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The Project Gutenberg EBook of Matter, Ether, and Motion, Rev. ed., enl., b Amos Emerson Dolbear
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Title: Matter, Ether, and Motion, Rev. ed., enl. The Factors and Relations of Physical Science
Author: Amos Emerson Dolbear
Release Date: February 27, 2010 [EBook #31428]
Language: English
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By Profe&or A. E. Dol´ar
MATTER, ETHER AND MOTION
The Factors and Relations of Physical Science Enlarged Edition Cloth Illustrated $2.00
THE TELEPHONE
With directions for making a Speaking Telephone Illustrated 50 cents
THE ART OF PROJECTING
A Manual of Experimentation in Physics, Chemistry, and Natural History, with the Porte Lumie`re and Magic Lantern New Edition Revised Illustrated $2.00
Lee and S˙«rd Publis˙rs Bo<on

Matter, Ether, and Motion
THE FACTORS AND RELATIONS OF
PHYSICAL SCIENCE

BY
A. E. DOLBEAR Ph.D.
PROFESSOR OF PHYSICS TUFTS COLLEGE AUTHOR OF “THE TELEPHONE” “THE ART OF PROJECTING” ETC.
REVISED EDITION, ENLARGED

LEE

AND

BOSTON SHEPARD PUBLISHERS
10 MILK STREET
1894

Copyright, 1892, 1894, by Lee and Shepard All Rights Reserved
Matter, Ether, and Motion
C. J. Peters & Son, Type-Setters and Electrotypers,
145 High Street, Boston.

PREFACE TO THE SECOND EDITION
The issue of a new edition of this book gives me an opportunity to make some needed corrections, and enlarge it by the addition of three new chapters, which I hope will make it more useful to such as have a taste for fundamental physical problems. The ﬁrst of these, Properties of Matter as Modes of Motion, presents the evidence that all the characteristic properties of matter are due to energy embodied in various forms of motion. The second, on The Implications of Physical Phenomena, points out what assumptions are made in explaining phenomena. It is the substance of a series of articles published in the Psychical Review in 1892 and 1893. The third, on The Relations between Physical and Psychical Phenomena, was read as a paper before the Psychical Congress at the World’s Fair in August, 1893.
Judging from some of the comments made about my statements as to Modern Geometry on page 67, and as to Vital Force, p. 336, I have thought it would be useful to some to see corroboratory statements; and I have therefore added, in an appendix, a few
iii

PREFACE TO THE SECOND EDITION

iv

pages of quotations from some of the most eminent mathematicians and biologists on these subjects, and from them one may judge whether or not my statements are correct.
As the work is a treatise on Physics, there is no special reason for going beyond it; but if this presentation of the subject is any approach to the truth, there is an important conclusion to be drawn from it. If the ether be the homogeneous and uniform medium it is believed with reason to be, then, in the absence of what we call matter, no physical change which we call a phenomenon could possibly arise in it; for every such phenomenon is a product, and in the absence of one of the essential factors, viz., matter, it could not be. If matter itself be a form of motion of the ether, the ether must have existed prior to matter; also, if the atom be a form of energy, then must energy have existed before matter existed. Hence there must have been some other agency radically different from any physical energy we know, and independent of everything we know, which was capable of producing orderly physical phenomena, by acting upon the ether; for a homogeneous medium could not originate it. Some philosophers call this antecedent power The Unknowable; others call it God. If energy as we know it implies antecedent energy as we do not know it, so, likewise, mind as we know it implies

PREFACE TO THE SECOND EDITION

v

antecedent mind under totally different conditions from those in which we ﬁnd it embodied.
In whatever direction one pursues physical science, he is at last confronted with a physical phenomenon with a superphysical antecedent where all physical methods of investigation are impotent. Such considerations raise the theistic hypothesis of creation to the rank of such physical theories as the nebula theory of the origin of the solar system, and the undulatory theory of light.

PREFACE
Within the past ﬁfty years the advance in physical knowledge has not only been rapid, but it has been well-nigh revolutionary. Not that knowledge that was felt to be well grounded before has been set aside,—for it has not been,—but the fundamental principles of natural philosophy that were applied by Sir Isaac Newton and others to masses of visible magnitude have been applied to molecules; and it has thus been discovered that all kinds of phenomena are subject to the same mechanical laws. It was thought before that physics embraced several distinct provinces of knowledge which were not necessarily related to each other, such as mechanics, heat, electricity, etc. Such terms as imponderable matter, latent heat, electric ﬂuid, forces of nature, and others in common use in text-books and elsewhere, served to maintain the distinctions; and even to-day some of these obsolete physical agencies are to be met in books and places where one would hope not to ﬁnd them. As all physical phenomena are reducible to the principles of mechanics, atoms and molecules are subject to them as much as masses of
vi

PREFACE

vii

visible magnitude; and it has become apparent that however different one phenomenon is from another, the factors of both are the same,—matter, ether, and motion; so that all the so-called forces of nature, considered as objective things controlling phenomena, are seen to have no existence; that all phenomena are reducible to nothing more mysterious than a push or a pull.
Some say that science is simply classiﬁed knowledge. To the author it is more than that, it is a consistent body of knowledge; and a true explanation of any phenomenon cannot be inconsistent with the best established body of knowledge we have. If physical factors are fundamental, then theorizers must square their theories to them.
The text-books have not kept pace with the advance of knowledge; and there is a large body of persons desirous of knowing more of natural philosophy, and especially of its trend, who have neither time nor opportunity to read and digest monographs on a thousand topics. To meet the wants of such, this book has been written. It undertakes to present in a systematic way the mechanical principles that underlie the phenomena in each of the different departments of the science, in a readable form, and in an untechnical manner. The aim has been to simplify and reduce to mechanical conceptions wherever it was possible to do

PREFACE

viii

so. One may often hear the question asked, What is
electricity? but a similar question as to the nature of heat or light or chemism is just as pertinent, although there chances now to be less popular interest in these than in the former; not, however, because they are in themselves better understood, or less interesting.
It is hoped that some of those whose interests lie along such special lines as chemistry, electricity, and even biology, will ﬁnd something helpful in the chapters dealing with those subjects.
In covering so much ground in so small a treatise, it was necessary to select such facts as give prominence to fundamental principles. Doubtless others might have selected different materials, even with the same end in view, for otherwise competent persons are generally more familiar with certain details of a given science than with others; and I have used what was closest at hand.
Aside from the topics usually treated upon in a book of physics, the reader will ﬁnd a chapter on Physical Fields, which is unique, as it extends the principle of sympathetic action—recognized in acoustics—to the whole range of phenomena, including living things.
The chapter on Life, in a treatise on physics, must justify itself; while the one on Machines points out

their functions in a more complete way than has been done before.
Lastly, however large the physical universe may be, and however exact such relations as we have established may be, it is daily becoming more certain that even in the physical universe we have to do with a factor,—the ether,—the properties of which we vainly strive to interpret in terms of matter, the undiscovered properties of which ought to warn every one against the danger of strongly asserting what is possible and what impossible in the nature of things. With the electro-magnetic theory of light now just established, and the vortex ring theory of matter still sub judice, but with daily increasing evidence in its favor, one may now be sure that matter itself is more wonderful than any philosopher ever thought. Its possibilities may have been vastly underrated.
In the book called “The Unseen Universe,” it is pointed out that possibly the ether may be the medium through which mind and matter re-act. What ﬁfteen years ago was deemed possible, is to-day deemed probable, and to-morrow may be demonstrated; and a perusal of that book is recommended to persons who are interested in questions of that kind.

CONTENTS

CHAPTER

PAGE

I. Matter and Its Properties . . . . . . . . 1

II. The Ether . . . . . . . . . . . . . 30

III. Motion . . . . . . . . . . . . . . 52

IV. Energy . . . . . . . . . . . . . . 70

V. Gravitation . . . . . . . . . . . . 99

VI. Heat . . . . . . . . . . . . . . 118

VII. Ether Waves . . . . . . . . . . . . 160

VIII. Electricity . . . . . . . . . . . . 207

IX. Chemism . . . . . . . . . . . . . 286

X. Sound . . . . . . . . . . . . . . 310

XI. Life . . . . . . . . . . . . . . . 336

XII. Physical Fields . . . . . . . . . . . 362

XIII. On Machines.—Mechanism . . . . . . . . 379

XIV. Properties of Matter as Modes of Motion . . . 401

XV. Implications of Physical Phenomena . . . . . 428

XVI. The Relations of Physical and Psychical Phenomena 463

Appendix . . . . . . . . . . . . . 477

Index . . . . . . . . . . . . . . 485

MATTER, ETHER, AND MOTION
CHAPTER I
Matter and Its Properties
All kinds of phenomena that we can become conscious of through any of our senses are traceable directly or indirectly to what we call matter. The sense of feeling implies contact with a body of some kind; the sense of hearing depends upon movements of the air, which is a body of matter having certain properties; and the sense of sight, also due to vibratory motion, implies that matter exists, however distant, which has given rise to the vibratory motions that are perceived as light. So of taste and smell, actual contact of material particles endowed with particular properties are the conditions for exciting these sense perceptions. Some philosophers have added a sixth sense to the ﬁve senses we have recognized for so long a time—the sense of weight, as distinguished from the sense of touch; and still others have thought to distinguish a sense of temperature—relative perceptions of heat
1

MATTER, ETHER, AND MOTION

2

and cold, from the sense of touch; and if these truly represent distinct senses, they illustrate still further the truth that it is through the reactions of matter upon the nervous organizations of living things that all of our knowledge of things about us and of the universe as a whole is obtained.
It might seem to one as if our knowledge of matter should be tolerably good, accurate, and complete, seeing that it is thrust upon us everywhere, and affects us for good or evil continuously from the dawn of sensation till death; yet it may truly be said that the knowledge of matter, its properties, and the wonderful complexity of phenomena that are due to them, which we possess to-day was wholly unknown to all mankind until the time of Sir Isaac Newton, whose discovery of the law of gravitation was the ﬁrst discovery of a universal property of matter; and by far the larger part of the knowledge we have, has been acquired in this century and mostly within the last half of it. The mass of mankind is, as it always has been, without any knowledge at all and without any desire for it. Whatever we have is due to the work of a small number of persons in Western Europe and America. Probably the large majority of mankind are quite unable to understand phenomena and their signiﬁcance, yet among the brighter and more competent individuals in

MATTER AND ITS PROPERTIES

3

every country there is an apathy and indifference to the subject, due, of course, to the estimate they have of its degree of importance; and this estimate is in a good measure due to the philosophy of things in general held by the individual thinkers.
When Mr. Emerson was told by a Millenarian that the world was coming to an end the next day, he declared that he could get along without it, and so it probably has seemed to the majority of philosophers that the material world was a condition of things to be endured, rather than to be understood and utilized: that they were in it but were not a part of it.
Knowledge has, however, increased, and the wise ones are growing wiser; and some of the modern questions of philosophy and psychology are now so woven in with physical details that a knowledge of matter and its possibilities has become to them imperative.
There have been many attempts to deﬁne matter, such as, whatever occupies space, or whatever affects our senses, and so on; and there is no brief deﬁnition that has been generally adopted. In the ordinary affairs of life one rarely needs to make such distinctions as are necessary in philosophical and scientiﬁc affairs, where accuracy and clearness are of the utmost importance. There seems to be no way to deﬁne matter except

MATTER, ETHER, AND MOTION

4

by means of some of its properties. If we say that it is whatever occupies space, there is implied in the statement that the term is properly applicable to everything that exists in space; but so far as we know there may be any number of things in illimitable space that are not subject to any of the physical laws, such as a piece of wood or an air particle are known to be controlled by. If we say whatever affects our senses, we again are going beyond our warrant; for electricity is capable of affecting several of our senses,—sight, taste, feeling,—and yet there is no good reason for thinking electricity to be matter.
There is one property of matter that may seem to differentiate it from everything else, and hence, if adopted, will enable one to be precise about his use of the term. One part of the law of universal gravitation is—every particle of matter in the universe attracts every other particle. This makes gravitation a universal property of matter. The astronomers have observed the movements of exceedingly distant stars to be in accordance with this law, and there are no exceptions to it that have been discovered.
If, then, one adopts as the deﬁnition of matter, whatever possesses the property of gravitative attraction, he will have a deﬁnition that is in accordance with everything we know, and with the added advantage

MATTER AND ITS PROPERTIES

5

that if there be anything else in the universe that involves observable phenomena he will not need to confuse it with the phenomena of gravitative matter. This is the sense in which that term is used throughout this book.
Matter presents itself to our senses in a scale of magnitude from particles in the neighborhood of the hundred-thousandth part of an inch in diameter, and requiring the highest powers of the microscope to see, to such huge masses as that of the earth, eight thousand miles in diameter, the planet Jupiter, nearly eighty thousand miles, and the sun, eight hundred thousand miles in diameter, while some of the more distant stars are probably ten times larger than the sun. The large masses, however, are but collections of smaller ones, each particle bringing its own properties of whatever kinds they may be; and it does not appear that new qualities are developed by simply changing the distance between bodies. So the properties of matter may be studied exhaustively without employing specimens inconveniently large.
The thin stratum of gold spread upon cheap jewelry has all the characteristics and qualities of any specimen of gold however large; and a small test tube of hydrogen will exhibit all the kinds of phenomena that

MATTER, ETHER, AND MOTION

6

any larger quantity would show. For such reasons the study of the universe of matter can be carried on in the laboratory. The universe may be in the crucible one holds in the tongs; whatever difference there may seem to be, it will really be one of bigness only.
In treatises on physics one will generally ﬁnd the properties of matter arranged in two divisions, called essential properties and non-essential ones. Of the former are (1) extension, or space occupying; (2) inertia, or passiveness under conditions of rest or motion; (3) impenetrability, or total and exclusive occupancy of its own space; (4) elasticity, or ability to recover its form after distortion, this, however, varying in degree in different bodies; (5) attraction, of which there are several varieties,—gravitation, acting at all distances; chemism, acting at close distances and selective in its operation, and apparently not existing at all between some kinds of matter, as, for instance, between oxygen and ﬂuorine. Chemism is also capable of complete neutralization, and is thus in marked contrast with gravitative attraction, which is not affected in the slightest degree discoverable by contiguity; and lastly, cohesion, which is not apparent except bodies are in contact, but is the agency that holds the particles of bodies together so they form liquids and solids of any and all sorts.

MATTER AND ITS PROPERTIES

7

The so-called non-essential properties are color, hardness, malleability, ductility, and the like, which vary very much in different substances. Among the metals silver is white, copper is red, gold is yellow. Diamond is the hardest substance known, while graphite is one of the softest, though both are composed of the same ultimate substance—carbon. Iron is malleable, and may be forged into any shape. Gold may be hammered out into leaves no more than one three-hundred-thousandth of an inch thick, but zinc is wholly unmanageable in that way. Platinum, one of the heaviest metals we have, can be drawn out into a wire ﬁner than a spider’s web,—a single grain may be drawn into a mile of wire; while bismuth, also a metal, cannot be drawn at all.
There are other conditions of matter that offer opportunities for convenient grouping sometimes, such as the solid, the liquid, and the gaseous: the solid being the one where the parts strongly cohere; the liquid, where the parts have but slight cohesion; and the gaseous, where the individual particles do not cohere at all, but, being elastic, bump against each other and rebound continually.
Farther on it will be shown how all substances may assume either of these conditions, inasmuch as it is temperature that determines whether a given substance

MATTER, ETHER, AND MOTION

8

be a solid, a liquid, or a gas.

Density signiﬁes compactness of matter, or the

relative number of particles in a given unit volume. If

compression be applied to two cubic feet of common

air until it occupies but one cubic foot, there is twice

as much matter in that cubic foot as there was at the

outset, and we express that fact by saying that the

density is doubled. If twice the amount of matter is in

the unit space, evidently the weight of the matter in

that space must be twice what it was at ﬁrst. So one

may measure the density of matter by the weight of

a unit volume of it compared with the weight of the

same volume of some other substance taken as unity.

Thus, if a cubic foot of water weighs 62.5 pounds, and

a cubic foot of rock weighs 155 pounds, the density

of

the

rock

is

2

1 2

,

which

means

that

it

is

2

1 2

times

heavier than water, and that the amount of matter in

the

rock

is

2

1 2

times

greater

than

that

of

the

water.

Such determinations have been made of all the different

materials that could be found, and extensive tables have

thus been constructed; but it is seen that the appeal is

to gravitation, and presumes that every particle obeys

that law, and that degrees of compactness of matter

do not affect the law. Such comparative tables, based

upon gravitation measure, are frequently called tables

of Speciﬁc Gravity, so that density and speciﬁc gravity

MATTER AND ITS PROPERTIES

9

mean substantially the same thing. The following examples of the relative densities of bodies may be of interest:—

Gold, 19

Silver, 10.5

Copper, 8.8

Iron,

7.8

Diamond,

4

Common Stone, 2.5

Wood,

.8

Sulphuric Acid, 1.8

Alcohol,

.8

Ether,

1.1

Water,

1

The Earth, 5.6

Such numbers are to be understood as signifying that if a given volume of water weighs one pound, an equal volume of gold weighs nineteen pounds, an equal volume of iron seven and eight-tenths pounds, and so on.
Sometimes, however, it is convenient to choose for a standard of density some body, a small unit volume of which is much lighter than water, such as air, or more frequently hydrogen gas, a hundred cubic inches of which weigh 2.2 grains. In the metric system, a litre, which is nearly two pints is the standard of volume; and a litre of hydrogen weighs .0896 of a gram.
In chemical work this is the common standard for gases; while for solids and liquids a cubic centimetre of water is taken, which weighs one gram.

MATTER, ETHER, AND MOTION

10

DIVISIBILITY OF MATTER.
Particles of matter as small as the hundred-thousandth of an inch may be seen with a good microscope as the smallest visible thing, but there is no reason for thinking that such a degree of ﬁneness is any approach to the ultimate ﬁneness of the parts into which it is possible to divide matter. For a long time philosophers have considered whether or not there could, in the nature of things, be an actual limit to the divisibility of matter, so that the smallest fragment could not be again divided into two or more parts by the application of appropriate means, thus making matter inﬁnitely divisible, at any rate ideally.
In Mr. Spencer’s “First Principles” this subject is considered at length, and the conclusion reached that it is impossible to conceive the existence of real atoms— bodies that cannot be divided into halves; nevertheless, we shall see presently that it is possible to conceive precisely that thing. It will be best here to note how far division has been carried and the means employed to effect it.
If a bit of phosphorus be put into a solution of gold, the gold will be set free in such a ﬁnely divided state that the particles remain suspended in the solution, giving to it a blue, green, or ruby color, depending

MATTER AND ITS PROPERTIES

11

upon the degree of ﬁneness into which it has been broken up. Faraday estimated that the particles of gold in the ruby-colored liquid did not exceed the ﬁve-hundred thousandth part of the volume of the liquid. One-eighth of a grain of indigo dissolved in sulphuric acid will give a distinctly blue color to two and a half gallons of water, which would be about the millionth part of a grain to a drop of the water.
A grain of musk will keep a room scented for many years. During the whole of the time it must be slowly evaporating, giving out its particles to the currents of air to be wafted presently out of doors; yet in all this time the musk seems to lose but little in weight.
The acute sense of smell of the dog is well known; for he can detect the track of his master long after the tracks have been made, which shows that some slight characteristic matter is left at each footfall.
A spider’s web is sometimes so delicate that an ounce of it would reach three thousand miles, or from New York to London. No one would think it likely that such a web would be made up of a single row of atoms, like a string of beads; for it would not seem probable that such a string could have such a degree of cohesion as spiders’ webs are known to possess.
Chemists have concluded from their experience with matter in its various forms and conditions that it is

MATTER, ETHER, AND MOTION

12

really reducible to ultimate particles which have never broken up, no matter what conditions they have been subject to; and these ultimate particles are called atoms. The term is not now understood to signify what is implied in its derivation, as something that cannot be divided, only something that has not yet been broken up into smaller parts. Thus hydrogen, oxygen, iron, silver, are reducible to such ultimate atoms; and there are now known about seventy different kinds of atoms, and these are often spoken of as the elements. Though they are excessively minute when compared with ordinary objects of sight, yet they have a real magnitude which the physicist has measured in several different ways. Most of these methods are complicated, and, in order to be understood, require a pretty thorough knowledge of molecular physics; but the following one may probably serve to give one an idea of the degree of smallness which atoms must have.
When a soap-bubble is blown, the material of the ﬁlm slides down the sides, making the bubble thinnest on top. When a certain degree of thinness has been reached at the top, colors begin to appear in concentric rings, and these colors appear to move towards the equatorial regions, new rings being formed at the top as fast as room is made for them by the displacement of the earlier ones. These colors always appear in

MATTER AND ITS PROPERTIES

13

the same order as they are in the rainbow, namely, beginning with the red and ending with the violet, then another set with the same order, until there have been ten or more such sets of rainbow tints. They are explained as being due to what is called interference in the light waves that fall upon the ﬁlm. Light is reﬂected more or less from every surface it reaches. Some light is reﬂected from the ﬁrst or outer surface of the ﬁlm; some goes through the ﬁlm to the inner surface, and is there reﬂected back to the outer surface, and then takes the direction that the light has which is reﬂected from the ﬁrst surface, so that the light that reaches the eye from a point on a bubble comes from both outer and inner surfaces. That coming from the inner surface has had to travel farther than that coming from the outer surface by a distance of twice the thickness of the ﬁlm. As light consists of waves, if one set of waves all of a length be made to move in the same direction as another set having the same length, their crests may coincide and produce a single higher wave; or the crest of one may be behind the crest of the other at any distance up to one-half the length of the wave itself, in which case the crest of one will coincide with the trough of the other, and the two waves will cancel each other, and this process is called interference. Now, in the case of the bubble,

MATTER, ETHER, AND MOTION

14

when the thickness is such that the distance through the ﬁlm and back again is such as to equal half a wave length of a given kind of light, that particular wave is extinguished; and when one of the constituents of white light is wanting, that which is left is seen as colored light, and the color seen must depend upon the kind of color that has been cancelled. Red light has the longest wave length, about one forty-thousandth of an inch, and violet, the shortest of the waves we see, about one sixty-thousandth of an inch; and when these colors are seen upon the bubble we are assured that the interferences are produced by thicknesses due to fractional parts of such wave lengths. As the ray must go through the thickness twice in order to fall behind one-half of a wave, it follows that the thickness of the ﬁlm where the last set of colors appear can be no more than one-fourth of the wave length of the shortest wave we can see, that is,
1 × 1 = 1 of an inch. 4 60, 000 240, 000
When a bubble has reached this degree of thinness, so that no more colors are to be seen, a rather remarkable physical effect may be noticed. The ﬁlm becomes almost jet black, with a jagged edge well deﬁned between it and the brighter colored rings where the adjacent

MATTER AND ITS PROPERTIES

15

tint is purplish. The thickness of the ﬁlm has fallen suddenly off here to about one-fortieth of the thickness it has where the tint is visible, and the bubble breaks in a second or two after this black patch appears; that is, when its thinness at any point becomes as small as
1 × 1 = 1 of an inch. 240, 000 40 9, 600000
As the bubble, however, does persist for a short time, and the thin ﬁlm has cohesion enough to enable it to support the weight of the bubble, it seems highly probable, but is not absolutely certain, that it must be more than one molecule of water thick at the thinnest place, which is, as shown, only about the one ten-millionth of an inch thick. If one thinks it probable that it be, say ﬁve molecules thick in order to have the degree of cohesion it shows, then the size of such molecule of water out of which the bubble is made can be but the one-ﬁfth of the above small fraction, which gives about the one ﬁfty-millionth part of an inch as the diameter of a molecule of water.
But a molecule is not the same thing as an atom: it is made up of atoms, chemically combined, and is deﬁned generally as being the smallest fragment of a compound body that can exist and possess the physical characteristics that belong to such body. Thus, a drop

MATTER, ETHER, AND MOTION

16

of water possesses all the characteristics of any larger quantity of it, and a drop may be divided into smaller and smaller globules, perhaps a million of them, each one being visible with a good microscope; but if the division be carried to a higher degree, as it can be by various methods, chemical, electrical, and thermal, the qualities of water disappear, and two different substances, oxygen and hydrogen, are left, both gaseous under all ordinary conditions, and neither of them exhibiting any properties like water or from which any of the properties of water might be inferred. It may be well to remark here that this is only one illustration out of multitudes that might be named throughout the whole domain of physical science, that the properties of things under common observation are not simply the properties that belong to the elements out of which the things are built up; such properties being the result of collocation rather than inherent qualities.
The molecule of water is then a compound thing, and is made up of three atoms,—two of hydrogen and one of oxygen,—and therefore the actual size of an atom of hydrogen must be less than that represented by the above small fraction of an inch. Evidently a thing made up of three individual parts and two dissimilar substances cannot be spherical, and it will be well to bear this in mind in thinking of molecular

MATTER AND ITS PROPERTIES

17

forms. One may imagine the atoms themselves to be

spheres, or cubes, or tetrahedra, or rings, or disks, or

any other forms he likes, for the purpose of getting

some sort of a mental picture of what a molecule might

look like if it could be seen with a microscope; and

it is probable that very many persons have hoped or

thought that the microscope would sometime be so far

perfected as to enable one to actually look upon the

molecules of matter and perhaps upon their individual

atoms. Let us therefore consider the problem of how

much more powerful a microscope must need to be

than any we possess to-day, in order that one should

see a molecule! We will assume atoms to be about

the one ﬁfty-millionth of an inch in diameter, and that

when combined into molecules they are geometrically

arranged so that the diameter of a molecule made up

of a large number of atoms is proportional to the cube

root of the number of atoms, as is the case with larger

bodies, say a box of bullets.

A molecule of water contains three atoms, a molecule

of alum about one hundred, while, according to Mulder,

a molecule of albumen contains nearly a thousand

atoms. Then, according to the assumption, the molecule

of alum would have a diameter equal to

√3 100 =

1

of an inch,

50, 000000 10, 776000

MATTER, ETHER, AND MOTION

18

and that of albumen would be equal to

√3 1, 000 =

1

of an inch.

50, 000000 5, 000000

Now, the best microscopes made to-day will enable one to see as barely visible a point the one hundredthousandth of an inch, so that such a microscope would need to be as much more powerful than it now is as one hundred thousand is contained in ﬁve millions, that is, ﬁfty times, in order to see the albumen molecule, and for the alum molecule as many times as one hundred thousand is contained in ten million seven hundred thousand, that is, one hundred and seven times. Now, one who is familiar with the microscope would probably admit that one might be made through improved methods of making and working glass hereafter to be discovered, two or three, or even ten times better than the best we have now; but the idea of one being made ﬁfty or one hundred times more powerful than we have to-day, I do not think would be allowed to have any degree of probability. The case may be illustrated as follows: Suppose in the days of the stage-coach some one had imagined that by some improvement in methods of travelling one might some day travel one hundred times faster than the stage-coach could then go. Twelve miles an hour was

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not an uncommon rate then; but one hundred times that would be twelve hundred miles an hour, and that is sixteen times faster than the best we can now do, and about twenty-ﬁve times faster than express-trains now go. As a matter of fact, we travel about three or four times faster than the best stage-coaches did, and, on a spurt, may go six or eight times faster. The powers of the microscope have not been doubled within the last ﬁfty years, and I suppose more time and ingenuity have been given to the problem of improving it than will ever be given to it in the same interval again.
There is another and still more serious reason why there is no probability that any one will ever see a molecule, even though the microscope had the magnifying power sufﬁcient to reveal it; namely, the motions that molecules are known to have would absolutely prevent one from being seen. A free molecule of hydrogen has a velocity of motion at ordinary temperatures of upwards of a mile in a second, and its direction of motion is changed millions of times in a second. A microscope magniﬁes the movements of an object as much as it does the object itself. An object in the ﬁeld of a microscope that should have a movement no greater than the hundredth of an inch in a second could only be glimpsed, so there is no possibility of one’s being able ever to see a free

MATTER, ETHER, AND MOTION

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gaseous molecule. Supposing one should be seized and held in the ﬁeld, even then it is to be remembered that it is in a state of vibration, changing its form constantly on account of its temperature, so that its wriggling would prevent any inspection.
Lastly, there is every reason to believe that the molecules of all bodies are so perfectly transparent that they can no more be seen than can the air, even if there were no difﬁculty from their smallness and their motions.
If the atoms of a single element like hydrogen are so minute, so restless, and so transparent that no one can hope to see them so as to make out their forms and what gives them their characteristic properties, what shall be said of the case of seventy or more elements similarly minute and restless and transparent, yet each one easily identiﬁed in several ways, physical and chemical? Does it seem in any way probable that such differences in properties as are exhibited by gold, carbon, iron, and oxygen can be due simply to differences in size or shape of the atom? Presumably not; and the constitution of matter has therefore always been a mystery to philosophers, for if one is to attempt to philosophize upon the subject in accordance with such other knowledge as we have, one would need to conclude that if the different kinds of matter, the

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elements as we know them, were formed out of some prior kind of substance, as bullets and marbles are formed out of lead and clay, then there must be as many different kinds of substances out of which the different elementary atoms are formed as there are different elements, which proposition does not seem to have such a degree of probability that any one could adopt it. If one sought for the explanation of the different properties by assuming that all the different kinds of elements were formed out of one and the same fundamental substance, then it is equally difﬁcult to understand how mere differences in size and shape could give such profound differences in quality as the elements possess.
Then, again, it appears that the individual atoms of each element are precisely alike. One atom of hydrogen is precisely like every other atom, so far as we have deﬁnite knowledge. Sir John Herschel likened them to manufactured articles on account of their exact similarity. A machine may turn out buttons or hooks or wheels or coins so exactly like one another that no one can tell them apart. It is really appalling to think of the immense numbers of atoms of every one of these seventy elements. It is a simple matter to calculate how many atoms there must be in say a cubic inch. It requires no other process than the application of

MATTER, ETHER, AND MOTION

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the multiplication table. If the diameter of one be the ﬁfty-millionth of an inch, then ﬁfty million in a row would reach an inch, and a cubic inch would contain the number represented by the cube of ﬁfty millions, which is
125000, 000000, 000000, 000000,
(125 followed by twenty-one ciphers) a number which is more conveniently represented by 125 × 1021. The utter impossibility of conceiving such a number will be apparent if one would try to represent to himself what the magnitude of only one million really is. Go out on a clear but moonless night and the heavens appear to be ﬁlled with stars. Count all that can be seen in a certain portion of the sky, say one-tenth, as nearly as can be estimated, and then determine the number in the sky that are in sight by multiplication. It will be discovered that only about two thousand can be seen in the whole sky. If one million stars were to be thus visible, it would require ﬁve hundred ﬁrmaments as large and as well ﬁlled as the one looked at to contain them. With the largest telescopes less than a hundred millions of stars are visible; but what shall one say when he learns that beyond a peradventure the number of atoms in a single cubic inch of matter of any sort is more than a million of millions times

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all the stars in all the heavens visible in the largest telescope.
If one fancies that kind of work he may compute the number of atoms that make up the world. Of course it will make the number much larger; but when written out not so much longer as one might think, for when it is multiplied a million times it will add but six ciphers to it. Some mathematicians have been to the pains to compute the number of atoms there are in the visible universe, or, rather, the number that cannot be exceeded; for if the number stated above ﬁlls a cubic inch, if one knows the diameter of the visible universe, the space it occupies can readily be known in cubic miles and cubic inches, and if all this space was ﬁlled with atoms one could know and write down their number. Astronomers tell us that some stars are so distant that their light requires as long as ﬁve thousand years to reach us, although the velocity of light is as great as 186, 000 miles in a second, and this distance is to be measured in every direction about us. If this be our visible universe, then the maximum number of atoms in it are calculable, and are stated to be represented by the ﬁgure 6 followed by ninety-one ciphers, or, as it is usually written,
6 × 1091.

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If we return to microscopic dimensions, and compute the number of atoms, there will be in the smallest amount of matter that can be seen with the highest powers of the microscope, the one hundred-thousandth of an inch, it will be seen that ﬁve hundred atoms in a row would just reach the distance; and the cube of 500 is 125, 000, 000, that could be contained in a space so small as to appear like a vanishing-point and the structure or details be utterly invisible. We have read of spirits that could dance upon the point of a needle, but the point of a needle would be a huge platform when compared with this last visible point with the microscope; and the spirit that should dance upon it might be a million times bigger than an atom of matter, and not be in danger from vertigo. One may be astonished at the amount of intelligence associated with the minute brain structure of some of the smaller forms of animal life—say the ants; but from the above it will be seen that so far as such intelligence is associated with atomic and molecular brain structure, the size of the brain in the smallest ant, though measured in thousandth of an inch, is sufﬁciently large to involve billions of atoms, and the permutations possible are almost unlimited. The same idea is applicable to the brain of man, and seems to indicate that such differences in quality of mind as we

MATTER AND ITS PROPERTIES

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see are not so much due to the differences in amount of brain, measured in cubic inches, as in atomic and molecular structure.
The work of physicists and chemists, carried on for many years, has convinced them that none of the processes to which matter has been subjected has affected its quantity in the slightest degree. A deﬁnite quantity of hydrogen, or, what is precisely the same thing, a deﬁnite number of hydrogen atoms, may be subject to any conditions of temperature, may be made to combine with other elements successively, forming with them solids or liquids or gases, and no atom is destroyed nor its individual properties changed in any degree. Neither has any phenomenon been discovered indicating that new atoms of any kind are ever produced by any physical or chemical changes yet known. Time does not alter them. Elements that have been imbedded in rocks from primeval times, reckoned by millions of years, when liberated to-day and tested, exhibit precisely the same characteristics as those obtained from other sources and that have been subject to many artiﬁcial conditions. Sometimes a meteorite reaches the earth, a sample specimen from distant space, having moved in some orbit about the sun for millions of years. Thousands of such bodies are in our possession, and they have been carefully

MATTER, ETHER, AND MOTION

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analyzed, but no element unfamiliar to the chemist has been found among them; and the iron, the nickel, the carbon, the hydrogen, and all the rest of the elements that compose them, behave in every particular like those found on the earth.
So far as spectroscopic evidence goes, it testiﬁes to the presence of the same elements in the sun and planets and comets; and it is as certain as anything physical can be, that the expert chemist here would be an equally expert chemist in the planet Mars, if he could ﬁnd a way to cross the immense space that separates that star from us.
These facts and conclusions are frequently stated in such a form as this, namely, that matter cannot be created or annihilated. All that can fairly be meant by such language is that under all the conditions at present known, the quantity of matter remains constant; and this proposition has a high degree of importance in social affairs as well as in philosophy. If matter were liable to change in its quantity or quality by being subject to various physical conditions, all industries involving commercial interests would be in an unstable state. If the ton of iron ore should turn out, when smelted, only ﬁfty per cent of iron instead of sixty per cent, as now,—the rest being either annihilated or transformed into lead or gold, or something else,—the

MATTER AND ITS PROPERTIES

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smelting company would soon go bankrupt, even if gold were the product instead of iron, for if gold were liable to be produced in that kind of a way, its value would be next to nothing as a standard of value.
The old alchemists sought to transmute what they called the baser elements into gold. It is safe to say, if it were physically possible to do it and some one should discover the art, and it were an economical process, commercial disaster such as the world has never known would follow its announcement. It would be as if the volcanoes of the world should suddenly begin to eject gold in the place of lava.
Stability of physical properties is as essential for the stability of society as the regular recurrence of day and night; and philosophy would be impossible if fundamental data were not in every way immutable.
These physical principles lead to some curious and most interesting conclusions with regard to the great difference there is between bodies of matter of any and all kinds that are familiar to our senses and the atoms out of which these larger bodies are composed. In every case, where there is a difference in movement between two of these larger bodies made up of atoms, there is what we call friction, which invariably results in wearing away some of the material of both. It is the result of mechanical friction, to tear away some of the surface

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molecules of the two bodies. Bodies in use much, and therefore most subject to friction, become worn out. Our clothing is a familiar example; the journals of machinery, the tires of wheels, the sharpening of tools, the polishing of gems, the weathering of wood and stone,—all show that attrition removes some of the surface materials of such bodies, but there is nothing to indicate that attrition among atoms or molecules ever removes any of their material. It appears as if one might afﬁrm in the strongest way that the atoms of matter never wear out, are not subject to such friction and the consequent destruction as comes to all bodies made up of them. The molecules of oxygen and nitrogen that constitute the air about us have been bumping and brushing against each other millions of times a second for millions of years probably, and would have been worn out or reduced, as the rocks upon the seashore have been beaten and ground into sand, if they had been subject to friction. So one may be led to the conclusion that whatever else may decay atoms do not, but remain as types of permanency through all imaginable changes—permanent bodies in form and in all physical qualities, and permanent in time, capable, apparently, of enduring through inﬁnite time. Presenting no evidences of growth or decay, they are in strong contrast with such bodies of visible

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magnitude as our senses directly perceive. Valleys are lifted up and become mountain-tops; mountains wear away and are washed into the ocean; the beds of the ocean sink and rise; and the boundaries of continents may be worn and washed away through the incessant beatings of waves against their coasts. Wear and tear go on in all inanimate nature unceasingly, so that it is only a question of time when everything we see upon the earth will have changed beyond identiﬁcation. The sun is shrinking, and must some time cease to shine. The stars, too, are changing likewise, because they shine, and their places in the ﬁrmament will be vacant. All living things grow because of change, and decay because of more rapid change, and there appears to be nothing stable but atoms. If it could be shown that life itself and the mind of man were in some way associated with atoms of some sort, as inherent properties, the hopes and longings cherished by mankind for continuous existence beyond the short term of three score years and ten would give way to convictions as strong as one has in any physical phenomenon whatever; the evidence would be demonstrative in the same sense as it is for the existence of atoms and their physical qualities.

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CHAPTER II
The Ether
An incandescent electric lamp consists of a ﬁne thread of carbon ﬁxed in a glass bulb from which the air has been exhausted. When a proper current of electricity is permitted to traverse the carbon ﬁlament, it becomes white-hot and gives out light like any other hot body. Other luminous bodies are in the air, and one might infer that the light was transmitted from the heated body to the eye by the material of the air itself. The light in the vacuum shows that this is not necessarily so, for the more perfect the vacuum is made the more freely does the light from the ﬁlament reach the glass bulb that encloses it. One is therefore led to infer that matter is not the agent that transmits light. The light of the sun reaches us after travelling through ninety-three millions of miles of space in about eight minutes. There are the best of reasons for believing that the atmosphere of the earth does not reach at most more than two hundred miles upwards from the surface, and its density at the height of only one hundred miles is such that there would be only about

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one molecule to the cubic foot. It is not unlikely that there are free-roving molecules
in space, as there are meteors in all directions about us, varying in size from fractions of a grain to masses weighing some tons, but the distance apart of these bodies is so great on the average that they cannot be considered as either help or hindrance to the passage of the light of either sun or stars. It is known with certainty that what we call the light from shining bodies is a kind of wave motion. The phenomena of interference, which can be brought about in several different ways, and which was referred to in the ﬁrst chapter when speaking of the colors of soap-bubbles, show this. It is possible to annihilate two rays of light by making one of them to follow the other in a certain way; and one cannot conceive that two particles of matter of any sort could annihilate each other by simply changing their positions, but this is precisely what happens in light.
Wave motions of all kinds can cancel similar wave motions; for the wave consists of periodic movements, a crest and a trough, and when the crest and trough of one wave are superposed upon the trough and crest of another similar one, the result is the destruction of both waves. The lengths of these waves have been measured by a great many persons in various parts of

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the world, and they all concur that light can only be explained by wave motions such as they measure.
If there be wave motions, evidently there must be something moved. One cannot conceive of a wave movement when there is nothing that can be moved; so men have been compelled to believe that there is some medium between the sun and the earth that is capable of wave motion, and this medium they have agreed to call the ether.
If one admits the existence of ether between the sun and the earth as the agency for the transmission of light, he will need to do much more than that. The sun is but about ninety-three millions of miles distant, but most of the planets are hundreds of millions and some of them thousands of millions of miles from us, and the light comes from them too; so the ether must extend through the space occupied by the solar system, the diameter of which is six thousand millions of miles, and to cross this space light requires nine hours, though going at the rate of one hundred and eighty-six thousand miles per second.
Then there are the stars beyond our solar system, the nearest one so distant as to require three and a half years for the light to get to us at the same rate; and some of these are so remote that thousands of years are needed for their light to arrive. That light

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we see from them to-day left them before America was discovered, before Jesus was born, before the pyramids were built, and for all we should be able to see they might have ceased to exist long ago, though their light continues to shine. So the ether must extend to those most distant stars we can see, and that, too, in every direction. There is no exaggeration in the statement that our visible universe is so great that light requires ten thousand years to cross its diameter. There is no reason, either, for setting that as a boundary to its magnitude; but wherever light comes from to us, there must this medium, the ether, be.
But there are other and just as good reasons for thinking there must be some medium between bodies, even when all atoms and molecules have been removed. For instance, everybody knows that one magnet affects another at a distance from it, and there is no kind of substance known that will prevent such action when interposed between them.
If one of these magnets be placed in the most perfect vacuum that can be made, it still acts as it would in the air, only with still greater freedom. One cannot believe that one body can thus act upon another body without some kind of a medium between them. Is it not absurd to think otherwise? One may, if there appears to him to be a good reason, suppose that

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there is a magnetic medium or ether different from that one employed in the transmission of light; but there is a similar need for imagining one for the effects produced by electriﬁed bodies upon other bodies in their neighborhood. An electriﬁed glass rod will attract a pith ball or anything else just as well in a vacuum as out of it; and it is certain that electrical attraction and magnetic attraction are not identical, for an electriﬁed body will attract one kind of thing as well as another, while a magnet is selective in its effects, and affects iron chieﬂy. Hence, if each different effect in a vacuum is to be attributed to some different kind of medium, there would need to be an electric ether in addition to the other two.
Then there is gravitative attraction, which has before been mentioned. If it is not rational to think that one body can act upon another body not in contact with it and without some medium between them, then one is bound to admit that the gravitative effects observed, say between the moon and the earth, the sun and the earth, and in every other case, are due to the action of some medium between them. Neither is it at all needful to be able to explain how the medium acts thus and thus, or even to imagine how it might, in order to ﬁrmly believe that there must be one.
Here are four cases of apparent action at a distance

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of one body upon another, requiring some sort of an intermediate agency; and, unless there be some good reason for thinking there are several such media occupying the same space apparently, it is much more philosophical to believe it likely that one medium exists capable of transmitting effects of the different kinds; and especially will this appear to be truer if it is known, as it is known, that the magnetic and electric effects are transmitted with the same velocity as is the light. So that physicists to-day quite concur in the belief that what was called at ﬁrst the luminiferous ether, on account of its function in transmitting light, is the same medium that is concerned in the other phenomena of magnetism, electricity, and gravitation.
It is likewise true that there are some physicists who hold rather lightly upon this belief, taking it as a convenient working hypothesis, and who would seem to be ready in a minute to surrender the idea, unless it had been demonstrated in the same way as the existence of matter and of motion has been. But this is not the attitude of philosophic minds.
Sir Isaac Newton deduced from the observed motions of the heavenly bodies the fact that they attract each other according to the law now known as the law of gravitation, but he says nothing about how bodies can affect each other. That is, in his “Principia” he does

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not attempt to explain gravitation. He explicitly does
say, however, that he has not employed hypotheses in
his work, yet we know from other of his writings that
the idea of a medium was constantly in his mind. His
“Principia” closes thus:—
“And now we might add something concerning a most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies mutually attract one another at near distances and cohere if contiguous; and electric bodies operate to greater distances as well repelling as attracting the neighboring corpuscles, and light is emitted, reﬂected, inﬂected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit mutually propagated along the solid ﬁlaments of the nerves from the outward organs of sense to the brain, and from the brain to the muscles. But these things cannot be explained in few words, nor are we furnished with that sufﬁciency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates.”
This shows plainly enough that he believed that
some medium, different from matter, was essential for
a mechanical conception of the phenomena he alluded
to. In a letter to Bentley he states his philosophical
judgment upon the subject in still stronger terms, and
it shows, too, the sense in which he is to be understood
when he says: “I frame no hypotheses”—which has
frequently been repeated to adventurous hypothecators

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as the example of the model scientiﬁc man. Hear him!

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must do if gravitation in the sense of Epicurus be essential and inherent in it. . . . That gravity should be innate, inherent, and essential to matter so that one body can act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”
Newton uses the word Spirit in the sense of a
substance entirely different from matter (see page 36).
Evidently Newton was so strong a believer in the
medium that we call the ether, though he could not
work out its mode of action, that he was ready to discount the intelligence of any man who doubted it.1
If our knowledge of the existence of the ether is
1In 1708 Newton wrote thus: “Perhaps the whole frame of nature may be nothing but various contextures of some certain etherial spirits or vapors, condensed, as it were, by precipitation; and after condensation wrought into various forms, at ﬁrst by the immediate hand of the Creator, and ever after by the power of nature.”
These with his other acute remarks concerning what we now call the ether lead us to infer that his mechanical instincts were more to be trusted in this ﬁeld than his more labored efforts.

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38

not so positive as it is for matter, but is inferential, it will be readily understood that the knowledge we have of its properties cannot be very exhaustive. Some have imagined that it was only a ﬁner grained kind of matter than that we know as the elements, and that it must be made up of atoms, though almost inﬁnitesimal in size. Others think it cannot be granular at all, but forms a continuous substance throughout space. By “continuous” is meant that there are no interstices in it: that it is constituted like a jelly, only not made up of distinct parts or atoms, so there can be no such thing as separating one part from another, leaving a vacuous cavity or rent between them. One of the reasons for thinking this to be the case is, that if it were made up of ﬁner atoms or of atoms at all, such waves as those of light could not be transmitted by it. Longitudinal waves, like those of sound in air, can be transmitted by atomic or molecular structures but not transverse waves, that is, such as are at right angles to the direction of propagation. Some of these light waves are as short as the hundred-thousandth of an inch, and some are as long as the one two-thousandth of an inch, and perhaps longer. Yet all of them are transmitted with the same velocity in any and every direction. From the fact that light travels with the same velocity in every direction, it is inferred that the ether

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39

is not only homogeneous, but its properties are alike in every direction. As light is transmitted in straight lines, it seems to follow that there is no difference in its quality in different parts of space.
That wave motions travel with such high velocity in it has been interpreted as proving it to have a high degree of elasticity, while the fact that it offers no appreciable resistance to the movements of bodies of matter in it is supposed to indicate that its density is very small.
There are some, however, who think that such terms as elasticity and density are not appropriately applied to the ether. These terms signify properties of atoms and molecules. If density signiﬁes compactness of atoms, then the word could not apply to something not composed of atoms. In like manner, if elasticity means ability to recover form after deformation, then it is not applicable to substances that cannot be deformed, and it is customary to speak of the ether as being incompressible. Still, it is certain that stresses may be set up in it in various ways, and that these conditions may be propagated, in certain cases in straight lines, in other cases in curved lines, so whether the explanation be forthcoming or not, there is no doubt about the facts.
There is no evidence at all that the ether is subject

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40

to gravitative action, or that it offers any resistance to a body moving in it. That is to say, it gives no evidence of friction. Here is the earth rotating upon its axis, and the velocity of rotation at the equator is a thousand miles an hour, and if there were an appreciable amount of friction the earth must slowly be coming to rest like a top spun in the air. Yet the astronomers tell us that the length of the day has not changed so much as the hundredth of a second within the last two thousand years. Again the earth revolves in its orbit about the sun at the average rate of nineteen miles a second, and if the ether through which it moves offered any resistance to the motion, the length of the year would be changed, but no such change has happened in historic times. Again, such bodies as comets move very much faster than the earth; some have been known to have a velocity of three hundred miles per second when near the sun, but the comets complete their circuits and give no evidence of slackened speed due to friction in space.
If, then, the ether ﬁlls all space, is not atomic in structure, presents no friction to bodies moving through it, and is not subject to the law of gravitation, it does not seem proper to call it matter. One might speak of it as a substance if he wants another word than its speciﬁc name for it. As for myself, I make a

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sharp distinction between the ether and matter, and feel somewhat confused to hear one speak of the ether as matter.
Nearly thirty years ago Helmholtz investigated, in a mathematical way, the properties of vortical motions, and, among others, pointed out that if a vortical motion was set up in a frictionless medium, the motion would be permanent, and it could not be transformed. Sir William Thomson at once imagined that if such motions were set up in the ether, the persistence of their form and the possibility of a variety of motions would correspond very closely with the properties that the atoms of matter are known to possess. Such vortical motions as are here alluded to, all have seen, as they are often formed by locomotives when about starting, if the air be quiescent. Horizontal rings, three or four feet in diameter, may be seen to rise wriggling into the air sometimes to the height of several hundred feet. They may be formed also by smokers by a vigorous throat movement forcibly pufﬁng the smoke from their mouths, and they can be made artiﬁcially by providing a box having a hole on one side an inch or two in diameter and the side opposite covered with a piece of cloth. A saucer containing strong ammonia water and another with strong hydrochloric acid may be set inside, and dense fumes will ﬁll the box. If the cloth

MATTER, ETHER, AND MOTION

42

Diag. 1.

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43

be struck by the hand, a ring will issue from the hole,

and may go forward several feet, and its behavior may

be studied. Such as are formed in the air under such

conditions present so many interesting phenomena that

it is worth the while here to allude to them for the

sake of helping the mind to a clearer idea of how

some of the properties exhibited by matter may be

accounted for.1

1. The ring once formed consists of a deﬁnite amount

of the gaseous material of the air in a state of rotation,

and in its movements afterwards

retains the same material. It

is to be noted that the ring is

formed in the air, the white fumes

serving merely to make the ring

visible. The ring moves forward

in a straight line in the direction

it is started, just as if it were a

solid body. It may move very fast

too,—ten feet a second or more,

Diag. 2.

and reach the distant side of the

room, but it always moves of its own motion in a

direction perpendicular to the plane of the ring.

1The method of producing these vortex rings and their phenomena are fully explained in “The Art of Projecting.” By Prof. A. E. Dolbear. Illustrated. $2.00. Published by Lee and Shepard, Boston.

MATTER, ETHER, AND MOTION

44

2. It possesses momentum, and will push against the object it hits.
3. If made to move rapidly adjacent to a surface like a wall or table, it will move towards it as if it were attracted by it, and generally will be broken up by impact against it.
4. A light body, like a feather or thread, will be apparently pushed out of the way in front of it, and drawn towards it if behind it—phenomena like attraction and repulsion.
5. If two such rings bump together at their edges, each one will vibrate with well-marked nodes and loops, showing that, as rings, they are elastic bodies, and that their period of vibration depends upon the rate of the rotation.
6. If two such rings be moving in the same line, but the hindmost one swifter so as to overtake the other, the foremost one enlarges its diameter while the hinder one contracts until it can go through the former, when each recovers its original dimensions.
7. If two meet in the same line, going in opposite directions, the smaller one goes through the larger and may be brought to a standstill in the air for a short time until the other has got some inches away, when it starts on in the same direction as before.
8. If two similar ones are formed at the same time,

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side by side, at a distance of an inch or two, they always collide at once as if they had a mutual attraction. The result of the collision may be the destruction of one or both, or—
9. Each one may break at the point of impact, and the opposite ends may weld together, forming a single ring which will move on as if it had been singly formed, or—
10. Instead of breaking they may rebound from each other, but always at right angles to the plane in which they were moving at ﬁrst; that is to say, if they were moving in a horizontal plane before impact, they will rebound from each other in a vertical plane.
11. Three rings may in like manner be made to join into one.
12. The material of the ring may often be seen to be in rotation about the ring, while the ring, as a whole, does not rotate at all, a rotary wave.
13. The parts of a ring may be in a state of vibration in the ring without changing its circular form, somewhat as if the ring were tubular and two bodies should move up on opposite sides till they met and rebounded to meet below, and so on.
All these, and some other just as curious phenomena, may be observed in vortex rings, and may fairly be said to be due to the properties of the rings themselves. For

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instance, the vibratory motions alluded to in the ﬁfth show that elasticity is a property of the ring, and that the degree of elasticity does not depend upon what the ring is made of, but upon the kind and degree of motion that constitutes the ring. If such a ring could be produced in material not subject to friction, none of the motion could be dissipated, and we should have a permanent structure, possessing several properties such as deﬁnite dimensions, volume, elasticity, attraction, and so on, all due to the shape and motions involved.
Imagine, then, that vortex rings were in some way formed in the ether, constituted of ether. If the ether be, as it is generally believed to be, frictionless, then such a thing would persist indeﬁnitely: it would have just that quality of durability that atoms seem to possess. It would possess physical attributes, form, magnitude, density, energy, that is, it would not be inert. It would be elastic, executing a deﬁnite number of vibrations per second. This property of elasticity has generally heretofore been assumed to be a peculiar endowment of ordinary matter, and one was at liberty to imagine some matter without it because not so made. This view implies that elasticity is a necessary property of vortex rings; for as the velocity of rotation is reduced, so is the degree of elasticity, and if there was simply a ring without being in rotation, it would have no

THE ETHER

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elasticity at all, neither would it have any qualities

different from the medium it was imbedded in.

That such a quality as elasticity may be due solely to

motion, and varying with it, one may assure himself with

that piece of apparatus to be found in most collections in

schools known as Bonnenburger’s. It consists of a disk

of metal, mounted in gimbals so it can be set spinning

in any plane. If this be set

spinning in a vertical plane it

becomes tolerably rigid in that

plane, and cannot be moved out

of it but by the employment of

quite a degree of pressure. If

the framework be quickly struck

by the ﬁnger while thus spinning,

the wheel will begin to rock back

and forth like the prong of a

tuning-fork, and the more rapid

Diag. 3.—Bonnenburger’s Apparatus.

the rotation the higher the rate of vibration. When the velocity of rotation becomes slow the vibratory

motion may be as slow as once a second, and, of

course, when the ring is not revolving it will not

vibrate at all. Thus there is fairly good physical reason

for thinking that what we call elasticity in the atoms of

matter may be due simply to the motion they possess,

MATTER, ETHER, AND MOTION

48

and how that may be one can understand if atoms be vortex rings.
One may properly ask how one vortex ring can differ from another so there could be so many as seventy or more different kinds of atoms. To this it may be said that such rings may differ from each other not only in size but in their rate of rotation: the ring may be a thick one or a thin one, may rotate relatively fast or slow, may contain a greater or less amount of the ether. The word “mass” in physics is used to denote a quantity of matter as measured by its resistance to pressure tending to move it as a whole. Thus if a pressure of one pound be applied to two different bodies for say one second, and one of them was moved an inch and the other but half an inch when otherwise they were alike free to move, we would say that one had twice the mass of the other—its resistance to being moved was twice as great as the other.
In the case of the Bonnenburger’s rotating disk, the resistance to the pressure tending to move it depends upon the rate of rotation, and a thin and swift moving disk would offer much greater resistance than a much larger one with a slower speed. So one might infer that the difference in what is called mass among the atoms of matter might be due simply to the different

THE ETHER

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speeds with which the rings rotate, rather than in the absolute volume of ether in the state of rotation. There are other reasons than these for thinking that motion is the chief characteristic of matter. Chemists have discovered that both the chemical and physical properties of all kinds of matter are functions of their mass or relative atomic weights, and that they may be arranged in a harmonic series. Harmonic relations may imply either relations of position or of motion. But the fundamental properties of matter do not change by changing its position, and one is therefore led to the conclusion that one must look to the various kinds of motion involved among atoms for the explanation of all their properties and all their phenomena.
There is another very important and peculiar property possessed by vortex rings; viz., there cannot be such a thing as half a ring or any fragment of one. Break such a ring in two and there is not left the two halves; not only is the ring broken, but each part at once vanishes into the indistinguishable substance that composed it, and all the properties that characterized it as a ring have vanished with it.
This greatly aids one to understand that matter may not be inﬁnitely divisible. Over and over again have philosophers asserted that it was impossible to imagine an atom of matter so small that it could not

MATTER, ETHER, AND MOTION

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in imagination be again broken into two or more parts. A vortex ring, however, shows how the thing can be done. If an atom be a ring, when it is disrupted it is at once dissolved into ether, and that is the end of it. There are no fragments of the ring.
One, however, must not infer from the above treatment that it represents knowledge of a demonstrated kind, for it does not. It was remarked in the ﬁrst chapter that atoms are too minute to be seen and studied as one would study an animalcule or a blood corpuscle, and one’s knowledge must be altogether inferential concerning them; but what knowledge we do have, and the inferences that may properly be drawn from it, all tend to convince one that matter and the ether are most intimately related to each other, and that some such theory as the vortex ring theory of matter must be true.
Now, it is either that theory or nothing. There is no other one that has any degree of probability at all. If what is presented herewith is not the precise truth concerning a most difﬁcult subject, it may have the merit of helping one to conceive the possibilities there may be of deducing qualities from motions, and rid him of the idea that matter consists necessarily of some created things that have no necessary relations to the rest of the universe beyond the properties impressed by ﬁat.

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In the latter case one could never hope to understand them, because there could be no necessary reason for their being as they are, rather than some other way, whereas, in the former case, the mechanical relations can be understood, and there is left the possibility that by and by, with more light and knowledge, one may know the physical conditions under which matter itself came into existence.

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CHAPTER III
Motion
Everybody has so clear a conception of motion that there would not seem to be any difﬁculty in deﬁning it absolutely, but philosophers and others from remote times till now have been perplexed by its problems. How can Achilles ever overtake the tortoise, though he runs ten times faster? How can the top of a cart-wheel move faster than the bottom? If the sun cannot set above the horizon and cannot set below it, how can he set at all? In the last chapter some phenomena were alluded to which were attributed to motions of different kinds, and one must needs have a deﬁnite notion of what he is talking about in order that his words shall convey to himself, as well as others, the information he would impart. Rest and motion are contrasted conditions of bodies, so if a body is at rest we say it is without motion, and vice versa. If two persons sit side by side in a house they may be said to be at rest, but if they sit side by side in a railroad car they will be at rest relative to each other as they were before, but may be in motion with reference to

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53

things outside the car. If, as a vessel sails past the end of a wharf, a person on board would talk with a person standing upon the wharf, he will walk so as to keep opposite the man standing still, and the two will be at rest in relation to each other, while one will be in motion with reference to everything on board the vessel. Thus it appears that rest and motion are relative terms, and can only be understood to apply to the relative continuous position of two bodies or objects. Hence, if there were but one object in the universe there could be no such thing as change of position, for that implies another body with which position may be compared at intervals. But such a single body might have some internal motions by which there was a relative change of position of its parts with reference to themselves. For instance, a tuning-fork might be at rest as a whole with reference to all other bodies, yet its prongs might vibrate towards and away from each other, the centre of mass or the centre of gravity of the fork itself not moving in the slightest degree either with reference to itself or anything outside itself. Again, a body might spin like a top, and there would be no change of position of the body as a whole with reference to any other body, nor change of position of the parts with reference to each other, yet there would be a change of position of the parts with reference to

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all bodies outside itself. Hence, a brief deﬁnition of motion is not so easy to give.
One might say that motion was the change of position of a body with reference to other bodies, or the change of position of the parts of a body with reference to each other, or the change of position of the parts of a body with reference to other bodies. But these would not cover all possible cases. There need be no trouble, however, in particular cases, because there will always be data at hand to determine the character and direction of the motion.
One may study the geometry of positions and changing positions of mathematical points, and attend only to rates and direction of motion of all sorts, without considering the motions of bodies of real magnitude possessing physical properties like matter. The science that has to do with such ideal conditions is called kinematics. Whenever the motions of matter are considered, the science is called kinetics. Of course all phenomena involve the motions of matter. Although one sees a great variety of motions, a few examples of particular sorts may be helpful in analyzing them.
1. The drifting of clouds, the ﬂight of birds, of arrows, of bullets, of meteors, the sailing of vessels, the running of locomotives, are examples of one kind of motion; namely, where the change of position is that

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55

of the body as a whole with reference to other bodies external to it. The cloud may drift with the air, but with reference to the surface of the earth it moves. Where a body thus moves straight on continuously with reference to other bodies, whether the distance moved be long or short, the motion is called translatory or free-path motion. The latter term is most frequently applied to the movements of the molecules of a gas. In ordinary air the distance apart of the molecules is on the average about the one two-hundred-and-ﬁfty-thousandth of an inch, but the molecules themselves being only one ﬁfty-millionth of an inch in diameter, it will be seen that they have a space to move in about two hundred times their own diameter before coming in collision with another one; and after collision their direction is only changed when they go on to another collision, and we say that their free path is on an average about the two-hundred-and-ﬁfty-thousandth of an inch. With some modern air-pumps it is possible to reduce the amount of air in a space so that the average free path of a remaining molecule will be a foot or more; but neither the size of the moving body, nor the distance hundred times their own diameter before coming in collision with another one; and after collision their direction is only changed when they go on to another collision, and we say that their free path is on an

MATTER, ETHER, AND MOTION

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average about the two-hundred-and-ﬁfty-thousandth of an inch. With some modern air-pumps it is possible to reduce the amount of air in a space so that the average free path of a remaining molecule will be a foot or more; but neither the size of the moving body, nor the distance it moves, nor the velocity with which it moves, makes any essential difference in the speciﬁc kind of motion: so the movements of air particles among themselves, of billiard-balls between impacts, of a bullet on its way to the target, and of a planet or comet in its orbit, are all examples of the same kind of motion, namely, translational.
2. The swaying of the branches of trees when moved by the wind, the swinging of the pendulums of clocks, the movement of the piston in a steam-engine, of the prongs of tuning-forks, the reeds and strings in musical instruments, are examples of a different kind of motion, inasmuch as the changes of position relate to the body itself rather than to external bodies. The tuning-fork is the type of them all, and together they are called vibratory motions. Sometimes, when the bodies that move thus are large and the motion conspicuous, as, for example, in the pendulum of the clock, and the steam-engine piston, the motion is spoken of as oscillatory. In such cases, as in the former one, it should be borne in mind that mere differences

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57

in the size of bodies, or of the rate of motion, does not in any manner change the character of the motion, so the name that is applicable to one will be equally applicable to all. If one calls the movement of a vibrating tuning-fork vibratory, the same term may be applied to an atom if it goes through a like periodic change of form, for that is the chief characteristic of vibratory motion; and hereafter it will appear how needful it is to bear this in mind, for what a given amount of motion will do will be seen to depend altogether upon the kind of motion.
3. The spinning-top, the balance-wheels of engines, the wheels of machines of all kinds, the turning of the earth, and each member of the solar system upon its axis, are examples of another sort, where the displacement is not, as in the last, between parts of the same body, but a change in the relative position of each part of a body to what is outside itself. The pendulum of a clock swings to and fro, but its point of suspension does not move; whereas every part of a turning-wheel is presented to opposite parts of space in the plane of its revolution. This motion is called rotary, and just as in the other two cases, I wish to emphasize the fact that the term is properly applicable to masses of matter of all degrees of magnitude; so an atom may spin on its axis as well as the earth

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or sun, and the phenomena it will be competent to produce by such spinning will be very different from that produced by its vibrations or free-path motions.
These three kinds are all of the primary ones: all the others we see are made up of these or their compounds. For instance, a compound of a free-path motion with a vibratory motion will give a wave or sinuous motion if the direction of the vibration be at right angles to the free path. A combination of a free-path with a rotary may give a spiral motion, as illustrated by the movement of a screw when pushed and turned into a piece of wood.
In a sewing-machine may be seen all of these kinds of motion and some other compounds more complex than the ones spoken of, but one may readily analyze them into the three primary ones.
These forms of motion have been spoken of as if they were peculiar to matter; but it ought not to be inferred that motion is not attributable to the ether. Indeed, we know that some sorts of motions are propagated in the ether. For instance, what we call light is an example. Its form is undulatory; and, as we have seen above, an undulatory motion is a compound of a rectilinear and a vibratory. A spiral movement in the ether is also known, and it is sometimes called rotary-polarized light: its motion is like that of a screw, and we know

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that such a motion is a compound of a rectilinear and a rotary. Rotary motions in the ether are also known as taking place in front of magnetic poles, and are the results of the magnetism imparted to the iron or other substance. I am not aware that any simple rectilinear motion is known to occur in the ether: there may be, and likely enough is, such.
For convenience, motions that are large enough to be visible are called mechanical motions, while those too minute to be seen are often called molecular or atomic. Sometimes these molecular and atomic motions are spoken of as if they were mysterious, and not to be understood in the same sense as the larger ones that are visible to us; but it is difﬁcult to justify any such distinction, and difﬁcult to imagine that any kind of a motion a large piece of matter may have, a small particle or atom cannot have, and vice versa. It would seem probable that whoever ﬁnds a difﬁculty in this cannot have strong mechanical aptitudes, and is not gifted with an adequate scientiﬁc imagination.
A free body of any kind and of any magnitude may have any kind of a motion whatever, and may move in any direction and with different velocities, but the term velocity is used in different senses when applied to different kinds of motion. Thus the velocity of an atom in its free path, of a musket-bullet, of sound-waves, is

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measured in feet per second. The velocity of vibrating bodies is indicated by the number of vibrations they make per second. A tuning-fork making two hundred and ﬁfty-six vibrations in a second is said to have that rate of vibration, whether the actual distance moved be one distance or another, which, of course, will depend upon the amplitude of each individual swing; while rotational velocity is generally speciﬁed by giving the number of rotations per second, or per minute, or some other unit interval of time. A top may spin a hundred times a second, a balance-wheel of a steam-engine turn four times, while the earth makes one revolution in a day of twenty-four hours. The range in velocities of these different kinds that have been measured is very great indeed. In free-path or translational motion, there may be the snail’s pace, perhaps less than an inch a minute, the pace of a man walking say three miles an hour, which is at the rate of eighty-eight feet per minute. A race-horse may trot a mile in two minutes and ten seconds, which is forty feet per second. A steam-locomotive may run seventy miles an hour, which is nearly one hundred feet per second. A riﬂe-bullet may go a thousand feet, and a cannon-ball two thousand feet in a second. The earth in its orbital motion goes seventeen miles per second; meteors come to the earth, from space, sometimes having a velocity

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of ﬁfty or more miles per second, while comets may reach the velocity of nearly four hundred miles in the same time when near the sun. These are the velocities of bodies of visible magnitude, but some of the motions of molecules are fairly comparable with some of these. Thus a molecule of common air is moving in its free path about sixteen hundred feet per second, while a molecule of hydrogen, which is much lighter, goes more than six-thousand feet—upwards of a mile—in the same time. As remarked before, the free path for air molecules having but about the two-hundredthousandth part of an inch, it must change its direction an enormous number of times in a second,—as many times as one two-hundred-and-ﬁfty-thousandth of an inch is contained in sixteen hundred feet;
250, 000 × 12 × 1, 600 = 4800, 000000.
Four thousand eight hundred millions of times. How one may assure himself that such a statement is not fabulous will be pointed out farther on; so far one needs only to trust the multiplication table.
For vibratory rates there are also enormous ranges: there are the slow oscillatory movements of swinging pendulums of various lengths, sometimes occupying several seconds for the execution of one vibration; piano-strings having a range from about forty per

MATTER, ETHER, AND MOTION

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second to four thousand; the chirrup of crickets about three thousand. Short whistles and steel rods have been made that will make as many as twenty thousand vibrations per second,—a rate much higher than can be perceived by most persons, though occasionally abnormal hearing in an individual enables him to hear sounds to which ordinary ears are entirely deaf. When the number of vibrations per second becomes so great that they cannot be individually seen nor heard, one must trust his judgment and the properties of matter in determining whether there really are any still more rapid. It has been found by experiment that the number of vibrations a given body can make when it is struck so as to produce a sound depends upon its shape, its size, its density, and its degree of elasticity. If a steel rod, having a given diameter and length, makes, when struck, ﬁve hundred vibrations per second, another similar one with but half the length will make twice as many in the same time. If one were made of something still more elastic than steel, and of the same size, the vibratory rate would be higher still.
A steel tuning-fork three inches long may make ﬁve hundred vibrations per second; if it were only the one ﬁfty-millionth of an inch long it would make not less than 30000, 000000 vibrations per second; and if it were made of a substance like ether it would make

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as many as 1000, 000000, 000000—a thousand million of millions per second. As large as this number is, and as improbable as it would seem to be, there is indubitable evidence that the atoms of matter do actually make such a number of vibrations per second.
If one knows the rate at which vibrations are propagated in a medium and the wave length, one can readily determine the number of vibrations the body is making that sets up the waves. Thus, if the velocity of sound in the air be 1100 feet per second, and the length of one wave be 1 foot, then the body must be making 1100 = 1100 vibrations per second: that is,
1 the velocity divided by the wave length will give the number of vibrations.
The velocity of light is known to be 186000 miles per second; the wave lengths of light are also known with great precision, and are all only small fractions of an inch. If they were only one inch long, their number would be the number of inches there are in 186000 miles, or 12 × 5, 280 × 186000 = 11784, 960000 per second. In reality they are only one forty-thousandth or the one ﬁfty-thousandth of that.
11784, 960000 × 50000 = 589, 248000, 000000,
nearly six hundred millions of millions per second. No one can pretend to comprehend such a number; but

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in proportion as he understands the process and the

data by which such a result is reached, will he have

an abiding conﬁdence that it is legitimate and that it

expresses the actual truth.

Sometimes it is convenient to know the actual space

that is moved over by a vibrating body in terms

of free-path or translatory motion, that is, how far

would the body move in the same time if, instead of

vibrating, it went on in a straight line. If the prong

of a tuning-fork moves through the one-hundredth of

an inch each swing, and vibrates one hundred times

in a second, obviously its rate of motion measured

that way would be only one inch, which would be

a relatively slow motion when compared with many

others. If the same computation be applied to atoms,

however, whose rate of vibration is so enormously

high, it leads to some very respectable translational

velocities. Thus, suppose the amplitude of vibration

of an atom of hydrogen be as great as one-half its

diameter, that is, one hundred-millionth of an inch, if

it vibrates ﬁve hundred millions of millions of times

per second, the actual space moved through will be

500, 000000, 000000 100, 000000

=

5, 000000

inches

=

80

miles,

which is more than four times that of the earth in its

orbit. It does not appear probable, however, that the

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amplitude of motion is anywhere near as much as that assumed, at any rate for ordinary temperatures; but if it be only the one-hundredth of that amplitude the velocity exceeds that which can artiﬁcially be given to any visible object, as it will then be nearly a mile a second.
Rotary speeds have wide ranges. The earth takes twenty-four hours to make one revolution; the moon about twenty-eight days, and the sun twenty-six, and some others of the planets perhaps much longer than that. Some astronomers have concluded from their observations of the planets Venus and Mercury, that their axial rotation corresponds with their time of revolution about the sun, being 224 days for Venus, and 88 for Mercury. Tops have been made to spin eight hundred or a thousand times per second; and if molecules ever rotate their rate has not been measured. The velocity of rotation, when measured as a translation, must evidently depend upon the diameter of the body rotating. The diameter of the earth being nearly eight thousand miles, a point on the equator moves twentyﬁve thousand miles in twenty-four hours—something over a thousand miles an hour, or about seventeen miles a minute. A driving-wheel of a locomotive that is six feet in diameter will advance nearly nineteen feet every revolution. To have a speed of a mile a

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minute, which is 88 feet per second, it must turn round

88 19

= 4.6

times

per

second.

A

disk

4

inches

in

diameter,

spinning 800 revolutions per second, which was the

speed given by Foucault to one of his gyroscopes,

would advance, if allowed to roll, with the speed of

837 feet per second—nearly ten miles a minute.

There are some facts, and inferences we draw from

them, with regard to motion and the geometry of space

that it may be well to mention here. When we speak

of the velocity of a body at a given time we mean by

it that its rate is such that if continued for the whole

interval of the unit of time, whether it be a second, or

a minute, an hour, or any other, the body will move

through the whole speciﬁed distance. A body will

not need to go a mile in a minute in order to have

a velocity of a mile a minute. It may not move ten

feet, yet may have that or any higher velocity. This is

obvious enough of course. Every one trusts arithmetical

processes to lead him to correct results in velocities

and time and all such familiar matters. One will say

frequently, “It is six hours to New York” instead of,

“It is two hundred miles to New York,” and will not

be misunderstood. Some persons have computed how

long a time it would take to reach the sun if they were

to take an express-train running at the rate of ﬁfty

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67

miles an hour, without stopping for food or fuel; and they ﬁnd it comes out nearly two hundred years,—a time of transit equivalent to ﬁve generations of men. In like manner, presuming one knows the distance to any remote point in space, the time required to get there at a given velocity one would call a simple problem in arithmetic, and it is. But there is an assumption one has to make which is rarely considered: that is, the properties of space and of time are the same everywhere, and that the geometry of the space in which we live is a geometry that holds everywhere and always: that its propositions are absolutely and irrefragably true always and everywhere. We assume, because we ﬁnd them practically true on a small scale, that they are equally true on the largest scale.
Within the past ﬁfty years the great geometers have made some very wonderful discoveries—one might say, astounding discoveries; for they tell us that we do not know that the sum of the interior angles of a plain triangle is equal to a hundred and eighty degrees, that we do not know it within ten degrees if the triangle be a very large one, such as is formed by the spaces between remote stars and the sun; furthermore, we are assured that, for all we know, and therefore for all we can reason from, space itself may be curved so that if one were to start in what we call a straight line, in

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any direction, and travel in it on and on he would ﬁnd himself after a long time coming to his starting-point from the opposite direction; that what one would see if his sight were prolonged in any direction would be the back of his own head much magniﬁed. Methods have been proposed for discovering if it be true or not. Some folks have called this nonsense, and have used descriptive adjectives to express their contempt for it; but none of those who have spoken thus of the new geometry are themselves mathematicians, and one is therefore left with the fair inference that they did not so well know of what they condemned as did the mathematicians who reached the conclusion.1
Now, we all of us trust such mathematical processes as we can ourselves handle, even when they lead us to magnitudes and distances too great for comprehension. All that one needs to know is, that the process is a legitimate one and is correctly worked out. This new geometry I have alluded to has been worked at by the best mathematicians of all the civilized nations, and they agree in the conclusions. They certainly would not do so if there were the slightest apparent reason for rejecting them; for national jealousies are too strong, and a sense of the value of truth too great, to allow
1See Appendix.

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any such notions to gain currency anywhere if there were any possibilities of breaking them down.
If the space we live in and the geometric relations are only practically true upon a small scale; if we may have a kind of space of four or more dimensions, whether we now can conceive of it or not, then should one understand that spaces and distances and velocities and all computations formed upon them, though practically true, for all of our experience must not be pushed up into statements that shall embrace all things in the heavens as well as on the earth. Perhaps even the visible universe is not to be measured by our span, much less things invisible in it and beyond it.

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CHAPTER IV
Energy
Whenever a body of matter having any motion strikes another body, it always imparts some of its motion to it, and the second body moves. The ability one body has to move another one is sometimes called its energy, and the amount of energy received is proportional to the amount of similar energy the ﬁrst body possesses. A body at rest can impart no motion to another one, so it appears that the energy a body has depends upon its own amount of motion. Neither can a body impart to another one more motion than it possesses itself, and rarely or never can it do so much as that. Inasmuch as every kind of a phenomenon is the result of the transfer of some kind of motion from one body to another, one may rightly infer that to understand phenomena and their relations, one must need to know, not only the kinds of motion that are transferred, but must also know their quantitative relations, and he must therefore have some units and standards for comparison. This requires some measure for the amount of matter involved, also

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some measure for the motion it has. For the former it is customary to employ a weight. A certain mass of matter called a pound is adopted in England and America. Exact duplicates of its standard weights are made and preserved by each nation; so as weights become worn by usage, they may be exactly replaced. Any unit space may be adopted, as the foot, which is common. If a pound has been raised a foot, a certain amount of work has been done, which is called a foot-pound, and it is important to keep in mind just what it signiﬁes. If ten pounds be raised one foot, or if one pound be raised ten feet, the same amount of work—ten foot-pounds—has been done; and with this as a starting-point, it will be easy to see how energy may be measured, for the measure of it will be the amount of work, measured in foot-pounds, it can do. It is found by experiment that if a body be left free to fall in the air, it will fall sixteen feet in a second, and its velocity at the end of the second will be thirty-two feet. If a very elastic ball weighing a pound should fall thus in the air upon an elastic pavement, it would rebound nearly to the height of sixteen feet. If it does not quite reach that height, it is because the air retards it somewhat, and some of its motion has been imparted to the pavement upon which it falls. Adding those losses to the height it did rise, and it would

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make the sixteen feet. Now, to raise a pound sixteen feet required sixteen foot-pounds of work; there must therefore have been sixteen foot-pounds of energy at the instant of impact. Its velocity was thirty-two feet per second. Hence a body weighing one pound, having a velocity of thirty-two feet in a second, is capable of doing sixteen foot-pounds of work. It is found also that if the same body falls for two seconds, it will fall sixty-four feet, and its velocity at the end of the second second will be sixty-four feet,—twice as great as it was for the fall of one second; but the pound weight in this case will rise under similar conditions to the height of sixty-four feet, which is four times higher than for thirty-two feet per second; so it is seen that in this case, when the velocity is doubled, the power of doing work, measured in foot-pounds, has been increased four times, and this is generally expressed by saying that the energy of a body is proportional to the square of its velocity. The particular direction in which a body moves has not been found to make any difference in this regard, so the statement is a general one. If a mass weighing two pounds were dropped, as in the ﬁrst instance, it would rise no higher than if it weighed but one; but two pounds raised sixteen feet would give thirty-two foot-pounds, so the work would be proportional to the weight as well as to the square

ENERGY

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of the velocity.

The amount of matter there is in, say, a pound

weight would be just the same in one place as in

another; but the attraction of the earth upon it depends

upon where it is. At the surface, where we measure

it, it has a certain value; but at the centre of the earth

it would weigh nothing. The farther it were removed

from the surface of the earth upwards, the less would

its weight be. At the height of a thousand miles it

would be but four-ﬁfths of a pound; at a million miles

it would be but sixteen-millionths of a pound, or only

about the tenth of a grain.

For that reason it has become necessary to ﬁnd

some measure for matter that shall be independent

of position, and this has been found by dividing the

weight of the body at a given place by the value of

gravity at that place, and calling the quotient the mass;

so if w represents the weight of a body at a given

place, and g the value of gravity at the same place,

that is, the velocity that gravity will give to a body in

one

second

if

left

free

to

fall,

then

w g

=

m,

the

mass.

The distance in feet that a body will fall in a second

is equal to the square of the velocity divided by twice

the

value

of

gravity,

or

d,

the

distance,

=

v2 2g

;

and

as the weight equals mg, the product of the two is

MATTER, ETHER, AND MOTION

74

mg × v2 = mv2 , one-half the product of the mass into 2g 2
the square of the velocity will give the energy of a

body. But it is generally more convenient to use the

weight of the body instead of its mass.

As

m=

w g

,

let it be substituted for m in the expression of energy,

and

we

shall

have

wv2 2g

=

pd

(pressure

in

pounds

into

distance in feet), or foot-pounds, a very convenient

expression to keep in mind if one has any problems

in motion and energy for solution.

An example will make plain the utility of this. A

body weighing ten pounds is moving with the velocity

of one hundred feet in a second; how much energy

has it? wv2 = 10 × 1002 = 1562 foot-pounds; that is, it

2g

64

has energy enough to raise 1562 pounds a foot high,

or ten pounds 156.2 feet high.

This is applicable to all bodies, big and little, whose

weight and velocity of translation are given.

When a person who weighs one hundred and ﬁfty

pounds climbs a ﬂight of stairs—say, to the height of

ten feet—he has done 150 × 10 = 1500 foot-pounds of

work. Whether he has gone up fast or slow makes

no difference in the amount of work done; it will

only make a difference in the rate of doing work.

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75

Now, a horse-power is a rate of work, and is equal to 550 foot-pounds a second; and hence if the above individual climbs the stairs at the rate of four feet a second, he will be doing 4 × 150 = 600 foot-pounds per second, which is over a horse-power, and indicates the probability that he would not climb so fast. If any one thinks he can do it, it will be worth his while to try it.
Work can be measured on a horizontal as well as a vertical plane. Suppose the horses on a horse-car pull two hundred pounds, as indicated by a dynamometer, and the car is moved ﬁve feet in a second: the pull into the distance measures the work done; that is, pd = 200 × 5 = 1000 foot-pounds, a little less than two-horse power. These illustrations are given because not every one has clear enough ideas concerning the meaning of energy and work, much less the ability to apply them to examples that may often come up. When one sees the long trail of a meteor in the sky, and remembers that its velocity may be as much as twenty or more miles per second, he will now see that it may have a good deal of energy, though its weight be but a few grains.
The energy of a pound moving twenty miles a second would equal

1×

(20 × 5280)2 64

=

174, 240000

foot-pounds.

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76

A grain is one seven-thousandth of a pound, and its energy would therefore be but the one seven-thousandth of that quantity. 174, 240000 = 24891, which is the number
7000 of foot-pounds of work a meteor weighing one grain, at that velocity, may have: enough to raise a ton twelve feet high.
As a matter of fact, the great friction it is subject to in its path through the air heats it shortly to incandescence, and it is presently dissipated. If it were not for the air, therefore, even if we could subsist without it, mankind would be in constant danger from the ﬂying missiles; for though they would weigh but a little, their velocity would enable them to do destructive work upon everything they struck. As there are some millions that come into the atmosphere every day, no one could be safe from them in any place.
The energy of a workingman is measured in the same way; namely, by the amount of work in foot-pounds he can do.
One of the most direct ways of knowing this for an individual is to ascertain the amount of earth or stones he can load into a cart, or the bricks he can carry up a ladder to the mason. Suppose he throws ﬁfteen shovelfuls per minute, each one holding ten pounds, and each one is raised four feet high: then in a minute

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he has done 15 × 10 × 4 = 600 foot-pounds of work, or 10 per second. This is rather a small quantity, only the one ﬁfty-ﬁfth of what a horse-power would do, and most men have been found able to do forty or ﬁfty foot-pounds per second; still, there is a great difference in individuals in their working ability. Climbing, in general, is hard work because it is continuous lifting of one’s self. One who weighs one hundred and ﬁfty pounds, and climbs one hundred feet, has done 15000 foot-pounds of work; and if he has done it in a minute, he has spent nearly half a horse-power, which is 33000 foot-pounds a minute.
Once more: a bird in ﬂying has to do work; and one may see how much is demanded of such birds as geese, that make long voyages through the air in the fall and spring,—sometimes for twelve hours or more continuously. As work is measured by pressure into distance, one may apply it thus. Geese are known to ﬂy at the rate of thirty miles per hour, which is forty-four feet per second. In ﬂying, of course, there has to be a push forward by means of their wings, not only to advance, but to maintain their elevation. Supposing that a large bird ﬂying at this rate should have to exert a push of one pound continually: it would be expending then forty-four foot-pounds per second, nearly one-twelfth of a horsepower; and to

MATTER, ETHER, AND MOTION

78

maintain such a rate for twelve hours would imply

that it had a supply of energy to start with of

44 × 60 × 60 × 12 = 1, 900800 foot-pounds for one day’s

expenditure. This does not seem at all probable, and

one may therefore infer that the pressure exerted when

going at that rate is much less. If the pressure were

but one ounce instead of a pound, the rate of work

would be 44 = 2.75 foot-pounds per second, which is 16
much more likely; but this supposes the bird to have

a

supply

of

energy

of

1,

900800 2.75

=

700000

foot-pounds.

In the chapter on “Chemism,” the source of the

energy of animals will be more particularly treated.

So far the energy involved in translatory or free-

path—or, as it is more often called, mechanical—energy

has been considered; but vibratory motions of matter

involve energy also, and the same expression is

applicable

as

in

the

ﬁrst

case,

wv2 2g

.

Here

the

value

of

the v, or the velocity, has to be determined by analyzing

the motion itself. This is not simply the number of

times the body vibrates, but also the extent of each

individual vibration,—that is to say, the amplitude of

vibration,—and the product of these two factors will

give the value of v needed. So if n be the number

of times the body vibrates a second, and a be the

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79

amplitude of the individual vibrations, the true velocity

will be represented by an, and then the expression for

the energy will be

wa2n2 2g

.

For most bodies of visible magnitude the amplitude of vibration is so small a quantity that for frequencies of only a few hundred per second, the velocity, measured as a translation, is small, and therefore the energy is small, and there are few cases where it is very important to take it into account.
Suppose a vibrating body has an amplitude of the one-hundredth of an inch, and vibrates a hundred times in a second: the total distance moved through in a second would be but an inch, which would be the value of v, so the amount of energy it had would depend more largely upon the weight of the body. On the other hand, if a body is so small that its rate of vibration is exceedingly high, as was shown in the case of atoms on page 63, there might be a relatively large amount of energy involved. In the case refered to, a velocity of eighty miles a second was computed, on the supposition that the amplitude of vibration was equal to one-half the diameter of the atom; and what amount of energy is possessed by a body weighing one grain was computed. The amount in an atom with

MATTER, ETHER, AND MOTION

80

that vibratory rate and amplitude would be calculated by dividing the amount in the grain by the number of atoms in a grain. Numerically it is a very, very small quantity, and only becomes appreciable to any of our senses when vast numbers of atoms act conjointly.
There are some cases where energy is apparently expended when there is no apparent motion, as is the case when a man holds up a weight. If the weight be a heavy one, exhaustion will be the result as much as if energy was spent in any other way. This muscular work is called physiological work, and for a long time it was not understood. It is now known, however, that when a muscle is put in a state of tension, it is in longitudinal vibration a great many times a second. This may be perceived by putting the end of a ﬁnger into the ear, pressing but gently, at the same time squeezing with the rest of the hand as if grasping something tightly; a low sound will be heard, made by perhaps no more than thirty or forty vibrations per second. The muscles in a state of tension produce this. When one holds up a weight—say, a pail of water—the muscles involved yield and contract rapidly, so the weight is really raised in a vibratory way a short distance, but a great many times in a second; and the heavier the weight, the more the work done, and this too is measured in the same way as other

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81

more visible kinds. There is good reason for believing

that a book resting upon a table is supported by the

vibratory motions going on among the particles of the

table, and therefore energy is expended to do it, and

that this is supplied by the heat present in the body;

that is, the temperature of the table is a little different

from what it would be if it did not have any weight

to support.

Walking involves the expenditure of energy in the

same way. Each step requires the whole body to be

raised somewhat. Suppose it be only an inch. A person

weighing 150 pounds would, for each step, do 150 12

foot-pounds

=

12

1 2

.

If

he takes

two

steps

per

second,

then

each

minute

he

does

2

×

12

1 2

×

60

=

1500

foot-pounds

of work. Thus one can see how physiological processes

are measurable in terms of mechanical units.

The energy of a rotating body is more complicated

than translational energy, because a part of the body

is at rest,—the axis; and the velocity of movement

at any point away from that is proportional to its

distance from it. In the case of the balance-wheels

of steam engines, where the most of the weight of

the wheel is in the rim, the velocity of the latter

would be equal to its circumference multiplied by the

number of turns per second or per minute. Thus if

MATTER, ETHER, AND MOTION

82

a ﬂy-wheel, having nearly the whole of its weight in

the rim, weighs, say, a ton (2000 lbs.), is six feet in

diameter, and rotates four times a second, its velocity

will be 75.4 feet per second, and its energy will be

wv2 2g

=

2000 × 75.42 64

= 177661

foot-pounds,

an

amount

of

energy which is stored up, and may be drawn upon

to prevent ﬂuctuations in speed to which engines in

workshops are liable.

If a body having rectilinear motion be left to itself

in the air, it will speedily be brought to rest, for gravity

will bring it to the earth whether it be moving this way

or that. The air, too, will retard its motion, and would

ultimately bring it to rest if nothing else did, as it would

either of the other kinds of motion. If, however, one

could contrive to give to a body above the atmosphere

a sufﬁcient velocity in a tangential direction, the body

would become a satellite, and revolve round the earth.

The curvature of the earth is about eight inches to

the mile, and such a body would then need to move

a mile in a horizontal direction in the same time it

falls eight inches in order that it should continue to

go about the earth. As it takes about two-tenths of

a second to fall this distance, its velocity would need

to be ﬁve miles a second to prevent it from falling to

the earth; this velocity would carry it quite round the

ENERGY

83

earth in a little less than an hour and a half. Thus it is seen that, in order that matter should
possess energy, it must have motion of some kind; indeed, that energy has two factors, mass and motion. When either of these is zero, there is no energy. This is a consideration of great importance both in a scientiﬁc sense and a philosophical one. One may often hear it said and read it in carefully written books that matter and energy are the two realities or physical things in the universe, and energy is spoken of as if it were an entity, or something that might exist though there were no substance to move. If energy be a product, and motion be one of the factors, then in the absence of this there is no energy. This perhaps will be seen still clearer after considering what are called the laws of motion, which were ﬁrst formulated by Newton, and which, in conjunction with the law of gravitation, were the fundamental principles that enabled him to produce the “Principia,” which is what to-day we would call a treatise on mechanics.
Of course, the science of mechanics is applicable to motions of matter of any magnitude and in any place; and Newton chose to follow out his newly discovered principles into astronomy to the largest extent, and it remained for later generations to employ the same principles in other directions, largely molecular and

MATTER, ETHER, AND MOTION

84

atomic. The ﬁrst law of motion is, that whether a body
be in a state of rest or of motion, it will remain in that state of rest or motion until compelled by the action of some other body upon it to change its state. This is sometimes expressed by saying that all matter has inertia, or an inability to move or change its direction or velocity if it has motion. This appears to be experimentally true of all bodies whose magnitude and state we can see. But it may very well be doubted if the ordinary conception of the inertness of matter be true. Many of the facts of chemistry indicate that matter in its atomic form is not altogether so helpless as it has been supposed to be. A stone may lie in the road for an indeﬁnite time and no one would suspect it possessed any energy to do anything, and so of any other kind of matter. Here is a piece of charcoal. Has it inertness in any extreme sense of that word? Here is some sulphur and some nitrate of potash; they, too, will lie as quiescent as the coal and as long. Pulverize them and mix them together, and we have powder the energy of which would wreck a building. The products of the explosion are gaseous mostly, and the carbon, the sulphur, and the nitrate of potash have vanished as such, and have entered suddenly into new combinations; they have developed also a large amount

ENERGY

85

of heat, while at the beginning their temperature was that of other bodies around them. This source of energy must have been resident in the atoms; and if it is perceived that for a body to have energy it is necessary for it to have motion of some sort, it will be apparent that the material itself must have possessed a large amount of motion, even when it appeared to be at rest. If one thinks that the law of inertia might still apply to atoms, and that they cannot individually move except as they are acted upon by other atoms, and even then only as much as by the measure of the motion thus imparted, he had better ﬁgure out to himself the energy of such explosions per molecule, and see if anything initially done will account for it.
When the mechanism of a clock is running, the motion may be traced to a falling weight, and the work done is measured by the product of the weights into the distance it falls as the clock runs down; but in the case of the powder, though the amount of energy developed by the explosion is deﬁnite, it is not measured by the work done in pulverizing and mixing and igniting it. The case is much more nearly analogous to that of a sleeping man. While asleep he would neither move nor stop moving unless some other agency acted upon him, any more than would a stone or other mass of matter; and in that sense he

MATTER, ETHER, AND MOTION

86

would be inert, yet no one would think of calling a sleeping man inert, except in a very loose sense.
Furthermore, there is an experimental analogy that may help one to see a little deeper into this. Every one knows what is meant by the “sleep” of a spinning top. It appears to be absolutely at rest, and may not even hum; but touch it, and the effect upon it will be out of all proportion to the slightness of the touch.
It has been observed as a property of vortex rings that they have a tendency to move forward in the direction of their axes, and when prevented from going forward they press upon the body that arrests them. If they be brought to rest, and then the barrier be removed, they, of their own accord, start on in the same direction as if pushed from behind. Such a body cannot be said to be inert without modifying the common meaning of the word.
This is not alluded to here as proving anything; but inasmuch as the vortex-ring theory of matter has a good probability in its favor, this property I have mentioned helps one to understand how the atoms might be other than inert, and yet large bodies of them together exhibit that property with the rigorousness our observations upon such bodies demonstrate. Suppose each atom had the ability to move forward of its own impulse when not acted on by any other atom. If there

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87

were a million atoms joined together, no matter how, provided they were promiscuously faced, they would mutually neutralize each other’s ability to move in any direction, and the resultant of the whole would be that passivity which we call inertness.
We may by and by see that there may be still other good reasons for thinking matter not to be so passive as it has been often assumed to be.
The second law of motion is, when two or more bodies act upon a third body, the effect of each is the same as if it alone acted, and the combined effect is called the resultant; and the third law is, that action and reaction are always equal and opposite in direction. This third condition of action, or the relation of motions in two bodies, is of a high degree of philosophical importance, perhaps not more so than the others, but of so much that it is worth while to attend to it more particularly than to the second law. If a rope be tied to the wall and one pulls upon it so as to make it taut, the wall pulls back in the opposite direction as much as the arm pulls forward. A spring-balance attached to the wall would indicate the strength of the pull, the pull of the arm representing the action, and measured by the muscular vibration, as already described, and the pull of the wall representing the reaction, and equal to the action in quantity and maintained by