23 G 
MR. C. DAYISON ON THE DISTRIBUTION OF STRAIN IN THE 
( 10 ) The continuous curve also represents approximately the volume that, in a 
given time, is stretched or folded of any shell. For, let r be the radius of the 
internal surface of any shell, a its thickness; let r' and a be what these values would 
naturally become by cooling if the shell were isolated ; and let r + 8 be the radius of 
the globe on which this shell is obliged to fit, 8 being small compared with r . If the 
shell were isolated, its volume after cooling would naturally be 47r/ /3 a'. But the 
volume of the shell of radius r -f- 8 and thickness a is irra (r' 2 + 2 r'S). Hence the 
amount of the shell that is stretched or folded is equal to — 87 Tar'S, the shell being 
stretched or folded according as 8 is positive or negative. This expression, at a given 
time, varies nearly as 8, and therefore the continuous curve of the figure may be 
considered to represent very fairly the amount of rock stretched or folded at any 
depth. 
(11) Without attributing much weight to the numerical results of these calcula¬ 
tions—for, on account of our ignorance on many points, they are given rather for 
their qualitative than their quantitative value—the following conclusions may be 
deduced from them, taking t provisionally at 174,240,000 years :— 
1. Folding by lateral pressure changes to stretching by lateral tension at a depth 
of about 5 miles. 
2. Stretching by lateral tension, inappreciable below a depth of about 400 miles, 
increases from that depth towards the surface; it is greatest at a depth of 72 miles, 
that is, just below the surface of greatest rate of cooling ;* after this, it decreases, 
and vanishes at a depth of about 5 miles. 
3. Folding by lateral pressure commences at a depth of about 5 miles, and 
gradually increases, being greatest near the surface of the Earth.t 
(12) Since, at the depth at which folding by lateral pressure vanishes, the thin 
spherical shell cools and naturally contracts without straining, it follows that the 
folding of the outer crust is exactly the same as it would be if the whole globe 
beneath the unstrained shell were to cool uniformly throughout, and at the same rate 
as at the unstrained surface. 
It will be seen, in the next paragraph, that the depth of this surface increases with 
the time since consolidation. Hence a part of the crust at one time stretched by 
lateral tension may at some later period be folded by lateral pressure. 
* If t = 174,240,000 years, the depth, of the surface of greatest rate of cooling is about 71 miles. As 
the surface of greatest stretching should be just below the surface of greatest rate of cooling, this close 
approximation indicates the degree of accuracy of the assumptions made in § (9). 
f The limited depth to which crust-folding extends may, perhaps, be considered as an argument 
against the contraction theory on the hypothesis of solidity, inasmuch as room is apparently not afforded 
for the accumulation of sediment to the estimated thicknesses of 40,000 feet in the Alleghany Mountains 
and 60,000 feet in the Rocky Mountains. But, assuming such estimates to be correct, it should be 
remembered that the depth of the unstrained shell has been calculated on the supposition that the 
surface of the Earth is smooth and spherical; and it is probable that the existence of the surface 
inequalities would account for folds amply large enough to bury the thickest known masses of sediment. 
