The advance of photography : its history and modern applications (1911)

312 THE ADVANCE OF PHOTOGRAPHY observers who look with telescopes at a star x. and measure the angles which the rays x a, x b make with the line a b : it can be determined from both angles and the line a b (which is easily found) what is the distance of the star from a or b. This is the trigonometrical method, and it gives reliable results, if the distance of the star is not too great ; thus, for example, the distance of the moon, which is about thirty of the earth's diameters, is easily ascertained. If the star to be measured is too remote, the rays a x and b x are nearly parallel, no difference exists between the two angles at a and b. and the trigonometrical method J.s useless. This is the case with the sun, which is ninety-three millions of miles from the earth. We can therefore only ascertain its distance by indirect methods. According to a law discovered by the celebrated astronomer Kepler, the squares of the periods of revolution of the planets vary as the cubes of their distances from the sun. Thus, if the period of the earth's revolution is U, and that of Venus u. the distance of the earth E, that of Venus e. according to this law, U* : ir=E* : e3. If the cube root is extracted from both, we have — 3 8 JU : su'2=E: e, hence, : 3 3 JU2— SV : s'u-=E — e : e. But E — e is the distance between the earth and Venus. When this has been determined, three terms of the proportion are known ; for the periods of the revolutions of Venus and the earth are accurately known. Then, by simple rule of three, the fourth term, e, can be found ; that is, the distance of Venus from the sun. If to this is