On Machines in General, 211 



the second fundamental law bodies should go in company* 

 we shall have V cosine q' + V" cosine q" = (A) : thus 

 by the first fundamental law, we shall also have F' V co- 

 sine q' + F" V" cosine q" t^ (B) : for if m' and rti!' are 

 both moveable, it is clear, by this law, that we have F" = F"; 

 therefore on account of the equation (A) we shall also have 

 the equation (B) ', anal if one of the two, 7n' for instance, be 

 fixed, or form part of an obstacle, we shall have V co- 

 sine ^' = o ; therefore on account of the equation (A) we 

 shall also have Y" cosine^' = 0^ therefore the equation 

 (B) will still take place : therefore this equation (B) is 

 true for all the corpuscles of the system taken two by two. 

 Imagining therefore a similar equation for all these bodies 

 taken in fact two by two, and adding tT)gether all these equa- 

 tions, or, what comes to the same »hing, the integral equa- 

 tion (B), we shajl have for the whole system, 



s Y' V' cosine q' -{• s ¥' V" cosine ^" = o : that is to say, 

 the sum of the products of the quantities of movement 

 which are reciprocally impressed by the corpuscles separated 

 by each of the small inextensible wires or incompressible 

 rods; from these quantities, I say, each of them multiplied 

 by the velocity of the corpuscle on which it is impressed, 

 estimated in the direction of this force, is equal to zero. 



This being done, abandoning the preceding denomina- 

 tions, let us name 



The mass of each of the cc^rpuscles of the system - m 



Its virtual velocity, i. e. that which it would assume 

 if it were free, ------- W 



Its real velocity - - - - - - V 



The velocity which it loses in such a manner that 

 \V is the result of V and of this velocity - - U 



The force or quantity of movement which each of the 

 adjacent corpuscles impresses upon tti, and by the inter- 

 medium of which it evidently receives all the move- 

 ment that' is transmitted to it from the different parts 

 of the systQm, -- - - • - -F 



The antvle comprehended between the directions 

 of W 'and> - - X 



The angle comprehended betweea the directions of 



WandU Y 



2 Tbc 



