496 Mr. J. Prescott on the 



that is, the condition corresponding to (49), is large when m 

 is large. 



From (60) and (61) we get 



„ „ ~ „ lia , _ 



^=0-321- (62) 



which is very little different from the result in (57). 



As both the results I have just obtained for the ellipticity 

 are much smaller than the values given by Dr. Hecker's 

 pendulums or by observations on ocean-tides, I have made 

 another calculation with a smaller rigidity. In this case 

 I have taken 



P = iv(l0-1'D~\ (63) 



n = 4x 10 8 grams per square centimetre, . (64) 

 and I find 



*=10- 4 - J7804-2683- 9 -779^ 



a 2 a 4 a 6 a" 



- i2 ^ + «4> (G5) 



and therefore the ellipticity of the surface is 



* 1 = 0-473— (66) 



9 



Now a plumb-line would set itself perpendicular to the 

 equipotential surface in its neighbourhood, that is, perpen- 

 dicular to the surface which would bound an infinitely light 

 liquid which may be imagined to cover the surface of the 

 earth as far as the plumb-bob. There would be a tide on 

 this light liquid similar to the tide on the ocean, but not 

 exactly equal to the ocean-tide — except over the ocean itself. 

 For, an ocean -tide depresses the solid earth beneath it to a 

 slight extent, and moreover the attraction of the ocean-tide 

 itself constitutes a tide-producing force. Both the depression 

 of the solid earth and the mutual attraction of the waters 

 would act in the same direction and make the ocean-tide 

 larger than the tide on an infinitely light liquid extending 

 down to the solid earth. The attraction of the Atlantic tide 

 would have some slight effect on Dr. Hecker's pendulums at 

 Potsdam, but it is considered small enough to be neglected. 

 Now these pendulums really give the direction of the plumb- 

 line relative to the solid earth ; that is, they indicate the tide 

 on the imaginary light liquid relative to the solid earth. 



