No. 8.] REMARKS ON THE EARTH’S CRUST. 71 
(nie sis oii eee circ. (48 + 20h’) m., 
Q1 hy 
if, as previously, we assume that h, =0°02 Ry, and h, =3°5 km.; for every 
additional 1000 m. in the height of the plateau, the thickness of the added 
mass must consequently be increased by 20 m. 
In the following pages we shall assume, for the sake of simplicity, that 
there is on an average the same quantity of matter over every surface unil 
of the inner nucleus. If we then imagine all the deficiencies of matter in the 
depths compensated by filling up from the corresponding accumulations above 
sea-level, the surface of all continents would in the main coincide with the 
spherical surface through sea-level. 
I have above taken the thickness of the earth’s crust to be 0:02 of the 
earth’s radius. How far down we must go before we reach a depth where 
we may assume that the density is constant all over the earth, will depend 
upon the manner in which the density on an average alters downwards from 
the surface of the continents and from the bottom of the oceans. By the 
inequality in the moon’s motion, dependent on the ellipticity of the 
earth, we may now infer how the density on the whole ought to change 
inwards towards the interior of the earth. Helmert gives the following 
formula: 1 
: 4 (%\? 1 9: a \* 
C— dean 104 (7) + 0275 alk 
where 6 is the density, a@) the equatorial radius of the earth, and a the 
equatorial radius of the equipotential surface through the point under con- 
sideration. When a= dp, 7. e. at the surface of the earth, the density becomes 
2°66. If s denotes the density at the surface of the inner nucleus, and the 
same symbols are employed as before, we obtain for the density, 9,, h km. 
above this surface, since a= R, —h, +h, anda, = R,, 
e =s — 000177 h. 
This gives a very trifling change of density in the external strata of the 
earth. In the earth’s crust, however, which has been subject to a more 
rapid cooling and less pressure than the interior of the earth, we may possibly 
1 F. R. Hermerr. Hoéhere Geoddsie. Bad. Il, p. 487. 
