D'ALEMBEET. 397 



body sliding or moving freely along a revolving rod, 

 at the extremity of which rod a fixed body moves 

 round in a given plane a locus which the calculus 

 founded on the Principle shows to be in certain cases 

 the logarithmic spiral.* 



No one can doubt that the Principle of D'Alembert 

 was involved in many of the solutions of dynamical 

 problems before given. But then each solution rested 

 on its own grounds, and these varied with the different 

 cases ; their demonstrations were not traced to and 

 connected with one fundamental principle. He alone 

 and first established this connexion, and extended the 

 Principle over the whole field of dynamical inquiry. 



The 'Traite' contains, further, (part 1. ch. ii.), anew 

 demonstration of the parallelogram of forces. The rea- 

 son of the author's preference of this over the common 

 demonstration, is not at all satisfactory. His proof 

 consists in supposing the body to move on a plane 

 sliding in two grooves parallel to one side of the 

 parallelogram, and at the same time carried along in 

 the direction of the other side. This is not one whit 

 more strict and rigorous than the ordinary supposition 



ydx* 2Dydy* 

 * The general equation is d 2 y = - -j- ~T^_|_ D a in wW< * # 



is the distance of the moving body D from the fixed point, or the length 

 of the rod, at the end of which is the body A, describing an arch of a 

 circle, and x that arch. The velocity of D is likewise found in terms of 

 the same quantity. 



I have freely admitted that the principle of D'Alembert flows from the 

 equality of action and re-action ; but nothing can be more incorrect than 

 the remark made by a learned critic, (' Quarterly Review,' vol. v., p. 345,) 

 that " this boasted principle is little more than Newton's third law of 

 motion modified so as to suit the algebraical method of investigating pro- 

 positions;" on which is grounded a complaint that the French, while 

 praising D'Alembert, never mention Newton, the real author of the prin- 

 ciple. The third law of motion was assuredly no discovery of Sir I. 

 Newton ; and as certainly the praise of the step made was due to D'Alem- 

 bert, unless indeed Bernouilli, and still more Fontaine, in some sort anti- 

 cipated him, probably without his being aware of it. The critic to whom 

 I allude is well founded in urging the like complaints against the French 

 chemists for omitting all mention of Black. But Fourcroy and others are 

 great exceptions. See Life of Lavoisier, p. 319. 



