characteristics is the fact that the distances between the masses which compose the system are very much greater than the dimensions of the masses themselves, of quite a higher order of magnitude. The diameters of the planets are measured by thousands of miles, the distances between them by tens of millions. The second characteristic consists in the approximately spherical shape of the planets themselves, and in the fact that by a mathematical consequence of the actual law of gravitation a sphere acts upon any outside body as if all its mass were concentrated at its centre, a most interesting peculiarity not true under many other supposable laws. These two facts very materially simplify the problem of the motions of celestial mechanics.

But just as the first of these peculiarities helps us to comprehension of the relative dimensions of the solar system, so does it hinder us in determining its actual dimensions. For this determination depends upon a problem in celestial surveying, the finding the distance to a body by measuring the angle it subtends from the two ends of a base-line. Now, as unfortunately we cannot get off the earth for the purpose, our base-line is at most the diameter of the earth itself, and as the distance to the other body immensely exceeds our own size, the angle to be measured becomes so excessively small as