STABILITY OF THE SYSTEM. KJ3 



stability or the instability of the system. The 

 decision of this point required a great number of 

 preparatory steps and simplifications, and such 

 progress in the invention and improvement of 

 mathematical methods, as occupied the best ma- 

 thematicians of Europe for the greater part of 

 last century. But, towards the end of that time, 

 it was shown by Lagrange and Laplace that the 

 arrangements of the solar system are stable : that 

 in the long run, the orbits and motions remain 

 unchanged ; and that the changes in the orbits, 

 which take place in shorter periods, never trans- 

 gress certain very moderate limits. Each orbit 

 undergoes deviations on this side and on that of its 

 average state ; but these deviations are never very 

 great, and it finally recovers from them, so that 

 the average is preserved. The planets produce 

 perpetual perturbations in each other's motions, 

 but these perturbations are not indefinitely pro- 

 gressive, they are periodical : they reach a maxi- 

 mum value and then diminish. The periods which 

 this restoration requires are, for the most part, 

 enormous ; not less than thousands, and, in some 

 instances, millions of years ; and hence it is, that 

 some of these apparent derangements have been 

 going on in the same direction since the beginning 

 of the history of the world. But the restoration 

 is in the sequel as complete as the derangement; 

 and in the meantime the disturbance never attains 



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