SEQUEL TO THE EPOCH OF NEWTON. 43& 



preface to the second edition of the Principia, Cotes remarks, 18 that 

 the perturbation of Jupiter and Saturn is not unknown to astrono- 

 mers. In Halley's Tables it was noticed 19 that there are very great 

 deviations from regularity in these two planets, and these deviations 

 are ascribed to the perturbing force of the planets on each other ; but 

 the correction of these by a suitable equation is left to succeeding 

 astronomers. 



The motion of the planes and apsides of the planetary orbits was 

 one of the first results of their mutual perturbation which was ob- 

 served. In 1706, La Hire and Maraldi compared Jupiter with the 

 Rudolphine Tables, and those of Bullialdus: it appeared that his 

 aphelion had advanced, and that his nodes had regressed. In 1728, 

 J. Cassini found that Saturn's aphelion had in like manner travelled 

 forwards. In 1720, when Louville refused to allow in his solar tables 

 the motion of the aphelion of the earth, Fontenelle observed that this 

 was a misplaced scrupulousness, since the aphelion of Mercury certainly 

 advances. Yet this reluctance to admit change and irregularity was 

 not yet overcome. When astronomers had found an approximate and 

 apparent constancy and regularity, they were willing to believe it ab- 

 solute and exact. In the satellites of Jupiter, for instance, they were 

 unwilling to admit even the eccentricity of the orbits ; and still more, 

 the variation of the nodes, inclinations, and apsides. But all the fixed- 

 ness of these was successively disproved. Fontenelle in 1732, on the 

 occasion of Maraldi's discovery of the change of inclination of the fourth 

 satellite, expresses a suspicion that all the elements might prove liable 

 to change. " AVe see," says he, " the constancy of the inclination al- 

 ready shaken in the three first satellites, and the eccentricity in the 

 fourth. The immobility of the nodes holds out so far, but there are 

 strong indications that it will share the same fate." 



The motions of the nodes and apsides of the satellites are a necessary 

 part of the Newtonian theory ; and even the Cartesian astronomers 

 now required only data, in order to introduce these changes into their 

 Tables. 



The complete reformation of the Tables of the Sun, Planets, and 

 Satellites, which followed as a natural consequence from the revolution 

 which Newton had introduced, was rendered possible by the labors of 

 the great constellation of mathematicians of whom we have spoken in 

 the last book, Clairaut, Euler, D'Alembert, and their successors ; and 



18 Preface to Principia, p. xsi. 19 End of Planetary Tables. 



