DUE TO THE WEIGHT OF CONTINENTS. 
205 
to 152 X '1039 X 10 -6 metric tonnes per square centimeter, and a central stress- 
difference of eight times as much. 
Since a metric tonne is a million grammes this surface stress-difference is 16 grammes, 
and the central 128 grammes per square centimeter. These stress-differences are 
exactly the halves of those which have been computed above. Thus the remaining 
stress-difference which is due to the moon’s tide-generating influence is 16 grammes 
at the surface and 128 grammes at the centre per square centimeter. 
A flaw in this reasoning is that stress-difference is a non-linear function of the 
stresses, and therefore the stress-difference arising from the sum of two sets of bodily 
stresses is not the sum of their separate stress-differences. 
I conceive however that the above conclusion is not likely to be much wrong. 
These stresses are very small compared with those arising from the weights of 
mountains and continents as computed below, nevertheless they are so considerable 
that we can understand the enormous rigidity which Sir William Thomson has 
shown that the earth must possess in order to resist considerable tidal deformations 
of its mass. 
§ 6. On the stresses due to a series of parallel mountain chains . 
Having considered the case of the second harmonic, I now pass to the other extreme 
and suppose the order of harmonics i to be infinitely great, whilst the radius of the 
sphere is also infinitely great. 
The equatorial belt now becomes infinitely wide, and the surface inequalities consist 
of a number of parallel simple harmonic mountains and valleys. 
If i be infinitely large, we have from (12) 
Now let f be the depth below the surface of the point indicated in the sphere (now 
infinitely large) by x, y, z. 
As the formulas given above apply to the meridional plane for which y— 0, we 
have p=a— f. 
Now let b=a/i , then when both i and a are infinite 
A 1 -^- 
:ale-^ b 
and since in the limit p/i=a/i=b, 
( *1 ^2 1 yi 
Y z a [ 21 6 3 ^4! Z> 4 &G ' 
cos 
b 
This expression for W involves the infinite factor a\ and in order to get rid of it we 
