No. 8.] REMARKS ON THE EARTH'S CRUST. 67 
If the integration in this equation is effected in the same way, we obtain: 
“ h h ‘ 
8 — eh — hy) “M2 (,’— 1), B=, 
where 9 is the difference between two densities, which may be considered 
as a kind of mean value of g, and eg, between h=0 and h=h, — hy, 
differing from 9, although the difference cannot be great, as in any case 
@; — @ is only very small. 0,’ may be straightway put down as equal to @,/ 
in equation III. According to this equation, 
(eo, —Hh, =d — o’ (hy — hy), 
which, substituted in the previous equation, gives 
h ah h é 
att — FE) = hy — hy) ("GEM — g 
As already mentioned, there can only be a slight difference between 9” 
hy 
Re 
and @’. The numerical value of 0” is probably less than that of 0’, as the 
difference in density is least, and the densities themselves greatest, in the 
lowest strata, where the factor (hk —h,) in the first integral TV. has its 
greatest value. Recollecting that 0, 9 and 0 are negative, we may write, 
if we substitute 0’ for 0” 
hy h 
se zens — we oY aed 
6(1— FS — (ey — adept. 
If now equation III. is employed for the elimination of 9 (h, —h,) ,we 
finally obtain 
hy == hs 4 Ay 
=) (th 1a )Se/—-Yhz 
or 
h h h 
—8 S (ex — 1h, pt (1+ Es), v. 
If, as previously stated, we assume that h, equals 3°5 km., and that the 
average density in the uppermost 3°5 km. of the continents is 2°7, then, with 
a sufficient degree of accuracy, 
—éd<6 ees km. of density one. Vib: 
0 
Even if the exterior spherical shell has a thickness corresponding to 0:02 
of the earth’s radius, or h, =circ. 126 km., 
— 0d < 120 m. of density one, 
