DUE TO THE WEIGHT OE CONTINENTS. 
225 
approximately spherical. This kind of elevation requires the 2nd as one of its harmonic 
constituents, and this harmonic means ellipticity of the whole globe. Now it may 
perhaps be fairly contended that on the earth we have no such continent as would 
require a perceptible 2nd harmonic constituent. I therefore give in Plate 20, fig. 5, a 
second curve which represents an equatorial belt of elevation counterbalanced by a pair 
of polar continents in such a manner that there is no second harmonic constituent. 
I have not attempted to trace the curves of equal stress-difference arising from 
these two kinds of elevation, but I believe that they will consist of a series of much 
elongated ovals, whose longer sides are approximately parallel with the surface of the 
globe, drawn about the maximum point in the interior of the sphere at the equator. 
The surfaces of equal stress-difference in the solid figure will thus be a number of 
flattened tubular surfaces one within the other. 
At the equator however the law of variation of stress-difference is easy to evaluate, 
and Plate 20, fig. 6, shows the results graphically, the vertical ordinates representing 
stress-difference and the horizontal the depths below the surface. The upper curve in 
Plate 20, fig. 6, corresponds with the “representation curve” of Plate 20, fig. 5, and 
the lower curve with the case where there is no 2nd harmonic constituent. 
The central stress-difference, which may be observed in the upper curve, results 
entirely from the presence of the 2nd harmonic constituent in the corresponding 
equatorial belt of elevation. 
The maximum stress-differences in these two cases occur at about 660 and 590 miles 
from the surface respectively. 
We now come to perhaps the most difficult question with regard to the whole 
subject—namely, how to apply these results most justly to the case of the earth. 
The question to a great extent turns on the magnitude and extent of the superficial 
inequalities in the earth. As the investigation deals with the larger inequalities, it 
will be proper to suppose the more accentuated features of ridges, peaks, and holes to 
be smoothed out. 
The stresses caused in the earth by deficiency of matter over the sea beds are the 
same as though the seas were replaced by a layer of rock, having everywhere a 
thickness of about or nearly of the actual depths of sea. 
The surface being partially smoothed and dried in this manner, we require to find 
an ellipsoid of revolution which shall intersect the corrugations in such a manner that 
the total volume above it shall be equal to the total volume below it. 
Such a spheroid may be assumed to be the figure of equilibrium appropriate to the 
earth’s diurnal rotation; if it departs from the equilibrium form by even a little, then 
we shall much underestimate the stress in the earth’s interior by supposing it to be a 
form of equilibrium. 
Professor Bruns has introduced the term “ geoid ” to express any one of the “ level ” 
surfaces in the neighbourhood of the earth’s surface, and he endeavours to form an 
estimate of the departure of the continental masses and sea-bottoms from some mean 
MDCCCLXXXII. 2 G 
