DUE TO THE WEIGHT OE CONTINENTS. 
219 
In this paper I have solved a problem of the kind indicated for the case of a 
homogeneous incompressible elastic sphere, and have applied the results to the case 
of the earth. 
It may of course be urged that the earth is not such as this treatment postulates. 
The view which was formerly generally held was that the earth consists of a solid 
crust floating on a molten nucleus. It has also been lately maintained by Dr. August 
Ritter in a series of interesting papers that the interior of the earth is gaseous.*'* 
A third opinion, contended for by Sir W illiam Thomson, and of which I am myself 
an adherent, is that the earth is throughout a solid of great rigidity ; he explains 
the flow of lava from volcanoes either by the existence of liquid vesicles in the interior, 
or by the melting of solid matter, existing at high temperature and pressure, at points 
where diminution of pressure occurs. 
There is another consideration, which is consistent with Sir William Thomson’s 
view, and which was pointed out to me by Professor Stokes. It may be that under¬ 
neath each continent there is a region of deficient density; then underneath this 
region there would be no excess of pressure. 
For the present investigation it is to some extent a, matter of indifference as to 
which of these views is correct, for if it is only the crust of the earth which possesses 
rigidity, or if Professor Stokes’s suggestion of the regions of deficient density be 
correct, then the stresses in the crust or in the parts near the surface must be greater 
than those here computed—enormously greater if the crust be thin,t or if the region 
of deficient density be of no great thickness. 
With regard to the property of incompressibility which is here attributed to the 
elastic sphere, it appears from §10 that even if we suppose the elastic solid to be very 
highly compressible, yet the results with regard to the internal stresses are almost the 
same as though it were incompressible. I think the hypothesis of great incompressi¬ 
bility is likely to be much nearer to the truth than is that of great compressibility. 
I shall therefore adhere to the supposition of infinite incompressibility, bearing in 
mind that even great compressibility would not much affect most of the results. 
I take then a homogeneous incompressible elastic sphere, and suppose it to have the 
* ‘ Anwendung der mechanischen Warmetheorie auf kosmologisclie Probleme.’ Carl Rumpler, 
Hannover, 1879. This is a reprint of six papers in Wiedemann’s Annalen. 
Dr. Ritter contends that the temperature in the interior of the planet is above the critical tempera¬ 
ture and that of dissociation for all the constituents, so that they can only exist as gas. Data are wanting 
with regard to the mechanical properties of matter at, say 10,000° Eahr., and a pressure of many tons to 
the square inch. Is it not possible that such “ gas” may have the density of mercury and the rigidity 
and tenacity of granite P Although such a conjectural “ gaseous ” solid might possess high rigidity, it 
almost certainly would have great compressibility: but it is proved in § 10 that the compressibility will 
make exceedingly little difference in the result of the present investigation excepting in the case of the 
2 nd harmonic inequality. 
f The evaluation of the stresses in a crust, with fluid beneath, would be tedious, but not more difficult 
than the present investigation. I may perhaps undertake this at some future time. 
2 F 2 
