78 Lagrange's Memoirs. 



to '-"ft 



the theory of vibrating cords. It is thus that in the last work which 

 he has presented to the class, he succeeded in simplifying remarka- 

 bly his theory of the variations of the elements of the planets, and 

 in drawing from his solution a general method for all problems of me- 

 chanics, where the disturbing forces are small in comparison with the 

 principal forces. But as we often see him make the most happy 

 efforts to generalize a solution, to exhaust a subject, so also we some- 

 times see him create difficulties where none existed, and apply his 

 adroit and learned methods to the solution of elementary problems 

 that required only a construction of the most simple nature. 



Thus, at the time of the last transit of Venus, he treats analyti- 

 cally curves of entrance and of departure, for the different countries 

 of the earth. But to arrive at the very easy and moderately exact 

 solution given by Delille and Lalande, he is obliged to employ suc- 

 cessively crooked shifts, remarks full of subtlety, to cause his co- 

 ordinates to undergo a number of transformations, whilst by a trigo- 

 nometrical calculation of some lines, we arrive at a more complete 

 formula, wherein are found terms neglected by Lagrange, and which, 

 though very small, are not yet absolutely insensible. Let us not- 

 withstanding avow, that he knows how to gather from his formula, 

 for calculating the parallax of the sun, a very advantageous part, of 

 which neither Delille nor Lalande had obtained a glimpse, but which 

 still proceeds with more facility from the trigonometrical calculus. 

 Let us add, still, that this memoir, which had been wholly unknown 

 to me, even to the time when I was obliged to read all that had is- 

 sued from his pen, appeared to have served some modern astrono- 

 mers, in establishing which they were obliged to acknowledge, that 

 Lagrange therein gave the first example, somewhat extended, of an 

 elementary problem of astronomy, solved by the method of three 

 rectangular co-ordinates, of so great and so indispensable use in 

 transcendant astronomy. 



He made then a similar attempt for the problem of eclipses ; he 

 found that the methods, somewhat prolix, of Dusejou, had neither 

 the simplicity nor the facility that ought to have been expected from 

 the actual state of analysis. He shows, in this work, all his resour- 

 ces and all his address. The reading of his memoir is very touch- 

 ing, to an astronomer, who had no idea of these methods. I have 

 not forgotten the effect it produced on myself, thirty years ago, when 

 I first read it ; I remember still with what praises, some years after, 

 M. Oriani spoke to me of this work. The author attempted to fa- 





