1297 
Let 
b==the aequatorial radius 8 
: of any surface, 
e = the compression ; 
Further 
b dé 
en 
NEE 
then we have approximately 
18 
€, = 75 (rbi: 
. b a 
For the earth we have 1, == 0.561. Taking — = = 0.0179, and 
) 
s = 0.00338, we find 
&,— & = + 0.000084 
The difference of the numerators is 
== eN 
ë‚ le, == sl) 5 
1) A better approximation is obtained by also taking into account the variation 
of ,. Let 
A = the density at ‘ B 
5 ae: any equipotential surface, 
D = the mean density within 
b dD 
Dap. 
then the theory of Crarraur gives, neglecting the second order in « 
A 
c= (d>) 
pO KLI) 
= == | Y)—Iy—7. 
db Ì he! 
If the crust were constituted in accordance with the theory of Cuarravt, it 
would consist of a solid crust entirely covered by an ocean of a depth of about 
2.4 km. The bottom of this ocean would be an equipotential surface, say Ss. For 
Sj we have now 
Cres 
4, == 1.08 D, seni 
from which we find 
Then, with .; = 0.561, we find 
dn 
ig eet EES ae 
dh), 
Therefore, since 6,—bs = 0.00038 b,, we have 
d 
no = 4, — (6,—b1) (7) = 0.550, 
1 
} 
For the surface Sy we then have 
