38 



THE TIDAL PROBLEM. 



from a to & will lose velocity — and hence kinetic energy — and gain potential 

 energy. At the point b it will have the minimum of motion and the maxi- 

 mum of potential energy. From 6 to c it will fall back toward the center, 

 a portion of its potential energy being converted into kinetic, and its veloc- 

 ity being increased and reaching a second maximum at c. In the second 



half of its orbit, cda, similar 

 exchanges of kinetic and poten- 

 tial energy will take place. 



If p is affected by no friction 

 or obstruction in its course, 

 these exchanges of kinetic and 

 potential energy will be com- 

 pensatory and maybe continued 

 indefinitely without affecting 

 the rotation of E. The case is 

 that of an inner satellite or an 

 inner planet when all the bodies 

 involved are considered as rigid 

 bodies or massive points. But 

 if now friction be introduced 

 at any point in the orbit of p, 

 heat will be developed and 

 dissipated, and energy lost to 

 the system. Looked at in 

 detail, it would seem that the 

 retardation of p by friction on 

 E in some phases of its orbit 

 would be accelerative to E's 

 rotation, and in other portions, 

 retardative, for in some por- 

 tions p's angular motion ia 

 greater than E's, and in others 

 less, but traced out in its full 

 history it appears that what is 

 seemingly accelerative in one 

 phase is retardative in another 

 and that the ulterior effect is 

 precisely measured by the loss 

 of mechanical energy by con- 

 version into radiant energy and 

 dissipation. For example, fric- 

 tion between p and the normal 

 periphery of E as represented 

 by A BCD, at or in the vicinity of c, will be accelerative in its immediate 

 phase because p in this part of its orbit is moving faster than the contact 

 portion of E, but the retardation of p in this portion will reduce the rise 

 of p in the section at and near d which is retardative in its immediate 

 phase because in this position p is moving more slowly than the normal 



