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Art. XIII.—On an Objection to Le Sage's Theory of Gravitation.
[Read before the Philosophical Institute of Canterbury, 5th May, 1897.]
The only theory to account for gravitation which has received any serious support is that due to Le Sage, who published his hypothesis in the “Transactions of the Royal Berlin Academy” in 178.4. He supposed gravity to be caused by streams of exceedingly minute bodies, which he calls ultramundane corpuscles, colliding with grosser matter, and the screening effect of one body on another gave rise to a tendency of the two bodies to come together. It can be shown that this force would fall off as the square of the distance increases, and that if we assume a sufficient openness in the structure of matter, the force will be proportioned to the product of the two masses involved. Though it might perhaps be too much to say that Le Sage's theory has been looked upon as being the final solution of the cause of gravity, yet it has had serious and careful consideration from such men as Kelvin, Isenkrahe, &c. There is one difficulty in it which Lord Kelvin has completely got over, and that is the objection that had been raised that if these ultra-mundane corpuscles did not rebound with less velocity when they approached gross matter there could be no gravitation, and that if they did lose velocity at impact sufficient heat would be generated to raise all gravitating bodies to a white heat.
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It is not my object at present to show how this difficulty may be overcome (as it has been naturally and without any fanciful assumptions); I merely quote it to show that scientific men of the highest standing have thought the theory sufficiently probable to spend time in its improvement, and as recently as 1895 Preston wrote a thesis on it, for which he was awarded the degree of Ph.D. at the University of Munich.
Now, there is an objection to this theory of Le Sage out of which I see no escape, and which lies at the root of the whole hypothesis. It will easily account for the force of gravity falling off as the square of the distance increases, and provided we assume a sufficient openness in the structure of matter it will account for proportionality to mass. But it is just that sufficient openness that we cannot grant, and, curiously enough, the evidence comes from a very unexpected quarter. It is, of course, well known that the gaseous laws, symbolically expressed as pv = RT, are merely approximations to the truth, and that they become less accurate approximations the more nearly a gas approaches its point of liquefaction. In order to obtain a more exact expression of the behaviour of gases Van der Waals,* in a paper “On the Continuity of the Gaseous and Liquid State of Matter” (a paper which has been translated by Threlfall and Adams, and published in English as one of the Memoirs of the Physical Society of London), improved this expression by the introduction of two small constants, and wrote the gaseous laws as
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(p + a/v2) (v — b) = RT.
As showing the degree of approximation reached by this formula, the following table of values observed for pv by Amagat, and of those calculated for pv by Baynes, from the above formula may be of interest. The gas under experiment was ethylene:—
| 1,000 pv. | 1,000 pv. | ||||
|---|---|---|---|---|---|
| p. | p. | ||||
| Obs. | Calc. | Obs. | Calc. | ||
| 31·58 | 914 | 895 | 133·26 | 520 | 520 |
| 45·80 | 781 | 782 | 176·01 | 643 | 642 |
| 59·38 | 522 | 624 | 233·58 | 817 | 805 |
| 72·86 | 416 | 387 | 282·21 | 941 | 940 |
| 84·16 | 399 | 392 | 329·14 | 1,067 | 1,067 |
| 94·53 | 413 | 413 | 398·71 | 1,248 | 1,254 |
| 110·47 | 454 | 456 |
[Footnote] * Kontinuitat der gas förmigen und flüssagen Zustande, Leipzig, 1881.
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The pressures are given in atmospheres, and the temperature was 20° C.
This table shows two things: It shows in the first place how hopelessly untrue the older formula pv = RT is when the pressure becomes large, for that formula at constant temperature gives
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pv = a constant;
and it also shows how very near an approximation to the truth Van der Waal's expression is, especially at abnormally high pressures.
It is, perhaps, unnecessary to lay further stress on the truth of Van der Waal's formula. It has played a most important part in physical research, and there is the strongest evidence in its favour.
Now, Nernst has shown* that it follows from this equation, combined with the critical pressure, volume, and temperature, “that at their respective boiling-points and at atmospheric pressure the molecules of the most various liquids, such as water, ether, carbon-disulphide, benzene chlorethane, ethylacetate, sulphurdioxide, &c., occupy a space very nearly 0.3 of the total apparent volume.” In other words, the intermolecular spaces are about double the volume of the molecules bn their superficial areas 2⅔: 1—i.e., the holes in the network have an area of about 1.58 times that of the threads.
Applying this to Le Sage's theory of gravity, it will be evident that if we consider the action of the ultra-mundane corpuscles in layers of matter situated at any considerable depth in a liquid at its boiling-point we must arrive at the conclusion that it will be nil, for the molecules near the surface must screen those more deeply situated, and there can be no bombardment. But unless these corpuscles reach every single molecule in a body, of whatever size, without any alteration in the direction of their motion in order to reach that molecule, the theory fails to account for the proportionality of gravity to mass. Gravity ought, were Le Sage's hypothesis true, to be a function of the temperature, and to depend on whether the gravitating body were in the gaseous, liquid, or solid state.
[Footnote] * Nernst, “Theoretical Chemistry,” translated by Palmer, p. 196.