DALEMBERT. 407 



velocity of a body sliding or moving freely along a 

 revolving rod, at the extremity of which rod the body 

 moves round in a given plane a locus which the cal- 

 culus founded on the Principle shews 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 con- 

 nected with one fundamental principle. He alone and 

 first established this connexion, and extended the Prin- 

 ciple over the whole field of dynamical inquiry. 

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

 demonstration of the parallelogram of forces. The reason 



mi j.- jo V d x 2 . 2 D y d y z 



* The general equation is d*y=. - + . , ^ ~ in 



a* A cr-H D v 2 



which y 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, describ- 

 ing an arch of a circle, and x that arch. The velocity of D is like- 

 wise 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 Re- 

 view/ 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 propositions;" on which is grounded a 

 complaint that the French, while praising D'Alembert, never men- 

 tion Newton, the real author of the principle. The third law of 

 motion was assuredly no discovery of Sir I. Newton; and as cer- 

 tainly the praise of the step made was due to D'Alembert, unless 

 indeed Bernouilli, and still more Fontaine, in some sort anticipated 

 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. 



