a star varies inversely as the square of its distance. If the distance of a star be doubled, then its brightness is decreased to one-fourth. If the star be removed to a distance three times its original amount, then the apparent brightness declines to one-ninth. We may therefore infer that if a star be withdrawn to a distance which is twelve times that which it has at present, then the lustre of the star will be reduced to one hundred and forty-fourth part of its primitive value. This reasoning shows that any star which is now situated at the distance and maintains the proper motion we have supposed, will in the course of a million years have its apparent lustre reduced to the one hundred and forty-fourth part of that which it now displays. It need hardly be said that such a reduction of brightness would be certainly sufficient to render most of the stars wholly invisible. Indeed, it is only stars which possess exceptional lustre at their present distance which would continue to be visible, even as telescopic objects, when they had suffered so serious a loss.
These considerations lead to consequences of a remarkable character. We have adopted an average value of the proper motions, and it appears that on such an assumption it is highly improbable that any two stars not physically connected as a binary pair, should remain in comparative proximity for a period so long as a million of years. The case may perhaps be conveniently likened to that of a number of ships which are each bent on their different courses. At any particular time each of these vessels will generally have several other ships in view, but as each moves on its way the distances gradually alter, so that in the course of an hour or two the vessels
