16 Statics. 



inversely as the times. Indeed we have in this last case s = v t. 

 and s' = v t 1 ; from which we obtain, when s = *', 

 v : v' : : t' : t. 



Thus the single proposition v = furnishes the means of compar- 

 ing all the circumstances of uniform motion. 



Of Forces and the Quantity of Motion* 



27. The sum of the material parts of which a body con- 

 sists, is called its mass ; but in the use we shall make of the 

 word is to be understood the number of material parts of which 

 the body is composed. 



Force, as we have said, is the cause which either moves ex- 

 tends to move a body. 



As forces interest us only by their effects, it is by the effects 

 of which they are capable, that we are to measure them. Now the 

 effect of a force is to cause in each particle of a body a certain 

 velocity. Accordingly, if all the parts receive the same velocity, 

 as is here supposed, the effect of the moving cause has for its 

 measure the velocity multiplied by the number of material parts 

 contained in the body, that is, by the mass. Therefore, a force 

 is measured by the velocity which it is capable of impressing upon a 

 known mass multiplied by this mass. 



28. The product of the mass of a body by its velocity is call- 

 ed the quantity of motion of this body. Forces are therefore measur- 

 ed by the quantities of motion which they are capable of producing 

 respectively. Thus, if we designate the above product by p, the 

 mass by m, and the velocity by v, we shall have p = mv. This 



equation gives v = , and m = ; from which it will be seen 

 that, 



1. The moving force of a body and its mass being known, we 

 shall Jind the velocity by dividing the moving force by the mass ; 



2. The moving force and the velocity being known, we shall find 

 the mass belonging to this velocity and moving force, by dividing the, 

 moving force by the velocity ; 



