3 IP On Machines in General. 



soft to the touch, and has yellow ochrey spots in it, app$» 

 rently proceeding from grains of altered cupreous and ter* 

 ruginous pyrites. M. Ansaldo informed me, that this py- 

 rites was formerly wrought for the sake of its sulphate of 

 copper, but abandoned on account of its poverty. 



LIX. Essay upon Machines in General, By M. Carnot^ 

 Member of the French Institute , &c, &€, 



[Continued from p. 221.] 



Problem, 



XX. 1 HE virtual movetnent being known of any given 

 system of hard bodies^ (i. e. that ivhich it would assume if 

 each of the bodies were free^) to find the real movement which 

 it should have ihefolloujing instant. 



Solution. Let us denominate each molecule of the 

 system, - - - - - m 



Its virtual given velocity, - '- - W 



Its real velocity sought, - , - V 



The velocity it loses, in such a manner that W is 

 the result of V and of this velocity, - - U 



Let us now imagine that we make the system assume 



an arbitrary geometrical movement, and let the velocity 



which m will then have be - - - u 



The angle formed by the directions of W and V, X 



The angle formed by the directions of W and U, Y 



The angle formed by the directions of V and U, Z 



The angle formed by the directions of W and u, x 



. The angle formed by the directions of V and «, y 



The angle formed by the directions of U and u^ z 



This being done, we shall have the equation s m u\J 



cosine x = O (F) ; by means of which we shall find in all 



cases the state of the system, by attributing successively to 



the indeterminates u different relations and arbitrary direct' 



lions. 



Definitions. 

 XXI. Let us imagine a system of bodies in movement \r\ 



any 



