmitter, which in turn causes the direct current
to fluctuate just in step with the pulses of the voice waves. This
fluctuating direct current passes through the primary of an induction
coil, producing in the secondary an intensified alternating current.
This passes over the line wires to the receiver where it produces
variations in the magnetic field affecting the receiver diaphragm,
causing the latter to reproduce the voice of the person speaking in the
transmitter. Now to make the comparison clear, two facts must be noted
with regard to the wire telephone: first, there must be an action in the
transmitter which causes variations in a current through the instrument;
second, this fluctuating current produces a more intense alternating
current which flows over the line and affects the receiver diaphragm,
producing there sound vibrations of greater intensity than those used at
the transmitter. This added energy comes from the current flowing
through the transmitter. The case is analogous to that of an electric
bell. The armature of the bell vibrates with greater energy than is
required to push the button, the extra energy being derived from the
battery.
=426. The Action of the Wireless Telephone.=--In the wireless telephone
we have a continuous stream of electric waves of high frequency. (See
Fig. 425_A_.) This stream of electric waves corresponds to the current
that flows through the transmitter in the wire telephone. These waves
are of such high frequency that even though we had a receiver diaphragm
vibrating in step with the waves, we could not hear the sound because
the human ear cannot hear a sound which consists of more than about
40,000 vibrations per second. The sound waves act upon this stream of
waves very much, as in the wire telephone, the transmitter acts to
modify the line current. The impulses caused by the voice are much
slower than the electric waves first mentioned and these slower impulses
are reproduced in the receiver. Not only are these slower impulses
reproduced but they are _amplified_, that is, produced with greater
energy than the impulses impressed on the stream of waves. Fig. 425_A_
represents as nearly as is possible in a diagram the continuous stream
of electric waves. Fig. 426_B_, represents the impulses produced by the
sound alone, and Fig. 426_C_, shows how these voice impulses are
impressed on the stream of waves.
[Illustration: FIG. 425.--_A_, unmodified high frequency waves; _B_,
waves of voice frequency; _C_, high frequency waves modified by waves of
voice frequency.]
[Illustration: FIG. 426.--Vacuum tube, transmitting type. (_Western
Electric Co._)]
[Illustration: FIG. 427.--Vacuum tube, receiving type. (_Western
Electric Co._)]
[Illustration: FIG. 428.--Diagram of wireless telephone transmitting
set.]
=427. The Vacuum Tube or Audion.=--The device by which all of this is
accomplished is the _vacuum tube_. (See Fig. 426.) This tube contains
three electrodes. _First_, a _filament_ (_F_, in Fig. 428) which is
heated by a current from a battery (_B_{1}_, Fig. 428) and because it is
heated, sends out a stream of electrons. _Second_, the _plate_ which
forms the anode of the circuit from battery, _B_{2}_. This plate
receives the electrons which are thrown off by the heated filament,
hence a current flows through the circuit of _B_{2}_; the discharge
through the tube depending on the e.m.f. between the filament and the
plate. _Third_, a _grid_ is placed between the filament and the plate
and is connected to the _secondary_ of the induction coil, the primary
of which is connected to the transmitter. When the transmitter diaphragm
is vibrating, the e.m.f. induced in the secondary of the induction coil
causes a variation in the potential of the grid. This means a variation
in the electric field between the filament and the plate. (See Fig.
428.) The changing electric field causes a variation in the discharge of
electrons through the tube; the variation corresponds to the vibrations
of the transmitter diaphragm. This produces a surging current of the
frequency of the sound waves in the primary of the transformer (_T_,
Fig. 428). The secondary of this transformer is connected to the antennæ
(_A_) and the earth (_E_). By means of the transformer, rapid surgings
are set up in the antennæ and these surgings produce a continuous stream
of electromagnetic waves which goes out in space. (Like Fig. 426_C_.)
These electromagnetic waves produce oscillations in the antennæ of a
receiving station. The antennæ transmit the impulses to a _tube_ (Fig.
427) which acts as a _detector_, and makes possible the reproduction of
the sound by an ordinary telephone receiver.
[Illustration: FIG. 429.--View of wireless telephone set.]
The _vacuum tube_ in the transmitting circuit also _amplifies_ the
impulses, that is, the energy of the waves given out is greater than
that of the impulses which produce them, the additional energy being
derived from the battery sending current through the plate and filament.
In operation, the filament and the plate are connected to a battery with
a _condenser_ (_VC_) and an _inductance coil_ (_I_) in the circuit, as
shown in Fig. 428. Photograph of a complete modern wireless telephone
set is shown in Fig. 429.
ALTERNATING CURRENTS
=428. Alternating currents= are of interest to us because of their
general commercial use. To understand the reason for the extensive
application of alternating currents it is necessary to learn the
fundamental principles which pertain to them. The production of such
currents has already been explained in Arts. 300-304. It should be
remembered that the current developed in the armature of a dynamo is
alternating. A dynamo may _deliver_ a direct or an alternating current,
depending on the method of collecting the current from the armature. If
a _commutator_ is used, the machine delivers _direct_ current, if _slip
rings_ are employed, an _alternating_ current is delivered.
=429. The Magnetic Field of an Alternating Current.=--The magnetic field
of a direct current has been considered in Arts. 255-256. It has been
shown to be arranged in circles about the conductor, according to the
_Right Hand Rule_. (See Figs. 229 and 230.) These facts will help one to
understand the following experiment:
If a number of magnetic compasses be arranged in a circle about a
straight vertical wire carrying a direct current, the compass
needles will point out a circle about the wire. (See Fig. 430,
_A_.) If now the current be reversed the compass needles will
reverse themselves and point in a direction just opposite to that
taken at first. (See Fig. 430, _B_.) This will be clear if you
imagine yourself walking around the wire in the direction the
compass needles pointed at first, and then walking around the wire
in the reverse direction. This illustrates what happens in the
field of an alternating current. The field reverses each time the
current reverses.
The magnetic field of an alternating current not only rapidly reverses
itself, but also continually _changes in intensity_. At the instant when
the current reverses, the force of the magnetic field is zero since the
current at that instant is zero. As the current begins flowing and
increases to its maximum intensity, the magnetic field appears and
increases in intensity; and as the current decreases to zero, the
magnetic field changes in a similar manner. The field as it grows in
strength extends farther and farther from the wire, as it decreases in
strength it contracts or draws closer to the wire. Thus the magnetic
field may be said to expand and contract. We may picture the lines of
force as continually moving. In a typical a.-c. circuit, the complete
series of changes takes place in a small fraction of a second, and is
repeated many times over in a second. Contrast this with the magnetic
field of a constant direct current. Here the magnetic field has the same
direction as long as the current flows and does not change in strength.
This comparison is important because most of the differences between
direct and alternating currents depend on differences in the action of
their magnetic fields.
[Illustration: FIG. 430.--Arrangement of compasses about a wire carrying
an alternating current.]
=430. Transformers.=--The transformer has been described in Arts.
309-310. The principle of the transformer may be illustrated by the
following experiment:
A coil having several hundred turns of No. 18 d.c.c. copper wire is
placed over one arm of a "U" shaped iron core (see Fig. 431) and
then connected to a 110 volt a.-c. lighting circuit. Another coil
(_S_) having about 50 turns of No. 22 d.c.c. copper wire is
connected to an electric bell or buzzer, or a low voltage electric
light bulb. When the small coil is held over the other arm of the
"U" shaped iron core, the bell rings or the bulb glows. It is
evident that the electromotive force developed in the small coil
(_S_) is due to the alternating magnetic field surging back and
forth through the iron core. In Fig. 431 the core is "open" since
the magnetic field must pass through the air from one end of the
core to the other. A typical transformer has a _closed core_ to
provide a _closed magnetic circuit_. To secure this, take a
suitable bar of iron and lay across the end of the "U" shaped core,
and notice any change in the induced current produced in the small
coil, due to increased movement of magnetism through the closed
iron core.
[Illustration: FIG. 431.--Diagram of a transformer.]
This experiment illustrates the construction and action of a
transformer. In a commercial transformer, the two windings are on a
closed magnetic circuit. (See Figs. 304 and 305, p. 346.) To keep the
coils insulated, the transformer is placed in an iron "housing" and
covered with oil. These "housings," or transformer cases are generally
attached to poles near buildings in which alternating current is used.
=431. Voltage Relation in a Transformer.=--In the experiment described
above, a bell was rung by an induced current produced in the secondary
coil. The induced e.m.f. was less than the voltage of the primary coil
partly because there was some magnetic leakage, but mainly because
there were fewer turns of wire on the secondary. In a commercial
transformer the magnetic leakage is practically zero. In such a case,
the ratio of the number of turns on the primary coil to the number on
the secondary equals the ratio of the e.m.f. induced in the primary to
the e.m.f. induced in the secondary. Suppose, for example, we wish to
make a bell ringing transformer to use on a 110 volt lighting circuit,
10 volts being required for the bell; the secondary will then need
one-eleventh of the number of turns of the primary. So that if 550 turns
are on the primary, then 50 turns will be needed for the secondary. This
will be a "step-down" transformer. On the other hand, suppose we wish to
"step-up" the voltage as is done in a certain power station where the
voltage of the generators is 6000 volts, the voltage being stepped up to
44,000 by means of large transformers. This means that the secondary
coils have approximately 7-1/3 times as many turns as the primary.
=432. Power Loss in a Transformer.=--When the voltage is "stepped up" in
a transformer, do we gain power? To answer this question we must
remember that electric power does not depend on voltage alone but on the
_product_ of e.m.f. and current intensity. (See Art. 291.) By tests with
a.-c. voltmeters and ammeters, we find that when the secondary e.m.f. is
_greater_ than the primary e.m.f., the secondary current intensity is
_less_ than that in the primary. It is also found that the _power_
developed is less than the power received by the transformer, _i.e._,
the "output" is less than the "input" as we would expect from the law of
machines. The power loss is mainly due to the work required to reverse
the magnetism, that is, to continually reverse the position of the iron
molecules. (See Art. 205.) The energy lost in this manner is known as
"core loss" since it occurs in the iron core. The lost energy appears
as heat. So much heat is developed in large transformers that special
means of cooling are provided. In order to make the heat developed as
small as possible, the cores are "laminated" (see Fig. 305, p. 346),
that is, built up of thin sheets of iron, because if the iron cores were
solid, the changing magnetic fields would induce electric currents in
the iron cores, which would produce an excessive amount of heat with a
correspondingly large power loss.
[Illustration: FIG. 432.--Diagram of "bell-ringing" transformer.]
=433. Choke Coils and Inductance.=--If we refer to Fig. 432 we see that
the primary winding of the bell ringing transformer is connected across
the line. This winding forms a closed circuit whether the bell is
ringing or not. The resistance of this winding is small. Let us assume
it to be one ohm. With a one ohm resistance connected across a 110 volt
line we might expect a current of 110 amperes. This is certainly what we
should get if we were to connect a one ohm resistance across a line
having 110 volts direct. The primary would form a short circuit if the
current were direct. But the fact is that practically no current flows
through the primary winding when the bell is not ringing. Herein lies
one of the important differences between alternating and direct
currents. With an alternating current the primary winding of our
transformer acts as a _choke coil_ and "chokes" down the current almost
to zero. Let us see how this is done.
[Illustration: FIG. 433.--A circuit containing a choke coil.]
Let Fig. 433 represent a choke coil. Since alternating current is used,
the magnetic field is continually changing. Each turn of wire has its
own magnetic field. The lines of force of turn number 1 expand and
contract and as they do so they move across turns 2, 3 and so on. In
like manner the lines of force from each turn of wire move across the
other turns. In other words the coil is cutting its own lines of force.
Now whenever an electric conductor cuts magnetic lines of force an
electromotive force is induced in the conductor. There is then an e.m.f.
induced in the coil by its own magnetic field. This induced e.m.f. on
the whole opposes the applied e.m.f.; in the primary of our bell ringing
transformer the induced e.m.f. opposes the e.m.f. of the line to such an
extent as to reduce the current almost to zero. _Inductance_ is the
action of an alternating current in inducing an opposing e.m.f. in the
coil in which the current is flowing. Since this opposing e.m.f. is
induced in the coil by its own magnetic field this action is also called
_self-induction_. In a transformer the action of the field of the
primary upon the secondary is _mutual induction_; while the action of
the field of the primary in choking the current in the primary itself is
self-induction or inductance. A coil having a single winding and used to
introduce inductance in a circuit is called a _choke coil_. A choke
coil inserted in a lamp circuit in series with the lamps dims the lamps
because it reduces the intensity of the current.
[Illustration: FIG. 434.--Diagram showing graphically an alternating
current with a "lag" of 30° behind its electromotive force.]
Self-induction causes the current to _lag_, that is, the current does
not quite reach its maximum at the instant the voltage reaches its
maximum. Fig. 434 shows graphically an e.m.f. and a lagging current. In
this figure the maximum current is shown following the maximum voltage
at an interval of 30 degrees. In other words the armature in a two-pole
field must turn 30 degrees from the position of maximum voltage before
the current in the coil, where the self-induction occurs, reaches its
maximum.
=434. Reactance and Impedance.=--A choke coil has resistance as well as
inductance. Its resistance can be found by the voltmeter-ammeter method,
using a direct current. (See Art. 278.) Let us take for example the
primary winding of a bell ringing transformer. Using a direct current
and testing the coil with a voltmeter and ammeter we find its resistance
to be, let us say, one ohm. If we connect the same coil across a 110
volt a.-c. line we find the current to be very small, say 0.05 ampere.
The coil now has resistance and _reactance_. Reactance is the effect of
self-induction in hindering the flow of current. It is measured in ohms.
The combined effect of resistance and reactance is called _impedance_.
In the example above, the coil has 110 (volts)/0.05 (ampere) = 2200 ohms
of impedance. In applying Ohm's law to an alternating current circuit,
impedance must be substituted for resistance. Ohm's law as applied to an
a-c. circuit should be stated: "Current intensity equals e.m.f. divided
by impedance", or _I_ = _E_/_Z_. (_Z_ = impedance.)
[Illustration: FIG. 435.--The relation between resistance, reactance and
impedance.]
Impedance, however, does not equal the _sum_ of resistance and
reactance. The relation between these three quantities is similar to
that between the three sides of a right triangle, in which the impedance
represents the hypotenuse, and the resistance and reactance the other
two sides. See Fig. 435 which indicates that Resistance² + Reactance² =
Impedance², or (_R²_ + _X²_ = _Z²_). (_X_ = reactance.) To illustrate
this relation; suppose the primary of a transformer has 10 ohms
impedance and 8 ohms resistance, then the reactance equals 10² - 8² =
6², or the reactance is 6 ohms.
Exercises
1. Find the reactance of a choke coil having a resistance of 10 ohms,
when its impedance is 50 ohms. How great a current flows through this
coil if the terminal voltage is 110 volts?
2. When the bell is ringing, the primary of a bell ringing transformer
has an appreciable current. Suppose this current is 0.2 ampere. What is
the impedance if the voltage of the line is 115 volts? What is the
reactance if the resistance is 1 ohm?
3. The primary of a large transformer has a terminal voltage of 6000
volts and a current of 600 amperes. What is the impedance? If the
resistance is 6 ohms, what is the reactance?
[Illustration: FIG. 436.--A telephone set showing a condenser used in
the circuit of the "ringer."]
=435.--The electric condenser= (see Art. 231) is a very useful device in
a.-c. circuits; _e.g._, in telephone sets used in cities, a condenser is
used in the ringing circuit, as shown in Fig. 436. Alternating current
is required to ring such a bell and a condenser permits an a.-c. current
to act through it, although it entirely prevents the flow of a direct
current. This peculiar action will now be explained.
=436. The action of a condenser= in an alternating current circuit may
be illustrated by the following experiment. Connect twelve, 1 m.f.
(microfarad) condensers, in parallel, and then attach them to a 110 volt
a.-c. line so that an incandescent lamp is in circuit as shown in Fig.
437. The lamp will be found to glow brightly, although there is no
electrical connection between the two sets of condenser plates. If the
same arrangement is connected to a 110 volt direct current circuit, the
lamp does not glow because it is really an open circuit. The lamp glows
on an a.-c. circuit because, although no electricity flows _through_ the
condenser, it does flow _into and out of_ the condenser, surging back
and forth through the lamp with sufficient intensity to cause it to glow
brightly. When the a.-c. current moves one way in the circuit, one set
of plates of the condensers becomes charged positively, the other,
negatively. When the a.-c. current reverses, the charges on the
condenser plates reverse. In the ordinary lighting circuit 120 reversals
take place each second, so that electricity rapidly flows into and out
of the condensers. On removing one condenser after another from the
circuit, the lamp is found to glow less and less, till when but one
condenser is left, no glowing is observed, since one small condenser
does not have sufficient _capacity_.
[Illustration: FIG. 437.--Twelve condensers in circuit with an
incandescent lamp.]
The unit of capacity is the _Farad_. Capacity is defined as the quantity
of electricity per second that flows into a condenser when the voltage
at the terminals changes at the rate of one volt per second. If a change
of one volt per second causes one coulomb to flow per second, that is, a
current of one ampere, the capacity is one _farad_. The condensers used
in the above experiment have a capacity of one microfarad, or one
millionth of a farad.
A condenser, on account of its capacity, causes an a.-c. current to
_lead_ the voltage, that is the current reaches its maximum value before
the voltage does. In this respect a condenser has an effect opposite to
that of the self-induction of a choke coil (the latter causing the
current to "lag"). (See Fig. 435.)
=437. Transmission of Electric Power.=--A field of peculiar usefulness
for a.-c. currents is in the economical transmission of electric power.
This fact is due to the following reasons: (_a_) The loss of electrical
power in a transmission line is due to the production of heat; the heat
produced being proportional to _I²R_, or to the _square_ of the _current
intensity_. Any lessening of the current flow required to transmit a
given power will therefore increase the efficiency of transmission.
(_b_) In order to employ a small current in transmitting a large amount
of power, we must use a very high e.m.f. Such high electromotive forces,
say from 60,000 to 100,000 volts, can be obtained only by the use of
a.-c. transformers, since it is not practicable to build a direct
current generator capable of producing 60,000 volts. In large power
transmission systems, a.-c. generators are used to produce powerful
alternating currents. The e.m.f. is then stepped up to a suitable
voltage (2300-100,000) by transformers and sent over transmission lines
to the various places where the power is to be used; at these places
suitable transformers "step-down" the e.m.f. to a convenient or safe
voltage for use. (See Fig. 442 of a transmission line and Fig. 438 of a
large power transmission system, and Fig. 439 of an a.-c. generator and
power plant.)
[Illustration: FIG. 438.--Diagram of an alternating current high tension
power system. (_A_) Alternator, (_Tu_) water turbine, direct connected
to alternator, (_E_) exciter, (_T_{1}_) step-up transformers in power
station, (_T_{2}_) step-down transformers in substation, (_M_) motor,
(_L_) lamps, single-phase, three-wire system, (_T_{3}_) step-down
transformers delivering three-phase current to rotary converter (_R_)
which delivers direct current to the trolley line.]
=438. Power Factor.=--The _power factor_ is a matter of interest and
importance in the use of a.-c. machines. Its meaning and use may be
learned from the following explanation: In a direct current circuit,
watts equals volts times amperes. In an alternating current circuit,
this equation is true only when the current is "in step" with the
voltage, that is, only when there is no _inductance_ or _capacity_ in
the circuit. If current and voltage are out of step, _i.e._, if there is
_lag_ or _lead_ (see Fig. 434), the product of volts and amperes gives
only the _apparent power_, the ratio between true and apparent power
depending on the amount of lag or lead. This ratio is called the power
factor. In an a.-c. circuit, then, the power equation is: watts = volts
× amperes × power factor, or power factor = true power/apparent power.
The product of volts and amperes is the _apparent power_ and is called
volt-amperes in distinction from the true power or watts. Therefore the
following is true: power factor = true watts/volt-amperes.
[Illustration: FIG. 439.--Power house showing alternators, direct
connected to horizontal hydraulic turbines. Note the direct current
"exciter" on end of shaft of alternator. (_Courtesy of General Electric
Co._)]
=439. Single-phase Currents.=--There are several kinds of a.-c.
currents. One of the most common is the _single-phase_. It is simply the
common a.-c. current used for light and power in the average home, and
uses a two-wire circuit around which the current is rapidly alternating.
Fig. 440 illustrates the changes of e.m.f. in an a.-c. single-phase
current. It may be produced by a single coil rotating in a magnetic
field. The curve of Fig. 440 represents one _cycle_, that is, one
complete series of changes in the electromotive forces. At the end of
the cycle the armature is in the same condition as at the beginning so
far as the magnetic field is concerned. It then begins a new cycle. The
ordinary commercial alternating current has a frequency of 60, that is
60 cycles per second. One rotation produces as many cycles as there are
pairs of poles. For example, if there are 48 poles in the generator
field, one rotation produces 24 cycles.
[Illustration: FIG. 440.--Graph showing the e.m.f. changes of a
single-phase current for one "cycle."]
=440. Three-phase Currents.=--Now suppose we have three coils as in Fig.
441, the coils being evenly spaced, or 120 degrees apart, at _A_, _B_,
and _C_. If the coils are rotated in a magnetic field, each will produce
an electromotive force. The result produced by three such coils is
called a _three-phase_ current. Ordinarily six wires, or three circuits,
would be required to carry the current produced by three separate coils;
for when coil "_C_" is in the 90 degree position, where its e.m.f. is a
maximum, coil "_B_" is 120 degrees past its maximum, and coil "_A_" is
240 degrees past its maximum. The graph (Fig. 441) shows the maximum
points of the three e.m.f's. separated by intervals of 120 degrees. In
practice, however, it is found possible to use _three wires_ instead of
six, as explained in Art. 441.
[Illustration: FIG. 441.--Graph showing the e.m.f. changes of a
three-phase current for one "cycle."]
=441. Three-wire Transmission.=--The currents produced in the three
coils just described undergo precisely the same changes as those
represented in the _graph_ (Fig. 441) for the three electromotive
forces. Careful examination of the graph will show that at any point the
sum of the _plus_ e.m.f's. equals the sum of the _minus_ e.m.f's. In
other words the algebraic sum of the three e.m.f's. is zero. Therefore
if we properly connect a transmission line of three wires to the
generator, the sum of the currents leaving the generator will equal the
sum of the currents returning to it. Since the algebraic sum of the
currents produced by the three coil combination described in Art. 440 is
always zero, it is possible to use three wires on three-phase
transmission lines. Fig. 442 shows a "tower" carrying three, three-wire
transmission lines. Long distance, high tension transmission lines are
generally three-wire lines carrying three-phase a.-c. currents.
[Illustration: FIG. 442.--A "tower" supporting three, three-phase
circuits of a high tension transmission line.]
=442. Alternators.=--A dynamo which delivers alternating current is
known as an _alternator_. Commercial alternators have many pairs of
poles in the field and as a rule the field rotates while the armature is
stationary. The field must be supplied with _direct_ current for the
polarity of each coil in the field must remain unchanged. Usually a
separate "exciter" is used, which is a small direct current generator.
The current from this exciter is fed into the rotating field by means of
slip rings. Fig. 439 shows a d.-c. (direct current) exciter on the end
of the armature shaft of the large alternator.
[Illustration: FIG. 443.--Diagram of a "Series Motor."]
=443. The A.-C. Series Motors.=--The only type of motor that will run on
either alternating or direct current is the _series motor_. The
"universal" motor used in household appliances such as electric fans,
vacuum cleaners, etc., is a series motor. The reason a series motor will
run on either direct or alternating current is because the direction of
rotation of the armature of a motor depends on (_a_) the direction of
the current in the armature, and (_b_) the polarity of the field.
Reversing either of these alone, reverses the direction of rotation of
the armature, while reversing both at the same instant leaves the
direction of rotation unchanged. Fig. 443 is a diagram of a series motor
since the field coils and armature are connected in series. On an a.-c.
line, both field and armature current must therefore reverse at the same
instant. In a shunt motor (similar to Fig. 286) we have a divided
circuit, and the greater self-induction of the field coils causes an
a.-c. current through these coils to lag behind that flowing in the
armature so that the two currents do not reverse at the same instant.
[Illustration: FIG. 444.--Diagram of a gramme ring. It is shown
connected to a single-phase current so as to produce a rotating magnetic
field, similar to that obtained with a three-phase current. (_Ahrens,
Harley and Burns._)]
[Illustration: FIG. 445.--The "stator" of an induction motor.]
=444. The Induction Motor.=--Another common type of a.-c. motor is the
_induction motor_. Its advantage lies in its simplicity. It has neither
commutator nor brushes, the armature having no connection with an
external circuit. If the wires of a three-phase line be connected to a
coil wound in the form of a _gramme ring_, the connections being 120
degrees apart as in Fig. 444, the magnetic field within this coil will
change in the same manner as if a magnet were spinning upon a pivot at
the center of the coil. Suppose the _N_ pole at one instant is at _A_,
in one-third of a cycle it moves to _B_, in another third to _C_, and in
one cycle it makes a complete revolution. Thus we have a _rotating
magnetic field_. If a cup of some non-magnetic metal such as aluminium
or copper be placed on a pivot in the center of this coil, the cup is
cut by the moving lines of force and currents are induced in it.
Because of these currents, the cup has a magnetic field of its own, and
the action of the two magnetic fields is such as to pull the cup around
and cause it to rotate in the same direction as that in which the field
of the coil rotates. The coil represents the stationary part, the
_stator_ (Fig. 445) and the cup the rotating part, the _rotor_, of an
induction motor. While the cup rotates in the same direction, it does
not rotate so rapidly as the magnetic field. If it should it is plain
that it would not cut the lines of force. The difference between the
rate of rotation of the rotor and that of the magnetic field is called
the "slip." The rotating part in small induction motors is frequently
made in a single casting. In large motors, it is built up of heavy
copper bars. Thus, from its appearance the common form of rotor is
known as the "squirrel cage" rotor. (See Fig. 446.)
[Illustration: FIG. 446.--The "rotor" of an induction motor.]
[Illustration: FIG. 447.--Diagram illustrating the principle of the
synchronous motor. The armature coil passes the position shown in the
figure at the instant the current in the line reverses. Thus the
armature keeps with the line current, making one revolution with each
"cycle."]
=445. A synchronous motor= is one that keeps step with the alterations
of an alternating current. The line current is fed into the armature by
means of two slip rings and brushes. The principle of the synchronous
motor is illustrated in Fig. 447. This shows a motor having a two-pole
field. The armature current must be reversed twice in each revolution.
The reversal must take place when the armature winding is perpendicular
to the lines of force of the field. In a direct current motor this
reversal is brought about by the commutator. In a synchronous motor the
armature reaches the 90 degree position at the exact instant at which
the current reverses in the line. Thus in the case of a two-pole motor
the armature must make exactly one revolution for each cycle; it is,
therefore, a constant speed motor. Such motors are frequently employed
in converter stations where alternating current is converted into direct
current by what are called _rotary converters_.
In practice the synchronous motor has a number of pairs of field poles.
It is essentially an alternating current generator running as a motor.
One of the principal uses of the synchronous motor is that of a
converter, receiving alternating current and delivering direct current.
Synchronous motors are also used in transmission lines to aid in
maintaining constant voltage.
Important Topics
The wireless telephone, essential parts, action, arrangement.
Alternating currents, alternating fields.
Transformers, voltage relation of coils, power and core losses.
Self-induction, inductance, and coke coils, uses, applications.
Impedance, reactance, and resistance; relation and effects.
Condensers, uses and applications with a-c. circuits.
Alternating current power transmission; uses, advantages.
Power factor, lag, lead, volt-amperes, true watts.
Single- and three-phase currents; uses and nature of each.
Three-wire transmission systems, alternators, construction, and action.
A-c. motors, series, induction, synchronous.
INDEX
Aberration, spherical, 408
Absolute scale of temperature, 164
Absorptions of gases by solids and liquids, 29
Accelerated motion, 86
Acceleration, 87
Adhesion, 21
Aeroplane, 97
Air, aspirator, 67
brake, 74
cushion, 46
height (of atmosphere), 64
pressure, 56
pump, 66
weight, 56
Alternators, 481
Alternating current, 337, 466
Amalgamation, 273
Ammeter, 291
Ampere, 291
Archimedes' principle, 48
Arc light, 321
Armature, 335
Artesian wells, 44
Audion, 463
Aurora borealis, 453
Balloon, 72
Barometer, 59
Beats, 376
Boiling, laws, 208
point, 207
Boyle's Law, 63
Breezes, land and sea, 181
British thermal unit, 162
Brownian movements, 16
Calorie, defined, 162
Camera, 426
Candlepower, 394
Capillary action, 25
Cartesian diver, 71
Cathode rays, 453
Centrifugal force, 91
Charles' Law, 165
Chladni's figures, 381
Choke coils, 470
Coefficient of expansion, definitions, 170
gases, 167
liquids, 168
solids, 169
Coherer, 449
Cohesion, 21, 33
Color, 435
bodies, 435
complementary, 436
primary, 440
prismatic, 433
theory of color vision, 440
three-color printing, 440
Commutator, 335, 336
Compass, 230, 240
Concave lens, 418
Condenser, 260, 474
Conductors, 246
Conservation of energy, 127
Continental code, 459
compared with the Morse, 452
Convection, 179
currents in nature, 181
draft of a chimney, 180
Convex lens, 416
Cooling, artificial, 210
Corpuscular theory, 442
Coulomb, 290
meter, 291
Couple, 101
Critical angle, 414
Crookes' tube, 456
Crystallization, 28
melting point of some crystalline substances, 203
Daniel cell, 276
Declination, 240
Density, 38, 52
methods for finding, 53
Dew, 192
Dew point, 193
Diffusion of gases, 13
Dipping needle, 240
Direct Current, 337
Dispersion, 433
Distillation, 208
Draft of a chimney, 180
Dry cell, 275
Dynamo, 330, 333
Dyne, 93
Eye, the, 423
action of, in vision, 423
defects of, 425
Ear, the, 386
trumpet, 361
Earth's magnetism, 238
Echoes, 362
Eclipses, 391
Efficiency, 142
engines (tests), 219
machines, 142
Elasticity, 31
Electric bell, 269, 287
charge, distribution of, upon a conductor, 253
circuit, 269
currents, 267
single phase, 479
three phase, 479
effects, 277
induced, 326
discharge in rarefied air, 452
motor, 339
screen, 256
Electrical capacity, 259
fields, 247
Electrification, 243
Electrolysis, 308
laws, 311
practical uses, 311
Electromagnet, 281
Electromagnetic theory of light, 456
Electromotive force, 267
unit of, 295
Electron theory, 252
Electrophorus, 263
Electroplating, 307
Electroscope, 244
Electrostatic induction, 248
Energy, 120
conservation, 127
falling water, 152
forms, 125
human body, 126
Energy, kinetic, 121
potential, 120
transference and transformation, 124
Engines, 213
Engines, gas, 222
steam, 213
turbine, 225
Equilibrant, 81
Equilibrium, 106
neutral, 107
stable, 106
stability, 108
unstable, 107
Erg, 119
Ether, 177
Evaporation, 18
cooling effect, 19, 197
rate, 198
Expansion, coefficient, 168
gases, 167
liquids, 168
peculiarity, in water, 168
solids, 169
water, on turning to steam, 206
Falling bodies, 109
experimental study, 111
laws, 113
Floating bodies, 48
Fluoroscope, 455
Foot candle, 396
Force, 79
dyne, 93
effectiveness, 134
graphic representation, 80
liquid, against any surface, 38
measuring, 79
moment, 99
parallel, 100
resolution, 96
units, 83
Forces, parallel, 100
Franklin's theory of electricity, 252
Fraunhofer lines, 439
Freezing, evaporation, 197, 199
mixtures, 210
Friction, 147,
coefficient, 149
fluid, 150
kinds, 147
Friction, laws, 150
reducing, 148
uses, 149
Galvanometers, 289
Galvanoscope, 269
Gas engine, 222
efficiency of, 224
Gas meter, 75
Geissler tubes, 453
Gravitation, 103
law, 104
Gravity, 88, 104
acceleration due to, 111
cell, 277
center of, 105
Hail, 193
Hearing, 386
Heat, capacity for water, 201
conduction, 173
constants for transmission, 220
convection, 179
effects, 161
engines, 213, 222
equivalent of fuels, 219
fusion, 201
measurement, 200
methods of transmitting, 173
produced by electric current, 318
radiation, 176
sources, 159
units, 162
vaporization, 205
work, 212
Heating of buildings, 182
direct and indirect radiation, 186
hot air, 183
water, 186
plenum system, 187
steam, 186
vacuum steam, 187
vapor steam, 187
Hertzian waves, 262, 449
Hooke's law, 33
Horse power, 123
electric equivalent of, 123
Humidity, 194
Hydraulic press, 42
elevator, 44
ram, 72
Hygrometers, 194
Hygrometry, 191
conditions for saturation, 192
dew point, 193
fog, 193
formation, of dew, 192
humidity, 194
hygrometers, 194
importance, 191
Hypothesis, 3
Images, concave mirrors, 405
construction, 405
definition, 392
plain mirror, 401
small apertures, 391
Impedance, 472
Incandescent lamp, 320
Inclined plane, 143
Inductance, 471
Induction coil, 343
Inertia, 87
Insulators, 246
Intensity of sound, 363
Interference, light, 442
sound, 374
Joule, 120, 319
Laws, boiling, 208
Boyle's 63
Charles', 165
electric action, 243
falling bodies, 113
floating bodies, 48
gravitation, 104
Hooke's, 33
induced currents, 326
intensity of light, 394
Lenz's, 328
liquid pressure, 37
machines, 131
magnetic action, 229
motion, 87
Ohm's, 298
pendulum, 116
reflection, 399
refraction of light, 411
vibration of strings, 378
Lenses, achromatic, 434
effect on light, 417
equation, 421
formation of images, 418
forms, 416
Leclanché cell, 275
Lever, 132
Leyden jar, 261
oscillatory nature of the discharge, 448
Light, compared with sound, 388, 444
electromagnetic theory, 456
intensity, 394
interference, 442
polarization, 445
rectilinear propagation, 389
reflection, 396
total reflection, 413
Lightning, 254
Lines, of force, 233
agonic, 240
isogonic, 240
Liquids, pressure, 36
Local action, 273
Luminous and illuminated bodies, 388
Machines, 129
advantages, 129
cannot create energy, 130
efficiency, 142
law, 131
mechanical advantage, 134
the six simple, 132
uses, 129
Magnetic action, 229
fields, 233, 466
induction, 231, 236
permeability, 237
poles, 229
properties, 230
retentivity, 231
substances, 230
effect of electric current, 279
Magnetism, 228
Magnetism, theory, 232
Major and minor triads, 369
Magneto, 328
Magnetoscope, 230
Magnets, 228
poles, 229
Major scale, 366
Manometric flames, 382
Matter, 4
effect of heat, 5
molecular theory, 5
properties, 34
states of, 4
states of, defined, 5
Mechanical advantage, 134
Megaphone, 365
Melting points, 203
Mercury arc rectifier, 347
Metric system, 8
Microscope, 427
Mirage, 414
Mirrors, 400
concave, 405
convex, 407
parabolic, 409
plane, 401
Molecular motion in liquids, 18
in gases, 13
in liquids and solids, 27
in solids, 31
Molecules, motion, 16
size, 13
Moment of force, 99, 133
Momentum, 87
law of, 92
Motion, 85
accelerated, 86
curvilinear, 88
direction, 86
first law, 87
modes, 85
second law, 92
third law, 93
uniformity, 86
Motor (electric), 339
A. C. series, 482
induction, 483
synchronous, 485
Muffler, 224
Musical instruments, 377
interval, 368
nomenclatures, table, 369
Musical sounds, characteristics 364
Newton's Laws of motion, 87
Nodes, in pipes, 384
in strings, 379
Noise and music, 363
Ohm, 294
Ohm's Law, 298
Opera glass, 428
Optical illusions, 390, 404
instruments, 423
camera, 426
eye, 423
microscope, 427
opera glass, 428
prism field glass, 429
projecting lantern, 427
telescope, 428
Organ pipes, closed, 384
nodes, 384
open, 384
Oscillatory discharge, 448
Osmosis, 19
Outline Review,
current electricity, 325
force and motion, 118
heat, 227
induced currents, 353
light, 446
magnetism and static electricity, 266
sound, 387
work and energy, 158
Overtones, 379
Pascal's principle, 41
Pendulum, compound, 115
laws, 116
simple, 115
uses, 116
Pepper's ghost, 404
Permeability, 237
Phonograph, 383
Physics, definition, 4
Photometer, 394
Photometry, 393
Pitch, 365
Polarization, of light, 445
of voltaic cells, 273
Portraits,
Bell, 431
Edison, 285
Faraday, 331
Galileo, 89
Gilbert, 217
Helmholtz, 397
Huygens, 397
Joule, 217
Kelvin, 331
Marconi, 431
Morse, 285
Newton, 89
Potential, 257
Power, 123
electric, 316
power factor, 476
transmission of electric, 476
water, 152
Pressure, air, 56
atmospheric, 58
Pressure, definition, 37
effect on liquids and gases, 62
law of liquid, 37
Prism field glass, 429
Projecting lantern, 427
Proof-plane, 244
Pulley, 139
Pumps, air, 66
condensing, 67
water (lift, 68, force, 69)
Quality of musical tones, 380
Radiation, 176
sun's, 178
Radio-activity, 457
Radiometer, 177
Radium, 457
Rainbow, 436
Reactance, 472
Reflection, light, 396
multiple, 404
sound, 360
total of light, 413
Refraction, 410
cause, 412
index, 412
light, 410
in plates, prisms, and lenses, 413
Resolution of forces, 96
Resistance, cells in series, and parallel, 302
conductors, 293
in series and parallel, 299, 300
unit, 294
volt-ammeter method for finding, 304
Resonance, 371
Resonator, 373
Resultant, 81
Retentivity, 231
Right hand rule, 279
Rotary converter, 486
Science, definition, 2
Screw, 144
Shadows, 390
Single phase currents, 479
Siphon, 70
Siren, 366
Solidification, change of volume during, 203
Solutions, 27
Sound, compared with light, 388
interference, 374
media, 355
nature, 356
reflection, 360
rule for finding velocity, 367
source, 354
speed, 355
transmission in air, 359
Specific heat, 200
method of determining, 201
Spectroscope, 438
Spectrum, 433
Spherical aberration, 408
Spinthariscope, 458
Stability, 108
Standpipe, 46
Static and current electricity compared, 287
electrical machines, 262
Steam engine, 213
turbine, 225
Storage battery, 312
Stress and strain, 94
Sublimation, 199
Surface tension, 22
Sympathetic vibration, 372
Telegraph, 283
wireless, 450
Telephone, 349
receiver, 349
transmitter, 350
wireless, 460
Telescope, 428
Temperature, 162
absolute scale, 164
Tempered scale, 370
Theory, 3
Thermometer, air, 167
centigrade, Fahrenheit, 163
gas, 167
Thermos bottle, 176
Thermostat, 188
Three-color printing, 440
Three-phase currents, 479
Three wire transmission, 480
Torricelli's experiment, 57
Trade winds, 182
Transformer, 345, 467
uses, 347
Turbine, steam, 225
water, 154
Vacuum cleaner, 76
pan, 210
Velocity, 86
Vibration strings, 378
sympathetic, 372
Visual angle, 424
Viscosity, 20
Volt, 295
Voltaic cell, 270
advantages, 274
amalgamation, 273
local action, 273
polarization, 273
simple, 270
Voltmeter, 295
Water wheels, 152
overshot, 152
turbine, 154
undershot, 153
Watt, 123, 317
Wave theory, of light, 442
Waves, beats, 376
interference, 374
longitudinal, 358
sound, 358
transverse, 358
visible, 357
Wedge, 144
Weight, 104
Wheatstone bridge, 304
Wheel and axle, 136
Wind instruments, 383
Wireless telegraphy, 450
telephony, 460
Work, 119
units, 119
"X" rays 454
Transcriber's Note:
This book uses B.T.U. and B.t.u., electrophorous and electrophorus,
e.m.f. and E.M.F. and this has been left as written.
Hyphenation is also inconsistent, e.g. electro-plated and
electroplated.
On page 324, Exercise number 8 was not used in the original. The
exercises have not been renumbered.
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