64 ELEMENTS OF LABORATORY WORK 



45. The Relation between Mutual Displacements, We 



have observed that a small quantity of matter undergoing a 

 large displacement may be the means of displacing a large 

 quantity of matter. That is, mutual changes occur in which 

 unequal masses are equivalent in virtue of unequal displace- 

 ments. The examples investigated have been the pulley, lever, 

 and the displacement of a large quantity of liquid by a smaller. 

 The conditions necessary in these and all other examples of 

 the same kind of mutual change are that the numerical value 

 of the mass multiplied by the numerical value of the displace- 

 ment shall give equal products for each of the moving masses, 

 that is, mL = M. 



This principle may be extended to phenomena which are 

 not connected by material bodies. In the previous observa- 

 tions we have bars, cords, &c., connecting the mutually chang- 

 ing bodies. In these cases it follows of necessity that both 

 changes must take place in the same time. The simultaneous- 

 iiess of the changes is a consequence of their mutual nature. 

 We may, therefore, substitute speed for displacement in our 

 conception of the phenomena, for the numerical value of dis- 

 placement divided by the numerical value of time expresses 

 the magnitude of speed. But it is important to note that 

 the direction in which the bodies move is not the same 

 that is, this complex quantity (mass x speed), which is called 

 momentum, is positive in the one case and negative in the 

 other. 



This principle obtains in every case of mutual change, 

 whether the bodies concerned are connected in any way or 

 not. The displacements are in opposite directions ; they 

 are equal if the masses are equal, but if the masses are 

 unequal the displacements are inversely proportional to them. 

 This is the principle contained in Newton's Third Law 

 of Motion, according to which reaction is always equal and 

 opposite to action that is, the actions of two bodies upon 

 each other are always equal and in opposite directions. 



In order to demonstrate this principle completely, it would 

 be necessary to find a system which is under the influence of 

 its own mutual action alone. On the surface of the earth we 



