Kinetic Theories of Gravitation/Herapath, 1816

by William Bower Taylor

Passing over a few names of less note in this connection, (Berthier, Churcol, and others,) we find a somewhat more developed attempt at unveiling the standing enigma, presented in the writings of John Herapath, of Bristol, England. In a preliminary essay, published in Thomson's Annals of Philosophy, "On the Physical Properties of Gases," he announced the hypothesis of "one cause for heat, light, gravitation, electricity, cohesion, aerial repulsion, &c., from which all these flow, and are easily deducible ; and their effects may be computed by mathematical induction, [deduction ?] It shows us that gravitation, cohesion, and affinity, are but the same thing under different modifications; that the differences of the two latter arise from a difference in the figures and sizes only of the particles; that attraction and repulsion are not properties of matter."^[1] This hypothesis thus briefly stated by its author, at the age of twenty-three years, does not appear to have been further publicly elaborated for five years.

In 1821, Herapath contributed to the same journal a memoir entitled "A Mathematical Inquiry into the Causes, Laws, and principal Phenomena of Heat, Gases, Gravitation, &c.," memorable as presenting by far the fullest and clearest exposition of the mechanical theory of heat and of gases that had at that time been propounded. He states that about ten years earlier, while engaged in investigating an anomaly found in his calculations of lunar equation, his attention had been accidentally directed to Newton's suggestions as to the cause of gravitation ; and he proceeds :

"If gravitation depends upon the action of an elastic medium such as Newton supposed, which grows rarer aud rarer as you approach the dense bodies of the sun and planets, there ought to be some reason for this variation of density ; and as Newton has not, as far as I could perceive, given any, I began to consider what it might be. And after some little thinking, it occurred to me that if this medium be of the same nature as our atmosphere and other gaseous bodies, that is, if it be capable of being expanded by heat and contracted by cold, then the sun being a very hot body, and the heat being so much the greater the nearer we are to him, the density of the medium ought therefore to decrease with a decreasing and increase with an increasing distance, the same as Newton would have it. And because we find by experience that dense solid bodies receive heat more strongly than much rarer [224] ones, particularly than gases, the dense bodies of the planets being heated by the solar rays as well as by the medium about them, ought it appeared to me, to be hotter than this medium, and consequently ought to produce the same effects on the medium as the sun, though cot in so great a degree. Therefore if as Newton imagines, the particles of the planets be impelled toward the sun by the inequality of the pressure on their further and nearer sides, the denser parts of the medium pressing more forcibly than the rarer, the same reason will likewise hold good why bodies should be impelled toward the planets an<l other material parts of the system."^[2]

After speaking of the discouragement resulting from his unsuccessful attempts at arriving at the mathematical laws of heat, he proceeds: " Yet sometimes when my thoughts were involuntarily turned this way, the idea that two inanimate bodies could act on each other at a distance without some other means than that of a mere tendency or inclination in them to approach, would appear so strongly unphilosophical, and the apparent coincidence of several phenomena with conclusions I had drawn from my notions of gravitation so very seductive, that I could not avoid thinking the views I had taken were tolerably correct ; and that there was only wanting the direction of some happy idea, which patient perseverance might possibly attain, to set the whole in a clear and irrefragable light. Thus between hope and despair, between unceasing attempts and mortifying failures, I continued until May, 181-1, at which time my ideas of heat underwent a complete revolution. Previous to this time I had conceived heat to be the effect of an elastic fluid, and on this supposition, had repeatedly attempted to reduce its laws to mathematical calculation ; but uniform disappointment at length induced me to give this hypothesis a careful investigation, by comparing it with general and particular phenomena. The result of this investigation convinced me that heat could not be the consequence of an elastic fluid. . . . After I had revolved the subject a few times in my mind, it struck me that if gases instead of having their particles endued with repulsive forces, subject to so curious a limitation as Newton proposed, were made up of particles or atoms mutually impinging on one another and the sides of the vessel containing them, such a constitution of aeriform bodies would not only be more simple than repulsive powers, but as far as I could perceive, would be consistent with phenomena in other respects, and would admit of an easy application of the theory of heat by intestine motion. Such bodies I easily saw possessed several of the properties of gases; for instance, they would expand, and if the particles be vastly small, contract almost indefinitely; their elastic force would increase by an increase of motion or temperature, and diminish by a diminution ; they would conceive heat rapidly, and conduct it slowly ; would generate heat by sudden compression, [225] and destroy it by sudden rarefaction ; and any two having ever so small a communication, would quickly and equally intermix."^[3]

Fanciful as are the considerations which led Herapath to this conclusion, it may be doubted whether a better statement of the dynamic theory of heat, and the modern view of gaseous temperature, has been published in the last half century. Certainly none can be found preceding it. The scientific world was not then however prepared by a sufficient induction to fully appreciate this theory.

These views of thermogenetic gravitation were amplified by their author at a later period, and included in an elaborate and excellent treatise on the general principles of physics, published in 1847, in which work they form the concluding portion, or book iv, comprising four sections.^[4]

Herapath saw very clearly that a theory of molecular collision cannot dispense with resilient impacts ; but he announced the startling paradox that atoms "perfectly hard" would on striking each other, rebound just as though they were elastic. This very difficult thesis is discussed at some length (though certainly not convincingly) in his general work.^[5] in a chapter on " the collision of hard bodies." The conception of a repellant propensity in the atoms is of course, excluded by the very spirit of the hypothesis. " Only two properties to matter are assumed, namely, inertia and absolute hardness. . . . Our theory deprives the particles of repulsion, or of any active properties, and merely assumes that airs are composed of small particles moving about in all possible directions, and keeping up their state as airs by their mutual collisions and reflections from one another and the sides of the containing vessels. From this simple property, and that of heat consisting in corpuscular motion, the whole known laws of gases are deduced with mathematical rigor."^[6] Unfortunately "two properties" are wholly insufficient either to set or to keep a system of molecules in motion. Matter thus constituted, (with only " two properties,") with any amount of motion superimposed, could never make a cosmos. The " stubborn fact" of elasticity has indeed been the insuperable obstacle and embarrassment of all kinetic schemes of molecular physics.

" By extending the principles to find the temperatures of the planets, we arrive at an interesting conclusion, namely : supposing them to be all of the density of our earth, we bring out very nearly the amount of gravitation toward each of them which is actually found to exist. Mercury is not included, as our knowledge about him is uncertain." (Introduction, p. xxv.) Mercury however is excluded, because on the assumption that the absolute temperatures of the planets are inversely as their distances from the sun, the temperature of this inner planet is [226] found to be too high to satisfy the conditions of the calculation.^[7] If "the amount of gravitation toward each" planet is at all indicated by the relative distance-periods of their satellites, it is very clear that they cannot have the same density.

It might be expected that with the range of temperatures at our command, the influence of heat on attraction could be subjected to the test of direct experiment. It is admitted that " We have no distinct evidence of attraction being either augmented or lessened by heat.^[8]

The radical defect of this ingenious application of the differential of heat-motion as the impelling force of gravity lies in the fallacy that any pressure-differences would, under the circumstances, result from temperature-differences. Our author says : " In Newton's day the notion of a fluid which had no visible tendency to one part of space more than to another, keeping up an equilibrium with itself, and yet able to press heavier on one side of a body within it than on the other, was quite enough to gain incredulity."^[9] Nor is it easy to perceive how the notion is made more credible in our day. The rarefaction of a free gas by heat is the direct effect of its increased elastic tension or pressure, and the two are proportional. In other words, if upon the planetary hemisphere exposed to the sun there were fewer impacts of gaseous molecules in a unit of time than on the outer or night hemisphere, these impacts would have a correspondingly higher velocity, so that the whole moment of impulse (or pressure) on the two sides would be precisely equal.

It is doubtful whether this hypothesis (even supposing it operative) could really satisfy any of the six conditions heretofore propounded. With regard to the second postulate, it is evident that the mass of the attracting body cannot determine the quantity of attractive action, if heat be the efficient cause. This is very frankly conceded by Herapath, who says of the mass ratio : " This law has been proved experimentally by Sir Isaac Newton ;• but though this be true, the converse case does not according to our principles hold good, namely that the attractive forces of bodies are directly proportional to their quantities of matter. Our principles do not therefore corroborate Newton's third law of motion, respecting the equality of action and reaction in attracting forces; for by our theory, a body might by the agency of the fluid medium, be impelled toward another, without any reciprocal action ; which is by no means surprising if we consider attraction not to be an inherent or essential property of matter, but merely the action of a third body."^[10] The sufficient answer to all which is, that not only is it unconfirmed by any experimental research, but all experience contradicts the assumption. [227]

The force of the objection contained in our fourth condition precedent is thus courageously confronted and defied : " It might be conceived that the attraction would be less on a body moving toward the central body, and greater on one moving from it, which is contrary to what we find by experience. Though regarded mathematically, such an inference would be strictly true, yet since the difference between the forces ' will depend on the activity of the medium, and since this activity will be increased in proportion to the tenuity of the parts of the medium, it is evident that the aetherial atoms may be so small, and the activity of the medium consequently so great, that the swiftest motions we know of could produce no sensible difference in the vigor of its action." And with a marvelous boldness of assumption he adds : " We may hence fairly conclude that there might be a fluid medium pervading the heavens, and all bodies, of such activity that no sensible difference could be observed in the intensity of its action on bodies in a state of quiescence, or moving with a velocity not only six million, but several million million times greater than that of light !"^[11]

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1. Annals of Philosophy, July, 1816, vol. viii, pp. 58, 59.
2. Annals of Philosophy, 1821, vol. xvii, cr of new series, vol. i, p. 276.
3. Loco citat., p. 278.
4. Mathematical Physics. By John Herapath. 2 vols. 8vo. London, 1847.
5. Math. Phys., vol. i, pp. 106-137. Huyghens and Wren had both (a century and a half earlier) maintained the same doctrine.
6. Math. Phys., Introduction, pp. xvii, xviii.
7. Math. Phys., vol. ii, p. 318.
8. Math. Phys., Introduction, p. xv.
9. Loco citat., Introduction, p. xxxvi.
10. Annals of Philosophy, new series, vol. i, p. 411 ; and Math. Phys., vol. i, p. 9.
11. Annals of Philosophy, new series, vol. i, p. 410.