80 Lagrange's Memoir. 



We must believe that on these occasions Lagrange wished not 

 seriously to propose to astronomers these troublesome means in the 

 place of these more easy and exact of which they were in possession. 

 He made of these plain, common, and already solved problems, the 

 same use that other analysts have made of questions of pure curi- 

 osity. For the questions furnished them examples of calculations, 

 and opportunities of unfolding new artifices of analysis that were 

 always well to be known. 



But a work grand in its object, useful by its continual applications, 

 and worthy entirely of his genius, is that in which he has calculated 

 the successive changes that operate in the dimensions and the posi- 

 tions of the planetary orbits. All the geometers since Newton, had 

 engaged upon this problem ; their differential formulas applied suc- 

 cessively to each planet, could until a certain period and during a 

 certain time, satisfy the wants of astronomy ; but after some time 

 they were found insufficient, and the calculations to be made again 

 upon new data. M. Lagrange viewed the question under a point of 

 sight that embraced it entirely, and permitted its most complete so- 

 lution. Instead of combining the orbits two by two, like his pred- 

 ecessors, he considered them all together and whatever be their 

 number, he succeeds in giving to the equation a form which permits 

 of integration, supposing on one side, the fundamental principle of 

 gravitation, and on the other, the orbits known as they were, for a 

 certain epoch. His analysis determines what they have been and 

 what they will be in all past and future ages. The solution leaves 

 nothing to be desired, unless it be a more exact knowledge of the 

 mass of the planets that have no satellites. But this knowledge itself, 

 in time, can be obtained by his formulas. In the mean time M. La- 

 place drew from his work a more limited but more easy solution ; 

 since, allowing him to go back to the first years of astronomy, it ex- 

 tends into the future the same number, nameJy two thousand. 



To be concluded in the next No. 



