124 



THE TIDAL PROBLEM. 



Therefore 



+ 



Ai 



A- n , , 1 (4Po-Do) ^^, 



[-.-««+©>'-^«)(f")°] 



Since these equations are applied only when Pq-D^ is small and Z)« 

 small compared to P', we have approximately 



.-^i^ 





Sm,' ( P,-D,)P '* Zm,' (Po-D^Y i5Po-8D,) P'« 

 V 



m^D,^ P. 



m^ D,* P^ 



(5Po-8Do) 



D,{P,-D,)^' 3P„(Po-^o) 



^^i 



A^' 



(137) 



By successive application of (135) and (137) the corresponding values 

 of P and D can be followed until P-D passes through zero. The value 

 of P, for which P = D, can then be determined by interpolation. The corre- 

 sponding values of P and D in the following table have been computed 

 from equations (130), (131), (135) and (137). The third column gives 

 p, the ratio of the rate of the change in the rotation of the earth due to the 

 sun's tides to that due to the moon's tides. 



The initial common period of rotation and revolution is found by this 

 computation to be 0.20037 day, corresponding to a distance of 9,045 miles. 



