$246-249] Planetary Theory : Minor Problems 319 



a sort of miniature solar system but with several character- 

 istic peculiarities, was fully dealt with ; the other satellites 

 received a less complete discussion. Some progress was 

 also made with the theory of Saturn's ring by shewing that 

 it could not be a uniform solid body. 



Precession and nutation were treated much more com- 

 [ letely than by D'Alembert ; and the allied problems of 

 the irregularities in the rotation of the moon and of Saturn's 

 ring were also dealt with. 



The figure of the earth was considered in a much more 

 general way than by Clairaut, without, however, upsetting 

 the substantial accuracy of his conclusions ; and the theory 

 of the tides was entirely reconstructed and greatly improved, 

 though a considerable gap between theory and observation 

 still remained. 



The theory of perturbations was also modified so as to 

 be applicable to comets, and from observation of a comet 

 (known as Lexell's) which had appeared in 1770 and was 

 found to have passed close to Jupiter in 1767 it was inferred 

 that its orbit had been completely changed by the attraction 

 of Jupiter, but that, on the other hand, it was incapable of 

 exercising any appreciable disturbing influence on Jupiter 

 or its satellites. 



As, on the one hand, the complete calculation of the 

 perturbations of the various bodies of the solar system 

 presupposes a knowledge of their masses, so reciprocally 

 if the magnitudes of these disturbances can be obtained 

 from observation they can be used to determine or to 

 correct the values of the several masses. In this way the 

 masses of Mars and of Jupiter's satellites, as well as of 

 Venus ( 235), were estimated, and those of the moon and 

 the other planets revised. In the case of Mercury, however, 

 no perturbation of any other planet by it could be satis- 

 factorily observed, and except that it was known to be small 

 its mass remained for a long time a matter of conjecture. 

 It was only some years after Laplace's death that the effect 

 produced by it on a comet enabled its mass to be estimated 

 (1842), and the mass is even now very uncertain. 



249. By the work of the great mathematical astronomers 

 of the 1 8th century, the results of which were summarised 

 in the Mecanique Celeste, it was shewn to be possible to 



