The apparent brightness of a star, as we see it from the earth, depends upon two causes--its intrinsic brilliancy or the quantity of light which it actually emits, and its distance from us. It follows that if all the stars were of equal intrinsic brightness we could determine their relative distances by measuring the respective amounts of light which we receive from them. The quantity of light in such a case varies inversely as the square of the distance. This will be made evident by Fig. 1, where S represents the position of a star, regarded as a luminous point, while A and B are screens placed at such a distance that each will receive the same amount of light from the star. If the screen B is twice as far as the screen A, its sides must be twice as large as those of A in order that it shall receive all the light that would fall on A. In this case its surface will be four times the surface of A. It is then evident that any small portion of the surface of B will receive one fourth as much light as an equal portion of surface A. Thus an eye or a telescope in the position B will receive from the star one fourth as much light as in the position A, and the star will seem one fourth as bright. [Illustration: FIGURE 1.] The fact is, however, that the stars are very unequal in their actual brightness, and in consequence the apparent magnitude of a star gives us no clue to its distance. Among the nearer of the stars are some scarcely, if at all, visible to the naked eye, while among the brighter ones are several whose distances are immeasurably great. A remarkable example is that of Caropes, the second brightest star in the heavens. For these reasons astronomers are obliged to content themselves, in the first place, with determinations of the actual amount of light that the various stars send to us, or their apparent brilliancy, without regard to their distance or actual brilliancy. The ancient astronomers divided all the stars they could see into six classes, the number expressing the apparent brightness being called the magnitude of the star. The brightest ones, numbering in all about fourteen, were said to be of the first magnitude. The fifty next in brightness were said to be of the second magnitude. Three times as many, an order fainter, were of the third magnitude. The progression was continued up to the sixth magnitude, which included those which were barely visible. As the stars are actually of every degree of apparent brilliancy, no sharp line of demarkation could be drawn between those of one magnitude and those of the magnitude next higher. Hence, different observers made different estimates, some calling a star of the second magnitude which others would call of the first, while others would designate a star of the third magnitude which others would call of the second. It is therefore impossible to state with absolute numerical precision what number of stars should be regarded of one magnitude and what of another.