IN THE EARTH’S CRUST RESULTING FROM SECULAR COOLING. 
249 
This, we have shown above, will be at a depth of 2 or 3 miles. The amount of 
crumpling at the surface is given by putting x — 0, and 
„ §Kt dv 
K — — e — — • 
c dx 
Now we have seen that, if r be the number of millions of years since consolidation, 
— 114 r feet, 
c 
and 
dv 
= 0 o- 02 Fahr. per foot. 
ctoc 
Hence 
K = — re X 2'28. 
The total amount by which a great circle is contracted is 25,000 K miles ; and, 
judging by the coefficient of expansion of metals, e may be about 5 X ID -5 . 
Thus, with these rough data, the amount of crumpling of a great circle of 
radius c is 
27 tcK = r X X (2*5 X 10 4 ) X 2 - 28 = 2’85 r miles. 
Thus, in 10,000,000 years, 28-| miles of rock would be crumpled up. 
The area of rock crumpled is 47 tc 3 . 2 K, and with these numerical data 
47tc 3 .2 K = 4c (27 tc K ). 
Now c = 4000 miles, and therefore 
47tc 3 . 2 K — 22,800 r square miles. 
Thus, in 10,000,000 years, 228,000 square miles of rock will be crumpled up and 
piled on the top of the subjacent rocks. 
The numerical data with which we have to deal are all of them subject to wide 
limits of uncertainty, but the result just found, although rather small in amount, is 
such as to appear of the same order of magnitude as the crumpling observed 
geologically. 
The stretching and probable fracture of the strata at some miles below the surface 
will have allowed the injection of the lower rocks amongst the upper ones, and the 
phenomena which we should expect to find according to Mr. Davison’s theory are 
eminently in accordance with observation. It therefore appears to me that his view 
has a strong claim to acceptance. 
2 k 
MDCCCLXXXVII.—A, 
