440 HISTORY OF PHYSICAL ASTRONOMY. 



it was carried into effect in the course of the last century. Thus La- 

 lande applied Clairaut's theory to Mars, as did Mayer ; and the inequal- 

 ities in this case, says Bailly 20 in 1*785, may amount to two minutes, 

 and therefore must not be neglected. Lalande determined the inequal- 

 ities of Venus, as did Father Walmesley, an English mathematician ; 

 these were found to reach only to thirty seconds. 



The Planetary Tables 2 ' 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 perturbations. Hence these latter Tables might be 

 considered as accurate enough to enable the observer to find the ob- 

 ject, but not to test the theory of perturbations. But when the calcu- 

 lation 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 determine the 

 mass of each planet ; for upon that, according to the law of universal 

 gravitation, its disturbing power depends. Thus, in 1813, Lindenau 

 published Tables of Mercury, and concluded, from them, that a consid- 

 erable increase of the supposed mass of Venus was necessary to recon- 

 cile theory with observation. 22 He had published Tables of Venus in 

 1810, and of Mars in 1811. And, in proving Bouvard's Tables of 

 Jupiter and Saturn, values were obtained of the masses of those plan- 

 ets. The form in which the question of the truth of the doctrine of 

 universal gravitation now offers itself to the minds of astronomers, is 

 this : — that it is taken for granted that it will account for the motions 

 of the heavenly bodies, and the question is, with what supposed masses 

 it will give the best account. 23 The continually increasing accuracy of 

 the table shows the truth of the fundamental assumption. 



The question of perturbation is exemplified in the satellites also. 



2° Ast. Mod. iii. 170. 21 Airy, Report on Ast. to Brit. Ass. 1832. 



» Airy, Report on Ast. to Brit. Ast. 1832. 



23 Among the most important corrections of the supposed masses of the planets, 

 we may notice that of Jupiter, by Professor Airy. This determination of Jupiter's 

 mass was founded, not on the effect as seen in perturbations, but on a much more 

 directdatum, the timeof revolution of his fourth satellite. It appeared, from this cal- 

 culation, that Jupiter's mass required to be increased by about l-80th. This result 

 agrees with that which has been derived by German astronomers from the pertur- 

 bations which the attractions of Jupiter produce in the four new planets, and has 

 been generally adopted as an improvement of the elements of our system. 



