Kinetic Theories of Gravitation/Croll, 1867
In a communication to the Philosophical Magazine, in 1867, by James Croll, of Edinburgh, "On certain Hypothetical Elements in the Theory of Gravitation," the author revived the difficulties which had been felt and proclaimed by Faraday. He says : " It was demonstrated by Newton, and has been proved by general observation and experience, that [262] bodies tend toward each other with a force varying inversely as the square of the distance, and directly as the mass of the bodies. But it never was demonstrated or proved by any one that the bodies attract each other. The thing which has been demonstrated is that B tends toward A; but the theory does not rest here ; it goes on to account for this tendency by referring it to a hypothetical cause, viz, to the ' attraction' of A. This however is a mere hypothesis, and no way essential to the theory. All that the theory requires is that it be demonstrated that A tends to move toward B. It is not necessary that we should go beyond this, and attempt to explain the cause of this tendency. Trifling as this assumption included in the theory may at first sight appear, it will be found that almost all the difficulties and objections which have been urged against the theory of gravitation are due in some form or other to that assumption. At the very outset we have the objection urged against the theory that it implies the absurdity of action at a distance. Now the mere facts of gravitation imply no such thing. That A and B placed at a distance should tend toward each other does not imply action at a distance. A moves by virtue of a force, but it does not follow that this force is at a distance from A. But if we assert that A and B 'attract' each other, then we imply action at a distance; for A is then affirmed to move in consequence of the force of B, and B in consequence of the force of A. ' The very idea of attractive force,' as Professor Brücke remarks, ' includes that of an action at a distance.' No principle will ever be generally received that stands in opposition to the old adage, 'A thing cannot act where it is not,' any more than it would were it to stand in opposition to that other adage, 'A thing cannot act before it is, or when it is not.'"[1]
These venerable "adages" are about as valuable in directing us to the actual facts of nature, as that other celebrated adage of Zeno, " a body cannot move where it is not;" and conversely, "it cannot move where it is." An equally profound dictum is, that a " cause " cannot properly be said to precede its " effect," since succession implies discontinuity.
It may be a fact of natural law that everything acts where it is not," including even an aetherial vibration ; and certainly there is no difficulty in believing it; and the other metaphysical axiom maybe easily discredited by the simple reflection, that were our sun suddenly blotted from existence by supreme power, though all " attraction" of the planets would instantly cease, its full dynamic action on the earth would continue unimpaired for eight minutes. Were Sirius annihilated this year, it would still continue to pour upon us its lull measure of dynamic action for twenty years " when it was not." The difficulty is not in the possibility of posthumous action, but in the possibility of annihilation.
As Mill has very properly stated in answer to Sir William Hamilton, "Action at a distance is intrinsically quite as credible as action in [263] contact, and there is no reason, apart from specific experience, to regard the one as in any respect less probable than the other."[2]
In our profound ignorance of all beyond the ascertained facts of gravitation, there could be no objection whatever to the substitution of the word "tend" for the word "attract," did it adequately express the observed fact that A induces in B a " tendency" to approach ; the quantity of tendency in B being found to be proportional not merely to its own mass, but notably to the mass of the distant body A.
Mr. Croll proceeds : " The attraction theory is also in opposition to the principle of the conservation of force, as has been shown, I think clearly, by Faraday. When a stone for example is thrown upward from the earth, it not only loses all its motion, but it loses its attraction in proportion to the square of its distance from the center of the earth. What becomes of the motion imparted to the stone ? It is not transformed into attraction, for the attraction diminishes as well as the motion. When the stone again falls to the earth it gains both motion and attraction. In the former case, the attraction is said to consume the motion, and instead of becoming stronger becomes weaker in consequence ; and in the latter case it imparts this same motion, and yet after imparting the motion, it is actually found not only not to have lost but to have gained force thereby. Faraday justly asks what becomes of the force or motion imparted to the stone ! It is not converted into attraction, for the attraction becomes less instead of greater in consequence. And in the case of the falling stone, where does the motion come from ? If the motion arises from the attraction of the earth, then there must be a -certain amount of this attractive force converted into motion; and if so, the attractive force should be so far reduced; but instead of this it is actually increased. There is therefore no account given of what becomes of the motion externally imparted to the stone when thrown upward, or whence the increase both of attraction and motion is derived as it descends. If the attraction theory be correct, then there is a destruction of force in the one case and a creation of force in the other ; and if so, then the conservation of force is violated."[3]
Although this is merely a more prolix statement of the objection urged by Faraday, it may be again specifically answered. It will be found on careful examination, that the whole difficulty really proceeds from an hypothesis tacitly adopted by the writer, while ostensibly opposing " certain hypothetical elements in the theory." From the necessary limitations of language, we have constantly to make words do double or multiple duty in carrying different ideas; and to many this is a source of constant confusion and misconception. The tacit assumption underlying this supposed violation of the conservation of " force " is that the force of gravity is the same in kind as the force of the [264] falling Stone ; and that as the latter is an example of kinetic energy, capable of transmuting itself into heat, so gravity must be in essence also a kinetic energy capable of similar transformation. On this " hypothesis " all the consequences so incongruous with experience, as above indicated, would result. The ascending stone would have its energy "transformed into attraction," and the latter would be correspondingly increased. It would then be truly " said to consume the motion " of the stone. And when the stone was falling there could be "a certain amount of the attractive force converted into motion, and so the attractive force should be so far reduced." The reasoning is undoubtedly correct. " But instead of this, it is actually increased. There is therefore, [by the kinetic hypothesis,] no account given of what becomes of the motion externally imparted to the stone when thrown upward." And the undisputed facts of observation therefore, show us that if the kinetic hypothesis "be correct, then there is a destruction of force in the one case and a creation of force in the other." The conclusion i& incontrovertible.
Seeing then the incongruity and inadmissibility of the assumed hypothesis, let us try a new departure. Let us, recurring to that only safe guide experience, recall as the necessary outcome of the fourth, fifth, and sixth propositions, that " gravitation is a property immutable and inconvertible." Let us, to avoid confusion of idea by the unconscious double entendre of the word " force," limit the term for the present to that innate and primitive tendency or tension which appears as the last result of dynamic analysis, and which obviously differs as much from the action of the falling stone, as the flying arrow differs in function from the elasticity of the bow which has impelled it. We shall thus have a term comparable in derivation and use to the "element" or the "atom" of the chemist, designating simply that which as a matter of fact, has not yet been further resolved. If now we deny (for the present purpose) the application of this term "force," to the dynamic action of the falling stone, and call the latter " energy," a term which conversely we deny to the primitive vis motrix, all confusion and inconsistency will disappear. Obviously, "conservation" can be intelligently applicable only to that which is capable of expenditure,, transformation, or dissipation ; as to matter, or to energy. To speak of the conservation of immutable gravitation is as unmeaning as to speak, of the conservation of the equally immutable molecular cohesion or atomic elasticity. As a fact of daily observation, motion is a variable function, and like heat, color, form, or density, is not conserved.
When a stone is thrown upward therefore, it loses tension, because this Ms been found empirically to be the inflexible law of distance-ratio for the gravitative force, and for no other human reason. It gains in potential energy by the ascent because there has been a corresponding expenditure of kinetic energy in effecting the ascent; and all experimental research proves the absolute constancy of the sum of these two [265] forms of energy. And this constancy is all that is signified by the oft-quoted but not always justly apprehended " conservation of force." So far from there being any fixed relation between gravitative force and the conversion of motion, the ratio varies in every planet; and while the height to which a pound of gunpowder would project a ball upward would differ widely in different planets, the velocity of projection and the returning energy of the fall would be precisely the same in all. Were we to rigorously deny that gravitation is energy, or that energy is force, we could not correctly affirm the conservation of "force." The thing truly conserved would be energy, and this is undoubtedly the more accurate and less misleading form of expression.
Mr. Croll says in concluding his essay : " In the case of the loaded piston rising under the pressure of the steam, we have the pressure of the steam and length of space both diminishing as the vis viva or mechanical work increases. This is in harmony with the principle of conservation, for pressure or force diminishes as energy or work increases. But in the case of gravitation matters are reversed, for the force increases along with the work. As the weight descends and performs work, the pressure of the weight, the thing which performs the work, increases also; and when the weight is rising and energy diminishing, the force or pressure of the weight is not increasing but actually diminishing also." A very sufficient demonstration that steam and gravity are not correlated ; that they are not both " forces " in the same sense of the term. Similarly a bar-magnet employed in educing magnetism in another steel bar, so far from losing what the other gains, has its own magnetism re-enforced by the operation. Vires acquirit eundo.
" This difficulty," says Mr. Croll, " along with all the others which we have been considering, will entirely vanish if we adopt the view of gravity which has been ably advocated by Faraday, Waterston, and other physicists, viz, that it is a force pervading space external to bodies, and that on their mutual approach this force is not increased, as is generally supposed; the bodies merely pass into a place where the force exists with greater intensity ; for in such a case, the intensity of the force in the space external to any body is inversely as the square of the distance from the center of convergence of these lines of force. As the stone recedes from the earth its vis viva is transferred to space, and exists there as gravity. When the stone approaches to the earth, the force existing in space is transferred back to the body, and appears again as vis viva.'[4]
Here then is an hypothesis which based on an a priori sentiment of fitness rather than on any direct induction, can be submitted to the test of observation. As a fact of observation, gravitation is always found to be a property of gross tangible matter, with its tensions mathematically directed to the mass-centers, and in quantity always directly proportioned to the number of material molecules, agreeably to the first and second propositions. As a fact of observation, the moon may pass [266] through the very center of the space occupied by our earth only two weeks previously without any perturbation or consciousness of increased tension in this mystic " space.'" To affirm that the projected stone transfers its vis viva to space without suggesting any conceivable method by which such transfer could physically be effected, is not to proffer an hypothesis. To affirm that the falling stone receives from the illimitable ocean of space its just supply of vis viva — whether required at the instant or ten years afterward — is to bid us hope that the steam exhausted from the cylinder into the atmosphere may be induced to return to its duty when needed, in order to justify our faith in its conservation.
Nine years later, in a communication read before the British Association at Glasgow, September, 1876, " On the Transformation of Gravity," Mr. Croll repeats very much the line of argument just referred to, showing that the interval had not served to remove his difficulties. He commences his memoir with the query: " Is gravity convertible into other forms of energy? Can gravity be converted into heat, electricity, magnetism, etc.? or can those forms of energy be converted into gravity?" It might be supposed that the question would as soon occur to the physicist. Can the flight of the arrow be converted into elastic tension"? The answer to his inquiry is directly involved in the fifth and sixth propositions. Mr. Croll, however, gives a different answer. "It may be true that gravity cannot be directly transformed into heat, electricity, magnetism, chemical affinity, etc., nor these forms directly transformed into gravity; but nevertheless, the thing may be done indirectly. ... If the electricity produced by the descent of the water be gravity transformed into electricity, then the ascent of the water produced by electricity must be electricity transformed into gravity ; for it is the same process merely reversed."[5] The alternatives are doubtless equally correct.
" If gravity be correlated to other forms of energy, it must like them come under the great principle of conservation. But here we enter upon debatable ground. It is admitted that gravity can perform mechanical work, and the mechanical work can be converted into other forms of energy. Here we have correlations; but it is generally denied that there is a decrease or loss of gravity resulting from such transformations. But this appears to me to be a virtual denial of the principle of conservation. . . . The reasons which appear to have led to this opinion are I think, mainly the two following : 1. It has been assumed [!] that the weight of a body is not affected by the work which it performs. 2. The force by which bodies are drawn toward each other does not diminish as they approach, but on the contrary increases. . . . May not a stone when in the act of falling be acted upon by gravity with less force at any given moment than it would be were the stone at rest at that instant ? The point has never yet been determined [267] either by experiment or by observation."[6] There is no conceivable reason why the falling stone should not " be acted upon by gravity with less force" than if it were at rest, (or why our fifth and sixth propositions should be true,) excepting the cogency of ascertained fact. Natural philosophy is an experimental science ; and this point has been determined both " by experiment and by observation.-' The sensitive galvanometer needle of Faraday would have betrayed a sigh of commuting energy in the falling weight employed, while the actual increments of vis viva were really so large that they would have been a notable duty for the coarsest scales. And the ceaseless fall of planets from the tangents of their orbits, without any reduction of their own centripetal tensions, or of their satellitic control, is a constant and conclusive observation to show that this law or condition of gravitation — embraced iu our sixth proposition — has not (as above suggested) been " assumed."
Mr. Croll continues: " But if the force of gravity does not sustain any loss as work is performed by it, what then is it that is supposed to sustain the loss? Some form of energy must diminish as work is performed ; and if it be not gravity it must be something else. The generally received explanation is this : when a body is projected upward, the potential form of energy into which the upward motion of the body is transformed does not consist in the simple force of gravity or tendency of the body to descend, but consists in this force or tendency multiplied by the distance through which it is capable of descending. . . This mode of viewing the matter, it is perfectly true, com pletely meets the mathematical and mechanical conditions of the problem.; but for this very reason it seems to me to hide somewhat the real physical nature of the process. [!]... Space and time are conditions, but conditions absolutely necessary to the transformation of potential energy into kinetic, and of kinetic energy into potential ; but they themselves cannot be forms of energy. But if it be true that the mere force of gravity or tendency of the stone to fall to the ground is not the potential energy, but that this potential energy is the force multiplied by the space through which it can act, then space must become a form of potential energy. This is evident; for the potential energy in this case consists of two factors, one of which is the space through which the force acts. It thus becomes just as much a form of energy as the other factor, viz, the force."[7]
The conclusion that space is " a form of" action, because all action is necessarily conditioned by space, does not appear so " evident." Mr. Croll correctly states : " But it is not in reference to gravity alone that this space-condition is essential to the transformation of potential into kinetic energy. It is as we shall shortly see, a condition absolutely necessary to the transformation of energy under every possible form. In the unbending of a spring the amount of work which can be [268] performed is proportionate to the pressure of the spring multiplied by the space through which the pressure can act. The potential element, which in this case decreases as work is performed, is the tension or elastic force of the spring. Space is necessary simply to allow this tension to expend itself in work. It is this tension, not space, which reappears as work or kinetic energy."[8] In the case of a sling with a perfectly' elastic cord whose elongation is proportional to the strain, the tension or potential element does not " decrease as work is performed ; " on the contrary, it Increases directly with the work ; and whatever the centrifugal velocity of the ball, the period of revolution remains constant.[9] The elasticity does not " expend itself in work." Vires acquirit eundo. As this is simply the " law of force " for this particular tension, it has no relation whatever to " conservation," which pertains entirely to work."
Again comparing gravitation to steam, whose pressure is weakened by the absorption of molecular motion in the rising piston, the writer repeats his questionings, " May not the same be equally true of gravity ". In fact, if gravity has a dynamical origin, it must hold equally true of gravity and of heat." Again recurring to Mr. Waterston's conception that " gravitation is a function of space," he would almost lead us to forget that " space cannot be a form of energy." Again endeavoring to fortify his assumptions by scholastic dogmas, he reiterates, " the conception of attraction does not represent the modus operandi of gravitation, because attraction implies action at a distance, or in other words, that a thing acts where it is not, which is just as impossible as that a thing can act when it is not." Again affirming that " there is no necessity for forming any conception of the cause of which it is the effect," his whole dissertation appears impelled by the necessity to " represent the modus operandi of gravitation."
The general conclusion arrived at by Mr. Croll appears to be: "Gravity in all probability is of the nature of an impact or a pressure. Some of our most eminent physicists state that the force of gravity must either result from impact of ultramundane corpuscles, in some respects analogous to that of the particles of a gas, (which has been found to be capable of accounting for gaseous pressure,) or it must result from difference of pressure in a substance continuously filling space, except where matter displaces it. That gravity is a force of the nature of pressure is I think beyond all doubt ; but that this pressure results from the impact of corpuscles, or from difference of pressure in a substance filling space, is purely hypothetical. Why not assume it to be a force, without calling in the aid of corpuscles or a medium filling space ?"[10]
If gravity be an abstract force, not requiring " the aid of corpuscles or [269] medium," it is not easy to perceive why it should so indubitably be "of the nature of pressure" rather than of tension. Is the phenomenon of the terrestrial tidal wave rendered any more intelligible by referring it to the action of a "pressure" from beneath, than by referring it, as the " most eminent physicists" do, to the action of a lunar tension from above ?
Rejecting a pressure-medium as purely hypothetical," the author yet thinks a pressure-force in gravity " is beyond all doubt"! not perceiving that the latter conception is as " purely hypothetical" as the former. A speculation born of metaphysical imaginings as to the "possible," framed in no physical relations to associate it with any known action, supported by no fact of observation, result of experiment, or sound induction, based on assumptions directly at variance with all ascertained laws or conditions of gravitative action, — if such a speculation be not "purely hypothetical," in what propulsive undulations, corpuscular chaos, or aetherial vortex, shall we seek to find a fitting subject for the appellation? And yet hypothetical as the speculation pre-eminently and undoubtedly is, — baseless, formless, insubstantial, — it comes to us with the prestige of a distinguished physicist as its propounder, and of a learned, association as its audience and recipient.
- ↑ L. E. D. Phil. Mag.. December, 1867, vol. xxxiv, p. 450.
- ↑ Examination of Sir William Hamilton's Philosophy, by John Stuart Mill, chap. xxiv, vol. ii, p. 245, of Am. edition.
- ↑ L. E. D. Phil. Mag., 1867, vol. xxxiv, p. 451.
- ↑ Phil. Mag., loco citat.. pp. 456,457.
- ↑ Phil. Mag., October, 1876, vol. ii, pp. 241, 242.
- ↑ Loco citat., pp. 242-244.
- ↑ Loco citat., pp. 244, 245.
- ↑ Phil. Mag., 1876, vol. ii, p. 247.
- ↑ The same isochronism exists with the revolving or conical pendulum whose vertical, height is constant, or with one whose ball revolves in the surface of a paraboloid.
- ↑ Loco citat., p. 252.