This would imply that the great annular system of the Milky Way is unstable. But if so, its existence at all is a greater mystery than ever. Although in detail its structure is very irregular, as a whole it is wonderfully symmetrical; and it seems quite impossible that its generally circular ring-like form can be the result of the chance aggregation of matter from any pre-existing different form. Star-clusters are equally unstable, or, rather, nothing is known or can be predicated about their stability or instability, according to Professors Newcomb and Darwin. Mr. E.T. Whittaker (Secretary to the Royal Astronomical Society), to whom Professor G. Darwin sent my questions, writes:--'I doubt whether the principal phenomena of the stellar universe are consequences of the law of gravitation at all. I have been working myself at spiral nebulæ, and have got a first approximation to an explanation--but it is electro-dynamical and not gravitational. In fact, it may be questioned whether, for bodies of such tremendous extent as the Milky Way or nebulæ, the effect which we call gravitation is given by Newton's law; just as the ordinary formulæ of electrostatic attraction break down when we consider charges moving with very great velocities.' Accepting these statements and opinions of two mathematicians who have given special attention to similar problems, we need not limit ourselves to the laws of gravitation as having determined the present form of the stellar universe; and this is the more important because we may thus escape from a conclusion which many astronomers seem to think inevitable, viz. that the observed proper motions of the stars cannot be explained by the gravitative forces of the system itself. In chapter VIII. of this work I have quoted Professor Newcomb's calculation as to the effect of gravitation in a universe of 100 million stars, each five times the mass of our sun, and spread over a sphere which it would take light 30,000 years to cross; then, a body falling from its outer limits to the centre could at the utmost acquire a velocity of twenty-five miles a second; and therefore, any body in any part of such a universe having a greater velocity would pass away into infinite space. Now, as several stars have, it is believed, much more than this velocity, it follows not only that they will inevitably escape from our universe, but that they do not belong to it, as their great velocity must have been acquired elsewhere. This seems to have been the idea of the astronomer who stated that, even at the very moderate speed of our sun, we should in five million years be deep in the actual stream of the Milky Way. To this I have already sufficiently replied; but I now wish to bring before my readers an excellent illustration of the importance of the late Professor Huxley's remark, that the results you got out of the 'mathematical mill' depend entirely on what you put into it.