A REVIEW OF- THE THEORY OF- J. K./ AT WOOD. A REVIEW -OF- THE THEORY -OF- I] J. B. AT WOOD SAN DIEGO CAL.: GOULD & HUTTON, PRINTERS. 1888. lo ' '1 IS THE NEWTONIAN THEORY OF GRAVITATION TRUEP Before submitting objections to this theory, or venturing any suggestions with regard to it, a few preliminary considerations may not be out of place. It is then an established theory, is quite generally accepted, has the weight of authority in its favor, and for these reasons at least is more formidable to combat. As usual in such cases there is now a sort of chronic faith in its validity, that was conspicuously absent in the first place, and this blind barnacle like and thoughtless adherance to an accepted matter, is always a bar to the recognition of the new, although a substantial bulwark in support of the old and well established. The theory, too, is somewhat plausible, and has at least some appearances in its favor, but this is no more than can be said of many other theories that are false, notwithstanding some seeming evidence in their behalf. Now, a theory may be true and have seeming objections, but cannot be true and have real -objections, or, in other words, truth admits of but one theory, although there may be many false ones about a given matter. In combatting a false theory, it is not necessary to know the true one, however desirable that may be. Of course the existence and manifestations of the force called attraction are not here questioned, but only the prevailing views concerning that force. Now, the main proposition, or rather assumption, of this theory, is that each atom of matter in existence attracts and is in turn attracted by every other atom of matter wlitlre universe:' It is also further assumed in this connection, , tjiat, the force called weight is nothing but the mutual'att^acti^ri^ci" :mtter ; that this attraction is not merely a local but a universal force, and "thaft the heavenly bodies are kept in their respective positions by this means. For the purpose of vindicating these assumptions several others were at the same time made, as will appear in this investi- gation, prominent among which are certain so-called laws of motion. Concisely stated then, it is the supposed universal feature of attraction that constituted Newton's grand discovery or possi- bly his grand mistake. We are now squarely confronted with this problem of uni- versal gravitation, and while some of the objections here raised to the present theory may be only suggestive of its unsoundness, some of them appear to be absolutely conclusive. 731202 4 A REVIEW OF THE THEORY OF > The simple statement then that a single atom of matter at- tracts every other atom in the universe, embodies and expresses the real essence of this theory, and the first question will be, what is an atom ? That question cannot at present be positively answered, but the nearest approach to it is the inference that it is an individual and indivisible portion of what is called matter. For the present we will accept this view of it, observing, by the way, that if not correct, it is simply bad for the theory. The first step, then, will be to obtain something like an approx- imate conception of the size of a single atom of matter, in order to form a proper estimate of its probable capacity for the duty assigned it, and the chief difficulty will be on account of its ex- treme minuteness. That difficulty is so great for the reason named, that we can only infer from certain facts, how very near that something is to nothing at all, although it is required by this rigid theory to accomplish nearly everything, not even excepting impossibilities. If, for instance, a single line of atoms one inch in length, containing the ordinary number in solid bodies, was divided into loo equal parts, and one of these parts was divided also into 100 parts, and one of the last named was also thus divided, still another similar div ision would at the very least be required to get down to the dimensions of an individual atom. The present aim, however, is not so much the actual size of the atoms, as that point is by no means essential in this connec- tion, for if they were a thousand million times larger than our estimate, the theory of universal gravitation would scarcely be less absurd. . Jhis being the^se, ;we will rest satisfied with the statement that thwart!} ^nta*>hs*aver i2,CKDo,oco,ox),CKX),coo,c>cKD,CKDO,ooo pounds of ^matter, .antf that" there are more atoms in a pound of mteit$(iKthere:lre pprM4 s " m the entire Earth. ''ktiVit'is'riot 'the* extreme minuteness of the atom that is of such special significance in this case; it is the tremendous magni- tude of the burden imposed upon it by this presumptive theory; for in contrast with the almost nothingless atom itself, the contract alloted it is a prodigious one, and taken in connection with its other ill-supported and extravagant assumptions, is at least calcu- lated to excite suspicion, if not to raise a serious doubt. The next step will be to discover the force or sum of the energy that is decreed this smallest of all things, this victim of the gravitation hobby, the invisible atom; and what a remarkable proposition is here presented, in which much the least and most definite thing in existence, although numerically the greatest of all things, is yet required to divide and distribute its patronage among all the countless host of atoms in the boundless universe. UNIVERSAL GRAVITATION. 5 Right here, for once at least, we have something tangible, something that we can comprehend, and that is the amount of force called attraction in a given quantity of matter, although it is not at all clear how that amount should be divided and alloted. For example, about four cubic inches of iron weigh a pound at the surface of the earth, and this, according to the Newtonian theory, represents the entire force exerted, not, however, by this particular mass of matter separately and alone, but in combina- tion with the rest of the earth. How, then, is this pound of force to be adjusted? and what proportion, if any, is there due to the earth? The Newtonian theory is not very lucid on this point, as well as on some others, and we are thus left to seek a solution of this problem. Two suggestions at least on this question seem to require consideration. In the first place, then, is the energy equally due to the two masses? and, in the second place, is it in proportion to the masses ? If we accept the first proposition, certain unpleasant conse- quences legitimately follow, a few of which are here enumerated. That a small part is equal to a much larger part ; also that attraction is not the property of an atom of matter, but is the property of two or more atoms ; and further, that the sum of this energy possessed by a single atom is entirely contingent upon the whole number of atoms in the universe ; and still further, that if the universe was ten times as large as it is, an atom of matter, although no larger than before, would yet possess ten times the attractive energy. The second proposition that the force is proportional to the mass, seems much the more rational of the two ; but it has one very unpromising feature for this theory, inasmuch as that would plainly indicate that this vaunted energy is a very insignificant and contemptible item for the sphere alloted it. A much more sensible solution of this matter is, that the entire weight of a pound of matter is due only to that specific mass. But that would upset the whole programme of universal gravitation. In following the second plan of this gravity campaign then, we shall find that instead of a mass of matter weighing one pound, and commonly and probably correctly supposed to possess and exert a pound of force, it does no such thing according to this theory ; but on the contrary, only exerts such a fractional part of a pound as that specific mass is a proportional part of thf entire earth ; and if expressed in numbers, the result would be substan- tially like the following, 1 2, 000,000,000,000,000, ooo, 000,000 parts, or twelve septillions of the pound of force, is due to the earth's attraction ; and only one part of the pound of attraction is due 6 A Ri.YIKU ()! T1IK THEORY OF to the smaller mass commonly supposed to weigh a pound itself. Or, in other words, according to this theory the above ex- ample furnishes a pretty fair measure of the energy possessed and exerted by a mass of matter weighing one pound, which it will be perceived, is about as much less than a pound as a pound is less than the whole number of pounds in the earth. What is true then of four cubic inches of iron or one pound of matter, is also true of one atom of matter ; hence we see that the entire attractive energy of an atom of matter is as much less than the atom itself as the atom is less than the whole number of atoms in a pound of matter; and there are more atoms in a pound of matter than there are pounds of matter in the entire earth ; consequently, the atom and its whole attractive force may IK- appropriately expressed in the same manner as in the example of the earth and pound. Thus 1 2,c>oo,ooo,oc>o,ooo,ooo,ooo,ooo ooo represents the mag- nitude of the atom, and only one is required to represent the relative proportion of its attractive force ; or, in words instead of figures, twelve septillions indicates the size of an atom, and only a single unit its energy in comparison with its dimensions. If the effort then which this theory so rigidly prescribes for the atom is enormous in proportion to its size, what must it be in comparison with its attractive energy. But these illustrations will fail to convey anything like a just appreciation of the absurdity involved in this problem of the in- significant atom and its utterly insignificant force, unless a little consideration is bestowed upon the immense field of its operations. And what is that field ? Surely not the nearest atom even in an ounce of matter containing more than a septillion of similar atoms ; neither is it confined to the ounce, nor the pound, nor the entire earth. It is not even restricted to the solar system, some half million times larger than the earth ; but the field includes the whole uni- verse, with its countless millions oi suns and systems of worlds ; and we may well exclaim, what a vineyard is this ! and what a task for such an insignificant and so utterly debilitated a laborer ! To convey anything like an adequate idea of the immensity of the universe is simply an impossibility ; but for the present we will note the point, that it takes thousands of years for light trav- eling nearly 200,000 miles a second to reach the earth from some of the distant stars or suns, and this amazing distance is indicative of only an insignificant part of the unfathomable universe. Now, the entire attractive energy of the earth if concentrated upon a single distant star, if indeed there is any force at all in such a case, is less than one ounce ; but the earth, according to Newton's laws of force and motion, could not exert any greater part of its attraction upon a remote star than when radiated UNIVERSAL GRAVITATION. 7 equally in all directions would be in a line with that star ; and as many hundred thousand millions of stars would be required to fill the space at that distance, it is clear that the actual force, if any, in such a case would be many hundred thousand million times less than a single dram. We have already seen that the attractive force of a pound of matter is twelve septillions less than the earth's attraction. What, then, are we to think of the attractive energy of only a single atom in such a case, the size of -which is more than three septil- lions less than a cubic inch, with a corresponding decrease of energy as compared with its dimensions, and still the universe would be even then scarcely invaded? But there are still other absurdities involved in this assumed universal attraction of an atom, for if each atom of matter exerts its force upon every other atom, that force which is originally so insignificant as to be entirely beyond ascertainment, must not only be extended infinitely beyond conception, but be divided beyond the power of language to adequately express. It must not only act through unlimited distance upon an un- limited number of other atoms, but also through an unlimited number, equal to itself in magnitude and energy without being intercepted by them ; and as every other atom must do the same thing, what an infinity of currents, cross currents, counter cur- rents, confused, bewildered and mixed currents of energy is thus implied, and how entirely unlike the economy, the simplicity, the harmony and the order of nature in all other respects. An atom of matter, in keeping with this remarkable theory, must constantly and uninterruptedly exert its energy in every direction and in every pla-.e however minute, in order to contin- ually reach every other atom ; in short, the imperceptible atoms are so small it would be necessary for a single atom of matter to completely pervade and entirely fill the universe with its force, notwithstanding its own entire energy is so contemptible an item, otherwise some stray atom might escape its influence, which would be detrimental, if not absolutely fatal, to this whole gravi- tation scheme. If one single atom of matter then, should fill the universe entirely full of its all prevading, never ending, never decreasing, but ever active energy, and every other atom not forgetting that there is some of them should do the same thing with the fullness thereof, a most incomprehensible and indescribable fullness would prevail. An atom of matter notwithstanding it is so exceedingly minute that its whole area is only about a hundred millionth part of an inch, the smallest possible point, is yet required by this theory to hold energetic communication with all the untold number of atoms in the unlimited universe. 8 A REVIEW OF THE THEORY OF A mere point itself, that would be entirely enveloped by a single line far beyond the reach of the microscope, and with its infinitesimal force a septillion of times less than its own propor- tions, must for all that, and still other far more insurmountable difficulties, send out from its little sphere more than a septillion of lines to intercept and connect with merely the atoms in a single ounce of matter. What a problem then is here presented, when we consider that the Earth contains twelve septillions of pounds, while the Solar system is some 500,000 times greater than that, and the en- tire universe more than 100,000,000 times greater than the Solar system. Nor is this the only difficulty that menaces this proposition, for this single atom must at the same time make room for the reception of an equal number of lines of communication from every other atom in return, and what is still more embarrassing, not only this, but all the other atoms are in rapid and ceaseless motion over immense areas of space. These atoms have not only an endless motion of their own, but the situation is still further complicated by several additional movements. For instance, an atom of matter besides its own continuous motion, may be located in the end of a lively mosquito's wing, while the aforesaid mosquito is buzzing at his best speed, and at the same time he is also being moved bodily by the wind, and if in the equatorial regions, where an additional movement occurs of over a thousand miles an hour, which is further supplemented by the orbital motion of the Earth at the rate of more than 18 miles a second, besides the additional movement of the Earth in concert with the Solar system. At the same time all the other atoms in the universe are lead- ing a similar lively and interesting dance, to the utter confusion and complete discomfiture of this complex snarl of a theory, through creating a tangled and inconceivable web of intricacies, that no imagination can begin to fathom or understand. If there was but one single atom of matter in the universe, there would of course be no use for attraction of gravitation, as there would be nothing to act on, notwithstanding its assumed active and everlasting hankering for the embrace of kindred atoms. But with two atoms the troubles commence, and continue to multiply with the increase in numbers, for it would legitimately follow that the universe would be twice full of energy with no where to store or deposit it; and that no matter what the distance between them might originally be, their first efforts would be to rush together in mutual and final embrace, thereby establishing a most damaging precedent, and precipitating a most awkward pre- dicament; in the very first instance for this peculiar theory. UNIVERSAL GRAVITATION. If they would not do this what becomes of this theory ? If they would, why is there more than one body in the uni- verse i Let the next supposition embrace three instead of two atoms, and still substantially the same results would follow as in the case of only two atoms. In harmony with the theory of universal gravitation the two nearest atoms would rush together first, and then the third would be added to the mass, thus making as in the case of two atoms but one final body of matter; nor would any possible arrange- ment of their original positions prevent such a result, not even if they were arranged in an equilateral triangle, the only way in which they could be equally distant from each other, as that would not prevent them if really possessed of this supposed prop- erty of attraction, from coming together at their common center. The same would be true of four atoms, or for that matter of any other number, including all the atoms in the universe; in fact, that would only serve to increase the liability, as the greater the accummulation, the stronger the attraction for the balance, for the unanswerable reason that two atoms would have tw r ice the at- traction of one. This being the case, it follows that in strict harmony with this theory of universal attraction, all matter would be combined in one single mass; yet we well know that there are hosts of sep- arate bodies, in spite of this ridiculous theory, which legitimately should make but one; nor has it been shown that any other pos- sible result but a single body, would follow the application and operation of this assumed universal force. The atom will now be given a brief respite while attention is being directed to a very different sphere of action, and to other prominent features of this scheme of universal gravitation. The principal theatre of operations in this field was supposed to be in connection with the various and complex movements and relative positions of the heavenly bodies; and this theory pro- fesses to elucidate and explain all the motions of those masses, with their varied connections and relations to each other satis- factorily as a true theory should. In this professed explanation that is so graciously vouchsafed for our guidance and enlightenment, a special diagram is furnished consisting of a circle with a single mass in the center of large volume representing the Sun, while a much smaller mass or sphere is located on the circular line to represent the Earth. Now, the present theory of planetary movements embodies Newton's grand discovery, and these movements are assumed to be due to the combined action of two independent and opposing forces, operating in right lines and at right angles to each other, one of which is claimed to be attraction, while there is a large 10 A REVIEW OF THE THEORY OF degree of obscurity and ambiguity about the other force, although that force whatever it may be, is far the more important of the two in spite of this obscurity, if indeed it is not the only force in- volved in the planetary problem. In the operation of these supposed forces a central body is involved like the Sun, and outside of this at a distance as per diagram, are other bodies moving in their respective paths or or- . bits like the Earth for instance, while an impelling energy of some unknown sort causes a forward movement, which unresisted would simply move the Earth in a straight line at a tangent with what would become a circle of a certain size, when counteracted and just counter-balanced by another force called attraction. Special attention is here directed to the fact that the diagram for illustrating these movements is simply a circle showing the Earth's path at a uniform distance from the central mass; and that the impelling energy is a uniform or unvarying force, while the attractive force is a variable one. If the combined action of two such forces could move one body around another at all, which is exceedingly doubtful, it could evidently be only under certain specific conditions. One requirement would be a circular path of the outside or moving mass, the inner mass would have to be at the center, the path of the inner body would have to be precisely where the two forces would balance each other just as indicated in the diagram, and there could not be other influences to disturb the relative in- fluence and effect of these two forces. But these are not the conditions under which the heavenly bodies move and are kept in their respective positions and orbits. Take the Earth for example. The orbit is not a circle; the Sun is not in the center; the forces are not balanced; the bodies vary, and there are numerous influences to disturb and destroy the equilibrium of two such forces. These supposed forces could not move the Earth around the Sun in the present path and manner, because they will not bal- ance each other at all parts of an eliptical orbit. If the impelling force at any time or point should exceed the attractive, the Earth wonld fly off into space because the ascend- ency of the moving force would from that time be relatively great- er, in consequence of the diminishing attraction by reason of the increasing distance between the two bodies ; while on the other hand if attraction should on account of the nearer approach of the Earth to the Sun at any part of its orbit become relatively greater than the other influence, the Earth instead of continually revolv- ing around the Sun, would simply be drawn into contact with it in a track not unlike a coiled spring, on account of the continually increasing energy of attraction to that point. This will be better comprehended if we substitute one of the UNIVERSAL GRAVITATION. II comets for the Earth where the departure from a circular path or orbit is so decisively marked, and where the attractive force is al- leged to be so very much greater at the point nearer the Sun. But if it would be a difficult matter for two such forces to main- tain even a circular movement of one mass around another, which is the only one possible ; it would be vastly more difficult to in- augurate such a movement, as there would be conditions required of very doubtful occurrence. The moving body would have to be outside of the orbit or point at which the forces would balance each other; and moving at a fixed rate of speed not less than that of its speed in its orbit if one could possibly result from such causes it would have to be moving in precisely the right direction, and free from the influence of disturbing causes. In short this idea of propelling one mass around another in a circle as an illustration of the actual origin and present means by which the real movements were caused and are still maintained, is indeed a very bald affair; not merely misapprehending the actual state of things, but vainly endeavoring to make the bastard sub- stitute perform impossibilities through the use of means entirely inadequate and inappropriate, without any legitimate connection, and involving insurmountable difficulties. In fact the contingencies are so numerous and important, that they render the problem of inaugurating or maintaining by such means anything like the planetary movemets, or even such a single movement as the one illustrated, too absurd to seriously entertain; besides if such a thing as this circular movement was entirely practical and feasible, it would still be of no consequence, as there are no such movements known. The Newtonian theory then not only practically ignores all the other movements of the planets except this substitute, but even fails to deal with the real orbital motion, in spite of .the fact that this was its objective point. Now while the single movement that has been substituted for the real motion is entirely different, so that the effort to explain the real one is a flat failure; the whole attempt is farcical, in view of the assumption that the movements of the heavenly bodies are all due to the operation of two such forces as this theory contemplates. For what an awkward predicament is presented by the signifi- cant fact that the very movement that has been so badly botched and obscured, could only have occurred if at all around a fixed point, instead of around an already rapidly moving mass; and a central point or mass at rest, was precisely what was contemplated in connection with this false movement; but how about the other and prior motion, which this half fledged scheme neither contem- plated nor could do anything with if it had? An inspection of the Earth's orbit suggests another telling 12 A REVIEW OF THE THEORY OF point against this gravitation hobby, in the fact that the move- ment on opposite sides of the Sun is in precisely opposite direc- tions; and of course the force or cause of the movement must act in strict harmony with that fact. Now a force acting in a straight line must come from a given direction, while the Earth's orbit plainly and unmistakeably im- plies a force acting upon the Earth in the direction that it moves, and in the curved path and plane of that orbit; besides a force from one direction only would not accomplish this result, or for that matter anything resembling it ; but would simply offer the same resistance on one side of the sun to the earth's movement as that very force imparted to it on the other. In short, the idea of propelling one mass around another by a straight line force is not even on par with proposing to blow a man around a barn with the wind from one direction only. If it is suggested that a single impulse could cause the present orbital movement in conjunction with attraction, the reply will be the conditions render that impossible. There would in such a case be not only the principal obstacles already enumerated, but other contingencies still more formidible. Indeed, the problem is too serious and complex for solution, and could not in the nature of things occur ; as the fixed central mass is an illusion, the force would have to come from precisely the right direction and be exactly sufficient to produce the present definite movement; besides there is not the least evidence of the existence of any such force or any use for it ; and a solid body like a planet could not possibly stand the shock of such an impact. If the heavenly bodies, or any of them, the earth and moon for instance, were really kept in position with each other, as alleged, by mutual attraction, they should revolve nearly around the center of gravity of the two bodies as if rigidly connected ; that center would be considerably outside the mass of the earth, and the earth would have, if that were true, an orbit of a very different description, as would also the moon. After Newton's conception that attraction of gravitation was a universal instead of a local force, and that the same force that causes a body to fall or move towards the centre of the earth also keeps the heavenly bodies in their respective orbits, he labored long and arduously to demonstrate the truth of his supposed dis- covery, and finally selected the earth and moon as a satisfactory example of the harmonious combination and operation of the two forces claimed to cause and control the planetary movements. And he is generally supposed to have worked out a complete demonstration of his theory, chiefly by means of this single example. To accomplish this result he made several new propositions UNIVERSAL GRAVITATION. 13 upon which the truth of this theory depends, some of which are here enumerated : That attraction decreases as the square of the distance. That the correct unit of distance for this purpose is four thousand miles. That this unit is just the radius of the earth. And that the distance between the earth and moon is sixty times the radius of the earth. But the grand assumption was that through these alleged facts, he claimed to have completely demonstrated the truth of his theory of universal gravitation, simply by proving that the moon followed the law of falling bodies on the earth, and that this was due to the same cause that makes an object move towards the center of the earth, styled attraction of gravitation. Now, the moon does not follow the law of falling bodies, and the difference between the two movements in point of fact and resemblance is a very marked and substantial difference, and we will note some of the variations. A falling body either moves in a straight line or a parabolic curve, while the moon does neither, but simply moves in a curved path that is slightly cliptical. A falling body has a limited movement, while the moon has a continuous movement. A falling body has an accelerated movement, while the moon has a comparatively uniform movement. Newton evidently overlooked these serious discrepencies, as well as many others still more serious, in his eagerness to mount this gravitation hobby successfully ; for he seems to have risked this whole structure of assumed universal gravitatation finally on a single point or proposition, and a most ludicrous one at that. This point was, that the moon lalls towards the earth, or curves in its movement around it, allowing for the difference in the intensity of the force or attractive energy the sme propor- tional amount in a single second of time that a body falls at the surface of the earth in that time. That statement, even if true, is of no significance at all as proof of the truth of this theory ; but, on the contrary, it is well calculated to mislead rather than aid in the discovery of the truth, and this singular proposition did undoubtedly deceive Newton as well as others. What if the moon does move as alleged for one second of time the same amount in proportion to the force that a body falls, how is it for two seconds ? or three ? or any other number ? It is entirely different, as we plainly see. Thus this vaunted agreement only applies to a single second, if indeed it does to any one, and that only the first ; but how is it 14 A REVIEW OF THE THEORY OF for the next succeeding second ? Why, only one-fourth as much of course. How is it for the third ? The difference is still greater, and so on for each succeeding second. In feet, no just comparison can be instituted between a uni- form movement and an accelerated one, and, as stated, there is no significance at all in the circumstance that the two movements are the same for a single second, whether first, second or third; as they could not help being the same for some given period, for the simple reason that the uniform movement of the Moon is rel- atively faster than the other at first, but is soon exceeded by the other, and that would be true of any two similar movements. Indeed they will agree for just one period of time, and only one, for the reason stated that the uniform motion of the Moon is relatively faster than the accelerated motion of a falling body during the first part of a second that a body begins falling; and slower than the latter part of its accelerated movement, as it would have to be in order to be equal in amount; but no comparison at all can be made with the next second, or any other period of time; while it is clear that the movements should be the same for any and all periods if there was any real connection between them. We shall also perceive, notwithstanding the vaunted fact that the Moon and a falling body may move a proportional amount in a second of time, that there would only be a. brief portion of that time in which the two motions would be the same, while at all other times they would radically disagree. We shall perceive too, that if their movements agree in amount for one second of time, that they would not agree even in that respect; if a second, which is a mere arbitrary portion, and not a natural division of time, had been either longer or shorter, as it might just as well have been, for there are no natural divis- ions of duration, and the conclusion is irresistible, that if a second had marked a different period of time, this famous discovery, or still more famous blunder, would never have been made. What sort of a foundation is this for a professed scientific theory to rest on ? But aside from the fact that there is no real connection or re- lation between these movements, and that he might with equal propriety have instituted a comparison between the movements of the Moon and that of a lunatic, the additional fact remains to blast this theory, that the distance between the Earth and Moon varies at times about fourteen per cent, or eight times the radius of the Earth. This fact when taken in connection with the circumstance that his demonstration was held in abeyance a long time, by an in- correct estimate of the Earth's radius, is really inexplicable. UNIVERSAL GRAVITATION. 15 Yet still another obstacle was encountered with reference to the radius of the Earth being the real unit of measurement for de- termining the variation in the intensity of the attractive energy, because in order to make the assertion that attraction like light varies according to the square of the distance even a plausible one, it was necessary in this instance at least, to recognize the center of the Earth as the starting point. But here was a snag; for that would imply that attraction is nothing but a local force, which is probably true, and would, if accepted, collapse this whole scheme of universal gravitation. The radius of the Earth was therefore necessarily taken as the proper unit of measurement, not because it was true, but because the theory compelled it for this special purpose, while universal gravitation, if true, is not contingent upon centers, as the entire mass is involved regardless of form, whether applied to the Moon or an object near the surface of the Earth. To obviate this difficulty Newton claimed that the real effect of the Earth's attraction was just the same on the Moon and also on objects near its surface, as if the whole mass of the Earth was concentrated at its center. But this is not the case as a very simple illustration will show. For example, suppose an object at the surface of the Earth to weigh a certain amount; then, if the entire mass of the Earth was concentrated at its center, this object would weigh less than it did, provided it remained in the same place, on account of the in- creased distance from the force; and the fact that the same amount of matter next to the object would relatively lose in being removed to the center about four times as much as a similar amount on the opposite side of the Earth would gain in being transferred to that point; while on the other hand, if the object was moved as near the center as it was to the surface, it would weigh more than be- fore with the force all concentrated at the center. The center of the Earth then is not the point at which the entire attraction for an outside mass would be the same as at pres- ent, provided the whole mass was concentrated at that point, and the real point is very difficult to determine, but it seems clear that this point would be considerably one side of the center, which fact taken in connection with the moon's eccentricity, effects his assumed unit of 4,000 miles most seriously. It is very plain that conditions like these completely vitiate his rules and estimates, which, after all, seem to be nothing but loosely formed theoretical speculations or mere vagaries. This will be still more evident when the relative amount of the two forces involved in Newton's problem is taken into con- sideration as it should have been. According to his second law of motion, which is in a certain local scene correct, and which was intended to meet this particular l6 A REVIEW OF THE THEORY OF case, although it evidently fails to do so, as he would have found to his dismay, if he had thoroughly investigated it, as he should; still he fancied that attraction was the force that caused a planet to deviate from a straight line in harmony with that law. The law is as follows, and when applied to a local case and a secondary motion may be correct; the alteration of motion is ever proportional to the moving force impressed, and is made in the direction of the right line in which that force acts. If we apply this law to planetery motion, it is evident that the force called attraction would have to be somewhere near the same amount as the other impelling force or forward movement; and especially should it be uniform in its application and operations; but how is it ? In the case of the Sun and Earth, only one pound of at- tractive force, if any, is pitted against a force of over three hun- dred thousand horse power; between the Earth and Moon the same amount of energy is opposed to over six hundred thousand horse power, while in the case of the Sun and Neptune, the dif- ference is over forty-five million horse power, and there are in- stances that far transcend even this. But if this attempt to account for one single motion of a planet and only one, and that to\the motion in its orbit is such a dismal failure; so complete in short that the real motion is un- touched and a glaringly inappropriate substitute improvised in its stead, which is also utterly useless, as it will neither operate ac- cording to the design, nor would be of any consequence if it did, we may then justly ask in view of such an unsatisfactory solution of this movement, what shall be done with all the other movements where this theory is still more balky ? Take the motion of the Earth on its axis for instance, where neither of the requirements of this theory exist at all, there being no separate and independent central mass, and of course no mutual attraction between two bodies, and where there could be no possible application of a force that acting alone will only move an object in a right line. Here then we have a motion that cannot be produced by any such means as Newton's scheme contemplates; and, of course, it was not produced in any such manner; but still it must have been caused in some way, and that is a serious matter for this theory, as it implies another and entirely different, theory. Taking then this motion alone, no one would think of it in connection with Newton's programme; and the difficulty is only increased when the orbital motion is coupled with it, and is still further complicated by the motion with the Solar system. Or take the moon for instance, which has four movements one around its own axis, one around the Earth, another with the Earth around the Sun, and still another with the Solar system, all UNIVERSAL GRAVITATION. 1 7 of which this theory, if true, should clearly explain and account for, which it most assuredly does not, and at the same time it should be free from real objections. On the contrary it is besi^with the most fatal objections, and does not even attempt to deal with the real motions, but only a substitute for one of them, and a very poor likeness at that. The more this matter is analyzed the more absurd it appears. Take for instance the only motion that it is supposed to contem- plate, namely, the orbital movement, and that of the Moon for example, and what do we find? Instead of a body revolving around a fixed point or center as an object might be whirled around a revolving shaft if connected with the shaft by a cord, we perceive a very complex movement of an entirely different character. First there is the motion of the entire Solar system, Earth and Moon included, that this Moon-struck theory does not even attempt to approach. Next we find the Earth with another movement around the Sun which is not circular but eliptical, with a daily motion besides; and, finally, the orbital motion of the Moon around the Earth, while this motion is also eliptical instead of circular, besides being spiral and curved around the eliptical path of the Earth. Now, it is not pretended that a single force will produce alone anything but a straight line movement, and nothing but a circular motion in conjunction with attraction; but here is a movement that is neither straight nor circular, but, on the con- trary, it is spiral, eliptical and curved", besides partaking of the Sun's movement, and has a rotary motion added. But one of the most withering points for this Moon-blind theory is found in the very example that Newton selected to prop it up with. Now, he claimed that the mutual attraction of the Earth and Moon overcame the other force in a certain ratio, and that amount is about thirteen times as much as it is between the Earth and Sun, while between the Earth and Moon the mutual attraction compared to the other force is at the same time less than half as much as between the Earth and Sun. Here is a striqtly legitimate test of the truth of this theory of Newton's, and this fact alone completely demolishes his super- ficial and theoretical moonshine hash, labeled universal gravitation. 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. REC'D LD REC'D i_D JUL 20'64 -7PM AUG1 1960 20W64JC REC'D LD (*.** JAN 15 '64 -9 AM 10 O 7'70-4PM LD 21A-50m-4,'60 (A9562slO)476B rary Univertity of California Berkeley U.C. BERKELE CDblBI 31202 UNIVERSITY OF CALIFORNIA LIBRARY