226 
MR. G. H. DARWIN ON THE STRESSES 
geoid.* From the geodesic point of view the conception is valuable, but such an 
estimate is scarcely what we require in the present case. The mean geoid itself will 
necessarily partake of the contortions of the solid earth’s surface, even apart from 
disturbances caused by local inequalities of density, and thus it cannot be a figure of 
equilibrium. 
Thus, even if we were to suppose that the solid earth were everywhere coincident 
with a geoid—which is far from being the case—a state of stress would still be 
produced in the interior of the earth. 
An example of this sort of consideration is afforded by the geodesic results arrived 
at by Colonel Clarke, B.E.,t who finds that the ellipsoid which best satisfies 
geodesic measurement, has three unequal axes, and that one equatorial semi-axis is 
1524 feet longer than the other. Now 7 - such an ellipsoid as this, although not exactly 
one of Bruns’ geoids, must be more nearly so than any spheroid of revolution ; and 
yet this inequality (if really existent, and Colonel Clarke’s own words do not express 
any very great confidence) must produce stress in the earth. Colonel Clarke’s 
results show an ellipticity of the equator equal to Y37i t, an d this in the homogeneous 
elastic earth will be about equivalent to ellipticity ytuo o i such ellipticity would 
produce a centra] stress-difference of yVwo or nearly one-third of a British ton per 
square inch. 
From this discussion it may, I think, be fairly concluded that if we assume the sea- 
level as being the figure of equilibrium and estimate the departures therefrom, we shall 
be well within the mark. 
The average height of the continents is about 350 meters (1150 feet), and the 
average depth of the great oceans is in round numbers 5000 meters (16,000 feet); 
but the latter datum is open to much uncertainty.^ When the sea is solidified into 
rock the 5000 meters of depth is reduced to 3200 meters below the actual sea-level. 
Thus the average effective depression of sea-bed is about nine times as great as the 
average height of the land. I shall take it as exactly nine times as great, and put the 
depth as 3150 meters; but it is of course to be admitted that perhaps eight and 
perhaps ten might be more correct factors. 
In the analytical investigation of this paper the outlines of the vertical section of the 
•continents and depressions are always sweeping curves of the harmonic type, and the 
magnitude of the elevations and depressions are estimated by the greatest heights 
and depths, measured from a mean surface which equally divides the two. 
We have already supposed the outlines of continents and sea-beds to have been 
smoothed down into sweeping curves, which w T e may take as being, roughly speaking, 
of the harmonic type. The smoothing will have left the averages unaffected. 
* ‘ Die Eigur der Erde.’ Yon Dr. H. Bruns. Berlin: Stankiewicz, 1878. 
f Phil. Mag., Aug., 1878. 
+ In a previous paper, “ Geological Changes, &c.,” Phil. Trans., Yol. 167, Part I., p. 295, I have 
endeavoured to discuss this subject, and references to a few authorities will be found there. 
