OF NATURAL PHILOSOPHY. 275 



gularly deviating from the general analogy of the 

 others, and gffering cases of difficulty in theory, which 

 no one had before contemplated. Yet even the in- 

 tricate questions to which these bodies have given 

 rise seem likely to be surpassed by those which have 

 come into view, with the discovery of several comets 

 revolving in elliptic orbits, like the planets, round the 

 sun, in very moderate periods. But the resources 

 of modern geometry seem, so far from being ex- 

 hausted, to increase with the difficulties they have 

 to encounter, and already, among the successors of 

 Lagrange and Laplace, the present generation has to 

 enumerate a powerful array of names, which promise 

 to render it not less celebrated in the annals of 

 physico-mathematical research than that which has 

 just passed away. 



(30.5.) Meanwhile the positions, figures, and di- 

 mensions of all the planetary orbits, are now well 

 known, and their variations from century to century 

 in great measure determined ; and it has been ge- 

 nerally demonstrated, that all the changes which 

 the mutual actions of the planets on each other can 

 produce in the course of indefinite ages, are pe- 

 riodical, that is to say, increasing to a certain ex- 

 tent (and that never a very great one), and then 

 again decreasing ; so that the system can never be 

 destroyed or subverted by the mutual action of its 

 parts, but keeps constantly oscillating, as it were, 

 round a certain mean state, from which it can never 

 deviate to any ruinous extent.. In particular the 

 researches of Laplace, Lagrange, and Poisson, have 

 shown the ultimate invariability of the mean distance 

 of each planet from the sun, and consequently of its 

 T 2 



