254 THE FORCES OF INOEGAJSIC NATURE. 



order that a body may fall, it is no less necessary that it 

 should be lifted up, than that it should be heavy or possess 

 gravity ; the fall of bodies ought not therefore to be ascribed 

 to their gravity alone. 



It is the problem of Mechanics to develop the equations 

 which subsist between falling force and motion, motion and 

 falling force, and between different motions : here we will call 

 to mind only one point. The magnitude of the falling force 

 v is directly proportional (the earth s radius being assumed 

 oo ) to the magnitude of the mass w, and the height d to 

 which it is raised; that is, v=md. If the height cZ=l, to 

 which the mass m is raised, is transformed into the final ve 

 locity c=l of this mass, we have also -y=mc; but from the 

 known relations existing between d and c, it results that, for 

 other values of d or of c, the measure of the force v is me 2 ; 

 accordingly v=md=mc i : the law of the conservation of vis 

 viva is thus found to be based on the general law of the inde 

 structibility of causes. 



In numberless cases we see motion cease without having 

 caused another motion or the lifting of a weight ; but a force 

 once in existence cannot be annihilated, it can only change its 

 form ; and the question therefore arises, What other forms is 

 force, which we have become acquainted with as falling force 

 and motion, capable of assuming? Experience alone can 

 lead us to a conclusion on this point. In order to experi 

 ment with advantage, we must select implements which, be 

 sides causing a real cessation of motion, are as little as possi 

 ble altered by the objects to be examined. If, for example, 

 we rub together two metal plates, we see motion disappear, 

 and heat, on the other hand, make its appearance, and we 

 have now only to ask whether motion is the cause of heat. 

 In order to come to a decision on this point, we must discuss 

 the question whether, in the numberless cases in which the 

 expenditure of motion is accompanied by the appearance of 

 heat, the motion has not some other effect than the pro- 



