422 D'ALEMBERT. 



While mentioning Fontaine's great and original genius 

 for analytical investigations, we must not overlook his 

 having apparently come very near the Calculus of Varia- 

 tions. In a paper read at the Academy, 17th February, 

 1734, we find a passage that certainly looks towards 

 that calculus, and shews that he used a new algorithm as 

 requisite for conducting his operation : " J'ai etc oblige," 

 he says, " de faire varier les niemes lignes en deux mani- 

 eres differentes. II a fallu designer leurs variations dif- 

 feremment." " J'ai marque les unes commes les geometres 

 Anglais par des fluxions (points) ; les autres par des dif- 

 ferences (d x) a notre nianiere ; de sorte qu'ici d x ne 

 sera pas la rneme chose que x, d x que 'x" (p. 18.) 

 " II peut y avoir," he afterwards adds, " des problernes 

 qui dependroient de cette methode fluxio-differentielle." 



Nothing that has now been said can, in any manner, 

 detract from the renown justly acquired by D'Alembert 

 and Lagrange as the first who fully expounded the two 

 great additions to the Differential Calculus, first applied 

 them systematically to the investigation of physical as 

 well as mathematical questions, and therefore may truly 



He afterwards (p. 606) supposes Clairaut's addition to the inverse 

 square of the distance ( ^ + ^ \ to have been adding what he 



calls " a small portion of the inverse cube joined to the ordinary 

 term of the inverse square;" and he considers, most unaccount- 

 ably, that this is not a function of the distance at all. His account 

 of the calculus of variations is equally vague; and the example 

 unhappily chosen is one in which the relations of the co-ordinates 

 do not change, but only the amount of the parameter (Ib., p. 600.) 

 I must also most respectfully enter my protest here, once more, 

 against mathematicians writing metaphorically and poetically, as 

 this learned Professor does in almost every sentence. 



