1314 
If then 7, p‚ 4 are the polar coordinates of any point, the poten- 
tial V, at that point due to the attraction of the moon is given by *) 
3 D3° meu 
Zy T= evin jer 
Aan f r i 7 
nig 
HEB cos? gp sin® À Ë PR rol. 
Tr . 
If w be the velocity of rotation, and if we put 
Bro 
ST AafD 
then the potential of the centrifugal force is 
i IV = Dor COR ip 
Aaf 
Further if J/ be the mass of the earth, and 
OM 
~ dae RED’ 
the potential of the attraction of the earth is 
=e 
») 
— V, = Dz{l — 4 sin” p — 3 cos® p sin® dik: 
4arf | 
Along an equipotential surface the sum V = DV, + V,+ V, 
must be constant. If we are content with the first order of o and 
» we can also take == — in the factors of S, 7, P, Q;.0 and x 
The equation to the equipotential surface then becomes, if a is a 
constant : 
TDL + 49) + — Saint DES + 1) + 4 De + Del 
+ (} Boost y sin® 2) [FP + Q) + De]. 
The equation of the ellipsoid is 
r= 6 (1 — osin? p — v cos’ p sin? 2}, 
Comparing the coefficients of sin* p and cos’ sin’ 4, we find 
Do=2(S+ T) +4 Do +3 Dx, (6) 
Do=3(P + IE De debt 
The quantities referring to the outer surface will be distinguished 
by the suffix 1. We then have 
M'=taD,b*, 
ES, bs B — Al = 3. x P, bY, 
T= 0, Q,=0. 
1) The constant of the gravitation f in this formula of course is a different thing 
from the ratio f, which has been defined above. 
