370 KELATIVE MOTION AND UNIVERSAL GRAVITATION. [CH. XIII. 



not take place without friction ; and thus we are led to expect 

 that the kinetic energy of the Earth's rotation is being dissipated 

 at a finite rate. To give a meaning to this statement we must 

 suppose time to be measured by some process other than the 

 diurnal rotation of the Earth. As before we may take the 

 number expressing time to be a slowly varying function of the 

 number expressing sidereal time, and then the sense of the 

 variation is again such that the function has a positive second 

 differential coefficient with respect to sidereal time. As before, 

 it is simpler to say that time can be measured so that the length 

 of the day varies and the tidal motions obey the laws of energy 

 than to keep to the measurement of time by the diurnal rotation 

 and seek a theory of the tides in conflict with the theory of 

 energy. 



