MECHANICS. 67 



of these, in order to produce the second, are such 

 as, if they acted on the system alone, would pro- 

 duce no motion at all, or would be in equilibria 

 with one another. 



a. The principle here laid down was discovered by 

 D^ALEMBERT, Dynamique, partie 2 de , chap. l r . It 

 is a result of the equality of action and re-action, 

 or rather, it is that very equality expressed with 

 perfect generality and precision. It was supposed 

 before, that the motions combined with the first 

 of those above described, in order to produce the 

 second, must, when added together, be equal to no- 

 thing ; whereas it is not the motions simply, but their 

 momenta, which, when added together, must be equal 

 to nothing. 



I. This principle is of great importance for deducing 

 the laws of constrained from those of free motion, 

 and affords the only general method of determin- 

 ing the manner wherein motion distributes itself 

 through all the parts of a system to which it is any 

 how communicated. It may very properly be called 

 the Principle of 'the Distribution of Motion. 



A simple instance of its application is afforded by the 

 following problem. 



121. Let two bodies connected by a straight rod, 

 without weight, be moveable about an axis passing 

 through their centre of gravity ; and let a motion be 

 communicated to one of them, which, were it de- 

 tached and single, would give it a velocity c ; re- 

 quired, the angular velocity with which the bodies 

 will begin to revolve ? 



E Z SECT. 



