SEQUEL TO THE EPOCH OF NEWTON. 225 



Newton had introduced, was rendered possible by 

 the labours of the great constellation of mathema- 

 ticians of whom we have spoken in the last book, 

 Clairaut, Euler, D'Alembert, and their successors; 

 and it was carried into effect in the course of the 

 last century. Thus Lalande applied Clairaut's theory 

 to Mars, as did Mayer ; and the inequalities in this 

 case, says Bailly 19 in 1785, may amount to two 

 minutes, and therefore must not be neglected. La- 

 lande determined the inequalities of Venus, as did 

 Father Walmesley, an English mathematician; these 

 were found to reach only to thirty seconds. 



The Planetary Tables 20 which were in highest 

 repute, up to the end of the last century, were those 

 of Lalande. In these, the perturbations of Jupiter 

 and Saturn were introduced, their magnitude being 

 such that they cannot be dispensed with; but the 

 Tables of Mercury, Venus, and Mars, had no pertur- 

 bations. Hence these latter Tables might be con- 

 sidered as accurate enough to enable the observer 

 to find the object, but not to test the theory of per- 

 turbations. But when the calculation of the mutual 

 disturbances of the planets was applied, it was 

 always found that it enabled mathematicians to 

 bring the theoretical places to coincide more exactly 

 with those observed. In improving, as much as 

 possible, this coincidence, it is necessary to deter- 

 mine the mass of each planet; for upon that, 

 according to the law of universal gravitation, its 

 19 Ast. Mod. Hi. 170. * Airy. Report on Ast. to Brit. Ass. 1&32. 

 VOL. II. Q, 



