Page:A short history of astronomy(1898).djvu/46

6 another pair of stars,, is the angle. The two stars and appear nearer together than do  and, or farther apart, according as the angle  is less or greater than the angle. But if we represent the stars by the corresponding points p, q, r, s on the celestial sphere, then (by an obvious property of the sphere) the angle (which is the same as p  q) is less or greater than the angle  (or r  s) according as the arc joining / q on the sphere is less or greater than the arc joining r s, and in the same proportion; if, for example, the angle r o s is twice as great as the angle p o Q, so also is the arc p q twice as great as the arc r s. We may therefore, in all questions relating only to the directions of the stars, replace the angle between the directions of two stars by the arc joining the corresponding points on the celestial sphere, or, in other words, by the distance between these points on the celestial sphere. But such arcs on a sphere are easier both to estimate by eye and to treat geometrically than angles, and the use of the celestial sphere is therefore of great value, apart from its historical origin. It is important to note that this apparent distance of two stars, i.e. their distance from one another on the celestial sphere, is an entirely different thing from their actual distance from one another in space. In the figure, for example, is actually much nearer to s than it is to, but the apparent distance measured by the arc q s is several times greater than q p. The apparent distance of two points on the celestial sphere is measured numerically by the angle between the lines joining the eye to the two points, expressed in degrees, minutes, and seconds.

We might of course agree to regard the celestial sphere as of a particular size, and then express the distance between two points on it in miles, feet, or inches; but it is practically very inconvenient to do so. To say, as some people occasionally do, that the distance between two stars is so many feet is meaningless, unless the supposed size of the celestial sphere is given at the same time.

It has already been pointed out that the observer is always at the centre of the celestial sphere; this remains