308 A Short History of Astronomy [CH. xi. 



239. With the exception of Lagrange's paper on libration, 

 nearly all his and Laplace's important contributions to 

 astronomy were made when Clairaut's and D'Alembert's 

 work was nearly finished, though Euler's activity con- 

 tinued for nearly 20 years more. Lagrange, however, 

 survived him by 30 years and Laplace by more than 40; and 

 together they carried astronomical science to a far higher 

 stage of development than their three predecessors. 



240. To the lunar theory Lagrange contributed com- 

 paratively little except general methods, applicable to this 

 as to other problems of astronomy ; but Laplace devoted 

 great attention to it. Of his special discoveries in the 

 subject the most notable was his explanation of the secular 

 acceleration of the moon's mean motion (chapter x., 201), 

 which had puzzled so many astronomers. Lagrange had 

 attempted to explain it (1774), and had failed so com- 

 pletely that he was inclined to discredit the early observa- 

 tions on which the existence of the phenomenon was 

 based. Laplace, after trying ordinary methods without 

 success, attempted to explain it by supposing that gravita- 

 tion was an effect not transmitted instantaneously, but 

 that, like light, it took time to travel from the attracting 

 body to the attracted one ; but this also failed. Finally 

 he traced it (1787) to an indirect planetary effect. For, as it 

 happens, certain perturbations which the moon experiences 

 owing to the action of the sun depend among other 

 things on the eccentricity of the earth's orbit ; this is one 

 of the elements ( 236) which is being altered by the 

 action of the planets, and has for many centuries been very 

 slowly decreasing ; the perturbation in question is there- 

 fore being very slightly altered, and the moon's average 

 rate of motion is in consequence very slowly increasing, or 

 the length of the month decreasing. The whole effect is 

 excessively minute, and only becomes perceptible in the 

 course of a long time. Laplace's calculation shewed that 

 the ir.oon would, in the course of a century, or in about 

 1,300 complete revolutions, gain about 10" (more exactly 

 io"'2) owing to this cause, so that her place in the sky 

 would differ by that amount from what it would be if this 

 disturbing cause did not exist; in two centuries the angle 

 gained would be 40", in three centuries 90", and so on, 



