I 



or THE EQUILIBRIWM OF A STSTEM, 171 



there may be a difference in the elementary particles of 

 matter. Fortunately, however, the truth of the hypothesis 

 is of no consequence to the science of mechanics, and we 

 may adopt it without any danger of error, provided that, 

 by similar material points, we understand points, which, 

 when they meet wl*h equal velocities, destroy each other's 

 motion, whatever tlieir nature may be. 



§. 14, Of tha reciprocal action of material points. 

 Reaction is always equal and contrary to action. Equa- 

 tion of the equilibrium of a system of bodies, giving the 

 law of virtual velocities. Method of determining the 

 pressure of bodies on the surfaces or the curves to which 

 they are confined. P. 37. 



303. Theorem. Action and reaction are 

 always equal and contrary. 



Two material points, of which the masses are m and m\ \ 

 can only act on each other in the direction of the right 

 line joining them. If, indeed, they are united by a thread 

 passing over a pulley, their reciprocal action may be other- 

 wise directed : but in this case the fixed pulley may be 

 considered as having at its centre a body of infinite den- 

 sity, which reacts on the two bodies m and m\ so as to 

 make their mutual action indirect only. 



If the action of m on m', exerted by means of an in- 

 flexible line, without inertia, uniting them, be called p, 

 and if it be met by a contrary force, expressed by —p, 

 this force will destroy in the body m a force equal to p, 

 and the force p in the right line will be communicated 

 entirely to m. This loss of force in m, occasioned by its 

 action on m, is called the reaction of m ; so that, in the 



