230 ON THE STRESSES DUE TO THE WEIGHT OF CONTINENTS. 
In the present paper it has been impossible to take any notice of the stresses pro¬ 
duced by the most fundamental inequality on the earth’s surface; because it depends 
essentially on heterogeneity of density. 
It is well known that the earth may be divided into two hemispheres, one of which 
consists almost entirely of land, and the other of sea. If the south of England be 
taken as the pole of a hemisphere, it will be found that almost the whole of the land, 
excepting Australia, lies in that hemisphere, whilst the antipodal hemisphere consists 
almost entirely of sea. This proves that the centre of gravity of the earth’s mass is 
more remote from England, than the centre of figure of the solid globe. 
A deformation of this kind is expressed by a surface harmonic of the first order, for 
such an harmonic is equivalent to a small displacement of the sphere as a whole, with¬ 
out true deformation. Now if we consider the surface forces produced by such a 
deformation in a homogeneous sphere, we find of course that there is an unbalanced 
resultant force acting on the whole sphere in the direction diametrically opposed to 
that of the equivalent displacement of the whole sphere. 
The fact that in the homogeneous sphere such an unbalanced force exists shows that 
in this case the problem is meaningless; it is in fact merely equivalent to a mischoice 
in the origin for the coordinates. But in the case of the earth such an inequality does 
exist, and the force referred to must of course be counterbalanced somehow. The 
balance can only be maintained by inequalities of density, which are necessarily 
unknown. The problem therefore apparently eludes mathematical treatment. 
It is certain that so wide-spreading an inequality, even if not great in amount, must 
produce great stress within the globe. And just as the 2nd harmonic produces a 
more even distribution of stress than the 4th, so it is likelv that the first would 
produce a more even distribution than the 2nd. 
It is difficult to avoid the conclusion that the whole of the solid portion of the earth 
is in a sensible state of stress. 
I would not however lay very much emphasis on this point, because we are in such 
complete ignorance as to the manner in which the equilibrium of the solid part of the 
earth is maintained. 
From this discussion it appears that if the earth be solid throughout, then at a 
thousand miles from the surface the material must be as strong as granite. If it be 
fluid or gaseous inside, and the crust a thousand miles thick that crust must be 
stronger than granite, and if only two or three hundred miles in thickness much 
stronger than granite. This conclusion is obviously strongly confirmatory of Sir 
William Thomson’s view that the earth is solid throughout. 
