:OM:S m:K KBsmPiJiiBmr.ifiirKKi;!! 1liti!tl»ili!i mpw I, ll ...^.■.[.rllTlriJ^H THE GIFT OF A.^s^k's.s \1 ^6|vr.).o.i. 3513-2 The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031177938 Atoms and Energies BY D. A. MURRAY, A. M. SOME TIME INSTRUCTOR IN THE GOVERNMENT SHOGYO GAKKO, KYOTO, JAPAN un NEW YORK A. S. BARNES & COMPANY 1901 E.M, Copyright, igoi, By D. a. MURRAY. AH rights reserved. The Riggs Printing and Pub. Co., Albany, N. Y. Contents PAGE Preface, 7 Introduction by Prof. Frederick Starr, University of Chicago 9 Synopsis of Argument 13 Summary, 21 III. CHAPTER I. ATOM MECHANICS. 1. Size does not alter mathematical laws, 2. Law of infinitesimal motions, . 3. Vibration not a simple motion, . 4. Revolution not the ground of expansion 5. Atoms in contact, .... 6. Do atoms exist ? . II. SHAPES OP ATOMS. 1. Importance of shape in mechanics, . 2. Method of determining atomic shape, 3. Illustrated by expansion in freezing, 4. Another explanation of the same, 5. Effect of contact CHEMICAL AFFINITY. 1. Difficulties of the ordinary conception, 2. Size of faces of atoms in contact, 3. Uneven and complementary faces, 4. Contact only by a point or a line, 5. More points in contact, 6. Combining in varying proportions. 23 26 27 28 32 38 43 46 48 55 57 59 63 68 71 73 74 4 Contents CHAPTER PAGE III. CHEMICAL AFFINITY — (Continiied). 7. Action of compounds, 77 8. Fundamental elements of all chemical phe- nomena 81 9. Special conditions necessary for unions, . . 85 IV. SUBSTANCE OF ATOMS. 1. All qualities merely difference of size and shape of atoms 89 2. A more ultimate uniform basal atom, . . 92 3. Definition of material substance, ... 93 V. GRAVITY AND COHESION. 1. Gravity weak between small bodies, . . 97 2. Infinitely increased at zero distance, . . 100 VI. EXPANSIVE ENERGY. 1. Law of expansive energy, .... 107 2. Mode of application to atoms, .... 114 3. Varying tension among varying atoms, . . 117 VII. ELECTRICITY. 1. Explanation not more difBcult on these grounds, 121 2. Attraction of magnets, 122 3. Dual constituents of attraction, . . . 125 4. Effects of this in other fields 127 VIII. GASES AND LIQUIDS. 1. Problem of three states of matter, . . .131 2. Immediate change between liquid and gas, . ^33 3. Change gradual, and latent heat, . . .138 4. Evaporation below the boiling point, . . 140 IX. LIQUIDS AND SOLIDS. 1. Problem of liquid and solid state, . . .143 2. Attraction varies as diameter of atom, , . 145 Contents 5 CHAPTER PAGE IX. LIQUIDS AND SOLIDS — (Continued). 3. One point of atom attracts while other parts repel, 150 4. This would yield the liquid state, . . .154 5. Capillary Attraction 158 X. EXPANSION AND VIBRATION. 1. Motion can not produce expansion, . . .161 2. Expansive tension would naturally occasion Vibration, 163 3. Expansive tendency the fundamental fact, . 169 XI. ENERGY AN ESSENCE. 1. Wrong ideas of causation, . . . .175 2. An agent acts only when and where it exists, 177 3. Gravitation not a quality of atoms, . . ,180 4. Heat energy not a quality of matter, 5. " Interstellar Ether," 6. Energy is an entity, .... XII. CONCLUSION 185 188 193 199 Preface THIS essay aims to give not a Theory but a Discussion. In dealing with the move- ments of Atoms I have endeavored to not postulate any new Force or factors of any kind, but simply to take the energies and laws which we now know, and compute their effects in the Atomic Dis- tances. Where the real condition in any case has been unknown, yet it is certain that one of two al- ternatives must be true, the one chosen has been, I believe, in every case the one equally or more prob- able intrinsically than the other. The field entered is new and exceeding large, so, while not asking any leniency of criticism for the re- sults here set forth, I would bespeak a little suspen- sion of judgment and candid, independent study along the same lines. Doubtless some or all of the conclusions here reached may have to be materially modified before a final solution is reached. It will 7 8 Preface be enough to hope that some of the ideas here ad- vanced lie along the path of that future solution. D. A. Murray. Ottumwa, Iowa, January i, 1901. Introduction By prof. FREDERICK STARR, Univenity of Chicago. IT is long since I have read a work in Physical Science which has given me so much pleasure as Atoms and Energies. The subject is in- teresting, the point of view novel, the argument clear, the book itself satisfactory. We are apt to assume that we know what is know- able about atoms. No doubt most of us think of them as spherical and of one size. Such a supposi- tion, when examined, leads to serious difficulties. In Physics, as in other sciences, we give some grand name to a difficult phenomenon and feel about as well satisfied as if we had explained it. But naming is not explanation. We shall however always have more names than explanations; there will always be some gaps in our knowledge. In his little book Mr. Murray tries to fill up several of these gaps. 9 lo Introduction He begins by an inquiry as to the shapes and sizes of atoms. Accepting the law of gravitation, he insists that it is applicable to atoms as well as to worlds and that it acts through infinitesimally small as well as through infinitely great spaces. Besides attracting gravitation he recognizes a repelling en- ergy in matter. With these as fundamental princi- ples, he examines, one after another the mysterious phenomena of physics. He tests his assumptions by applying them to Chemical Affinity, Cohesion, Ad- hesion, The States of Matter, Latent Heat, Magnet- ism, Electricity. He shows, not only that his as- sumptions are not antagonistic to the facts, but that they aid in the explanation of them. Not that the author anywhere gives a detailed proof, but he every- where points out a possible line of demonstration. He closes his discussion with a pregnant suggestion that energy is a distinct entity. It has been said by another that Science distrusts simple explanations. This is true and her distrust is but too frequently warranted. Few phenomena are simple : and the simple theory often fails to take into account many of the details the phenomena pre- sent. But the elements of the phenomena may well Introduction 1 1 be simple. And it is with fundamental elements that Mr. Murray deals. Thus while making no pretense of explaining Chemical Afifinity in minute detail, he does claim to state principles which, admitted, make chemical phenomena less mysterious, taking them out of an independent category and locating them under a known and tested law. The author is not partisan; he seeks truth. He believes he has a helpful thought ; he presents it. If it proves truly helpful and is accepted he will be jus- tified in taking pleasure in that helpfulness and ac- ceptation. Should his views be proved wrong he will be the first to welcome better and sounder views. In either event knowledge will have been advanced by his effort. For I feel sure that the book will stimulate thought. To that end it is sent forth. Frederick Starr. University of Chicago, Synopsis of Argument THE first chapter starts with the proposition that Large and Small are merely terms of comparison not absolute dimensions. An atom is much smaller than a world or than our bodies, yet compared with some other size it must be called very large. In a geometrical or mechanical calculation its size would have no bearing as making its properties or mode of activity any different from those of a marble or a world. The same laws and activities that obtain in the larger mechanics must also operate in the same way in the infinitesimal dis- tances between atoms. Attention is called by way of illustration to several common conceptions which contradict this truth ; and it is maintained that atoms in solids are in actual contact with each other, as there is no combination of known energies that could keep them rigid out of contact and all the observed phenomena of compression, etc., would be perfectly possible with atoms in contact. »3 14 Synopsis of Argument Considering atoms to be in contact, Chapter II takes up the question of their shape. Since in the larger mechanics it is the size and shape of articu- lated parts that is the one essential determining fac- tor and all the myriad forms of machinery are pro- duced solely by varying the combinations of articu- lated shapes, it seems more than probable that the shapes of the articulated atoms must have a most im- portant determining effect upon their interactions and relations. First, merely by way of illustration, is taken up the hitherto insolvable paradox of water and other substances expanding by cold in the act of congealing. It is shown how in two different ways, certain shapes of atoms engaging each other could and must produce exactly that result. Chapter III takes up the subject of chemical affin- ity. Without assuming to discuss in detail the par- ticular combining weights and affinities of any of the atoms it attempts to establish that shape alone could account for all the phenomena. That with nothing more than one simple attractive energy and one sim- ple expansive energy operating between atoms — atoms which had no difference of substance or at- tribute from each other, except the one difference Synopsis of Argument 1 5 of size and shape, this difference of size and shape could differentiate the one simple attractive energy to produce all the diversity of chemical phenomena exhibited by different substances. Namely, it could explain ( i ) Why a given atom should combine with one kind of atoms and not with another. (2) Why of several that it will unite with it should prefer one to another. (3) Why it should unite with a given atom in several different but definite proportions. (4) How even united in the same proportions it might have different properties. (5) How an atom might not, and also how it might, be able to combine chemically with itself. (6) How an atom in com- bination with .others might go into combinations that it would not go into in a free state. These are the fundamental factors that by their combination make up all chemical reactions, and as each of these could be determined by the shape of the articulated atoms and as the possibilities of varying the shape are so infinite it is maintained that the one element of shape with a single simple attractive energy acting is adequate to account for all the intricacy of chemi- cal phenomena. And &s the atoms must have some shapes and very simple shapes would produce very 1 6 Synopsis of Argument important results the claim is pressed that this is the explanation, especially since no other explanation is known or imaginable. Chapter IV. If difference of shape accounts for all the diversity of chemical affinity, all the so called chemical potencies or attributes residing in the atoms, which differentiate them one from another, are simply the result of difference of shape. And so all that differentiates one substance from another, as for instance, iron from gold or carbon, is a difference in the size and shape of their atoms. The substance of those atoms, — their texture or what they are made of, is the same for all kinds of atoms. We thus get rid of the unthinkable metaphysical conception of an attribute or potency residing in a substance and we are able to make a definition and form a mental im- age of the ultimate essence of matter, — a. thing which has always hitherto been conceded to be impossible. Chapter V asks the question what is this one single simple energy that produces the results of chemical affinity. What is its relation to the attractive ener- gies called Cohesion, Adhesion and especially to Gravitation? Gravitation, while exhibiting enor- mous power between worlds, between small objects Synopsis of Argument 1 7 produces so infinitesimally small attraction that it would seem it must be disregarded entirely. But its law is " Intensity inversely as the square of the dis- tance." So in the zero distance between atoms in actual contact its intensity would be multiplied in- finite fold. That certainly would produce attraction great enough for all the phenomena of cohesion and chemical affinity. The demonstration is absolute unless it can be proved that the law of Gravitation is not the same for small distances as for large. There is no room for any other force for the known force of Gravitation is present and must produce just such results. Chapter VI discusses Expansive Energy which it identifies with the expansive tendency produced by heat. It is shown that its law is " Intensity inversely as the distance (first power not square as with grav- ity)." This holds true only when temperature is maintained constant. Temperature is convertible into tension and as it is also varied by forcing the atoms closer or farther apart the gross amount of ex- pansive tension present in any gas would probably be found to vary its intensity of application inversely as the square of the distance between the atoms. 1 8 Synopsis of Argument Chapter VII merely touches the subject of electric- ity and magnetism without attempting to explain their phenomena further than to show that they pre- sent nothing antagonistic to the conclusions previ- ously reached. Chapters VIII and IX undertake an explanation of the three states of matter, Solid, Liquid and Gaseous. It is shown why the two simple energies, expansive and attractive, under their known laws, acting on atoms of various sizes and shapes must at a given temperature hold different substances in the three several states, Solid, Liquid and Gaseous. It is shown why the transition from liquid to gaseous must necessarily be in all ordinary cases instanta- neous, the substance going at once from the liquid state with excess of attraction between the atoms to the gaseous state with great excess of expansive ■ tendency, with no intermediate state and with an absorption of so called " latent heat " in the opera- tion. The transition between liquid and solid is also explained and it is shown how there would be evap- oration from liquids below the boiling point and even from solids. Chapter X shows that vibration can not be consid- ered a simple fundamental form of motiQn, it is Synopsis of Argument 19 manifestly a manufactured product. Neither vibra- tion nor any other kind of motion could account for the phenomenon of expansive tension. But expan- sive tension could and must give rise to vibratory motion among atoms affected by it. So the ex- pansive tension must be considered the fundamental fact in heat phenomena and the vibration of atoms only a concomitant result. In Chapter XI it is shown that Energy cannot be considered merely a mode of motion. Gravitation is not a mode of motion, and expansive tension, which is the ultimate essence of heat, is not a mode of mo- tion, though they both are tendencies to produce mo- tion. Energy is not an attribute of matter or atoms. Heat energy passes readily from one body to an- other. Gravitation can not be a quality of the atom for that would mean that an atom here exerts power millions of miles from here, that is to say an agent acts where it is not. Both gravitation and expansion are distinct entities, articulated to but not a quality or attribute of atoms. There are two forms of Substance, Material Substance or Atoms and Kinetic Substance or Energies. (To which might be added a third, Psychic Substance Soul or Life.) Summary Atoms: All identical in Substance Dififering only in size and shape Only two energies : One Attracting One Repelling With this alone account for : All diversity of Chemical Affinity. Cohesion, Adhesion, etc. Three states of Matter, — Solid, Liquid, Gas. Immediate transition from liquid to gas. Latent Heat. Expansion of water by freezing, etc., etc. Energy is a distinct Entity not a mode of motion. a I Atoms and Energies CHAPTER I ATOM MECHANICS LARGE and small are merely terms of com- parison. Space has two infinities, infinitely larger and infinitely smaller, but there is no natural starting point for comparisons. Whatever size or length is taken it is capable of infinite subdi- vision and infinite multiplication, so that with respect to some other line or space it may be considered in- finitely large or infinitely small. The particular standard of large and small which we use grows largely out of the mere accident that our bodies and the atoms which compose them happen to be this particular size. Had our bodies been a million times taller and our faculties in proportion, objects which we now consider immense would then have been counted and seemed to us exceedingly minute. On the contrary had our bodies been a million times 23 24 Atoms and Energies shorter and our faculties in proportion, what we now call infinitesimally small would have been called and seemed very large. So there is no such thing as Large or Small as an absolute quality. It was the realization in part of this great truth that made Newton's law of Gravitation such an epoch in natural science. More important than the mere cataloguing of a new force and demonstrating its laws was the birth of the grand thought that Me- chanical Laws once discovered have universal appli- cation; that they recognize no confines of large and small ; whatever law or statement of the mode of an energy is found to be true within the confines of what we term a mile is thereby shown to be true for a thousand miles or a thousand million miles. If at- traction between material substance operates to draw a falling apple to the earth it must act in the same way and under the same laws upon the moon or the planets revolving around the sun or on the farthest star. Strange as it may seem, in all the marvelous ad- vance that we have made since his time we have in an important respect failed to grasp the direct comple- ment of this truth. The same mechanical laws which Atom Mechanics 25 we find true for an inch must also be true for a mil- lionth part of an inch. The same laws which we find to be true in the spaces which we can traverse and measure with our instruments, not only hold true in the vast expanses too great for us to traverse and in- vestigate but equally in spaces too small for us to measure, perceive or even picture in imagination. The same fact of Inertia in motion or rest, under precisely the same laws, must aiifect the motions of a planet, an apple and equally of an atom. The same laws of motion in a straight line, increment of veloc- ity under a constant force, divergence from the course only under the influence of a second force, etc., must obtain with a Planet or an Atom, whether through spaces of millions of miles or through the space of a millionth of a hairbreadth. Of course it is not speculatively impossible to con- ceive that the attraction of gravitation might act according to a different law than intensity inversely as the square of the distance when that distance is more than a billion miles or less than a billionth of an inch. But it would be contrary to all sound sci- entific principles to base a theory on such an hy- pothesis since there is no positive evidence for it and 26 Atoms and Energies the presumption is against it. Again, we can not positively affirm that there are no energies that act only through a limited distance, as for instance the distance between the atoms. But this is just as im- probable as that there should be an attraction that would operate as far as from the Sun to Mercury or the Earth and not to Mars or Jupiter. It would only be necessity that could justify such an assumption. II But whether or not every energy which operates in the smaller sphere must also necessarily operate in the indefinitely larger sphere of the whole universe, it must at least seem to be necessarily true that every energy and every law that obtains in the larger sphere must also obtain in the smaller, so called in- finitesimal distances. For in operating through the larger space it does actually operate through all the smaller spaces that aggregate to make up that larger space. We may go still farther in respect to those laws of motion which are considered the axioms of mechanics, such as Inertia in motion or rest. Mo- tion always in a straight line unless diverged by some independent force in a different direction, etc. Atom Mechanics 27 As to these it is not only improbable but speculatively impossible that if they are true in the larger spaces and distances they should not be true in the smaller spaces and distances, even down to the zero or van- ishing point. For the motion through the larger space is actually made up of the sum of the motions through the infinitely small spaces. Any possibility of change of velocity or direction in the smallest space would also be change in the largest space, which according to the axioms of mechanics is de- clared impossible. It will be proper, then, to treat Atoms as though they were the size of marbles or the size of worlds, provided it will assist our imagination in its effort to realize their mechanical relations. And we may count that the same laws that would govern the mo- tions of bodies of such considerable size must also govern the motions of these minute atoms. Ill While these truths are so evident that they need only to be stated to be accepted, yet even to-day we see men seriously discussing theories which entirely ignore and contradict them; for instance, theories 28 Atoms and Energies which make the vibration of atoms an ultimate fact; which treat vibration as if it were a simple motion, and use it as a basis to explain expansion, heat and other phenomena. They do not seem to sufficiently consider that the vibration of an atom must itself be the result of a complex of forces. It must be a manufactured product. It can only be the result of several interacting energies, not their cause. It just as necessarily requires an adequate explanation why an atom ceases its motion in a given direction and returns again on its course to make a vibration as it would if the Earth would stop in its revolution around the Sun and begin to swing back in the op- posite direction. And the arrangement and direction of forces must be exactly the same for the Atom to thus change its motion as for the Earth. The fact that the earth is large and the atom small makes no difference. The fact that the earth's orbit is im- mense while the atom's vibration is infinitesimal does not affect the question a particle. IV Again, the theory is frequently put forth that the atoms of a body are kept from touching each other Atom Mechanics 29 and the phenomenon of expansion under heat is pro- duced by centrifugal force in revolution just like the balancing of the planets in their revolution around the sun. Thus all the atoms of a body are conceived in constant revolution around each other, and the centrifugal force of such revolution is the expansive force that urges the atoms apart and accounts for the expansion in heat, etc. It seems to be entirely overlooked that in order to produce a like result in any small body as in the balancing of revolving planets we must have a like condition of revolution ; that is, the whole number of atoms must be revolving around one center. In other words the body must be revolving as a whole on its axis, at a rate all but sufficient to make it fly to pieces, — a condition that would be decidedly evident to the senses. As this seems to be rather a favorite conception of physicists just now it may be worth while to take space to consider it a little more in detail. Let the accompanying figure, "ab...xy" abcde represent the atoms of any body. Now K n 1 j ,., , , k I m n o we can readily concede that any two •' ■' p q r s t contiguous atoms, as " a b," " m n," u v w x y etc., might revolve around their com- ^^«- '• 36 Atoms and Energies mon center and thus generate sufficient centrifugal tendency to counterbalance the attractive energy drawing them together, and these atoms and the space occupied by them being so small the motion would be entirely unperceived as motion. The same would be true, perhaps, of any very limited group of atoms, as " d, e, i, j," which might revolve about its center of gravity and keep its individual atoms apart without the motion being large enough to be perceived as motion. Yet even then these atoms of the group would tend to collect into two opposite groups by their reciprocal attraction unless each member of the group had a revolution with each other member around a point which was between that particular pair. In general, though the revolution of any particu- lar pairs of atoms, as " a b," " f g," etc., might ac- count for the two atoms " a " and " b " not coming together and the two atoms " f " and " g " likewise, yet no amount of revolution of the individual pairs would have any tendency to prevent the pairs com- ing together or the atoms of one pair approaching the atoms of the other pair. For any atom to be kept from approaching any other atom, even the Atom Mechanics 31 most distant one, it must actually have a revolution with that atom around a point between them. No amount of revolution with atoms in its own vicinity would keep it from approaching that other distant atom. Thus it would not be sufficient that " a " and " b " be revolving around their center and " x " and " y " around their center but " a " and " y " must also be revolving about a point midway between them, likewise " a " and " x," " a " and " r," " b " and " X," " b " and " r," and every other pair. That would be a condition that would be decidedly in evidence no matter how small the individual atoms were, for it would be really the whole body rapidly revolving on its center as well as all parts constantly mixing in the most intricate complexity. Nothing short of that would prevent any body from collaps- ing under its own attraction or from the slightest external pressure. The same objection practically would lie against the modified conception that these revolutions or " Vortices " are in the assumed all pervasive " Ether," and that these " Vortices " are themselves the facts which we interpret as solid atoms. All vortices in fluids are comparatively unstable in their 32 Atoms and Energies characteristics and necessarily modified by every ac- cidental external influence, even the slightest. In contrast to this the characteristics of atoms are per- manent and untransmutable. So whatever these " Vortices " are they are not the mechanical motions which we usually denominate by that term nor any other known motion. They are simply an unknown quantity "x." Moreover if the movements of this " Ether " are governed by the same mechanical laws that are known to apply to matter then the same objection would apply to its revolution producing ex- pansion as applies to atoms above. If they are not, then, since we have experience of no other laws they are an entirely unknown quantity and we may call them " y." Thus our explanation of expansion re- duces simply to the proposition that the two un- known quantities " x " and " y " in combination pro- duce it. Whatever interest or value such a proposi- tion may have to a metaphysician it has little place in science. We are endeavoring to interpret phe- nomena in terms of known facts and laws. For some reason it seems to be assumed by many physicists when alluding to atomic arrangement that Atom Mechanics 33 atoms never actually touch each other, even in solids, but are suspended stationary at infinitesimal dis- tances from each other, yet so as to be prevented from either approaching or receding. The reasons for such an hypothesis are the compressibility of solids and their ability to vibrate. A little examina- tion will show that such an hypothesis is impossible. Magnify your atomic structure in thought until that infinitesimal space of separation appears as a foot or a mile, the size of the atoms being in proportion, and then try to imagine some explanation for their re- maining a part. For instance imagine two planets the size of the earth rigidly suspended at a distance of one mile or one thousand miles from each other. We have seen that the law of Centrifugal tendency in revolution can not be used, for in order for that to apply the whole body as a whole would have to be in very rapid revolution on its axis. An explanation must be found for atoms practically at rest being held so that they can not separate and yet can not be made to touch. The principle of vibration can not be used, for the question why any two atoms ap- proaching each other in the process of vibration should stop short of actual contact would be harder 34 Atoms and Energies to solve than the original question of two atoms at rest separated. The only two known causes to hinder the approach of two bodies at rest attracted toward each other would be, either actual contact or some repellant en- ergy such as is seen in the expansive power of heat, the action of like poles of a magnet, etc. Now the law of all known attractive or repellent force is that its eflfect varies in the proportion of some power of the distance between the bodies. We know of no force with other laws and we should limit the ma- terials of our hypotheses to known facts. The rela- tion to each other of two bodies at rest and not touch- ing each other nor interfered with by outside influ- ences must be determined by the interaction of repel- lent and attractive energies. The law of Gravita- tion is that it varies inversely as the square of the distance. If that be the law both of the attracting and repelling forces which operate between the atoms they could never be in a state of stable equilibrium or rest except in actual contact. If the repellent force preponderated they would tend to infinitely separate, and if the attractive force preponderated they would come to actual contact. The same would be true Atom Mechanics 35 whatever the ratio, provided it were the same for both the attracting and repelling forces. Much more would this be true if the repelling force varied in the ratio of a lower power of the distance than the at- tracting force. And this seems to be the law, as we shall see later, of the expansive tension in gases, the temperature remaining constant. * But even supposing the laws of the attracting and repelling forces to differ in the other direction ; sup- pose the repelling force varied inversely as the cube of the distance and the attracting force as the square. That would indeed be a condition that would pre- vent the atoms from ever coming to actual contact, but it would not produce the phenomena we now see of solid, liquid and gaseous bodies. Instead of com- ing directly by decreasing heat from the gaseous state or indefinite expansion to the liquid state with nearly the greatest density, they must pass through a progressive process of gradual condensation with no definite marked phases. But it is needless to thus call up these various theories and refute them in detail, for there is no really sufficient reason for supposing that atoms do *See Chapter VI: i. 36 Atoms and Energies not come into actual contact. The fact that solids are compressible is no reason for supposing the atoms are not in contact. Take any aggregation of small bodies, as a box of sand or wheat, and if first thrown in loosely it can afterward, by shaking or pressing it, be made to occupy less space without changing the shape of a single grain or bringing the grains into any more real contact than they were in before. An illustration of this looser and closer con- tact might be found in a quantity of bricks, first thrown down loose and irregularly, and secondly piled up regularly into a solid wall occupying much less space. Another illustration, possibly embodying to some extent the very principles that govern the forces in atom building, may be seen in a bunch of iron filings clinging to each other and hanging on the end of a magnet. They can be easily compressed into smaller compass and spread out again on the removal of the pressure, but the contact is not any more real at one time than at the other. It is only when we have the closest kind of con- tact, as of equal cubes built solid, or equal spheres laid regularly in layers, that compression is impossi- ble. But the contact of atoms in a solid or liquid Atom Mechanics 37 under the balance of opposing forces would at first be, as we may assume, and as we shall see later,* the loosest possible contact. There would then be possible all the range of contraction between this loosest possible contact and the closest possible con- tact; for instance between prisms touching by their corners and edges only and those same prisms touch- ing face to face. Now since these atoms are drawn toward this closest kind of contact by an attracting energy, and urged away from it by a repelling en- ergy, it is evident that when the repelling energy is diminished or when pressure is applied from with- out, the efifect will be to force the atoms toward the closer species of contact occupying less space. When the pressure is removed or the expansive repelling energy increased the effect will be to urge the atoms toward the looser species of contact occupying more space. In all respects the effect of pressure or of the increase or decrease of repelling energy would be precisely the same as though the atoms were not touching, but suspended at a distance from each other. We could thus have all the phenomena of expansion and contraction equally as well under one » See Chapter IX: i. 38 Atoms and Energies as under the other condition. And if we could have expansion and contraction we could also have vibra- tion, which is merely a quick repetition of expansion and contraction. So then not only is it impossible to account for atoms in liquids and solids being kept from contact by any forces or laws known to us, but there is no legitimate reason for supposing that they are not in contact, for all the phenomena we observe could and must be produced in bodies composed of atoms in contact. VI Perhaps it will be necessary to pause a little on the preliminary inquiry whether there really are such things as atoms or what is commonly conceived of under that term. To this inquiry we must frankly answer that we do not know. Then why institute an inquiry as to the relations and properties of that of which we are not even sure that it exists? In answer it may be said : — 1st. We have no indication that they do not exist. That conception is as legitimate as any if we must form some conception of the ultimate consti- tution of matter. Atom Mechanics 39 2nd. It is the most natural conception, and the one that first occurs when we try to think about the question. 3d. All our experience of construction is of the putting together of bodies of definite size and shape. All our experience of material is in the form of bodies of definite size and shape. So we legitimately form the inference that all material construction is probably the aggregation of definite bodies of definite size and shape. Since the mind revolts against an in- finite series of analysis into smaller bodies we rest in the conception of some indivisible, unconstructed unit of construction of definite size and shape. 4th. Since all our experience of expanded sub- stance is in the form of bodies of definite size and shape we have absolutely no data from which to de- duce or construct laws for the activity of substance without definite size and shape. We would be shut up entirely to fancy. Only by considering the ulti- mate units of construction to have definite size and shape can we have any real data from which to dis- cuss their properties or relations. All discussion of matter otherwise conceived proceeds by importing and applying to it just so many as suits our purpose 40 Atoms and Energies and no more, of the known laws of the activities of bodies with size and shape. This is indeed a very convenient method for securing the conclusions we desire, but is not a very scientific method. 5th. For the purposes of our discussion we do not even have to assume that there are atoms with the common implications of that term. It is admit- ted by all that there are the phenomena of some kind of Units of Construction. The only discussion is whether those " Units of Construction " are self- sustaining, hard, indivisible bodies, or whether they are merely the " Focal ends of beams of energy," " Vortices of Ether " or some other more or less com- prehensible metaphysical conception. For our pur- poses we may entirely waive all that question. There are these units of construction, whatever they are composed of. To us, as far as our manipulation and observation goes, they are practically indivisible. They are to us, and to all the physical phenomena which we have thus far investigated, practically ulti- mate. To an architect the stones in an arch or wall are the ultimate units of construction, and he may investigate the mechanical laws of the relations and interaction of those stones in the arch entirely ir- Atom Mechanics 41 respective of the question whether those stones are resolvable into smaller bodies, or whether they are made of clay or iron, hollow or solid, etc. So the atom is the practically indivisible, ultimate unit of construction for all the phenomena we know, and since our inquiry is not a metaphysical one, but a physical and practical inquiry into the nature and ground of phenomena, we may be justified in treat- ing the atom as ultimate. Like the architect, we pro- pose to use those units or atoms merely for purposes of construction and so may waive all questions of their composition or origin. CHAPTER II SHAPES OF ATOMS A MOST important inquiry concerns the Shapes of Atoms. It is common when this subject is broached at all, to pass it ofif with the con- jecture that they are " probably round." The ques- tion is usually treated as one of no special import- ance. It has been largely ignored or overlooked. On the contrary, however, in Mechanics the matter of shape is the subject of greatest importance. In all mechanical calculations it is the shape that is the most essential and the determining element. In the case of even the most complicated machinery it is the size and shape of the various wheels and other articulated parts, and that alone, which determines that machine to do the particular work it is desig^ned to do. In fact there are only two elements in al- most all problems of Mechanics, namely the Force and the Shape of the object acted upon; and it is the 43 44 Atoms and Energies shape which determines what result the force exerted shall produce. The screw, the lever, the wedge, the wheel and axle and all the factors which go to make up machinery or architectural construction, are noth- ing more than varieties in the shapes of the two or more bodies articulated together, and this shape de- termines their action. Now if we are to treat atoms in a common-sense light, as objects which we can investigate, and whose movements are not under any veil of mystery, but subject to the same mechanical laws as larger bodies, then it is evident that the ques- tion of shape is the one question of greatest importance. The reason, probably, why it is carelessly con- jectured that atoms are round is that a sphere, while the most perfect of forms, is one of the most easily constructed and common forms in nature. The heavenly bodies are nearly spherical, so is a drop of water when falling or left to form itself according to its own tendencies. A pebble, an egg, an apple or orange and most fruits approach more or less to the spherical form. And it is doubtless a semi-conscious induction from these facts which leads us carelessly to assume that the atoms have this most common shapes of Atoms 45 and yet most perfect shape, that of a sphere or spheroid. But we should notice that these are all manufactured products and their form is in every case determined by the evident laws of their con- struction. They are of that shape because the laws under which they are built up arrange their parts into that shape. But by hypothesis the atom is not a constructed object, at least not in the sense and under the laws of construction by which larger bodies are made up of smaller particles. It has no parts ; is not built up. Its shape is not the result of the observed laws of nature, but rather, as we shall see later,* the cause of those laws. On the other hand, if we conceive any value in such indications, we might notice the fact that when many bodies pass from the liquid into the solid state under conditions of least interference from outside forces, they assume a crystalline structure, that is, the form of some sort of polyhedrons with definite angles and faces. But we must absolutely dismiss all preconceptions of probability, and conceive that one shape is just as antecedently probable as any other; the most intri- cate and involved contour of a hundred facets, as a simple cube or sphere. * See Chapter III. 46 Atoms and Energies II The practical question will doubtless occur : How can we ever know the shapes of the atoms? They are hopelessly beyond the utmost range of our per- ceptive faculties aided by the most effective appli- ances. How can we ever hope to find out anything about their shapes? It is easy enough to magnify them in imagination to any size we desire, but that does not help us to find out anything new about their appearance, only to realize more vividly what we previously knew. We could easily draw a diagram of atoms and their mutual relations on any scale of magnitude if we only knew their forms and shape, but that will not show us the form and shape if it is unknown. It may, however, be a means to help determine those shapes indirectly. If the shape is the only un- known quantity in an equation it may be possible to solve the equation and determine the value of that unknown quantity. If we have the equation : — (Shape "X" + conditions " a ") X mechanical laws " b " = phenomenon " c," and if the phenome- non "c," the conditions "a" and the mechanical Shapes of Atoms 47 laws " b " are all known it may not be impossible to determine the value of the unknown quantity shape " X." We may at least be able to determine whether there is any possible value for shape " x " that would satisfy the equation and produce the value phenome- non " c." Our magnifying in imagination and dia- graming will thus be useful in that they enable us to see and realize the elements of the problem and to correctly apply the known laws of mechanics to the case. In other words we may assume that certain atoms have a certain given shape. We may then cal- culate what eflfect would be produced if the known mechanical energies with the known laws operated on atoms of that shape under known conditions. And if the phenomenon which we calculate would thus be produced agrees with the phenomenon which actually is met with in nature that is pretty good evi- dence that we have assumed the right shape for the atom. This will be especially so if it is a phenome- non which it is impossible to devise an explanation to account for in any other way. In that case we will have come as near to a demonstration as we ever come in physical inquiry. In any case we will have proved that the element of shape can be and so 48 Atoms and Energies doubtless is, an important determining factor in atomic phenomena. It would, of course, be an exceedingly long, deli- cate and intricate problem to carry through such cal- culations and determine the actual shape of all or of any of the atoms, and no attempt of that kind is proposed. It is simply proposed, ist. To point out that the element of shape can account for such phe- nomena as are seen in atomic changes; 2nd. To designate some of the elements of shape that may be the determining cause of some of them ; and 3rd. To show that the immense range of difference of pos- sible shapes affords indefinite possibilities to corre- spond with the vast diversity of atomic phenomena. Ill In the first place, as has been said, it will be very significant evidence if the factor of shape is able to afford an explanation for phenomena that are other- wise unexplainable. We may first consider one such case. It is the very familiar fact of the expansion of bodies by cold. Water and various other substances in a liquid state contract as they cool till very near the congealing point. But in the very act of con- Shapes of Atoms 49 gealing there is a considerable expansion, so that the body at the lower temperature occupies considerable more space than at the higher. Thus decrease of heat which is the agent of expansion here causes expansion. I am not aware that any adequate and satisfactory explanation has ever been advanced for this anomaly. If the mere element of the shape of the articulated atoms should prove sufficient to fur- nish a full, simple and perfectly natural explanation for this phenomenon that would be pretty strong evi- dence that it was the true explanation, and that shape might be looked to as a potent element in the elucida- tion of many if not all atomic phenomena. It will not be difficult to conceive a shape and rela- tion of contiguous atoms which would produce pre- cisely the effect noted. The accompanying figure gives a diagram of such a relation. The figure is an idealized representation of a cross section of atoms in contact with each other. It will be evident from a mere examination of the figure that if the angle at " A " is sufficiently acute and the attractive force is such that there will be a greater tendency for the atoms " n " and " p " to come together than for the atoms " n " and " m," the effect of that attrac- 50 Atoms and Energies r shapes of Atoms 5 1 tion would be to bring the mass into the condition illustrated in fig. 2 in which it occupies more space than in the original position in fig. i. That the conditions might be easily fulfilled is evident. For assuming that the attraction varies inversely as the square of the distance, if " n " were nearer to " p " than to " m " it would be attracted much more strongly toward " p " than toward " m." And though, according to the laws of the composition of forces, only part of the efficiency of the attractive force would be available in urging the atoms in the direction of the line " BA " which would be neces- sary to bring them together, and although a less and less part of the total attraction between " n " and " p " would be thus available as the angle " A " was more and more acute, yet however acute the angle, since the attraction is inversely as the square of the distance, there could always be found some point on the line at which if the atoms were placed their nearness would make their attraction so great that even this small available component of it would be greater than the much larger component of the attraction urging in the opposite direction. More- over, when the angle " A " is acute " AC " is longer 52 Atoms and Energies than " BC " and so as the atoms approach " A " the horizontal expansion would be greater than the per- pendicular contraction, and if " DE " were as great or greater than " EF " that would produce a net expansion of the whole mass. If it is desired we may go into the mathematical properties a little more in detail. For convenience we may neglect the attraction of the small atoms " s," " s," " s," etc., being so much smaller and more distant from each other, and we may suppose the figures all parallelograms and the larger ones, " m," " n," " p," etc., squares, and of the same size. Their volume of attraction would be the same and we may represent it by a. The attraction between ' n ' and 'p' would be ^, The attraction between ' n ' and a ' m ' would be DR» The component giving motion in the direction ' B ' to ' A ' . . . . ~j-, X Sin BAC The component giving motion in a ^ ^ -o \/^ the direction ' A ' to ' B ' =DR^ ■^ Cos BAC Let us suppose the atoms so placed that the opposing tendencies are equal, then : — 5uj Sin BAC = g^, = Cos BAC , DR« _ Cos BAC _ AC hence j^u" — sin bac — bc Shapes of Atoms 5 3 (i) DR2: DU^:: AC: BC Also by similar triangles we have : — Bh: hD:: Dg: gA (2) BC—Yi DU: i^DR:: J^DU: AC— J4 DR From these two equations we may deduce the formulas : — (3) DR = _^B<^ (4) DU = _1^^ VBC B? WAC AC AC ■•■ AC V BC "^ BC Which will give the relative distance of the atoms from each other to be in equilibrium for any value of the angle " A." For all values of the angle " A " from 0° up to 90° these will produce positive quan- tities less than "AC," so with the angle "A" acute there is always a point on the line " BA " at which if the atoms impinge their tendencies in the two directions will be in equilibrium. But it is evi- dent that if they impinged nearer " A " than that point, since the perpendicular attraction would be increased and the horizontal attraction decreased there would be an excess of tendency in the direction of " A." If the atoms impinged at the obtuse angle " B," and " m " and " n " were in contact and "o " and 54 Atoms and Energies " p " then the total space occupied by the five atoms " m, n, o, p and s " would be (2ED + 2BC) x 2EF. When impinging at " A " with " n " and "p " in contact: — (2EF + 2AC)x 2DE. The latter quantity will be greater than the former, (if " DE " is as great as " EF,") whenever "AC" is greater than " BC," that is when the angle " A " is acute. It might be greater even with " AC " less than " BC " provided " DE " were greater than " EF." Thus we see that with the shapes and conditions we have assumed, increased attraction would cause expansion of the mass provided the atoms impinged at or beyond the point indicated by equations (3) and (4) above. Now, of course, it is not supposed that the atoms have the simple, plain shapes here shown. The configuration of the atoms and other circum- stances might easily be such that when they would come together they must necessarily always first im- pinge at such points that this result could be pro- duced. For instance, the small atoms, " s," might be star shaped, so that motion on their surfaces would always be toward an acute angle and so produce expansion. Nor would it be only exceptionally shaped atoms Shapes of Atoms ss that could present the conditions to produce this re- sult of expansion. All that is necessary is that the two opposite faces of any atom upon which two other atoms impinge should be so disposed that if produced they would meet in an acute angle. It is evident that in polyhedrons of many faces, at least half the possible pairs of faces, if produced, would meet at an angle of 90 degrees or less. We have thus found a possible explanation of this anomaly of Expansion by Attraction based on the shape of the atoms. Moreover this explanation uses only the forces and laws which are well known in the larger mechanics. We have also seen that this result might be produced with a considerable per cent, of the possible shapes and conditions of atoms. IV There is, however, another way in which this phenomenon can be explained, the explanation de- pending upon the shape of the atoms. This will, of course, render it more doubtful what is the real shape of the atoms concerned, but it will make it more evident that atomic shape is an important fac- tor to be looked to for explanation of atomic phe- 56 Atoms and Energies nomena. And that is the object aimed at here rather than the merely curious task of determining any particular shape. Fig. 3, represents a highly idealized conception of the cross section of atoms in contact. Since the dis- tance between the atoms along the line " AB " or " CD " is so many times less than at any other points, if the attraction decreases with the square of Fc^.3. the distance, it is evident that the attraction at all other points will be comparatively insignificant and may be disregarded in the calculation. The attrac- tion along the lines " AB " and " CD " would tend to bring the points " B " and " D " together. But if the distance from " A " to " E " is greater than from " A" to " B " the result of bringing " B " and Shapes of Atoms 57 " D " together will be to increase the space occupied by the two atoms. Thus in this way again we might have expansion brought about by attractive energy, and the result is produced entirely by the shape of the atoms concerned. V There is another consideration which we have not taken into account here, and which will be discussed more fully in a later place.* If attraction is in- versely as the square of the distance there would be an immense increase when there was actual contact. If a change of position would bring new parts or more parts into contact, then, having once attained that contact, there might be a strong tendency to maintain it even though by so doing the atoms would occupy more space than otherwise. And the agita- tions and vibrations that are normally going on in all bodies would be sufficient to throw them into these positions of contact, even when they might be in equilibrium in some other position occupying less space. Now the available attraction being only the excess of attracting over repelling energy, there may * See Chapter IX: 2. 58 Atoms and Energies be states of temperature in which certain given parts would have an excess of repelling tendency, even when in contact. But when the temperature is so reduced that these parts would have an available excess of attraction when in contact, then, whenever by the accidents of vibration or otherwise they were brought into contact, they would remain fast even though the bulk was thereby increased. This would agree with the observed fact that this expansion is chiefly not gradual but all at once, at some critical point of decreasing temperature called the Congeal- ing point. It might also show how water, if per- fectly still, might remain liquid even below the freezing temperature, but a sharp blow, setting up internal vibrations and agitations, might cause the whole to suddenly congeal. Considerations which will be developed later seem to make it more probable that this is the true ex- planation of the phenomenon, rather than either of the other two. They are given here, however, as possible explanations chiefly to illustrate the posibili- ties of the item of shape and how great influence it is able to exert in determining atomic phenomena. CHAPTER III CHEMICAL AFFINITY A LARGE range of very mysterious atomic phenomena is classified under the name, " Chemical Affinity." These facts seem to be among the strangest that science is called on to explain, and seem at first almost to imply intelli- gence and consciousness in these minutest constitu- ents of bodies. Thus for instance, when a number of atoms of different kinds are thrown together under certain conditions, they seem to have the abil- ity to sort themselves out and group themselves in definite proportions, and build up combinations in which perhaps three or four different kinds will be united, each in a different amount, but always and in all parts of the resultant body in exactly the same proportion. Then again we find that any certain atom unites eagerly in definite proportions with one certain kind of atoms ; with another kind in another 59 6o Atoms and Energies proportion; with others it unites not at all; with still others it unites only as a member of a complex group that seems to have the power of building it- self up always in the same proportions. When vari- ous kinds of atoms are presented together in un- limited quantities to any certain kind it will select therefrom, perhaps, a certain one kind, and make all its cornbinations or unions with it, though the others are atoms that on other occasions it would unite to with more or less eagerness. Now by what means, if atoms have not intelli- gence, can one species of atom recognize another species? And what is the nature of the taste by which it prefers one kind to another ? And by what kind of arithmetic is it able to compute so exactly, and unite itself with just so many and no more, and to discriminate and always keep in mind the exact number of each kind with which it is allowable to ally itself? These and other observed facts present a phenomenon of selection, recognition and computa- tion so intricate and yet so perfect as to seem beyond and apart from the ordinary laws of the larger operations of nature. In approaching this subject from the view point Chemical Affinity 6i of atomic shapes it must not be thought fatal if at first the explanation that presents itself does not seem sufficient to meet all the problems. If it can be shown that the element of shape could have some de- termining effect toward producing such results, that will be an immense advance. For hitherto science has done little more than to simply catalogue the results and assign a name, Chemical Affinity, to the agent that produces them. That is merely to con- fess that we do not know what produces them but wish to assign a name to the unknown quantity so that we may be able to talk about it. But this un- known agent must be a very intelligent being indeed, and have a vast resource of expedients in its reper- toire in order to do all that is attributed to it. The results are so many and so diversified that it is diffi- cult to conceive of an energy endowed with an as- sortment of laws and discriminating powers sufficient to account for them all. If the shape of the atoms could have any directive effect in producing such re- sults there is certainly an endless diversity of possible shapes to correspond with the vast diversity of re- sults to account for. It is certainly more possible to conceive of a dozen or a hundred different shapes 62 Atoms and Energies than to conceive of an energy endowed with the power to discriminate and act in a hundred different ways, or to conceive of a hundred different species of energy, all similar in that the only thing they can do is to attract, but yet all attracting differently. Certain it is that the atoms must have some shape, and we are at least warranted in investigating what would be the result of various assumed shapes acted upon according to the known laws of mechanics by the same or similar forces and laws to those we see operating in the larger operations of nature. Instead of the many intricate laws and forces com- monly assumed we will assume as the agent of all these results only one simple uniformly acting at- tracting energy, modified by the activity of an equally simple opposing expansive or repelling en- ergy. The one universally acting attractive energy which we know and can measure, we find to operate under the law that its intensity varies inversely as the square of the distance through which it acts. In the absence of any definite intimation of a different law we may, at least provisionally, assume this as the law of the attractive energy operating between the atoms. We may define the problem to be solved. Chemical Affinity 63 then, as follows: — Atoms being capable of actual contact with each other, and the forces acting on them being such and under such laws as indicated above, what would be the effect of varying the shapes of the atoms? What determining effect on phenomena would result from certain given shapes of atoms ? II Let us first suppose two atoms to be equal polyhe- drons, and their faces to be not such approximately plane surfaces as we have to do with in all practical mathematics, but absolutely perfect planes. For, since the atom is not considered to be built up of smaller particles, nor yet dependent for its shape on the operation of laws constantly liable to outside in- terference, there is just as much intrinsic probability of its having perfect surfaces as broken or uneven ones. Indeed we would hardly conceive of the form of the ultimate elements being anything else than perfect geometrically. Now it is evident that two such bodies coming into contact face to face, might come into perfect contact throug'hout the whole area of their faces. The distance between them would 64 Atoms and Energies then be reduced to absolute zero. Hence in com- puting the effect on them of an energy whose in- tensity varies inversely as the square of the distance there is an infinite factor brought into the computation. There is no good reason apparent why we should not consider the acting distance of the attractive energy to be the distance between the nearest sur- faces of the atoms. We have been considering atoms as absolute units, not made up of smaller particles and incapable of division. There seems to be there- fore no good reason for supposing we must com- pute and average the distance of all the points con- tained in the atom in computing the distance through which the attraction acts. It is natural to think the atom must act as a whole, and the point from which to compute distance in any direction is not the center of the mass but the surface, for that is the point at which the atom as a whole is met, and therefore the point from which it is natural to suppose it acts. We may not, of course, pretend to say it is certain or provable that such is the case, but merely that that supposition is no more improbable, is just as plausi- ble, really if any thing is more plausible than the Chemical Affinity 65 other. We have just as much right to adopt that as any other, — as, for instance, the supposition that they act from their centers or any other point, or that distances must be computed from the centers. Some place must be the starting point, and we are at equal liberty to adopt either one or the other. However, if this one adopted into an hypothesis enables it to explain phenomena not otherwise easily explainable there can be no objection to using it since the other is no more intrinsically probable, and furthermore that very fact of its helping to explain facts otherwise unaccountable is in itself very strong evidence that this is the true statement of the case. If we are right in assuming this actual distance of separation between the surfaces of the atoms to be the distance which determines the intensity of at- traction then this intensity would be multiplied in- finite fold when the atoms came to actual contact. Even if that assumption were not true there must still be an infinite multiplication of part of the at- traction, for part, namely the surface layer, of both atoms is thus at actual contact and acts at infinite closeness. And even part of the attraction so multi- plied would be sufficient to validate the deductions 66 Atoms and Energies made in the ensuing discussion. Yet as it would seem the more plausible that the whole atom should act from its surface we may proceed on that assumption. However, on the other hand it would not follow that all the attraction should be exerted from one point on the surface. For there is no particular one point that could logically be adjudged to have this pre-eminence. Why this point rather than that point? If then every point can attract the total at- traction from any face of a given ""atom would be in some degree proportional to its area. If we have then atoms acting at infinitely short distance throughout all the area in which their faces are in actual contact, it is evident that the attraction resultant from those parts would be so much greater than all the rest of the attraction between the atoms that it alone need to be taken into account in com- puting the total of attraction and all the rest may be disregarded. If, as would be natural to assume, the attraction of an atom is distributed over the whole area of its surface, the amount of the attrac- tion between two atoms in contact would depend upon the amount of the surfaces of the atoms that were in actual contact. In the case of two equal Chemical Affinity 67 cubes one-sixth of the surface of both atoms would be in actual contact. If, however, we take two atoms with a larger number of faces the amount of surface that could come into contact would be far less, say one-twelfth, or one hundredth of the whole, and thus though the atoms might have the same bulk as be- fore, their attraction for each other would be far less. Now, if we take any atom as a base, and present other atoms of various shapes to it, it is evident that with their various differences of shape the amount of surface in contact would vary, and so the degree of their attraction to this first atom would also vary. For, as we have premised, only so much of the sur- face as comes into actual contact with the first atom will figure in computing the amount of attraction, for that only has the infinite factor resulting from the distance being reduced to zero. As the shapes vary, the amount of surface that would come into contact would vary. It will also be readily seen that if two or three kinds of atoms of different shapes were presented to the first atom it would be the one affording the strongest attraction that would be allowed to find place to attach itself, and it might with the help of some kind of intense vibrating or 68 Atoms and Energies agitating movement in the mass even be able to dis- place the others if they were previously attached, and take their place. In this way, then, we see that Shape is sufficient to determine any atom to prefer combination with certain kinds of atoms rather than with others. In the above we have only conceived of atoms in the form of symmetrical figures with plane faces. Though perhaps the properties of such shapes would not have diversity enough to furnish the explanation for all the results and reactions seen in chemical com- bination, yet we must notice the fact that they would be sufficient to produce one of the most fundamental of the laws of chemical affinity, namely the prefer- ence or greater affinity which certain kinds of atoms have for certain others. Thus even if there were no other considerations or resources, we would at least be led to expect that shape might have something to do, in fact to see that it must have some influence in varying the results of chemical combination. Ill But we have by no means exhausted the possibil- ities of atomic shape. Instead of being symmetrical Chemical Affinity 69 with plane faces, the faces of an atom may be con- cave or convex, made up of ridges and furrows, the whole or part of the surface may be made up of radiating spikes, cones or prisms, or any particular face may have part of its surface elevated or de- pressed, such parts having plane, concave, convex or any other variety of surface. Thus it is seen that the possibilities of shape are practically infinite. Now this will introduce an entirely new factor into the solution. If an atom with concave or convex surfaces be introduced to the first mentioned basal atom with plane surfaces, it can touch it only at a point or a line and there can be no extent of surface in contact. With all these latter described shapes there must be a matching with an exactly comple- mentary shape before there can be surface to sur- face contact. Thus if the surface of one were con- vex the surface of the other must be not only con- cave, but it must be a concave exactly correspond- ing to the convex of the other. If one atom has a surface of furrows and ridges the other must have not only ridges and furrows, but have them the same distance apart and of exactly such complementary shape that they will fit into the first perfectly. 7© Atoms and Energies It is evident that if the surfaces of atoms were anything else but plane surfaces this might prevent any species of atoms from making combinations with atoms of its own species. For in order to make a combination the contours must be not the same or similar, but complementary to each other, one con- vex where the other is concave, etc. This, however, would not necessarily divide the atoms rigidly into two groups, the members of the one able to combine with the members of the other, but never with those of their own group. For the same atom may have a hundred faces, all different, and each face adapted to match with some face of some other atom. There might be some one kind of atom, like Oxygen, with faces adapted to match and combine with almost ev- ery other kind of atom, while there were many other kinds which could not combine with each other at all except as they were bound together by this one. There are even cases which appear like one kind of atom uniting chemically with its own species. This, of course, would be readily conceivable even under these conditions, as one face might be complementary to another face of the same atom. Chemical Affinity 71 IV We have still not exhausted the possibilities of the effects of shape. If the attractive energy were great enough the firmness of attraction seen in chemical union might result without actual contact through- out the w'hole area of a surface, but merely such partial closeness and contact at a point only, as would result from a convex surface on another surface not exactly complementary to it, or one uneven surface on another. In this case the intensity of attraction with all its determining effect on phenomena would vary with the rate of divergence of the impinging surfaces. Two curved surfaces that were very nearly complementary would produce more intensity than curves that were less near. This conception would account for more diversity of results with more sim- plicity in the shapes of atoms. As there is an infinite factor in the attractive intensity resulting from actual contact, it seems not impossible that this kind of contact might yield strong enough attraction to give the observed results. In this case a slight vari- ation in the radius of curvature or in the inclination 72 Atoms and Energies of contiguous faces would yield all the necessary variations of preference and affinity. But, as previously remarked, it is not necessarily more probable that the shapes of atoms are simple than that they are intensely complex. Moreover, the most complex and intricate shape is perfectly conceivable, while it is doubtful whether we are able to form a conception or mental picture of any other quality or attribute suitable to thus differentiate atoms and account for chemical preferences. The most complex shape is a much more conceivable idea than an energy which has power to discriminate and act differently toward different individuals. Nor is it at all certain that very complex shapes would be neces- sary to produce all the range of varied results seen in nature. Possibly a perfect knowledge might be able to devise a series of very simple elementary shapes that would be able to produce all the variation of results necessary. While holding in reserve, then, this possibility that a lesser form of contact might be all that would be necessary, we may proceed to consider further the possibilities of combination interpreted as perfect surface to surface contact between atoms. The pos- Chemical Affinity 73 sibilities of diversity in the other species of contact are so limitless that there is no question of the im- mense variety of results that could be made possible by that agency. V Let us take for an experiment some comparatively simple form of surface, say one composed of " V " shaped grooves and ridges. Let us suppose that the sides of these ridges are inclined to each other at a uniform angle, and slightly curved. Now it is evi- dent that if another surface of the same kind were presented to this one, though the number and dis- tance apart of the ridges would be the same, yet it would not match to make a surface to surface con- tact, because that would require the opposite kind of a curve, concave where it was convex and vice versa. Thus this atom could not enter into combination with itself, at least not by that face. But let us sup- pose atoms to be presented having ridges to exactly fit into the grooves of the first atom. It is evident that there might still be quite a variety in the strength of the affinity growing out of variety in the number of grooves in the first atom that would be 74 Atoms and Energies filled by the second. Thus suppose the size of the grooves in the first atom to be such that in a given distance there would be 24 grooves and ridges. Among the atoms presented that matched these grooves there might be those that had, in the same distance, i, 2, 3, 4, 6, 8, 12, 24 grooves respectively. All these would yield surface to surface contact and SQchemical combination. But the strength of the affin- ity would vary directly with the number of grooves matched. We would have here then another possi- ble way of explaining the preference of any atom for combination with one kind of atom rather than another though it could combine with either. VI Let us take another simple experiment. Let figs. I, 2, 3, and 4, represent four different kinds of mole- cules, composed of the same two kinds of atoms " A " and " B," only in different proportions. Now while it is seen that three of the atoms " A " can find attachment to the atom " B " as in fig. 3, yet by a different method of attachment, as seen in fig. 2, or 4, no more can be attached after two have been at- tached, and in fig. i, a single atom attached prevents Chemical Affinity IS others from being attached without a structural change. Here we might have an explanation, or rather a type, of the varying proportions in which two kinds of atoms will unite, as for instance CO, CO2, etc. Fiq.l. ^^1^3L. ^i-aM. Or if, again, we suppose an atom with one face suitable for a given kind of atoms to attach them- selves to, one atom of this given kind might attach itself in the center of that face, so preempting the whole territory. Or two, three or more might attach y6 Atoms and Energies themselves less completely with their bodies meeting in the center of this available face and projecting be- yond its edges. This would be another type of the union of atoms in varying proportions. In this case it might be that the more atoms were attached the less secure would be their attachment, and the more easily they would leave it to combine with other atoms, just as we see in certain series of acids where those members having the higher proportion of oxygen are the more active reagents, that is more ready to break up and form new combinations when in contact with other substances. Of course these are very crude, elementary cases, and are only intended to illustrate the principle that in many different ways varying the arrangement might vary the number of atoms that would make preferential attachments with other atoms. Espe- cially if more than one of both species of atoms were used it is still easier to see that there might be quite a number of different proportions in which the atoms might be built together under those conditions of preferential contact which are necessary to constitute chemical union. Comparing figs. 2, and 4, we see that in each only Chemical Affinity 'j'j two of the atoms " A " are attached to " B " and no more could find room to attach in either case, yet the arrangement is different and the shape and presuma- bly the qualities of the resulting molecule are differ- ent. This will furnish a type or simple explanation of those cases where exactly the same elements in exactly the same proportions seem capable of uniting to form compounds with different qualities. In all these cases it must be borne in mind that the illustrations and designs here given are not intended to be received as the actual form of any specific chemical compound, but are simply designed to demonstrate that that kind of a compound could possibly be brought about entirely by the shape of the atoms concerned when acted upon by the sim- plest kind of a single attractive energy, acting on all alike, and acting just as the one attractive energy we know and have measured is known to act. VII Now it is true that all the cases we have thus far considered have been cases of the union of one simple element or atom with another. And of course we must recognize that rather the combinations of com- yS Atoms and Energies pounds with compounds occupy by far the most important part of chemical study. Their results are the facts the chemist is interested in much more than the simple unions of one element with another. It is the extreme variety of the results produced and of qualities presented in the union of complex compounds, and the diversity often seen in the union of nearly the same elements in different proportions and different combinations which he would seek to explain. The skilled chemist will very probably not receive with much favor the ex- planations and adaptations outlined in the previous pages for the reason that they do not seem to touch at all the problems which he is most interested in, — the problems which are really the most intricate and which practically constitute the science of chemistry to him. But it should be borne in mind : — ist. That an ex- planation that does not explain everything may still be good and valuable for as much as it will explain. 2d. The explanation of the union of one ele- ment with another is really a much more funda- mental and important problem than the more intri- cate and interesting question of the properties and Chemical Affinity 79 reactions of these more complex unions of com- pounds with compounds. 3d. Even the union of compounds with each other is now looked upon in the light of a union and readjustment of the individual atoms in each rather than of the compounds acting as integral wholes. 4th. All the diversity of chemical " quality " for the most part consists of diversity in the tendency to enter into combination with other substances. 5th. The chief phenomenon that is peculiar to these unions of compounds with each other is the ability compounds have to bring elements into com- bination which would not enter into combination if they met each other in a free state. This may be ac- counted for in a number of possible ways, all con- sistent with the conception of chemical affinity depending on atomic shape. (a) It may be accounted for by some new law or property not here set forth or not yet discovered. (b) The configuration of the built-up molecule may present a shape or contour more advantageous for contacts than any single atom. (c) The vibrations and agitations caused by the breaking down of one molecular structure may force 8o Atoms and Energies atoms into contacts they would not otherwise be able to reach. (d) An atom held in the grasp of other atoms which are being drawn into some combination may, by them, be drawn or pushed into some contact that it would not otherwise be able to reach. A type of this might be found perhaps among common opera- tions, in the Bit in the Brace, the Nut in the Wrench, or the Iron in the Plane frame, being forced to do work which they could not be easily made to do without being grasped by these accessories. (e) It is possible that the explanation might lie in the fact of atoms, or at least some atoms, in the so called free state being really in combination with their own species, that is, the face of the atom that is capable of attaching to other atoms is already at- tached to another atom of its own kind. The two must therefore be separated before they can unite with any other kind of atom. That would prevent their entering into combinations when in the so called free state. In the compound the atom has already been separated from its mate, so, as it comes from the compound in the reaction, the susceptible face is free and ready to unite with a suitable atom Chemical Affinity 8i if it offers itself. Some slight countenance would seem to be given to this last supposition by the fact that oxygen appears to be such a double atom made up of two atoms of Ozone united. VIII Now the phenomena of chemical affinity and combination, though so multiform and complex, may be analyzed and reduced to a few very simple elements, and it is the combination of these simple elements that builds up the intri- cate results and phenomena we see. Just as all the elements of machinery may perhaps be analyzed into two principles, The Lever, including the wheel and axle, the pulley, etc., and the Inclined Plane, in- cluding the wedge, screw, knee joint, etc. A practical machinist might not consider a theoretical discussion of levers and inclined planes very profitable to him and yet all the most intricate machines he works with are perhaps made up of these and of these alone. The elements of chemical phenomena may be com- prised in the following questions : — ( i ) Why an atom combines with one atom and not with another. (2) Why it prefers one union to another possible 82 Atoms and Energies union. (3) Why it makes all its combinations with other atoms in regular, definite proportions. (4) Why it will unite with the same atom in differ- ent proportions. We have seen that all these can be accounted for as the result of the one element shape, the shape of the faces or points of contact. Different shaped atoms acted upon by one uniform attractive force varying with the square of the dis- tance would necessarily produce all those different kinds of phenomena. All these elements have al- ready been shown in the illustrations given, (i) Inability to unite would result from not having faces that would match to make intimate contact with the other. (2) Preference for one over another might result as shown from one of several causes, as a larger area of surface contact, a larger number of corrugations or special conformations matching in a certain area, etc. (3) Union always in definite proportions would necessarily result from the definite shape of the atom, which would provide attaching places for just so many and no more under any given conditions. This number might naturally vary somewhat with the kind of atoms presented. (4) As to the series of different proportions with the Chemical Affinity 83 same atom, the illustrations given show how that could be accounted for in the case of a simple union. If a larger number of each kind were built into one structure it would afford much more possibility of variety in that respect. Thus we see that the one element of Shape in the atom is capable of determining all the varieties of result found in combinations. And not only could it produce those results, but since the atoms must have some shape, and in all probability a large variety of shapes, if they are acted upon by a force that varies with the square of the distance they not only could but must produce results of that precise nature. What right have we to look for other mysterious, occult agents to produce these results when these sim- ple agents which we know to be present must produce precisely those results? If other agencies produce those results where do we see the resulting differ- entiations that necessarily must result from differ- ent atomic shapes? The proof seems complete that atomic shape is capable of having, and so must have, some determining influence in producing the diver- sity of results in chemical combinations. Since it is capable, as we have seen, of determining any and 84 Atoms and Energies each of the four species of phenomena which by their combination make up all the complex results, and since, moreover, the possibilities of diverse shape are almost infinite, making possible an almost limitless series of each species of phenomena, shape would seem to present an adequate cause for the determina- tion of all the diversity of atomic combination. Notice that this is not merely an hypothetical theory. It is not a matter of indifference whether we prefer to assume that this agency does this work or some other agency does it. We know that the agency of shape is there present, and, as we shall see later, we know that just such an attractive energy with just such laws as we have assumed is also there present and acting. Even if it were possible to con- ceive of some other agency that might produce these results better and more simply, we would not be at liberty to attribute them to that agency unless there were positive evidence of its presence, for this agency is present and must produce just such results. Much more, then, since we have never been able to conceive any thinkable explanation of the phenomena, while shape explains them in a most simple manner, may Chemical Affinity 85 we rest in the conviction that we have here the true explanation. IX It may be noticed that there is one other point not yet touched upon, namely: — Why it should require special conditions to make any two atoms unite if they have such a configuration as would make them capable of uniting. For instance, why does not the oxygen and nitrogen in the air spontaneously unite into nitric acid ? Or at least, when the repelling en- ergy has been so far decreased that the atoms really touch each other, as in liquefied air, why should they not go still farther into chemical contact? Why, if the attraction is strong enough that the atoms will stick when they are together, should it not be strong enough to bring them together? Some points bearing on that case will be discussed later when we come to study the laws of repelling energy and the probable nature of the attachment of the energies to the atoms and their method of act- ing on them.* It will not be found difficult to con- ceive very simple, natural conditions or circum- * See chapters VI and IX. 86 Atoms and Energies stances that might enable the atoms to stick together when in the position that produces the liquid or even the solid state while when they were in the positions for face to face contact the repelling force would be so strong in the directions affecting that position as to keep them apart. Or again, if the supposition ad- vanced in (e) above, be true and the atoms of Oxy- gen and other substances in the so called free state be really two atoms with their available faces joined in contact, that would furnish a sufficient explanation here also, why the atoms would not enter into com- bination by mere contact without some intense agita- tion to break apart the double structures and release suitable faces to make attachments to. At any rate the explanation is not an impossible problem, and it would be just as easy under the con- ception that chemical affinity was governed by atomic shape as under any other theory. That has been the only task attempted here, to show that all the diversity in atomic combinations, and therefore all the qualities that distinguish one atom from another, could be accounted for merely by the size and shape of those atomic bodies. If as is suggested in a later chapter, this at- Chemical Affinity 87 traction between the atoms which draws them to- gether, is capable of being separated into two com- plementary, opposite components as seen in the phe- nomena of magnetism, some modification of this same effect may be produced in every contact of atoms with each other, under laws and conditions not yet well understood, and this may have something to do with atoms not uniting into the closeness of chemical union until suitable conditions are present. The same cause also may have some modifying or determining influence on all chemical phenomena. CHAPTER IV SUBSTANCE OF ATOMS IT is hardly necessary to point out how very greatly this will simplify our conception of the workings of nature. Instead of having a vast number of distinct agents or laws or little law- lets, one for each separate kind and degree of afifin- ity, a dozen or a score or more sometimes attached to a single atom, attached in a way that we cannot im- agine, and these lawlets or agents being of a nature that we cannot comprehend or even conceive of; in- stead of all this mysterious complexity we have the whole matter just as simple as the relation of the wheels in a watch or the stones in a wall, and, more- over, governed by precisely the same laws. All chemical phenomena are produced with atoms all identical as to their essence and varying only as to their size and shape. These atoms are merely at- tracted and repelled by two perfectly simple energies 89 90 Atoms and Energies with the very simple law of variation in intensity according to the ratio of some function of the dis- tance, while the size and shape of the atoms de- termines this one simple attractive energy to make the selections, preferences, computations and all the other wonderful results seen in chemical affinity. It is true the way we have conceived of the atoms being fitted and matched together may seem quite crude, artificial and cumbersome. But the first de- signed steam engines or telephones were very crude also, and very unlike the graceful compact machines of the present. Yet they had the essential principles. And so, we may maintain that though many changes may have to be made in the application and working out of details, the general principle will be found true that the size and shape of the atoms is the determin- ing, differentiating cause of what is known as chemical affinity. But possibly the objection may arise in some mind : Is not the explanation burdened by the neces- sity of supposing so many, so intricate and complex patterns and shapes for the atoms? Not at all. In the first place it is not sure that they must be either intricate or complex. As before remarked, the first Substance of Atoms 91 model of every invention is always complex and crude. Fuller knowledge and use enables us to pro- duce the same results on the same principles, with much more compact and simple working parts. So, possibly, perfect wisdom might construct, of very simple and compact form, shapes that would pro- duce all the mechanical results necessary. But more than that, since atoms are not constructed or in any way dependent for their form on the laws or pro- cesses of mechanics or physics, but were as far as we know, arbitrarily constituted to their present state, we know of no logical reason why one shape is any more probable than any other. Moreover, a hundred different shapes are perfectly conceivable, but a hun- dred varying and discriminating laws or faculties are hardly conceivable. And especially all those laws, energies or faculties inhering in one and the same atom is entirely beyond our power to make a mental picture of. We can readily conceive shape as an at- tribute of atoms. It is a necessary attribute. We cannot conceive any body without shape. But to call the act of counting, recognizing, discriminating and attracting other atoms a quality of a given atom, or an attribute that inheres in it, is to use a form of words without any mental conception to correspond. 92 Atoms and Energies II Perhaps it might be suggested that it would be a still simpler theory to suppose these present atoms of diverse shapes to be themselves constructed of still more ultimate smaller atoms of uniform shape. If by that is meant symmetrical, spherical or cubical atoms, it would not be a simplification but would add immense complexity. For it would require intelli- gence and a more numerous set of more complex and incomprehensible laws than those commonly assumed in chemical affinity to build up these uniform atoms into these diverse shapes requisite for chemical affin- ity and maintain them rigidly in that state. If, how- ever, it is possible to conceive of a single kind of atom of complex shape such that by a simple process of being built up upon itself under the influence of one single attractive energy, by varying the combina- tion of faces that come together in the building-up process, all the necessary forms of atoms would be produced, — if, in other words, we could have some one uniform atom which in its own shape possessed the directive tendency to produce all the shapes of atoms necessary to produce our known phenomena. Substance of Atoms 93 that would perhaps be a simpler theory. But it may be doubted whether such a shape is mathematically possible. Even if possible it may still be questioned whether that plan would be logically simpler, for there is no more intrinsic probability of atoms be- ing one shape than another, — all uniform or indefi- nitely diversified. But at all events we have abso- lutely no empirical evidence of such more ultimate uniform atoms. Until there is some evidence of the possibility of transmuting one elementary substance into another there is no ground for such a supposi- tion. It may find place in a merely speculative discus- sion, but the design here is to confine the discussion to the practical, to the interpretation of known facts. Ill We are prepared now, perhaps, to attempt a defini- tion of material substance and to form some concep- tion of what the essence of matter is. Hitherto this question has always been set aside as unanswerable. We can tell how " iron " differs from " gold," or " lead " or " carbon," or we can tell what iron will do, but what " iron " is in itself has been considered a type of the unanswerable question. We are accus- 94 Atoms and Energies tomed to speak of certain qualities inhering in it as an essence, but what that essence is in which that series of qualities inheres has been considered beyond the power of the human mind to know. What do we mean by qualities inhering in an essence, or what is the meaning of essence apart from qualities ? Per- haps conceived in that form the matter is incompre- hensible. But since we have been able now to greatly simplify our conception of atoms and reduce all so called qualities, attributes and laws to the too easily understood necessary qualities of size and shape, we may at least be able to come a step or two nearer to a conception of essence and a solution of these questions. In the first place Iron does not differ from Gold or Carbon in the sense in which we commonly con- ceive it to be a different substance. It is not a differ- ent essence, which is made up of or endowed with a dififerent set of qualities, or in which those qualities inhere. In the sense in which we commonly con- ceive of essence, the essence of Iron and Gold and of all the other elements is identical. To use popular terms, what is inside of the atoms, their texture, what they are composed of, is the same for all. Their Substance of Atoms 95 differences or their diverse ways of acting, which we term qualities, are all the result simply of their diverse sizes and shapes, these sizes and shapes de- termining the effects that one simple attractive force and one simple repulsive force will have upon them. It only remains then to define or form a conception of what that universal essence is. We can, of course, do no more than to formulate a statement of what its phenomenon is. But since that phenomenon is single and quite simple we may feel that we have come as near a definition and comprehension here, perhaps, as in any of the other cases where we assume to define. We may say : — Material substance or an Atom is: — ^An Impene- trable Expanse of the Ability to Modify and be Moved by Energy. This phenomenon is really single, for the two fea- tures " modify " and " be moved by " energy are really but the two complementary parts of the same one fact. Modify, means determine the point of application and the direction of the energy while the very essence of energy is simply ability to change the relative locations of these impenetrable expanses. The impenetrability is not a second phe- 96 Atoms and Energies nomenon, for it is not absolute impenetrability, but simply relative, with respect to other such expanses. We might say. Mutually Exclusive expanses in- stead of Impenetrable. In other words we might say that an Atom is merely a certain expanse that is capable of being moved about by what are called Energies. As to what is inside of these expanses, we might say, simply the potency of being moved by energies and of preempting a definite expanse of space each to the exclusion of all others. We thus can frame as adequate a definition and form as com- plete a mental picture of the essence of matter as in any other case where we profess to define. CHAPTER V GRAVITY AND COHESION IN the previous pages we have spoken of an at- tractive force acting between atoms, and pro- ducing the various phenomena of chemical affinity according to the shape of the atoms acted upon. We also know of an attractive force acting between the atoms of bodies, which we call Cohesion. Can these attractive energies be the same, and can they both be identified with what is called Gravity? In other words would the attraction of gravitation acting upon atoms under precisely the same laws as when it acts on planets be sufficient to produce the observed results ? If this can be established it would reduce our analysis of nature almost to the simplest possible terms. The main question would be whether this energy which produces gravitation can be powerful enough. At first thought, perhaps, the idea would seem 97 98 Atoms and Energies absurd. It would seem as though it certainly could not be powerful enough. Break a stone in two, and hold the two parts as close as we can together. We know that under the law of gravitation every atom in either part attracts every atom in the other part, but we find by testing, that the total aggregate of that attractive force is so infinitesimally small as to be beyond measurement. How then could it have been so strong before the stone was broken as to hold those two parts together so firmly that tons of trac- tion could not draw them apart? If a small object is held suspended close to the foot of a high, steep mountain, the attraction of the whole mountain upon it might be just barely sufficient to be measured by the most delicate instruments. Indeed the attraction of the whole earth upon it may amount to only a few pounds or a few ounces. And yet the attraction of the few atoms in the small body upon each other in cohesion is so great that many thousand pounds of energy would be necessary to draw them apart. So it would seem as though all hope of making the familiar energy of gravity the explanation of these atomic phenomena would have to be abandoned as absurd. A force so infinitesimal, however great its Gravity and Cohesion 99 results when massed into great aggregations as in the earth and suns, seems too insignificant to play any part in an observed attraction of many tons between the parts of a body whose whole attraction to the immense bulk of the whole earth would not exceed a few pounds or ounces. And this conclusion would seem to be strengthened by the fact that this attraction of cohesion seems to bear no relation to the bulk of the body, as does Gravity. The break- ing strain of a bar of iron of a certain cross section will be exactly the same whether its length be ten feet or a tenth of a foot. So it has been thought necessary for the explana- tion of this result to assume a distinct energy or set of energies of great intensity and limited range, of which nothing more is known or knowable, but that they produce these specific effects that are otherwise unexplainable. Thus, in every body, attached to each of its atoms there is conceived to be a complicated series of energies or laws. One is called Cohesion, and has certain functions and prerogatives. Another is called Adhesion, another called Gravity, another called Chemical Affinity, or rather, as commonly con- ceived, this last is an extended, intricate series of loo Atoms and Energies energies and energiettes, different ones being at- tached to different ' atoms, and the same atom pro- vided usually with quite an extended assortment, sometimes as high as fifty or a hundred, all posted at their appropriate stations and provided with grips and pass words and by-laws and rules of order to regulate the outgoings and incomings of other atomic suitors and visitors, according to the severe etiquette of the atomic social organization. II In spite of its comparative feebleness and the ap- parent absurdity of the thought, it seems that closer analysis will show that the one well known and simple energy which produces the result called Gravi- tation is the producing cause of all these results ; that Adhesion and Cohesion and Chemical Affinity in all its myriad forms, are simply different operations of the same energy that draws the apple to the earth and holds the earth itself and all the suns in their appro- priate orbits. The key to the solution is to be found in the infinite factor which comes into operation when the atoms are in actual contact with each other. The observed law of gravity is that its intensity in- Gravity and Cohesion loi creases in inverse ratio to the square of the distance. If that distance is very small the intensity would be immensely increased. When it becomes zero the in- tensity would be infinitely increased. That would be the case when the two atoms are in actual con- tact. The distance between them would then be zero. If the surfaces opposed to each other were perfectly complementary, there would be this zero distance throughout the whole extent of the surfaces so in contact. If they were not perfectly complementary there would still be this zero distance at the point or line in which the one atom did actually touch the other, and in the territory imme- diately adjacent to that line or point of contact the distance would be so very small that the intensity would be immensely multiplied. The only critical question is whether the distance between the atoms may be computed as the actual space which separates them, that is, the distance be- tween their nearest surfaces, or whether it must be computed from some point within the atoms as for instance from their center of mass, or the average distance of all the points which make up their volume. This question has already been anticipated 1 02 Atoms and Energies in the previous pages. In computing the attractive influence of one large body upon another we natur- ally and rightly compute an average of the influence of all the particles in the body, because every body is actually made up of separate particles which at- tract independently. But when we deal with atoms the case is different. They are not made up of smaller particles, at least as far as we know. By hypothesis the atom is the smallest possible division, and indivisible. It is not made up of units which act independently. It is itself the unit. There is noth- ing to suggest that we ought to treat its attraction as made up of a large number of little attractions emanating from all the points which make up its expanse. It should act as a unit, and from the place where as a unit it is met, namely at its outer surface. The presumption at least would seem to be in favor of that as the most plausible hypothesis, and if its adoption will enable us to simplify in any degree our conception of atomic relations, that is itself the best kind of proof that it is the true hypothesis. Now if the distance which determines the intensity of attraction between atoms is their actual distance apart, and is to be measured between the respective Gravity and Cohesion 103 nearest points or surfaces, when any two points are in actual contact, or when a certain area of surface of one is in actual contact with the surface of the other, it is evident that the distance is reduced to zero, and the intensity increased by infinity in the second power. In the one case that part of the at- tractive force that belonged to that point would be exerted with that intensity, and in the other that proportion of the whole attraction which corre- sponded to the area of the surfaces in contact. In either case the exceedingly small attraction which is all that is apparent between bodies at a finite distance would surely be sufficiently multiplied to produce even the intense attraction seen in what we call co- hesion or in chemical affinity. So the objection that this energy is not powerful enough is sufficiently answered. That force which produces Gravity, act- ing between atoms in contact would be sufficiently powerful to produce all the intensity necessary, pro- vided, as we are perfectly warranted in doing, we count the distance which determines the intensity, from the surface of the atoms. Indeed, since that intensity is multiplied by a quantity expressed by infinity in the second power, I04 Atoms and Energies it would seem rather on the other hand as if this power was too strong for us, that it would bind bodies together with such a force that it would be absolutely impossible to ever separate their parts. But we may be satisfied if we have demonstrated this power strong enough, for there are plenty of expedi- ents and conditions that might tone down its in- tensity sufficiently to make it tractable to our uses. As previously remarked, it is not imperative that we suppose there is ever surface to surface contact, pro- vided the exigencies of the case seem to make the other conception necessary. If the contours were such that there could only be contact at a point or a line, then since only an infinite fraction of the total surface was in contact, and thus only an infinite fraction of the total attraction infinitely multiplied, that would reduce the result to finite dimensions. Or we might conceive that Cohesion was contact only at one or more points or lines while surface to surface contact produced Chemical Combination, which is only dissolvable by special processes. And again, even with surfaces in contact, each point on one sur- face would not be in contact with the whole of the opposing surface, but only with one point or an Gravity and Cohesion 105 infinite fraction of it, and this consideration again might sufficiently reduce the too great infinite attraction. Again it is not certain that any surface would ever have to be lifted per- pendicularly away from another surface. Even if two surfaces were held together by an infinite power, less than an infinite power might be suffi- cient to cause them to slip or slide on each other and separate them in that way. And finally, since the attractive force is not alone but the apparent attrac- tion is merely the excess of the attractive over an opposing repulsive force whose intensity also varies with the distance, a little change of temperature might throw the repelling force in excess and thus cause the atoms to separate. Even in the case of a body breaking from an outside strain it might be that that strain caused waves or congestions of heat or repellent energy w^hich were the agencies that effected the separation. There need be then no fatal objection, either on the ground of too feeble or too great intensity, to the explanation that the well known energy seen in Gravitation also produces the intense attractions seen in cohesion and chemical affinity. Moreover, io6 Atoms and Energies certain it is that this energy which produces gravita- tion is present and acting between the contiguous atoms. According to its known and computed laws it must produce some results, indeed we have seen that according to its known laws it must produce as great an intensity of attraction as is seen even in cohesion and chemical combination. It is not a ques- tion whether this or some other agent is best adapted to do the work or furnishes the best explanation. Even if it were possible to conceive of some other agent that would account for it all more simply and satisfactorily we would not be at liberty to adopt it for explanation, for this agent is actually there, and to demonstrate that according to its known laws it would produce those results is to demonstrate that it does actually produce them and there is no other energy concerned in the case. The proof that the same energy that makes the apple fall also holds to- gether the atoms of the apple, is precisely the same as the proof that that same energy holds the moon and planets in their orbits. The reasoning is exactly the same, only carried down to very short distances instead of up to very long ones. CHAPTER VI EXPANSIVE ENERGY ONE of the phenomena of an increased amount of heat in any body is a greater expansion or tendency to expand between its atoms. We find a certain tendency to separate between the atoms of all gases, and even in liquids and solids there is an elasticity which is its equivalent, and which arises from the same cause, a repelling energy be- tween the atoms. We find that gases, liquids and solids all normally expand by increase of heat and contract by decrease of heat. This expansive en- ergy, therefore, seems to be one of the essential attributes of what we call Heat. We may ten- tatively assume that this expansive energy which is one of the phenomena of heat, is the only expansive energy that exists, and all expansion between atoms is brought about by this same energy which produces the expansion in heat 107 io8 Atoms and Energies phenomena. There is a presumption against there being two energies that do the same work and yet are different things. Since we have seen that all attractive energies may be one and the same it is much simpler to suppose that there is also but one repelling energy, and we may proceed on that pre- sumption till we meet some phenomena that dis- tinctly contradict it. The next question is, what is the nature and what are the laws of that energy ? Is its law the same as that of Gravity, Intensity decreasing according to the square of the distance, or is it something else? We may best examine its action in a gaseous body, for there the atoms are suspended freely at the dis- tance of many diameters from each other, so we can measure the intensity as that distance increases or decreases. One of the laws of the tension of gases is that at a uniform temperature the volume varies inversely as the pressure. Take any gas at the normal atmos- pheric pressure of fifteen pounds to the square inch, and increase that pressure to thirty pounds to the square inch, and it would be reduced to half its vol- ume. Decrease the pressure to half an atmosphere Expansive Energy 109 and its volume would be doubled. Let us suppose the pressure increased to eight atmospheres. The pressure being eight times as great the volume would be one-eighth as great or the distance between the atoms one-half what it was previously. It is evi- dent that the measure of the expansive tension of the atoms is the same as the measure of the pressure necessary to resist and restrain it. So decreasing the distance to one-half thus increases the expansive tension by the cube of two or eightfold. But it must be noticed that it is not the total sum of ex- pansion that is increased eightfold but the amount of expansive efficiency per square inch or for each unit of surface. Now if we suppose the volume of gas to retain the same shape as it contracts, the area of its surface will vary as the square of the distance between the atoms. When that is one-half, the sur- face will be one-fourth as great. So though the expansive energy is eight times as great for each unit of surface, yet the surface is only one-fourth as large, so the total amount of expansive energy ex- hibited is only eight divided by four, or two times as great as at first, that is, inversely proportional simply to the distance between the atoms, — that dis- no Atoms and Energies tance through which it acts. In general, suppose the pressure in any gas to be increased till the distance between the atoms becomes ^ of what it was at first. Then the pressure per unit of surface will be found to be #, but the amount of surface becomes -, so the whole amount of pressure, and therefore of expansive tension, is # x -. = ^- That is to say it varies inversely as the distance. Or, if we divide up the whole volume so as to allot to each atom the amount of space contiguous to it and through which it acts in reaching the next adja- cent atom, we may compute in the same way how the expansion associated with each atom varies. The volume of that space which is the sphere of a given atom's expansive influence, varies as the cube of the distance between the atoms, but the area of its sur- face varies as the square of that distance. When the distance is reduced to - the expansive energy per unit of surface will be n^ times as great, and the amount of surface \ times as large, therefore the total amount of expansive influence connected with that atom will be n^ x ^ or w times as great. That is, it varies simply as the distance between the atoms. Or, to approach the matter from another view Expansive Energy 1 1 1 point, — the energy that is apparent and subject to measurement is not the sum of all the amounts of energy associated with all the atoms, but only of the layer of atoms contiguous to the containing wall. The energy of all interior atoms is simply used in resisting the expansion associated with the atoms around them. The pressure of each of these exterior atoms, however, is the same as that of each of the others in every part of the mass, and so is a measure of the intensity of expansive tension. Now the pres- sure on each unit of surface varies inversely as the volume, that is, inversely as the cube of the distance between the atoms, but the number of atoms contig- uous and impinging upon that unit of surface varies inversely as the square of that distance between the atoms. So the amount of pressure exerted at each atom would vary inversely as the cube divided by the square, that is to say it would vary inversely as the simple distance between the atoms. This then is the law of the intensity of expansive energy at a uniform temperature. But this does not necessarily show the law of expansive energy to be different from that of at- tractive energy, for this result of intensity inversely 1 1 2 Atoms and Energies proportional to distance is only obtained if the tem- perature is maintained constant. But one result of compressing any volume of gas is always to raise the temperature. To maintain the temperature constant this surplus of heat must diffuse off into the sur- rounding space, and be subtracted from that body. But increase or decrease of temperature also always produces and is equivalent to increase or decrease of expansive tension. So the increase of tension at a uniform temperature is only part of the actual in- crease produced by the compression, the rest having escaped with the heat diffused away. The total in- crease of tension for a given compression or de- creased distance of the atoms would be this observed increase at the same temperature plus the additional tension that would have been caused by the heat that escaped in keeping the temperature uniform. It would be the increase of tension at the temperature which the compression would produce if no heat escaped. Now perhaps it can not be shown from our present computed figures, that this amount of heat diffused to bring the compressed mass to its original tempera- ture, added to the increased tension from compres- Expansive Energy 113 sion would give such numerical results as to show that the law of expansive energy is the same as that of attractive energfy, namely intensity inversely as the square of the distance. Our present figures do give results somewhat nearly approximating that law. We know, moreover, that there is prob- ably a miscalculation in our ordinary computa- tions of heat volumes and intensity. Almost as low temperatures have actually been produced as the temperature which our computations give as the absolute zero or absence of all heat, with the resulting substance still liquid. The ordinary mercury or spirit thermometer uses as the measure of change of temperature the change of bulk of a liquid, — a quantity which varies with the cube of what would correspond to distance between the atoms. Other forms use lineal expansion of a bar, which corresponds to the first power of the same quantity. So there is a difference in our standards of measure. This latter would seem the more scientifically correct. The former method, though, because of the very small range of the expansion, it may be correct enough for all ordinary uses, might give considerable error when applied to very great 114 Atoms and Energies differences of temperature. So, while we may not say with confidence that the law is the same for the attractive and repelling energies, yet we may say that the repelling energy varies at least as some function of the distance and apparently very nearly inversely as the square of the distance between the atoms. II There is an essential difference between the mode of application of heat energy and attractive energy. As far as we are able to determine, the quantity of attractive energy attached to any atom or any body is constant. While the intensity varies inversely as the square of the distance, the volume of energy which is varied in that ratio is always the same. When the atoms or the body is transferred, the energy is al- ways transferred with it, and the only way that the energy can be removed from place to place is to re- move the body. The energy seems inseparably at- tached to the atoms. This is not true of the energy of heat. It is capable of being transferred from place to place by radiation or diffusion, without any transfer of atoms. A body may contain a certain amount of heat at Expansive Energy 115 one moment and at another moment only half that amount or twice that amount. A quantity of heat energy may appear at one moment in one body, and at a later moment it may appear in some other body at a distance from the first.* It does not show any attachment for any body or any tendency to remain in any particular body or between any certain atoms. In fact precisely the reverse seems true. It shows a persistent tendency to escape from any or all bodies or atoms with which it is associated. And it is only prevented from thus separating itself at any time by the confining presence in the contiguous territory of an equal or greater amount of heat. This difference in the fact of attachment might lead us to suppose probable a difference in the method of application of the expansive from the attractive energy. We count that the attractive energy, asso- ciated inseparably with the atoms, varies directly with the bulk of the atom. Suppose we assume that the expansive energy, being a detachable, transfera- ble energy, in no way permanently associated with * See also chapters X and XI. The expansive energy ex- hibited by heat cannot be accounted for as a mode of motion, it must be a distinct entity. 1 1 6 Atoms and Energies any particular atom, does not measure the amount of its influence on any atom by that atom's bulk, but by the amount of surface which it finds on which to apply itself. The amount of its influence or power exerted on each point or unit of surface we may as- sume to be the same, no matter what the diameter of the atom acted upon. It seems as though this would commend itself as the more logical assump- tion. A quantity of this energy moving from place to place, when it meets an atom meets it only as a surface. That is all the atom would appear to be to it ; merely a surface opposing its motion, and an area on which it could impinge. It is hard to see how the character of that surface would be different to it, or modify it in a different way, whether the thickness of the atom lying beyond that surface were one unit or ten units. It is hard to conceive any reason why a quantity of energy acting on a surface for the first time, should act with greater or less intensity upon it because the distance through the atom to the oppo- site surface was greater or less, or why the quantity of that energy that should apply itself to a certain area should be more or less from the same circum- stance. It would imply something almost like in- Expansive Energy 117 telligence in the energy to always know at each new surface it met, just how far it was through that atom, and to proportion itself accordingly, when it might be meeting and acting upon a dozen different kinds of atoms every minute. It would be more natural to suppose that it should act uniformly on everything it met irrespective of its cubical size, that is to say, that its influence would vary simply as the amount of sur- face exposed to it on which it could act ; its influence would be the same on one unit of surface as on an- other. This would be entirely consistent with the other idea that the attractive energy, being perma- nently associated with a particular atom, should have its volume or quantity proportional to the size or volume of the atom with which it is and always has been permanently associated. Ill It is quite evident that this difference in the mode of application of these two energies would cause a difference in their comparative effect on different atoms. Their comparative efficiency would vary ac- cording to the size and shape of the atoms between which they were acting. The repelling energy vary- 1 1 8 Atoms and Energies ing as the square and the attractive energy varying as the cube of the same quantity. For instance, let us take two atoms of a certain given size. There is a given amount of attraction between them proportionate to their size. There is also an amount of repelling tendency between them which affects them in proportion to the amount of surface it finds to impinge on, while it varies in quantity with the temperature. Let us suppose the temperature such that the effect of the repelling en- ergy exactly equals the effect of the attractive energy. Alongside of these with the same temperature let us suppose there are two other larger atoms. Being larger the attraction between them would be more. Also, though the temperature, or quantity of heat, or amount of repelling energy present was the same, yet because there was a larger surface to act on the effect of that repelling energy upon these atoms would be greater than upon the others. But the quantity of the attractive energy, being in proportion to the bulk, would vary as the cube of the diameters of the atoms, while the effect of the repelling energy, being proportionate to the amount of surface it could find to act on, would vary as the square of that Expansive Energy 119 diameter. It is evident then, the shapes being the same, that with these larger atoms the attractive effect would exceed the repelling effect, because one varies as the square and the other as the cube of the same quantity. The larger the atoms the more pre- ponderance it would give to the attractive energy, and the smaller the atoms the more advantage it would give to the repelling energy. This would make it possible that different kinds of atoms would require different degrees of heat to separate them into the gaseous state. Also at the same temperature different kinds of atoms might exhibit the three dif- ferent states, gaseous, liquid and solid. We would have then, if the shapes of the atoms were all the same, the law that the temperature of vaporization would vary as the size of the atoms. This we do find to hold true to some extent. The small atoms of Hydrogen remain gaseous at a very low tempera- ture, while the larger atoms of metals and earths re- quire a very high temperature to melt or vaporize them. This would only be accurately true, however, if the shapes of the atoms were all the same. It is evi- dent that if the shapes were sufificiently different the 1 20 Atoms and Energies rule could not give accurately the vaporizing tempera- ture, for with different shapes the ratio between the area of the surface and the volume may vary greatly. Thus suppose a cube measuring one unit each way, be compared with another body ten units long, ten units wide and one-tenth of a unit thick. The volume of the former would be i, and of the latter lo. But the surface of the former would be 6, and of the latter 204. The volume is 10 times greater but the surface is 34 times greater. Instead of the volume increasing at a faster rate than the surface the sur- face has increased more than three times as much as the volume. This would seem to make it possible that atoms of larger size or greater weight might vaporize or change their state at even lower tempera- tures than other atoms smaller in size. Only, if there were some approximate symmetry, or approach to equal proportion in the comparative length, breadth and thickness of the different forms of atoms, would there be a close conformity to the rule that the temperature of vaporization should vary as the size of the atoms. CHAPTER VII ELECTRICITY THUS far we have given no consideration to that very interesting and important group of phenomena that are classified as electri- cal or magnetic. The nature and explanation of these phenomena is confessedly a difficult problem, and we may be permitted to postpone any attempts at a full explication until the properties and laws of electric action are better ascertained. We may, how- ever, premise at least this much, that the explanation will be just as easy under the conceptions of matter and energy here set forth as under any other. We are not attempting here a cyclopedia of science or an explanation of every fact of nature, but merely to account for some of the fundamental facts that are the basal elements of phenomena. How these facts are combined to produce all the diverse varieties of phenomena is a separate question. 122 Atoms and Energies If, as is commonly thought, vibration is the dis- tinctive feature of electrical action as it is of heat and light, we will see later* that vibration is a natural and necessary product of an expansive tension be- tween atoms. So there could be any required species of vibration in bodies that had this expansive ten- sion. There would remain only the question of the necessary interaction of forces and the shape and relation of the atoms acted upon to produce the particular rate, amplitude and other features of vibration seen in a given case. II As for the attractive power that is exhibited by electrified and magnetized bodies, it is not impossible to conceive that it might be accounted for by that same natural attractive energy in the body that pro- duces the other attractive effects. The probability of this is enhanced by the fact that the attraction of magnets like that of Gravitation varies inversely as the square of the distance. We do not know, but there may be laws governing the direction of lines of attractive energy that would make it possible for the * Chapter X. Electricity 123 attraction radiating out in every direction from an atom to be all bent and concentrated on one or two directions. We do not know, again, but some rela- tion or particular kind of contact between the atoms may render them so that the attractions from all the atoms of a whole body are united into one attraction acting from the surface or pole of the body, so that the whole body acts like one atom, and the distance through which the attraction acts, and which di- minishes its intensity, is not the distance from each individual atom, but is to be measured from the outer surface of the body to the object attracted. Either or both these causes would immensely increase the infinitesimal apparent attraction shown by normal bodies toward each other and help to yield some such appreciable strong attraction as is seen in magnets and magetized bodies. Moreover, we know that there is a reciprocal ele- ment in this normal attraction of gravitation. It va- ries not only with the body attracting, but also with the body attracted. It is the product of the potential of the attracting body multiplied by the potential of the attracted body that yields the effective result. Now if only the atoms of iron have the necessary 1 24 Atoms and Energies shape to yield this concentration of the lines of attrac- tion in a marked degree, and if this magnetic concen- tration in the lines of energy in one body has the power to induce a similar state of concentration of the lines of energy in another suitable body that is brought within the range of its influence, then when an iron magnet is brought near iron, since it induces a similar magnetic state in the other iron body its own high potential is multiplied by the high potential in- duced in the other body, and so the result is a very strong attraction. If, however, the other body were one whose atoms were of such a shape or so related that they did not conduce to this concentration of their attractive energy, then, though the magnet itself had a very high potential of attraction not being multiplied by a high potential in the attracted body, the actual resultant attraction between the two bodies would be very much smaller than before, and might be entirely too small to be perceived. This would ex- plain why the magnet would have an appreciable at- traction for iron or any other substance that could be magnetized, while its attractive efifect on other substances would be too small to be noticed. Electricity 125 III There is another consideration possible. We know that heat energy has an essential duaUty which mani- fests itself in the dual phenomena of Temperature and Expansive Tension, making possible greater or less tension at a given temperature and greater or less temperature at a given tension. After a like analogy there may be a duality in the essence of this one universal attractive energy. It may be a com- pound of two complementary, oppositely acting com- ponents, which have an innate propensity to seek to come together and neutralize each other (this effort of the two components to come together being per- haps what draws together the atoms which are articulated to them or something of that kind). Mag- netization consists in partially separating these two components which have the complementary tenden- cies, and concentrating them each on opposite sides of the atoms, at the same time uniting all the energies of all the atoms into one energy acting from the sur- face or pole of the body. Then, if opposite poles of magncLs be brought near each other, the component 1 26 Atoms and Energies of energy at each being complementary to that at the other, and each being partly denuded of its comple- mentary and neutralizing associate component, the attraction would be greatly enhanced so as to appear as the strong visible result of magnetism. On the contrary, if like poles were brought near each other exactly the opposite conditions would exist and di- rectly the opposite results would be produced. The bodies would repel each other as like poles of mag- nets or similarly electrified bodies are seen to do. Now it may seem like rather a large assumption to suppose that the attraction which is universally char- acteristic of atoms, which produces Gravitation and which we have seen could also produce all the results of adhesion, cohesion and chemical union, has such a dual character and is capable of being resolved into two components and producing the polarity seen in electricity and magnetism. But on the other hand we do know by experience that some energy is capa- ble of being thus resolved into two components, for we find it actually done in these phenomena of elec- tricity and magnetism. We do not know anything to prohibit us from supposing that our well known attractive energy may be capable of being so re- Electricity 127 solved. And so it is no more improbable nor nearly so much so to suppose that an energy known to exist is capable of being so resolved, than it is to conceive and invent an entirely new attractive energy, which also has to be so resolved. IV If this one universal attractive energy has this duality and consists of these two components whose proportions may be varied in varied circumstances, that would add a new element to help in the explana- tion of the phenomena of chemical affinity. It will be borne in mind that when showing the adaptability of difference of shape of the atoms to produce these differences of resulting combinations, it was by no means claimed that that was the final word on the subject, or that it excluded the action of other laws and principles to vary those results. What was attempted was merely to show the very wide variation of results and modes of combination that could be caused by the one element of variety in the shapes of the atoms. The one desire was to get free from the necessity of supposing there were a hundred different varieties of energy, or there was 128 Atoms and Energies some energy with the marvelously complex, discrimi- nating, calculating, practically intelligent powers that would be necessary in the ordinary conceptions of chemical affinity. If we find from other sources that there is this new feature or any other factor that would contribute to the variety of the results, that is to be welcomed as so much gain. All that is de- sired is to be able to explain the infinitesimal move- ments and changes of the atoms by means of energies and factors that are known and measurable in larger relations, and under the same laws that operate in the larger mechanics, so as to get entirely rid of the air of mystery that is usually felt to attach to atomic movements. As commonly conceived the causes that produce and govern the complexity of chemical com- bination are so utterly mysterious, complicated and unknowable that for all we could tell they might be capable of producing almost any other result that it is desired to explain. In fact they have actually been so used. Atomic motions have actually been held by some theorists to explain or be the essence of almost every known phenomenon from heat and gravitation to thought, consciousness and animal life. If, however, we can reduce all the complexity Electricity 129 of atomic relations and qualities to be explainable by geometrical and other mathematical properties and the same laws that are well known and measured in the larger mechanics there will be no room left for mystery. We can tell approximately what atomic movements can and what they can not account for and we will put an end to all this wild speculation. It is possible also that the same cause, law or agency which produces this polarization of energy in magnets may also afford the explanation of what is called " Capillary Repulsion," and the disinclina- tion of certain substances, as for instance, water and oil, to mix with each other. The energy associated with each atom may be so separated into its con- stituents and polarized by the action of the energy associated with the atom of the other substance that they would mutually repel each other like the sim- ilar poles of magnets. Or, on the other hand, in other cases this polarization of the energy might in- crease their attraction for each other, as in the case of dissimilar poles of magnets. This would furnish the explanation for some of the phenomena of Diffu- sion of Gases and the dissolving of solids in liquids. It also might have some very import- 1 3© Atoms and Energies ant effects in chemical reactions, bringing the appropriate atoms into the locations where they could unite, and displacing atoms with feebler at- tachment to make room for others that would have a stronger attachment. CHAPTER VIII GASES AND LIQUIDS MATTER is met with in three clearly marked, distinct states, Solid, Liquid and Gaseous. The distinction between the solid and liquid states is not always perfectly definite, as cer- tain bodies pass gradually from solid to liquid, through an indefinite, intermediate viscous state, with no marked phases. But the distinction be- tween the liquid and gaseous states is always marked and definite, and there is no gradual approach or in- termediate condition. In making any of these changes there is always a certain displacement of heat. This is especially marked in passing between the liquid and gaseous states. A large amount of heat is absorbed in pass- ing from liquid to vapor, and reappears on changing back to liquid, all without any change of temperature. This phenomenon of so called Latent Heat is one of 131 132 Atoms and Energies the characteristic features of vaporization, and the question arises, what becomes of this heat ? What is its function, or what is its condition in the vapor ? A very striking feature of this change from liquid to gaseous is its suddenness. In hquids the atoms are in contact with each other, and some of the effects of " Capillary Attraction " would seem to hint that in some respects there may be a very strong attrac- tion between them. In the gaseous state they not only have separated to the distance of many diame- ters from each other, but they have a strong repelling tension developed between them. And this change from contact to this wide separation with marked expansive tension, is made instantaneously, without any intermediate gradual change. When heat is applied to any liquid, after it has reached the vapor- izing point the temperature does not rise farther, but the liquid remains at that temperature while one by one its atoms change from the liquid condition of contact to the gaseous condition of wide separation and marked expansive tension. And precisely the corresponding process takes place in condensation. Another very striking fact about vaporization is that it may go on when the liquid is very much below Gases and Liquids 13^ the vaporizing temperature. Indeed, it even goes on from solids. Snow and ice will gradually evaporate even when the temperature is far below the freezing point. The same is known to be true of many other solids, and it is supposed that all solids evaporate more or less. This vaporization occurs without ap- parently passing through the liquid state, and at temperatures very much below that which would al- low the substance to remain in the gaseous state or even in the liquid state. How are all these phenomena to be accounted for and interpreted? Is there anything in the results of the theory of atoms and energy here set forth that will help toward their interpretation? Could simple inert atoms acted upon by two opposing forces whose intensity varied inversely as the square of the dis- tance, and without any other determining laws except such as we know in the larger mechanics, produce such phenomena ? Rather the question is, must they necessarily produce just such changes? II In examining this question let us start with a given body in the gaseous state. That means that the ex- pansive energy is in excess of the attractive energy, hence the atoms tend indefinitely to separate except 134 Atoms and Energies as they are restrained by some extraneous force. If more heat is introduced, raising the temperature, the tendency to separate becomes stronger, requiring more power to restrain it, or as we commonly say, the tension increases. If heat is removed the ten- dency to separate decreases. This tendency to sepa- rate is only produced, however, by the amount of ex- pansive energy which is in excess of the attractive energy. An attractive energy is present and acting between the atoms all the time. As more and more heat is removed, there would come a moment when the expansive energy would be reduced to equili- brium with the attractive energy, and any further re- duction of heat will leave the attractive tendency in excess and the whole must come into contact in the liquid or solid state. Moreover, if the gas had all the time been subject to a constant uniform external pressure it would seem that the result of decreasing temperature must have been to reduce the bulk con- stantly and gradually from the gaseous to the liquid condition without any marked phases. This is not, however, the observed result seen in condensation. The atoms go directly from wide separation with marked expansive tension, to actual contact in the Gases and Liquids 135 liquid state, and all without any change of temperature. But we have omitted some very important fea- tures of heat activity. There are two elements in the phenomena of heat, for the expansive tension of heat is varied, ist, by the closeness or distance of the atoms, and 2nd, by what we call temperature. Bring- ing the atoms closer together with the temperature constant increases the intensity of the repelling en- ergy, and raising the temperature with the atoms at the same distance apart, also does the same. But bringing the atoms closer together develops a higher temperature, which will diffuse off increasing the temperature of surrounding regions. Thus either of these elements, Tension and Temperature, is the equivalent of, and readily transformable into the other. Also we have seen that there is a difference in the law as to the ratio of distance to intensity, be- tween the repelling and the attracting energy under uniform temperature. All these things will consid- erably influence the manner of the atoms coming together to form a liquid, or separating to form a gas. In any gas at ordinary atmospheric pressure the 136 Atoms and Energies atoms are separated at a distance of many diameters from each other. And we have seen that, tempera- ture remaining constant, the law of the repelling en- ergy is that its intensity between any two atoms varies inversely not as the square, but as the first power of the distance between them. The attractive energy, on the other hand, varies inversely as the square of the same quantity. So closeness gives an advantage to the attracting energy and distance gives an advantage to the repelling energy. Let us suppose a given gas to be at such a temperature that the ex- pansive tendency is found to be in excess of the at- tractive, — say twice as strong as the attractive tend- ency. If by any means any two atoms in that gas were brought to half the distance they were before, the temperature remaining the same, then the ex- pansive tendency would be found twice as great, but the attractive energy would increase faster and would be found four times as great as before, so the attract- ive energy would then be exactly equal to the ex- pansive. If these atoms were brought still nearer together the attractive tendency would be in excess and the atoms must come together and remain together. Gases and Liquids 1 37 Thus we see that in such a gas at such a tempera- ture the atoms at the considerable distance of separa- tion would remain apart, and have considerable ten- dency to separate still farther, but if by any means brought into contact they would have a strong excess of attractive tendency, and might cling together with great firmness. The known law that, at a uniform temperature the intensity of the repelling energy varies inversely as the distance and of the attractive energy inversely as the square of the distance, would make this possible. It would cause that when sepa- rated a considerable distance the atoms would have a strong repelling tendency, while, if brought together the attractive tendency would be in excess. Thus, when the temperature was suitable, the atoms, even in a gas that had still great expansive tension, must go immediately at one movement into the state of contact, or on the other hand, go from the liquid state of contact immediately to the gaseous state of separation and strong expansive tension. The change must be instantaneous. There could not be a gradual, uniform transition from one to the other. As soon as two atoms got close enough together that the attract- ive tendency preponderated they would come to- 138 Atoms and Energies gether and stay together. If they were separated farther than that distance they would tend to recede as far as possible. If the closeness that was neces- sary to give the attractive force the preponderance were actual contact then any two atoms that were made, in any accidental way, to touch each other would remain together, and as long as they were not actually touching each other they would tend to recede to the greatest possible distance. So there could be no intermediate state between liquid and gas. The agitations and vibrations that are con- stantly going on in all bodies would naturally throw the atoms into these contacts and so cause the vapor to condense as soon as the temperature was low enough that the atoms would cling together when they were brought into contact. But even at that temperature the atoms would maintain nearly their maximum separation and expansive tension until they were thus brought into contact. Ill But there is still another consideration. The ex- pansive tendency increases inversely as the distance only if the temperature remains constant. But com- Gases and Liquids 139 pressing any gas, or forcing its atoms closer together, raises the temperature. Even if the temperature in any gas were such that any of its atoms brought into contact would have an excess of attraction and would cling together yet the act of bringing any of those atoms thus into contact must cause a rise in the temperature. Let us suppose the temperature in any gas to be just at the point where if any two atoms were in contact the attractive tendency would be equal to and just enough in excess of the expansive force to retain them together. Then, if by any means two of its atoms were brought together they might stay together, but their coming together would cause an increase of temperature, and this diffused through the mass would raise its temperature so much that no other two atoms could come together and stay to- gether till that amount of heat had diffused out of the mass and the temperature again lowered to the condensing point. Thus, both the condensation must be a gradual process, and a certain amount of heat must be diffused out of the mass into the surround- ing medium during the process of the condensation. It is evident that exactly the converse and counter- part of this would take place when a liquid was 140 Atoms and Energies heated to the evaporating point. When the tempera- ture was high enough that the repelling tendency exceeded the attractive, even in contact, the atoms would begin to separate. Any atom separated from the mass would by its separation acquire a strong ex- cess of the expansive tendency, and so would stay separated. But this expansion or separation of atom from atom would cause a decrease in the tempera- ture between those atoms, which being immediately made up by diffusion from the surrounding territory, would lower the temperature there below the evap- orating point, and no more atoms would separate till more heat were introduced. Here, then, we have an explanation for the spe- cific features that characterize evaporation and con- densation. We can see why the process must be gradual and not the whole mass changed at once, and we can see what is the explanation and function of what is called the Latent heat of vaporization. IV The same principles will readily explain how there could be evaporation from liquids, below the evapo- rating temperature, and even from solids. The tern- Gases and Liquids 141 perature throughout a considerable expanse of con- tiguous territory in any body must always be com- paratively uniform, any slight heat that is produced or absorbed by a few atoms coming together or sepa- rating is quickly compensated by diffusion, so that such atoms coming together or separating would do so under conditions of approximately uniform tem- perature. At uniform temperature the attraction di- minishes as the square, but the repelling efKciency as the first power of the distance. So the ratio of the repelling to the attracting efficiency would increase directly as the distance. The separation of the atoms therefore, as we have seen, gives a great advantage to the repelling energy, so that atoms which would have attraction greatly in excess if in contact, and so would cling firmly together, might, when separa- ted several diameters from each other, have the re- pelling efficiency considerably in excess. If thus the condensing temperature, — that tem- perature which just allows the atoms to cling to- gether when in contact, — would allow them to have a large excess of repelling tendency when separated, it is evident that a temperature much below that con- densing point might also allow the atoms to have re- 142 Atoms and Energies pelling tendency in excess when separated. A tem- perature as low as the congeaUng point of the sub- stance or even much lower might still allow the atoms to have excess of repelling tendency when separated from each other. The vibrations and agitations which are constantly going on in all bodies would have precisely this effect of separating one and an- other of the outside layer of atoms from the mass, and when once separated the repelling tendency be- tween them would be in excess and they would have no tendency to come together again. This would be in effect a slow evaporation, and it would go on from liquids below the evaporating point and even from solids. CHAPTER IX LIQUIDS AND SOLIDS THERE are two states in which substances exist with their atoms in contact, namely, Liquid and SoHd. While there is not as marked a difference as between liquid and gaseous, nor always as sudden and immediate a transition from one to the other, yet the distinction is usually very definite. In the liquid state the different parts of the mass move freely upon each other, and do not seem to have any cohesive attraction. And yet some of the phenomena of Capillary Attraction seem to point toward some kind of very intense attractive force existing some where in some form in the liquid. In the second place, when passing from the liquid to the solid state there seems to be an adjustment of the position and relation of the atoms to each other that in many cases produces a crystalline structure, and in some cases actually increases the bulk of the body. 143 144 Atoms and Energies Now if, as we have seen, the attractive influence not only increases with the closeness of the atoms, but its relative advantage over the repelling energy is greater the closer the atoms are together, it would seem as if when the atoms got close enough together to attract at all they must come at once as close as it was possible for them to come. Since the attractive force is greater than the repelling force there would be an excess of attractive force that would have no corresponding repelling force to resist it, and the more intimately the atoms came into contact with each other the greater would be both the volume and the efficiency of that unresisted attraction. So it would seem hard to explain why the atom should not go immediately from wide separation in the gas to the very closest contact and rigidity in the solid state. This might be readily explained, however, if there were certain points, positions or directions in which the attraction was greater than in others. That there might be some discrimination of this kind is at least suggested by the fact that in all cases of attraction between small bodies that we know and can investi- gate there does seem to be this discrimination of posi- tion and direction. Magnetism exhibits the charac- Liquids and Solids 145 teristic of polarity, — certain points in the magnetized body attracting much more than other points. Elec- tricity seems to have the properties of attraction and repulsion, and electricity always shows greater in- tensity at any sharp point or angle of the electrified body than at other parts. It would not then be an entirely gratuitous supposition to assume that there might be something of the same kind in the attrac- tion between atoms; something akin to polarity, or some concentration of the attraction at the points or solid angles on the contour of the atom. And more- over a little analysis and inference from the known facts of that attraction, provided it is the same as what appears as gravitation, will give plausible ground for thus assuming that the attraction does vary at different points on the same atom, and would also seem to point to just such a variation as would explain these characteristics of the liquid and solid states. II The law of attractive energy as we have been able to examine. and measure it under the name of Gravi- tation, is that it varies directly as the mass of the bodies concerned. If any atom is twice as large as 146 Atoms and Energies another atom its attraction will then be twice as great as that of the other. If the diameter of the atom were doubled the mass would be increased eightfold, and therefore the attraction be increased eightfold. But the surface would be increased fourfold, so if the attraction is distributed over the whole surface then the attraction from each unit of surface or from each point on the surface would be increased eight divided by four, or twofold. In general, when the diameter is multiplied by w the mass and the total volume of attraction is multiplied by n^ and the sur- face from which that attraction is exerted is multi- plied by n^, hence the amount of attraction from each unit of surface or from each point will be multi- plied by-j or n. That is. The amount of attraction from any point varies directly as the diameter of the atom. This is simply a mathematical corollary from the well known law that attraction varies directly as the mass. It has been assumed above that the attraction may be computed thus as distributed over the whole sur- face since that seems to be the most natural concep- tion. True the atom is conceived as an indivisible unit, and that might at first thought seem to imply Liquids and Solids 147 that its attraction could not be divided up into com- ponent parts. But even though the atom be a unit, and acts as a unit, not from every individual point within its expanse, but from where it as a unit is met, namely from its outer surface, yet that surface is an extended area, and we can logically conceive no reason why the whole attraction should be exerted from any one point or region of it to the exclusion of all other points. If the attraction then is exerted from all points of the surface, that is the equivalent of, and for mathematical purposes may be considered as, a distinct quantum of attraction associated with each point in the area, the sum of these quantums making up the whole attraction just as the sum of all the points makes up the whole area. We have seen then that the known law of. Attrac- tion directly as the Mass, would produce this further law: — In similar atoms the attraction from similar points varies directly as the diameters of the atoms or as their homologous dimensions. If in atoms of the same shape and different size the attraction at similar points would vary as the diameters through the atoms at those points, would it not be at least plausible to suppose that the diameter or distance 148 Atoms and Energies through the atom might be the measure of attraction, and that even at different points on the same atom the attraction would vary as the diameters through the atom at those points and in the direction of the line of attraction. FisJ. CL X c' ^$3 Thus let figs, i, and 2, represent cross sections of atoms similar in shape but different in size. We know from the known law of attraction just stated, that the attraction from the similar points h and h' Liquids and Solids 149 will be to each other as the distances through the respective atoms at those points, or as the lines ab to a'b'. May it not be that this is an indication of the still more fundamental law that the distance through any atom at any point in any direction measures the amount of attraction exerted from that point in that direction? Thus, not only would the line ab measure the attraction from the point b in the direction be and the line of a' b' measure the attraction from b' in the direction of b' c', but the line gb would measure the attraction from b in the direction bh. The line de would measure the attrac- tion from the point e in the direction ef, etc. And even in atoms of dissimilar shape as in fig. 3, the lines a" b" or d" e" would still measure the attrac- tion from any point b" or d" in the direction b" c" or e" f". This more ultimate law that: — Attraction from any point on any atom in any direction is measured by the diameter of the given atom at the given point in the given direction, — would still agree with the known law of : — Attraction directly as the mass, — for the sum of all these lines through the body is mathematically equivalent to the solid mass of the 150 Atoms and Energies body. It is certainly a very simple and natural con- ception of the relation between the atom and the amount of its attraction. And though it has a little more of the conjectural element in it than any other of the postulates that we have found it necessary thus far to assume, yet it is a very probable conjec- ture, and really very modest compared with the mag- nificent textures of pure speculation and assumption that are made use of in all other attempts to explain atomic relations. Ill If attraction at any point on any atom in any di- rection is in proportion to the distance through the atom in the line of that direction, there will be sig- nificance in the fact that the distance through any atom, unless it be a perfect sphere, varies consider- ably in different parts and different directions. So the attraction from some points would be greater than from others. Ordinarily the greatest distance through the atom would be between two opposite angles or projecting points. So the attraction from such points, measured in the direction of the line connecting them, would be greater than at any other Liquids and Solids 151 point. The attraction from the corners or solid angles of an atom would thus be greater than from any other part. Also one particular diagonal might be longer than any of the others, and the attraction from the points at its extremities be greater than from any of the other angles. Thus in a given case the attraction from these points might be greater than the repelling energy that the atom was subject to while the attraction from any other point on the atom was less than the repelling tendency. Now all atoms are constantly under the influence of two forces, an attractive and an expansive or re- pelling energy, and the apparent attractive or repel- lent tendency is the measure not of the real amount of either, but of the preponderance of one over the other. In any given case, as the heat or repelling energy is sufificiently diminished there would eventu- ally come a moment when the repelling efficiency would be reduced to equality with the attractive effi- ciency at any or all points on the atom, but as the attractive power is greatest at some two or more of the solid angles subtending the longest diagonals, it is evident that the repelling energy would be reduced to equality with the attractive energy at those points 152 Atoms and Energies sooner, that is at a higher temperature, than at any others. There might be a preponderance of attract- ive tendency at those points at a temperature at which all other points on the atom would have re- pelling tendency. The slightest preponderance of attractive power, multiplied by the infinite intensity resulting from the distance being zero in actual con- tact, would be sufficient to keep the atoms together. But the excess of repelling tendency at all other points would keep the atoms from touching at any other point, would indeed keep the atoms straining away from each other so as to stand as far as they could apart while having their points in contact. This effect would also be heightened by another cause. As we have seen, with the temperature con- stant the expansive power decreases inversely as the distance and the attractive power inversely as the square of the same quantity, so distance gives an advantage to the repelling energy. In two atoms touching each other only at a single point, all other points being separated at some distance, only the point in contact would have the advantage which comes to the attractive energy from short distance. At all other points there would be the advantage to Liquids and Solids 153 the repelling energy that results from greater dis- tance. So in the given case not only might all other parts except the solid angle that was in contact have the repelling tendency stronger than the attracting, and so tend to stand away from contact, but this very distance of separation would give additional advan- tage to the repelling energy, and still further increase the tendency urging all parts of the atoms not in con- tact with each other as far apart as possible. More- over, as that distance of separation is not the long dis- tance of several diameters which separates the atoms in the gaseous state, but the exceedingly minute dis- tance of the interstices between atoms in general con- tact, this shortness of the distance would so increase the intensity of the expansive tension as to yield something like the very strong resistance to compres- sion seen in liquids. Also from the fact that the atoms were in contact, when pressure was applied to them only part of the pressure, according to the prin- ciples of the composition of forces, would be efficient in forcing them closer together, the rest being ex- pended as pressure on the point of contact. Thus we see the explanation of the very great elastic resist- ance to pressure exhibited by liquids though there is 154 Atoms and Energies an actual preponderance of attractive over repellent energy, sufficient to cause the atoms to cling together. IV Let us conceive then of two atoms in contact vfiih each other with just the angle of one impinging on the angle or face of the other, that one angle being the only available part of the atom which has the attracting tendency in excess of the repelling tendency as the result of the diameter through the atom being longest at that point. In the first place, since the point is in actual contact with the other atom, thus making the distance zero, the intensity of the energies would be immensely increased, so that though the attractive exceeded the repelling by an exceedingly minute ratio, this in the infinite intensity resulting from zero distance would yield a very in- tense attraction between the atoms. It would take a very strong force to draw one perpendicularly away from the other atom. But a very slight force might be sufficient to make it slide about on the surface of the other atom, or even slide completely off at the edge of any face. For we must entirely dismiss all idea of frictional resistance from the case. That is Liquids and Solids 155 only an accident of the unevenness of surfaces made up of small particles ranged together. The atom's face, being perfectly smooth and perfectly continu- ous, would have no friction, so even an infinite force urging another body perpendicularly to its surface would present no hindrance to the body moving about parallel to that surface and at right angles to the line of force. If the one atom impinged on the surface of the other in such a position that its direc- tion of greatest attraction or the direction in which attraction was greater than repulsion was perpen- dicular to that surface it would move about freely on that surface, and if the line of the direction of the attraction were inclined to the plane of the surface it would at least move freely in the direction in which the attraction drew it. And in either case, when it reached the edge of any face it would easily be de- tached from the atom entirely. It is evident that such a state of attraction would yield precisely such freedom of movement as is found in liquids. And such a state of attraction is the one into which the atoms would first come as the temperature or amount of repelling energy pro- gressively decreased. In any atom, unless its shape 156 Atoms and Energies was quite symmetrical, there would be one diameter or diagonal that would be longer than all others, and at the extremities of this diagonal there would be a preponderance of attractive energy while yet the repelling energy preponderated at all other points. Thus the atom could first only attach itself to other atoms at these two points on its two opposite sides. And thus in the mass as at first condensed from the gaseous state there would be the fewest possible points of contact and attraction, all allowing lateral movement, so there would be the conditions for the freest movement of the parts upon each other such as we see in the liquid state. As the heat or repelling energy progressively de- creased there would come the moment when some one or more other diagonals would come to have attractive energy preponderating at their two ex- tremities. That would make possible many more points of contact and attraction between the atoms, and would prevent freedom of movement and pro- duce rigidity. Moreover, the atoms would natu- rally arrange themselves in that position in which they would have the most attracting points in con- tact; for the incessant ordinary movements of the Liquids and Solids 157 atoms would bring them into that position, and once there they would tend to stay in that posi- tion. We would thus have the third or Solid state of matter. That would be when the atoms were built together with so many points in contact that there could not be any movement without the neces- sity of lifting some point more or less directly away from the face with which it was in contact. This rearrangement of the atoms to make more points of contact would also furnish another possible explanation for expansion of bodies on congealing, as discussed in Chapter II. For the atoms would arrange themselves in the positions that would yield the most contacts entirely irrespective of any in- crease or decrease of bulk that might thereby be pro- duced. We might state the different kinds of contact of atoms as follows. When not in contact we have the Gaseous state; when but a single point of contact, the Liquid state; when so many points of contact that there is rigidity, the Solid state; when face to face contact, Chemical Combination. Where there is actual face to face contact we might suppose all the expansive energy driven out from the region in con- 158 Atoms and Energies tact, and this would account for the intense access of heat produced by combustion. Though there is this great freedom of movement between masses of these atoms with only few points of contact which make up bodies in the liquid state, yet it must be remembered that there is an intense attraction between these individual points. Though there were but few points that had attraction in any given atom yet the attraction would be so strong at those points that they could not well be separated perpendicularly away from the face of another atom, but could only slip along its surface and separate at its edge. It might require a considerable readjust- ment in contiguous atoms to bring about the condi- tions for such a separation. It is conceivable that this necessity of a readjustment of the atoms to per- mit separation might not have any perceptible effect on the movements of masses of considerable size, while in smaller masses, say of only a few thousand atoms it might have a very appreciable effect and might enable such masses to resist considerable lateral pressure without yielding and separating. Liquids and Solids 159 something as a small mass of sand or powder might be held intact between the thumb and finger while if we attempted to grasp a larger mass it would press out and escape. This may possibly be the explana- tion of the phenomena seen in Capillary Attraction. A few thousand atoms are in and around an aperture that will not contain them all. But after it is full the internal vibrations of the body and other internal movements opening the aperture wider for an in- stant allow other atoms to enter. Being once in, this strong attraction between the individual points and the necessity of a readjustment to allow a separation is sufficient in the mass of so few atoms to keep them firmly in and the aperture cannot contract again. The next vibration opens the aperture still wider al- lowing a few more atoms to enter, which again are held fast and remain as before. And so the aperture keeps on growing wider by the process as we would say of the liquid soaking in, but more properly by the aperture widening in infinitesimal degrees by its own vibrations and other causes, and the liquid flowing in and being caught and retained by the atomic attractions, and thus holding all the expan- sions that accidental causes produce. In a small tube 1 60 Atoms and Energies in like manner the same cause would enable a very narrow column of the liquid to sustain itself by the attraction of the atoms for each other and for the containing walls while the vibrations and other acci- dental movements would cause it to rise. If the attraction between all atoms is capable of being resolved into two mutually opposing comple- mentary components, as was suggested in a previous chapter in connection with magnetism, this might also furnish the explanation of the opposite efifect of different substances on different liquids; some liquids being raised and some depressed in different capillary tubes. The same cause would also account for certain liquids not mixing, as for instance water and oil. The effect of the lines of attraction of one atom on those of another or some other effect of their contact, may bring about in a small way be- tween individual atoms the same repulsion that is seen in like poles of a magnet brought together. Just how this is done or what is its nature, we may not yet know perhaps. We do know, however, that it is done in the case of the iron magnet, and so we are warranted in assuming that it might possibly be done in this case. CHAPTER X EXPANSION AND VIBRATION IN the opening chapter of this discussion atten- tion was called to the fallacy in considering the vibration of atoms a fundamental fact or law of motion that could be used as an elementary factor in explaining phenomena. It is itself a very com- plex movement, and can only be explained by a com- plex of forces, unless the mechanical laws that gov- ern the motions of atoms are different from all the known mechanical laws which we observe in the larger relations; that is to say, unless the properties of Inertia, Motion in a straight line, and other axioms concerning motion do not apply to bodies so small as atoms. Vibration means, an atom moving at great speed entirely ceasing that motion, coming to complete rest, then beginning an equally swift mo- tion in the opposite direction, and continuing this series of changes indefinitely. Moreover, if the vibra- tion is performed by the atoms in a gas, this creation i6i 1 62 Atoms and Energies and annihilation of motion goes on without any ap- preciable attractive tendency present to be a possible determining and controlling force. It was also pointed out that no kinds or arrange- ment of motions, under the conditions of the me- chanical laws which we know to operate in the larger distances, could account for the phenomenon of ex- pansive tension. The only kind of motion that might seem to produce that kind of a result would be the re- volving motion which produces a centrifugal tend- ency. But that effect is only produced between bodies that are actually revolving with respect to each other. So for that cause to produce the effect of expansive tension every atom in the body must be revolving with respect to each and every other atom, and every part must be revolving with respect to every other part, the top half with respect to the bottom half and the whole body as a whole revolving and mixing all its parts together in the utmost complexity. Let us start from the other direction, and, assum- ing the existence of an expansive energy as the de- termining fact, see what would be the result of its action on atoms, working according to the known Expansion and Vibration 163 laws of mechanics which we see and measure in the larger distances. The expansive tendency is a known fact. Let us assume that it is a concrete en- ergy without trying to resolve it into an effect of some kind of motion. Let us consider it a Cause, in- stead of an Effect, and see what would be the neces- sary effects that it must produce. II In a gas the expansive energy is in excess of the attractive tendency. The amount of expansive energy that is balanced by the attractive energy we may dis- regard, and merely consider the effect of the exces- sive residuum which we may treat as if it were acting alone. The atoms are held from dispersing by some restraining outside agency, as Gravity, or the sides of a containing vessel, but this restraining agent is unaffected by the changes we shall consider and so may be disregarded also. We know that the expan- sive energy, under conditions not of uniform tem- perature, but of the increase or decrease of tempera- ture that accompanies compression or expansion, varies as some function, approximately the square, of the distance between the atoms. 164 Atoms and Energies Let u, t, s, a, b, c, d, etc. fig i, represent a succes- sion of atoms at rest and held asunder by an expans- &o. utsabcde &o fig. I ive energy operating between them in the ratio of some function of the distance. Suppose the distances all equal and the atoms at rest, the forces being in equilibrium. Now suppose the expansive force at some point, as between " s " and " a " to be increased by an amount we may designate m. The first effect of this on the atom " a " would be to urge it in the direction of " b." But as soon as " a " approached " b " the distance " ab " being decreased the expans- ive efificiency between " a " and " b " would be in- creased, and that would tend to urge " b " toward " c." In like manner " c " and " d " and all the others would be urged in the same direction. There will come a moment when the expansive efficiency between " s " and " a " is decreased by dis- tance till it is the same as that between " a " and " b " and there will then be no energy urging " a " toward " b." But the momentum developed in the atom " a " must carry it on, though the pressure Expansion and Vibration 165 from this moment is greater in front of it than behind it. The farther it recedes from " s " the less the efficiency of the energy between " s " and " a," and the greater the net resistance. It must take as much resistance to overcome the momentum of " a " as the force that caused that momentum. That re- sistance, beginning with zero, is a constantly increas- ing quantity, just as the energy which caused the momentum was a force decreasing regularly from m to zero. If the rate of increase or decrease of force is uniform throughout the whole operation then at the moment when the atom " a " is brought to rest and its momentum overcome, there will have developed an excess of energy urging it back toward " s " equal to the original energy m that started its motion. So the atom " a " will start back toward " s." Until it reaches the moment when under the law of distance and intensity the pressure between "s" and "a" is equal to that between "a" and " b," the motion of " a " will be accelerated. Be- yond that point it will have to move against a re- sistance, but the momentum already acquired will still carry it on as before till it has been opposed by an amount of resistance equal to the force which 1 66 Atoms and Energies caused its momentum, and by that time the excess of tension between " s " and " a," having brought it to rest will begin to send it back toward " b " again to go through the same process as before. In this man- ner a continuous vibratory action would be origi- nated and maintained. The movement of the atom " b " would be in all essential respects similar to that of the atom "a." For as soon as the atom " a " begins to approach the atom " b," that would increase the expansive ten- sion between " a " and " b," and this increase of tension would produce essentially the same, results on " b " as previously described as resulting from the increased expansive tension between " s " and " a." As this increased tension between " a " and " b " is the result of, and so subsequent to, the motion of " a," and every increment of this tension is also the result of, and so subsequent to, some motion of " a," it is evident that the phases of the vibration of " b " would be later than those of " a." Again, the mo- tion of " b " would decrease the distance and so in- crease the expansive tension between " b " and " c." This would cause an essentially similar series of movements by the atom " c," whose phases would be Expansion and Vibration 167 still later than those of " b." And so also of the atom " d " and all the other atoms to the end of the series. The same would also be true of the atoms in the other direction, " s," " t," " u," etc., or indeed of any contiguous series of atoms in any direction. Thus it is evident that any increase of expansive energy at any point in a gaseous body must cause vibration throughout that body. It is also evident that a decrease of tension must produce the same effect, for a decrease between one pair of atoms means a comparative excess between the contiguous pair which would thus start the train of vibration above indicated. What would be true of a gaseous body would also be true in a slightly modified form in a liquid or solid body, for there is in them also the possibility of expansion and contraction as well as the balancing of expansive and attractive energies. If Heat is an expansive energy, it follows that every transfer of heat, since it increases the tension between certain atoms, must thereby cause vibration in the body affected. Thus, Vibration must be a necessary and invariable result of the transfer of heat. And as Heat is continually being transferred from place to place through all bodies to some extent. 1 68 Atoms and Energies and the quantity at any given point is constantly varying more or less, it follows that vibration will appear as a constant accompaniment of heat energy. Moreover, it is the law of at least one mode of the transfer of heat that it only passes from a region of higher tension or temperature to a region of lower tension. But it will be noticed that one result of vibration is to cause at any given point alternations of high and low tension and accompanying tempera- ture, between the atoms. So if there was a flow of heat energy toward that point it would not be con- tinuous and uniform, but would be broken up into intermittent jets synchronous with the alternations of low and high tension at that point. Thus not only would the coming of heat into a body set up vibra- tions in it, but the heat itself must come in successive waves or jets. So then, if a quantity of heat were moving transversely against the line of atoms u, t, s, a, b, etc., it would not strike all parts of the line at the same time, but broken up into waves and jets, would strike the space between " s " and " a " at one time, between " a " and " b " at another time and between " b " and " c " at still another time. This result would tend to maintain and augment any ex- Expansion and Vibration 169 isting vibration in a somewhat similar manner as the constant stream of air is broken up into jets or waves at the exit orifice of an organ pipe and maintains and intensifies a sound vibration existing there. There is another time element in the case that might possibly produce important results. The atoms in vibration move at a certain definite rate of speed, and the heat in being transferred also has its own definite rate of motion. The ratio between the rate of motion of the atom, its time of vibration and the rate of motion of the heat energy, might vary greatly in different cases, and this variation might produce great differences in the resulting phenomena. For instance a difference in this ratio might produce the difference between the characteristics of what are called Diffusion and Radiation of heat, or it might even produce those variations of result discriminated as Color, Heat, Actinism, The " X Ray," etc. Even Electricity and Sound may come in the same catalogue. Ill It must be evident that this conception of Expan- sive Energy as the fundamental fact and motion of the atoms merely an effect of that energy, is a much I/O Atoms and Energies more satisfactory and adequate statement of the case than the opposite conception that Motion is the fun- damental fact, and the expansion and all other phe- nomena must be sought to be accounted for as in some way effects of this motion; or the conception that the essence of heat is vibration, and the mo- mentum of the vibrating atoms is the energy ex- hibited. For, in the first place, as has been previ- ously shown, such motion cannot account for the ex- pansive tension which is one of the essential phe- nomena of heat. In the second place, as has also been previously indicated, vibration itself is a very complex movement, and must be the resultant of a complex of forces. It is impossible to account for an atom in motion coming to rest and starting back in the opposite direction without just some such action of an expansive energy as has been described. And further, in the third place, it is difficult to con- ceive how, without such an expansive energy as its foundation, any mere motion of atoms or their im- pinging on each other could develop the available working energy we see. For, according to all the known laws of mechanics, without such an energy, whenever two atoms in motion came together that Expansion and Vibration 171 component of the energy of their respective mo- menta which was opposite each to the other would annihilate each the other, and the resultant momen- tum would be diminished by that amount, while both the atoms would move on together in the new direc- tion which was the resultant of their previous move- ments. So if heat consisted simply or essentially of motion of the atoms it could not do what it does now, for without expansive tension or elasticity every con- ceivable movement among the atoms of a body must eventually and quickly resolve itself into a small residuum of motion of all the atoms in one direction, that is to say, of the body as a whole in that direction. The trouble is that when we attempt to explain the phenomena of heat as simply motion of atoms we unconsciously fall into the fallacy of using the very thing to be explained as one of the unnoticed factors in the explanation. In order to account for the ex- pansive energy of heat by motion we have to use the existence of some expansive energy somewhere to produce the very motions which we rely on to pro- duce expansion. For instance, motion arrested or resisted we know is transformed into heat, and this 172 Atoms and Energies we use as a fundamental law or fact with which to explain the nature or essence of heat. But without the presence of some expansive energy acted upon and resisting that motion it is impossible to find any known mechanical law by which that motion met by a counter motion in the opposite direction should not be annihilated. So also we have seen that vibra- tion of atoms is only possible under the influence of expansive tension, so for linear motion to be changed into vibration of the atoms must also require the existence of an expansive energy. In all our con- ceptions of how linear motion is transformed into a mode of atomic motion which we term Heat we un- consciously make use of the operation or the neces- sary effects of some kind of expansive energy. In other words, the laws which we attribute to atomic motions, and by means of which we explain the transformation of linear motion into the mode of atomic motion which we term Heat could not exist without the action of some kind of expansive energy. They are simply the laws which express the observed movements of atoms as they now exist, but atoms as they now exist are known to be under the influ- ence of at least an expansive tendency, which ex- Expansion and Vibration 173 pansive tendency has an important determining in- fluence on their movements. To use these move- ments and laws resulting from expansive energy as the basis for an explanation that is intended to do away with belief in the existence of any expansive energy as a concrete entity, would be as illogical as to affirm that the sun was unnecessary in the daytime because it was light enough then. The very laws of atomic motion which we use to explain vibration, expansion and other heat phenomena, are themselves the resultant of expansive energy, and those laws and motions could not exist without the very ex- pansive energy which they are intended to explain. The expansive tendency is a more fundamental fact than the vibrations or the laws which we conceive as governing atomic movements. Given the expansive energy and it would produce the vibration, trans- formation of motion into heat and all other phe- nomena of heat, but none of these could produce the expansive tendency nor be themselves produced without it. If all these phenomena must follow as a necessary resultant of an expansive energy and none of them would be possible without it, the argument seems conclusive that the expansive energy is the 174 Atoms and Energies fundamental fact. Instead of saying that heat is a vibration of atoms we should say that heat is an ex- pansive energy which as one of its normal results produces vibration of atoms. Instead of saying that heat is a mode of motion we should say that heat is a tendency to produce motion. CHAPTER XI ENERGY AN ESSENCE THERE are two fallacious tendencies more or less prevalent in modern scientific thought. One is to ignore the idea of causation and make the statement of law the final fact. In a given juxtaposition of circumstances a certain result or change invariably succeeds. All we can do, it is said, is to discover and catalogue what changes invariably succeed what groups of circumstances. The idea of a genetic connection between events is held to be a metaphysical conception, entirely subjective in its origin, and incapable of proof. Such a view, how- ever, and such a temper of inquiry is abnormal. The conviction of a genetic relation between events, or of causation, is just as much a necessary part of our mental state and a present though unrecognized postulate in every thought, as the conviction of the integrity of our perceptions and validity of our rea- 175 176 Atoms and Energies soning processes. The conviction of causation is one of the factors in almost every act of perception, reasoning or belief. Another equally fallacious practice is to prema- turely assign the agency for some change to factors previously known or perceived to be present. Of this nature was the old conception that the flame ate or consumed the wood, or the idea of suction as a drawing energy from the exhausting agent. In the same catalogue we may venture to assign the concep- tion of one atom exerting a pulling influence on an- other atom thousands or millions of miles away; the idea of the carbon, hydrogen, oxygen, etc., in pro- toplasm, causing the complex selections, structures and activities seen in living growth; or the idea of any atom causing the intricate activities seen in chemical combination. We see some result produced and it is undeniable that certain material impenetra- able expanses called atoms are present and concerned in the change, so we carelessly assign the producing agency of that change to the atom. We hypostatize the ability to produce such a change under the name of an " Attribute," and tack it on as an appendage or possession of the atom. Another kind of change is Energy an Essence 177 observed in connection with that same atom, and we hypostatize another " attribute " and tack it on, till perhaps the one atom is fitted out with a score or more of so called " attributes," diverse in their na- ture and minutely discriminating in their application. Retaining then the idea of causation as a legiti- mate conception, we must inquire critically what is the real efficient agent that produces any given cause. It is not enough to simply find out some invariable antecedents and assign the causation as in some mys- terious way an attribute or property of some of them. We want to definitely isolate the actual efficient agent which produces the change. It will then be a legitimate question what is the relation of this effi- cient agent to the other observed invariable ante- cedents of any change; or what is its status; is it a property or attribute of something else, or is it an independent Entity, coordinate with other sub- stances. II There is a loose popular use of terms that is per- haps all right for ordinary conversation, but which may be the cause of error if it is imported, as it some- times unconsciously is, into scientific discussions as 1/8 Atoms and Energies the statement of real fact. There is no harm, per- haps, in speaking of the sun rising, the ice pitcher sweating, speaking of looking out of our eyes or through a telescope. In most of these cases we are fully conscious that our terms represent only the seeming, not the real fact, and so there is not much liability of error from their use. But in some of such cases this is not so immediately apparent, and we are quite in danger of using them with their col- loquial meaning in exact reasonings where that use would lead to error. Especially is this true in all those cases where we confuse the " Final cause," the " Occasional cause," or some early member in the chain of causation which leads up to any event, with the actual efficient cause that produced it. We speak of the gun shot wound as being caused by the soldier or by the force in the gunpowder. We speak of hearing the vibrations of a distant bell or organ, or we consider the man's hand on the crank as mov- ing all the wheels of the articulated machine. That use of the terms is sufficiently definite for all ordi- nary purposes, and it would be sheer pedantry to ob- ject to it except in discussions of absolute efficient causation. But in a discussion of absolute causation Energy an Essence 179 that use of terms would be fallacious. And just be- cause it is so proper and appropriate on all other occasions there is the greater danger of our uncon- sciously using such terms here with disastrous re- sults. The following statement is more than an axiom. It is virtually an identical proposition which it would seem entirely gratuitous to formulate and state at all except for the fact that, as we shall see, it is almost constantly violated in discussions of energy and causation. An agent only acts where it. is, and cannot act where it is not. An agent only acts when it acts. And the simple converse of these propositions would be: — Every effect must be produced by an agent there present. Every effect must be produced by an agent then acting. A little reflection will suggest how constantly we use forms of expression directly contradictory to these truths, and it requires some attention and an- alysis to appreciate that we are not thereby express- ing actual efficient causation. Thus we conceive of the tug boat drawing the ship a hundred yards away; of the mainspring of the watch moving the i8o Atoms and Energies hands on the dial ; of the telegraph operator making an instrument click in the receiving office a hundred miles away; of an event to-day as being caused by something that happened yesterday. We would readily enough see on close analysis that it was really the cohesive attraction in the last layer of atoms in the hawser that drew the ship; it was something acting at the base of the hands of the watch that made them move ; it was the electric power actually present in the distant instrument that made it move and sound. What produced the change to-day was an efficient agent actually operating to-day, though that agent might have been genetically connected with some other event that occurred yesterday. While it would be pure pedantry to insist on this distinction in ordinary conversation yet in any dis- cussion of efficient causation the distinction is most important. Ill We speak of the earth attracting the moon, or of an atom in the moon attracting and moving an atom in the earth. And yet they are more than two hun- dred and forty thousand miles distant from each other. Now the facts are undisputed. The atom Energy an Essence i8i is there in the moon and in the earth, and both move with reference to each other, and each would not have moved if the other had not been there. And doubtless there is no harm in common conversa- tion in saying that the atom of the earth attracts and moves the atom of the moon, just as there is no harm in saying that the sun rises, or that we smell a distant rose. But according to the axiom stated above, what moves the atom of the moon must be some agency actually present at that atom. And whatever the atom in the earth does (if it does anything in the sense of efficiency), it must do it where it is. This may seem a captious discrimination but further thought will show that it is not ; that most important results follow from it. It is a very important dis- tinction whose neglect has done very much to con- fuse scientific thinking. We must simply give up the conception that one atom attracts another atom as that conception is commonly held, and make a statement and conception which accords with the facts of the case. This contradiction in supposing an atom to be acting at a distance from itself and where it is not, i82 Atoms and Energies has been often noticed before and remarked upon. It has been called one of the " Paradoxes of science." But it is not a paradox of science at all. It is simply a fallacy of thinking; simply an error in statement, just as it would be an error of statement to say that a bottle was empty when all the water was poured out of it, and then call it a paradox that though it was empty yet there was something in- side that resisted the cork being forced far in. It is simply the fallacy of refusing to recognize and state what actually is the fact because we are ac- customed in colloquial language to ignore the fact and make a different statement of the case. We must, then, candidly accept and state the fact that what moves the atom is something actually present at the atom, though recognizing, of course, that it is in some way articulated with the other dis- tant atom because it always acts in a certain definite relation to that atom. When the moon is said to raise the water in the tides what moves the atom of water must be some efficient agent actually pres- ent at that atom. Manifestly it is not that atom of water itself. Neither is it the atoms in the moon, for they are not present at the place where the effect Energy an Essence 183 is produced. It is not any atom at all but is some- thing else that is not an atom yet is present at the moved atom and is in some way articulated with the distant atom in the moon. That is the actual fact of the case. And that " something " should be given a name and be recognized as a real entity. There is just as much reason for recognizing it as a real entity as for recognizing the atom as an entity. They both stand on the same level in that respect. This " Something " is not an attribute or quality of either of the atoms concerned. It would be just as reasonable to say that the atom was a quality of this " Something." They are both distinct entities, and it would be just as fallacious to speak of one as a quality or attribute of the other as it would be to call water an attribute of the pitcher it was in, or call the hawser a quality of the tug boat that uses it. This " Something " is not, it is true, a material en- tity or material substance. But it is a purely grat- uitous assumption to conceive that material sub- stance is any more real and concrete than any other kind, or to imagine that there can only be one kind of substance, namely that which has definite space extension and impenetrability, which exists as what 184 Atoms and Energies we call atoms and which is called matter or material substance. That is one kind of substance only. That is the only species of entity which has the qualities of extension and impenetrabiHty, but there is no reason that there may not be other species of entity or substance which do not have those quali- ties but have other qualities. This " Something " above referred to is one of these other species of en- tity or substance which does not have the quality of impenetrability, etc., but has other qualities, as for instance, the quality of Ability to move atoms. We may give this " Something " a name and call it Energy. But calling it energy we do not mean thereby that it is the energy of something else, that it is the energy of a distant atom. It is the energy of itself, or rather, itself is energy just in the same sense that the atom is matter. The two statements are exactly analogous. The proposition that this energy here is a quality of, or inheres in, a substance or atom thousands of miles away, is a metaphysical fiction so impossible of being conceived that it is simply a form of words without any meaning. En- ergy is just as worthy of being recognized as a pri- mary entity as matter. Energy an Essence 185 IV That Energy is not a quality or attribute of mat- ter will be still more evident in the case of heat or expansive energy. We have already seen that heat is something more than the vibration of atoms. There is an expansive energy that cannot be ex- plained as a result of motion. In this case the en- ergy is not, like the attractive energy, permanently attached to any matter or atoms. A quantity of heat and expansive tension is now in a certain body ; a little while ago it was not there; again after a little while it will have radiated away and be gone. A certain quantum of heat is in a certain body at a certain time, but part of it leaves that body and goes to another body, and from that to a third, and still on continually changing from place to place. How then is it possible to consider this migratory expan- sive energy an attribute or quality of matter since it is not even permanently attached to any atoms but is constantly removing from one to another. A mere motion, of course, could be considered an at- tribute of atoms while yet appearing to be trans- ferred from one atom to another, but, as we have 1 86 Atoms and Energies seen, there is no known kind of motion that could produce this result of expansive tendency nor are we able to imagine or conceive of any kind of motion that would be able to produce that as an effect, though an expansive tendency, as itself the primary fact and cause, could and would produce all the mo- tions we see in heat as its natural effects. There is then an external something which holds the atoms in its grip, and tends to urge them away from each other in an expansive tension; and this "some- thing " has no tendency to remain articulated to any particular atoms but is constantly moving about from one to another and from place to place entirely independently. How is it possible then not to con- sider it an independent entity? And more than that, without the arbitrary hy- pothesis of an inter-stellar Ether, which science has thought itself compelled to invent for this very cir- cumstance, and which has no other objective evi- dence, besides being in its own character in various ways a logical contradiction, — without such an ether we are compelled to admit that this heat energy ex- ists entirely apart from all atoms in absolute space. This must occur whenever it passes from one place Energy an Essence 187 to another, either through the vast voids between the stars, or what is practically the same, through the infinitesimal voids between atom and atom in gases. The principle is the same whether it travels alone and exists unattached through the billions of miles between the stars or through the billionths of an inch between the atoms. If then we have in this expansive energy which produces the phenomena of heat something which cannot be explained as the result of motion, is not attached to any atoms, can be freely transferred from body to body and can exist entirely separate from all material substance in the great voids between the stars or even in the lesser voids between the atoms, how is it possible to consider it a quality or attribute of any atoms ? Of what atoms is it a quality, since it is never long with any one set but is constantly moving from one to another? Especially of what atoms is it a quality during the time that it is en- tirely separated from all atoms in the voids between the atoms or between the stars ? How is it possible to consider it as anj^hing else than a separate en- tity, co-ordinate with the material entities, but in no other way related or subordinated to them except 1 88 Atoms and Energies that it is so articulated to them that it is able to move them about. In the case then of both the attractive and the re- pelling energy we are prohibited by various different considerations from counting them as qualities or attributes of atoms, but are compelled to consider them as distinct entities, coordinate with material substance but having entirely different qualities. V This conception of an inter-stellar Ether is such a popular favorite at the present time that we ought, perhaps, to give it a little special consideration. It seems to have been devised specifically to provide some way to explain various phenomena, especially heat and light, in terms of modes of motion. It was recognized that these phenomena could not all be accounted for as motion of the kind of matter that we ordinarily conceive of, made up of atoms, and moving according to the known laws of motion. So it was undertaken to formulate a kind of matter that would fulfill the conditions, and could produce these phenomena by its motion. It must be admitted that this was a most magnificent undertaking, and it Energy an Essence 189 would most wonderfully simplify our conception of the universe if all its phenomena could be analyzed into the two categories of matter and motion. This stupendous result would be well worthy the greatest eflforts, and the hope of such an explanation well justified the wide currency that has been accorded to the conception of such an ether, unsatisfactory and self contradictory as it confessedly is. And possibly like other unsatisfactory partial truths it may serve as an introduction and preparation for the real truth. It may be worth while to remind ourselves, how- ever, that even if we could reduce all phenomena to matter and motion, even motion of common atoms without this ether, it would not be so simple as we might at first think. The motion which we think of as a very simple and easily understood phenomenon is merely the visible fact of progressive change of position. But motion is not really so simple a fact as that. Why should any object changing its posi- tion persistently tend to continuously do so? Why should it cause any other body it meets to change its position with the same persistent tendency? There is something there beside change of position. It 190 Atoms and Energies may be questioned whether it is simpler to conceive that mere motion is endowed with that mysterious superadded faculty, or to conceive that there is a something else which produced and maintains the motion in the first body and is also able to produce motion in other bodies which it meets. But recurring again to this assumed so called Ether, — as now conceived there are many difficulties and self contradictions in the characteristics of this ether. In the first place, it cannot be conceived as composed of small ultimate indivisible particles, as we seem necessarily disposed to consider all matter to be. For even though its particles were so much smaller than the commonly assumed size of the atoms that they would flow between them as parti- cles of air flow between marbles or between worlds, they would help us not at all in our explanations, for that smallness would not alter the action of me- chanical laws and forces upon them. And, for that matter, for anything we know the atoms themselves may be as small as we would conceive these particles of ether to be or a million times smaller if necessary. If the Ether was a substance infinitely divisible, that is absolutely continuous, and either filling all Energy an Essence 191 space or with a porous or cellular structure to allow freer motion in it, that would still not render it capa- ble of producing this result of repulsion or expansive tendency if it still had the qualities which are con- sidered the essential characteristics of matter, such as Inertia in motion or rest, Motion persistent in a straight line and the resultant of two lines of force determined according to the laws of the composition and resultant of forces. The motions of even such a continuous infinitely divisible substance would be in all essential respects the same as of an atomic or granular substance, and unless it were void of the essential characteristics of matter mentioned above, and were endowed with other attributes, — indeed unless it were endowed with practically the very energies which its motions are designed to explain, and which it was invented expressly to get rid of recognizing, it could not produce expansive tension or even vibration. If it be conceived as resilient and elastic in the sense of absolutely compressible, that would mean two portions of it being made to occupy exactly the same space at the same time, and would be exactly opposite to that essential charac- teristic of matter, Impenetrability. If it is not, there 192 Atoms and Energies is no known mechanical law, as we have seen, by which it could produce expansive tension. To be really resilient without being absolutely compressi- ble it would need to be endowed with an energy working exterior to or upon itself, and that is the very thing it was invented to get rid of. It is con- ceded that it cannot have weight, or momentum, for that would impede the motions of the heavenly bodies, so that would be another essential character- istic of matter which it must lack. If it had no mo- mentum, again, it could not transmit motion, the very thing it is invented to do. So there would be a direct contradiction in its characteristics. And even aside from this, it still could not furnish an ex- planation for the attraction of gravitation. So even if this ether exists there must still be at least one energy which is a non-material entity, and is not a mode of motion. It may also be questioned whether with all the qualities and powers that im- agination could endow it with it could ever by means of its motion produce the exact phenomenon of ex- pansion that we see. Now if it lacks the essential characteristic of mat- ter, weight, and probably also impenetrability, and is Energy an Essence 193 not subject to the necessary conditions of motion, inertia and the laws of the composition and result- ants of forces, it certainly is not material substance. If this Ether exists it is just as much a different kind of entity from matter as mind is. Even if we could get rid of the contradiction of transmitting motion without momentum and were able to explain expan- sion in terms of this ether, and gravitation too for that matter, we still would not have reduced these phenomena to the simple categories of matter and motion, for this ether is not matter. We would still have two distinct entities, Matter and another entity that is not matter. VI If then we are under the necessity of formulating a new entity why should we let our minds be so under bondage to the visual and tactual conceptions associated with matter that though this new entity can have none of the rest of the qualities of matter it still must be conceived under these categories as a quasi material substance? Why should we approach the subject with any predispositions at all? Would not the more scientific way be simply to take the 194 Atoms and Energies phenomenon or thing done reduced to its sim- plest elements, and say : — There is an entity whose essential characteristic is ability to do that thing; and not feel under the necessity of importing into our conception of this new entity all the characteris- tics of material entity that we are not positively pro- hibited from applying. The thing done is simply, Atoms are moved or given a tendency to move. We may then say simply : — There is an entity whose es- sential characteristic is a tendency to move atoms. Further than that we are not under any obligation to assign any other characteristics to this entity until we find out by experience that it actually has them. We may find that it exists in two varieties, tending to draw atoms together and to urge them apart, and we may find certain other elements of time, direc- tion, intensity, etc., that characterize it. Those are the attributes that we should assign to it and we should not attempt to give it those that are charac- teristic of material entity. It certainly would seem the proper way, if we are to have a new kind of en- tity, to build up our conception of it from the ob- served facts themselves, instead of trying to cut and fit and make over an emasculated conception of ma- Energy an Essence 195 terial entity into a clumsy expedient that will only partially account for the facts. Recurring again to the common conception of this inter-stellar ether, and approaching the problem in another way : — This ether is required to be infinitely divisible and practically continuous between the atoms. Energy, either attractive or expansive en- ergy, may be absolutely continuous between the atoms and is also infinitely divisible. The Ether is required to be not impenetrable. Energy is not impenetrable. Ether must be elastic or resilient. That is the essential characteristic of expansive en- ergy. Ether has no weight. Neither has energy. Yet it transmits motion. So does energy. We find that all the very qualities that would be necessary for this assumed Ether are the very quali- ties that are characteristic of expansive and attract- ive energy, provided we admit it to be a distinct entity. May we not say then that Energy is this very same mysterious something which we have felt the need of and have called Ether. The Ether is simply Energy as an entity. The nonmaterial some- thing which we have been groping blindly about for, and to which we have assigned so many 196 Atoms an Energies qualities and duties is nothing else than the entity- Energy. This is really far more than a question of Meta- physics or a matter of definition. It involves a mat- ter of fact and has led to very irhportant results in scientific thinking. It is because we have failed to recognize Energy as a concrete entity or substance that we have been led into much fallacy and con- fusion in the use of the terms law, and causation, and that we have been betrayed into the attempt to define all existence in terms of matter and motion. It does make a difference how we define in science as well as elsewhere. There are certain connotations attached to certain words which will always call up certain ideas when we use those terms and will do so unconsciously even in the mind of the one who has made an arbitrary definition, and thus will introduce confusion and fallacy into his reasonings and results. The term Substance, has gained an acknowledged connotation of reality and concrete existence, and the very practice of confining the word to material substance, or using it more frequently of that, un- consciously creates the impression that material sub- stance is more real and concrete than kinetic sub- Energy an Essence 197 stance or psychic substance. In reality the three are coordinate, and are the three known forms of con- crete existence: — Material Substance or Atoms, Kinetic Substance or Energies, and Psychic Sub- stance, Mind or Soul. CHAPTER XII CONCLUSION THE discussions in the preceding |)ages are built on three elemental facts, i. There is an attractive energy, known in some of its manifestations as Gravity. 2. There is an expan- sive energy which is an observed feature of access of Heat. 3. There is what is called Matter, whose ul- timate elements are called Atoms. These facts are undisputed. Stress is laid on the view that the two above ener- gies are concrete entities, not qualities or attributes of, but coordinate with. Matter. In discussing the action of these energies, while it was suggested that there might be certain additional laws or results of their interaction that would afford explanation of many of the details of special phenomena, yet for the greater part of the discussions here given the only laws of their activity used were the well demon- strated ones that their effects varied inversely as 199 200 Atoms and Energies some function of the distance through which they acted. In the case of the attractive energy it varied also vfith the diameter of the atoms attracting, and of the expansive energy with the area acted upon and the Temperature or varying amount present. In the discussions no activities were assigned to the atoms. They were treated as entirely passive, simply acted upon and manipulated by the energies. As nothing was thus assumed as the basis of the dis- cussions but these simplest admitted facts, the con- clusions, as far as legitimately drawn from them, ought to have weight. It was shown by mathematical calculation that varying the size and shape of the atoms, with no other differentiation of quality or law, must deter- mine aggregations of different styles of atoms, though at the same temperature, to exist in the three different states, Solid, Liquid and Gaseous. These simple laws also would cause them to pass from one state to another in precisely the way we see in nature, with Latent Heat, Evaporation from Sohds, Expan- sion by Congealing and all the other features that we see. There was found no necessity for other species of Conclusion 201 attractive energies to produce Adhesion, Cohesion and Chemical Combination. The same energy that produces Gravitation must produce these also, the variety in the effects resulting chiefly from variety in the distance through which it acts. In that most important field of all. Chemical Com- bination, the results reached were equally satisfac- tory and still more surprising. All chemical qual- ity, as we know, is simply variety in the readiness of substances to unite with each other. It was shown that variety in the size and shape of the atoms must produce just such variety in the readiness for com- bination as we see, and all the different types and degrees of variety seen in actual nature could and must be thus produced. Not that the whole science and technique of chemistry is to be elucidated by a single formula. But the fundamental elements and operations which by their combination produce all the intricacy of chemical reactions, are all fully ex- plainable on these simple principles, the difficult questions of detail are no more difficult of explana- tion under this than under the common conception of chemical affinity, and in most cases are even easier. All elemental Quality is thus reduced to simply 202 Atoms and Energies size and shape of atoms. All physical and chemical laws are merely the statement of the essential char- acter of the two entities, Expansive and Attractive Energy. Moreover these characteristics are, in the last analysis, found to be exceeding simple. It is needless to point out how far reaching must be the results of such a changed conception of the nature of fundamental atomic phenomena. It must mean a complete revolution in our thinking along many lines of physical research. It may well be an- ticipated that many will pause before resting in a conception so very radical though it is not the temper of science to really reject any proposition merely be- cause it differs from former ideas. The extreme simplicity also will be an obstacle to the belief of some. Yet is it not rather a tribute to our Creator's wisdom if out of elements so simple he has constructed a world so wonderful and com- plex ? Indeed the nearer we get to fundamental truth the simpler we will always find that truth to be.