MATTER AND ETHER THOMSON. 



243 



tern as a whole we see that it behaves as if it were free from the action 

 of external forces and that its kinetic energy remains constant ; what 

 on our restricted view we regarded as the potential energy of A is 

 seen on the more general view to be the kinetic energy of the system 

 B. It is now many years ago since I showed that the effects of force 

 and the existence of potential energy may be regarded as due to the 

 connection of the primary system with second- 

 ary systems, the kinetic energy of these S3'^stems 

 being the potential energy of the primary, the 

 complete system having no energy other than 

 the kinetic energy of its constituents ; a similar 

 view is the foundation of Hertz's system of 

 mechanics. 



Let us consider one or two simple mechanical 

 systems in which the motion of matter attached i 

 to the system produces the same effect as a 

 force. Suj^pose A and B (fig. 1) are two 

 bodies attached to tubes which can slide verti- 

 cally up and down the rod E F, and that two 

 balls C and D are attached to A and B by rods 

 hinged at A and B, then if the balls rotate 

 about the rod they will tend to. fly apart, and as 

 the balls move farther from the rod their points 

 of attachment A and B must approach each other ; thus A and B will 

 tend to move toward each other, i. e., they will behave as if there 

 were an attractive force acting between; the velocities of A and B, 

 and therefore their kinetic energy, will change from time to time; 

 the kinetic energy lost by A and B will really have gone to increase 

 the kinetic energ}^ of the balls. If the rotating system C and D had 



been invisible we should have 

 explained the behavior of the 

 system by assuming an at- 

 tractive force with corre- 

 sponding potential energy be- 

 tween A and B. This is due 

 to our considering A and B as 

 a complete system, whereas it 

 is in reality part of a larger 

 system, and when we consider the complete system we see that it 

 behaves as if it were acted on by no forces and possessed no energy 

 other than kinetic. 



It may perhaps be of interest to note that we can in a similar way 

 make two bodies appear to attract each other with a force varying 

 inversely as the square of the distance between them. Let A and B 

 (fig. 2) be the bodies, and suppose that parabolic wires without mass 



Fig. 1. 



B'IG. 



