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 H denotes the 



moon's mass, and y the gravitation-constant. If we put OC=D, OP = r, and 

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

 this potential is equal to 



(Z> 2 - 



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 yJ///) 2 * parallel to OC, and the potential of 

 a uniform field of force of this intensity is evidently 



yM 

 ~ jyi' r cos ^* 



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

 attraction on P, 



(i). 



This function Q 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". Laplace, 

 Hecanique Celeste, Livre 6 m3 , Art. 30, and Livre 13 me , Art. 10. 



