66 0. E. SCHI@TZ. [NORW. POL. EXP. 
hy hy hy 
[# R? dw e, dh—=f M, do fe dh=f >t My Ri do [ey a= 
0 0 
hy 
=g, R ao |e, dh, 
0 
and under the oceans to 
=I he 
g, Ri dw (fe an + | dh. 
0 hy—ha 
These two pressures are not equally great, and their difference 2, 
hy —he hy 
4= 9, Fi dw (lle, —@)dh+ (le, —1) ah} I. 
0 hi—ha 
must, as we shall immediately see, be negative. In order to produce the 
distribution of matter in the earth’s crust, that is found beneath the portions 
of continent under consideration, from the distribution of matter that exists 
beneath the oceans, masses must be removed from the deeper strata, and 
added above, where the sea is found; and in this way the attraction exerted 
by the interior nucleus upon the masses, and consequently their pressure 
upon it, are diminished. The sum of the two integrals in IJ, must thus, as 
already mentioned, be negative. 
It is easy to find an approximate value for this sum, and thus for the 
difference in pressure, 4, even if nothing more is known as to how the 
density changes down a vertical line from the surface. If we call the sum 
of the integrals J, we may put 
hy— ha hy 
= {le =) an + les —1)dh=o'(h, —hy)+(e1—Ah,, UL 
0 hy — Ia 
where 0’ indicates the difference between the mean values of the densities 
e, and @ in the crust reaching from h = 0 to h=h, —hy, and e,‘ is the 
average density in the uppermost stratum of continent of thickness hg. 
According to equation I., we now have, neglecting quantities of the second 
order, 
hy —he hy 
y 
i+ 7, [le — et —hy)an+ |e, — 1) (h—h,)dh]=0. IV. 
hy —he 
