282, a8 3 ] The Distance of the Sun 365 



members of the solar system; and Laplace had deduced 

 a value of the solar parallax from lunar theory. Improve- 

 ments in gravitational astronomy and in observation of the 

 planets and moon during the present century have added 

 considerably to the value of these methods. A certain 

 irregularity in the moon's motion known as the paraUactic 

 inequality, and another in the motion of the sun, called 

 the lunar equation, due to the displacement of the earth 

 by the attraction of the moon, alike depend on the ratio 

 of the distances of the sun and moon from the earth ; if 

 the amount of either of these inequalities can be observed, 

 the distance of the sun can therefore be deduced, that of 

 the moon being known with great accuracy. It was by a 

 virtual application of the first of these methods that Hansen 

 ( 286) in 1854, in the course of an elaborate investigation 

 of the lunar theory, ascertained that the current value of 

 the sun's distance was decidedly too large, and Leverrier 

 ( 288) confirmed the correction by the second method in 

 1858. 



Again, certain changes in the orbits of our two neigh- 

 bours, Venus and Mars, are known to depend upon the 

 ratio of the masses of the sun and earth, and can hence 

 be connected, by gravitational principles, with the quantity 

 sought. Leverrier pointed out in 1861 that the motions 

 of Venus and of Mars, like that of the moon/ were incon- 

 sistent with the received estimate of the sun's distance, and 

 he subsequently worked out the method more completely 

 and deduced (1872) values of the parallax. The displace- 

 ments to be observed are very minute, and their accurate 

 determination is by no means easy, but they are both 

 secular (chapter XL, 242), so that in the course of time 

 they will be capable of very exact measurement. Leverrier's 

 method, which is even now a valuable one, must therefore 

 almost inevitably outstrip all the others which are at present 

 known; it is difficult to imagine, for example, that the 

 transits of Venus due in 2004 and 2012 will have any 

 value for the purpose of the determination of the sun's 

 distance. 



283. One other method, in two slightly different forms, 

 has become available during this century. The displace- 

 ment of a star by aberration (chapter x., 210) depends 



