DEFINITIONS AND EDUCATION. 139 



cords, the elasticity of a spring, gravity that acts on 

 all the molecules of a body, friction, the normal 

 mutual action and reaction of two solids in contact. 



This is only a qualitative definition ; we have to 

 learn to measure a force. For this purpose we shall 

 show first that we can replace one force by another 

 without disturbing the equilibrium, and we shall find 

 the first example of this substitution in the balance 

 and Borda's double scales. Then we shall show that 

 we can replace a weight not only by another weight, 

 but by forces of different nature ; for example, Prony's 

 dynamometer break enables us to replace a weight 

 by friction. 



From all this arises the notion of the equivalence 

 of two forces. 



We must also define the direction of a force. If 

 a force F is equivalent to another force F^ that is 

 applied to the body we are dealing with through the 

 medium of a taut cord, in such a way that F can be 

 replaced by F^ without disturbing the equilibrium, 

 then the point of attachment of the cord will be, by 

 definition, the point of application of the force F^ and 

 that of the equivalent force F, and the direction of the 

 cord will be the direction of the force F^ and also that 

 of the equivalent force F. 



From this we shall pass to the comparison of the 

 magnitude of forces. If one force can replace two 

 others of the same direction, it must be equal to their 

 sum, and we shall show, for instance, that a weight of 

 20 ounces can replace two weights of 10 ounces. 



But this is not all. We know now how to compare 

 the intensity of two forces which have the same direc- 

 tion and the same point of application, but wc have 



