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 OF 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?