APPENDIX. 



ON TIDE-GENERATING FORCES. 



a. IF, in the annexed figure, and C be the centres of the earth and of 

 the disturbing body (say the moon), the potential of the moon s attraction at 

 a point P near the earth s surface will be - yM/CP, where M denotes the 



moon s mass, and y the gravitation-constant. If we put OC=Z&amp;gt;, OP = r, and 

 denote the moon s (geocentric) zenith-distance at P, viz. the angle POC, by ^, 

 this potential is equal to 



yM 



We require, however, not the absolute accelerative effect on P, but the 

 acceleration relative to the earth. Now the moon produces in the whole 

 mass of the earth an acceleration yM/D 2 * parallel to OC, and the potential of 

 a uniform field of force of this intensity is evidently 



yM 



~ rj2- r cos ^- 



Subtracting this from the former result we get, for the potential of the relative 

 attraction on P, 



This function G is identical with the disturbing-function of planetary 

 theory. 



* The effect of this is to produce a monthly inequality in the motion of the 

 earth s centre about the sun. The amplitude of the inequality in radius vector is 

 about 3000 miles ; that of the inequality in longitude is about 1&quot;. Laplace, 

 Mecaniqne Celeste, Livre 6 m % Art. 30, and Livre 13 me , Art. 10. 



