Lagrange's Memoirs. 79 



cilitate the practical part of it, by the aid of ingenious tables. Still, 

 however, we do not see that astronomers have adopted this method. 

 For, beginning with formulas apparently, the most direct, and the most 

 rigorous, and most proper, for application to all cases, it nevertheless 

 terminates in one merely approximative, and what is still worse, in- 

 direct. 



Another attempt of the same kind was not more happy, because 

 success was impossible. The problem was very simple. It was 

 proposed to find the difference between the heliocentric and geocen- 

 tric longitudes of a superior planet. 



Among the sports of his genius which sought difficulties to display 

 best its powers, ranked still the memoir, wherein he points out the 

 means of constructing astronomical tables, after a series of observations, 

 and without knowing the law of celestial motions. It is a problem 

 that astronomers of all ages have resolved by means the most elemen- 

 tary. The methods of Lagrange, are more analytical and learned ; 

 yet in the very example which he has selected, and which is most 

 simple, it is doubtful whether those employed are the most sure 

 and easy. Undoubtedly he wished only to show us the resources 

 which he had found in analysis, since Kepler and Newton had un- 

 folded to us the system of the world, and the laws by which the plan- 

 etary motions are accomplished. For it is not possible to suppose 



that he could have had the least doubt about that law of universal 



i 



gravity, of which he himself had given so many fine developments. 

 Nevertheless in many passages of his works, he took care to establish 

 his formulas for any law of attraction, in order to render them inde- 

 pendent of every hypothesis. 



Geometers will read with pleasure his analytical researches on the 

 problem of projections, which had never before been treated in a 

 manner so general or complete ; astronomers and geographers will 

 find in it for practice, only what they had previously learnt by the 

 merest elements. If these latter memoirs offer no results in reality 

 useful, otherwise than that they furnish pleasant reading, they still 

 give us this lesson, which may have frequent applications, viz. : 

 that easy questions should be treated only by means equally plain ; 

 that learned analysis, should be reserved for questions that need pow- 

 erful means, and that in doing otherwise, we may resemble the man 

 in the fable, who, to get rid of a flea, wished to borrow of Hercules 

 his club, or of Jupiter his thunderbolt. 



