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centre of gravity. Such, however, is not the case ; and we 

 are now to consider the effects of the disturbance occa 

 sioned by the sun s action upon the satellites, and the 

 disturbance occasioned by the action of the planets onjone 

 another. This forms the subject of Sir Isaac Newton s 

 investigations in the second branch of that section which 

 we have been considering ; an inquiry regarded by some 

 as the most extraordinary portion of the great work 

 which forms the principal monument of his genius. From 

 this opinion it is difficult to withhold our concurrence ; but 

 it may be admitted that here, as in the operations for find 

 ing orbits from given forces and conversely, the great 

 improvements of modern analysis have afforded easier and 

 more manageable methods of investigation. That this 

 must be true as regards the planetary disturbances, will 

 be apparent upon a little reflection. 



The grand problem in every case is to find the precise 

 effect of a disturbing force upon the path of a given body 

 moving by a combined centripetal and projectile force; 

 and \vhat has been called the Problem of Three Bodies 

 presents the simplest case of the question, being the deter 

 mination of the motions of two bodies acted upon by one 

 another and by a third body. But though this is the 

 simplest case of the general question, it has been found 

 to present difficulties of the highest order ; and a general 

 and rigorous solution of it has been found to exceed the 

 powers of the most improved analysis. In the time of Sir 

 Isaac Newton, that analysis of which he was the inventor 

 had not attained any thing like its greatest perfection. 

 Hence, in grappling with the subject, he had much of 

 the difficulty to contend with, which made him give less 

 convenient formulas than we now possess for the solution 

 of the other problems relating to orbits and motions. The 

 mere improvement of the integral calculus by the advan- 



