20 Statics. 



of the quantities of motion of those which act in one direction is 

 equal to the sum of the quantities of motion of those which act 

 in the opposite direction. For, they being in equilibrium, we 

 maj always suppose that, m and n acting in the same direction, 

 n destroys a part of the motion of o, and that m destroys the 

 remaining part. Now if we represent by x the velocity that o 

 loses by the action of n, we shall have o a?, for the quantity of 

 motion destroyed by the action of n ; we have accordingly 



n v = o x. 



The body m, therefore, will have only to destroy in o the remain- 

 ing quantity, namely, o w o x ; we have consequently 



m u = o w o # ; 

 or since o x = n u, 



m u = o w n v^ 

 that is, 



Of Compound Motion. 



35. We still consider the masses to which the forces under 

 consideration are applied, as concentrated each in a point. 



We call compound motion that which takes place in a body, 

 when urged at the same time by two or more forces having any 

 given direction with each other. 



Fig. 3. If a body m moving in the line C5, receive upon arriving 

 at the point A, an impulse in the direction AD, perpendicular 

 to CB, this impulse can produce no other effect, except that of 

 removing the body from CB. It can neither augment nor dimin- 

 ish the velocity with which, at the time of receiving the impulse, it 

 was departing from AD. Indeed, since AD is perpendicular to 

 CB, there is no reason why a force acting in the direction AD 

 should produce an effect to the right, rather than to the left, of 

 this line, and as it cannot act in both these directions at once, 

 it can have no influence either way. 



The same reasoning will hold true, if we suppose that the 

 body m, moving in the line AD, receives, upon arriving at A, an 

 impulse in the direction AB. This impulse will neither add to nor 

 take from the velocity with which the body m was departing 

 from AB. 



