70 0. E. SCHI0TZ. [NORW. POL. EXP. 



nent, but greater than normal if it is beyond the coast-line, out on the ocean ; 

 and this is on the very assumption that there is an equal amount of matter under 

 surface-elements of equal size, in both places. 



If, however, the density undergoes finite changes from one place to another, 

 the change in the integral on the right side of equation VI may be of the 

 same order as the integral itself, and the acceleration may then show an increase, 

 even if the element, R 2 dw', cut off by the tube of force, is greater than 

 normal, and a decrease if it is smaller than normal. 



We have, in the above, only considered the lowlands on the continents. 

 Experience seems to show with regard to the mountain regions and the elevated 

 plateaus, that this accumulation of matter above the level of the sea is compen- 

 sated on the whole by deficiency of matter in the depths. If this be so, there 

 should also, on an average, be the same quantity of matter above every unit 

 element of the surface of the inner nucleus beneath these portions of the con- 

 tinents as beneath the remainder of the earth's surface. 1 It has been to 

 some extent supposed that this compensation depends upon an equilibrium of 

 pressure of all parts of the earth's crust upon the inner nucleus. It is easy 

 to show that in this case too, the two suppositions are almost equally good. 

 If the mean elevation of the plateaus is h', and if their density is assumed 

 to be (i, as in the upper part of the continents, we have only to add g^'li' 



h< 



2 f 

 to the right side of equation (III), and the integral p Ip, h dh to the left side 



^o J 



o 



of equation (IV). Equation (V) will then become 



Thus the term p/fe'^-has been added here. If we assume the same 

 *e 



quantity of matter over every element of the surface of the inner nucleus, 

 then, in order to obtain an equilibrium of pressure upon the latter as regards 

 the continents, we must add, at sea-level, a layer of rock of a thickness 



F. R. HELMERT. Where Geod&sie Bd. II, p. 365. 



