The Gentleman's Magazine/Volume 253/July 1882/The Birth of the Moon

I ASSUME, as a matter of course, that all who read these Notes have read Mr. Proctor's paper on this subject in the last number of this Magazine, and that they agree with me in appreciating the great value of such contributions to the intellectual progress of the present generation. Proctor is doing for the English-speaking peoples, and Flammarion for the French, what has never been well and widely done before, viz., bringing the most sublime results of mathematical demonstration and mathematical speculation within the reach of all intelligent men and women.

We all have a natural tendency to exalt our own special branch of study, and this is perhaps desirable. It appears to me that mathematicians are prone to go further than others in this direction; their usual assumption being that whatever has been demonstrated mathematically must be infallibly true. No mathematician of corresponding attainments is more free from this or any other form of scholastic dogmatism than Mr. Proctor, and yet this mathematical self-righteousness crops out occasionally, as in the paper above named, where, referring to Mr. Danvin, he says, "the reasoning relating to this part of his views does not belong to the sure domain of mathematics, but to speculation."

This reads oddly when closely following a description of how Adams, "twenty years or so ago, discovered a notable flaw in Laplace's reasoning," which was purely mathematical; and further, that both Leverrier and Pontecoulant have rejected Adams' results, the latter "even denouncing Adams' method of treating the subject as analytical legerdemain."

All this was in "the sure domain of mathematics" of the purest and highest order, and among mathematical giants; the difference of result was quantitative, i.e. mathematical, and not a mere fractional percentage, the result obtained by Adams being "only one-half of what Laplace had made it."

Such instances of error to which mathematicians, like all other human beings, are ever liable, enforce the necessity of continual verification of mathematical conclusions by comparing them with facts revealed by observation and experiment.

I will thus examine the conclusions of Darwin and Ball as expounded, and with certain modifications adopted, by Proctor in the paper above named.

They assume with the customary matter-of-course confidence (which always astonishes me as coming from such unimaginative people) that the sun and all the planets of our solar system began life with a nebulous infancy, proceeded through a gaseous or vaporous childhood and liquid youth to a semi-solid puberty, when a film of solid crust crept over their liquid surface like whiskers on the cheeks of an adolescent.

It was, if I understand the theory rightly, at or about this period that the parturition of satellites occurred, according to Darwin and Ball; or somewhat earlier, according to Proctor. All agree in attributing the detachment of the satellite fragment or fragments to the tidal disturbances of the sun. They differ only as to the mode of operation of this agent. As the tide-raising power varies "not as the inverse square, but as the inverse cube" (see page 680), it is evident that the planets near to the sun must during their youth have suffered vastly greater tidal disturbance, or moon-generating agency, than the more distant, and therefore should have by far the largest families of satellites. Applying this test to the theory, it breaks down completely; for, instead of the satellites increasing in numbers with the proximity of the planets to the sun, the opposite is the case.

The two nearest planets, Mercury and Venus, have no satellites; the next, our earth, has one; then, farther on, Mars has two; Jupiter, separated by a great gap, has four; Saturn, still farther, has eight, besides the multitude of pebble-moons forming his rings. Thus far the facts are in direct and nearly quantitative contradiction to the theory. So far as we know, Uranus and Neptune have not the multitude of satellites required for establishing a law of increase with distance from the sun. I say, "so far as we know," because their distance is so great that if they had hundreds of such satellites as those of Mars we could not see them with any telescopic help at present available.

The effect of dimensions of the planet must of course be considered as well as that of distance from the sun in estimating the tide-raising efficiency of solar attraction; but by comparing Jupiter and Saturn we have both of the tide-raising agencies so combined as to operate greatly in favour of Jupiter, and yet we find that his satellites are so much fewer.

Then, again, if we compare Venus and the earth, two planets differing in dimension by a mere fraction, we find that, instead of Venus indicating the results of a nearly threefold greater moon-generating action of the sun, it has not three moons, but no moon.

Man presents another contradiction to those subsequent proceedings of the satellites which the theory expounds. The solidity of Mars is that of a middle-aged planet, according to the theoretical description of planet-growth; but the position of its satellites so near to their primary is quite juvenile. The theory imperatively and mathematically demands that the distances of both Phobos and Deimos from their primary should be far greater than observation has proved them to be.