300 A Short History of Astronomy [CH. xi. 



slow diminution in the obliquity of the ecliptic. To these 

 may be added the alterations in the rates of motion of 

 Jupiter and Saturn discovered by Halley (chapter x., 204). 



Newton had shewn generally that the perturbing effect of 

 another planet would cause displacements in the apses 

 of any planetary orbit, and an alteration in the relative 

 positions of the planes in which the disturbing and disturbed 

 planet moved ; but he had made no detailed calculations. 

 Some effects of this general nature, in addition to those 

 already known, were, however, indicated with more or less 

 distinctness as the result of observation in various planetary 

 tables published between the date of the Principia and the 

 middle of the i8th century. 



The irregularities in the motion of the earth, shewing 

 themselves as irregularities in the apparent motion of the 

 sun, and those of Jupiter and Saturn, were the most 

 interesting and important of the planetary inequalities, and 

 prizes for essays on one or another subject were offered 

 several times by the Paris Academy. 



The perturbations of the moon necessarily involved by 

 the principle of action and reaction corresponding though 

 smaller perturbations of the earth ; these were discussed on 

 various occasions by Clairaut and Euler, and still more 

 fully by D'Alembert;. 



In Clairaut's paper of 1747 ( 233) he made some 

 attempt to apply his solution of the problem of three bodies 

 to the case of the sun, earth, and Saturn, which on account 

 of Saturn's great distance from the sun (nearly ten times 

 that of the earth) is the planetary case most like that of the 

 earth, moon, and sun (cf. 228). 



Ten years later he discussed in some detail the perturba- 

 tions of the earth due to Venus and to the moon. This 

 paper was remarkable as containing the first attempt to 

 estimate masses of celestial bodies by observation of per- 

 turbations due to them. Clairaut applied this method to 

 the moon and to Venus, by calculating perturbations in 

 the earth's motion due to their action (which necessarily 

 depended on their masses), and then comparing the results 

 with Lacaille's observations of the sun. The mass of the 

 moon was thus found to be about / T an( ^ tnat f Venus 

 that of the earth ; the first result was a considerable 



