1502 
E—E, = J — = (A 
The change in H due to the change in C in the denominator is 
very small (of the order of */;,,) compared with the effect of the 
change in the numerator. Consequently 
J —J,=9(H — H)). 
and 
se (H =H) 0.5902 (f B eee 
The part contributed towards the moments of inertia by an element 
of mass m at latitude gy, longitude 4, and distance from the centre 7 is 
dC = mr" cos? p‚ 
2 
dA —= mr° {1 — cos* gf cos" (2 
il, 
dB = mr? [1 — cos’ p sin* (A — A)|, 7 
from which 
d[C — 4(A+ B)| = mr° (1 — 3 sin’ g) 
d|B — A] = mr* cos° pp cos 2 (A — A,). 
If now over a surface element w of the ideal surface the height 
of the continent is /, and the mean density A, then the mass is 
m—=oh, WW Z, is the depth of the isostatic surface below the 
ideal surface, the defect of density needed to compensate this mass, 
if equally distributed over the whole depth, isd = 4 Ih . The change 
in 2mr* produced by the continent and its isostatic en 
then is, if 7, be the radius vector of the ideal surface : 
Tj + hy r) 
d (Smr*) =| Aw «dx ==] dwx?da = Awh, (Z + h,) (7, —42, +AA), - (5) 
Ty nl 
Similarly for an oceanic element, let d, be the depth of the bottom 
of the ocean below the ideal surface and 4’ the difference of density 
between the water and the mean density of the crust. The com- 
d 
1 ange 
Ye 
yensating excess of density below the sea then becomes d' = 
le) A 
and the change in Zn” is 
d (Emr?)= A'od, [(—Z, +2d)r, +AA: +4Z,d].- . (6) 
It has been found sufficiently exact for our purpose instead of 
(5) and (6) to use the approximate formulas 
d (Sar) 9 el nr Dee 
d (mr) = — 0Stgvds - 2 ce ee 
The height A, above the ideal surface is the sum of the height 
h above the normal surface and the height 4’ of the normal above 
the ideal surface. This latter is 
