290 A Short History of Astronomy [CH. XL 



of the three bodies can always be regarded as exercising 

 only a small influence on the relative motion of the other 

 two, but also by the facts that* the orbits of the planets 

 and satellites do not differ much from circles, and that 

 the planes of their orbits are in no case inclined at large 

 angles to any one of them, such as the ecliptic ; in other 

 words, that the eccentricities and inclinations are small 

 quantities. 



Thus simplified, the problem has been found to admit 

 of solutions of considerable accuracy by methods of 

 approximation. * 



In the case of the system formed by the sun, earth, 

 and moon, the characteristic feature is the great distance 

 of the sun, which is the disturbing body, from v the other 

 two bodies ; in the case of the sun and two planets, the 

 enormous mass of the sun as compared with the disturbing 

 planet is the important factor. Hence the methods of 

 treatment suitable for the two cases differ, and two sub- 

 stantially distinct branches of the subject, lunar theory and 

 planetary theory, have developed. The problems presented 

 by the motions of the satellites of Jupiter and Saturn, though 

 allied to those of the lunar theory, differ in some important 

 respects, and are usually treated separately. 



229. As we have seen, Newton made a number of 

 important steps towards the solution of his problem, but 

 little was done by his successors in his own country. On 

 the Continent also progress was at first very slow. The 

 Principia was read and admired by most of the leading 

 mathematicians of the time, but its principles were not 

 accepted, and Cartesianism remained the prevailing philo- 

 sophy. A forward step is marked by the .publication by 

 the Paris Academy of Sciences in 1720 of a memoir written 

 by the Chevalier de Louville (1671-1732) on the basis of 

 Newton's principles ; ten years later the Academy awarded 

 a prize to an essay on the planetary motions written by 

 John Bernouilli (1667-1748) on Cartesian principles, a 

 Newtonian essay being put second. In 1732 Maupertuis 

 (chapter x., 221) published a treatise on the figure of the 



* The arithmetical processes of working out, figure by figure, a 

 non-terminating decimal or a square root are simple cases of successive 

 approximation. 



