BARTH’S CRUST RESULTING FROM SECULAR COOLING. 
239 
(17) First, the problem investigated is not one according to nature. For it takes 
no account of the time during which the cooling has taken place; and, therefore, 
being independent of the time, the effect must be the same as if the cooling were 
suddenly accomplished. But sudden cooling involves the impossible supposition that 
k, the rate of conductivity, should be infinite. 
(18) But, again, let us for a moment imagine that the temperature of the Earth’s 
crust (supposed solid) did suddenly change from a uniform one throughout to its 
present condition as given by Sir W. Thomson’s solution. Let us further assume the 
Earth’s surface to have been initially spherical, and the Earth to be divided into a very 
great number of very thin shells by spheres concentric with the Earth ; the shells being 
so thin that the cooling throughout each may be considered uniform. 
Then the loss of heat experienced by any one of these shells is V — v, where V was 
its initial and v is its present temperature. And, as v increases with the depth from 
the surface, it follows that V — v diminishes as the depth increases. 
Consider any two consecutive shells. Since the upper shell is cooled by the greater 
amount, its inner surface would, if free, contract more than the outer surface of the 
shell below; but, being forced to remain of the same radius as the latter after its 
contraction (and straining), it follows that the upper shell must be stretched in order 
to rest upon the lower. 
The same reasoning applies to every pair of consecutive shells from the greatest 
depth at which Y — v is a sensible quantity to the very surface of the Earth. Hence, 
on the assumption of sudden cooling throughout the whole of the Earth’s crust that 
has so far undergone cooling, there ought only to be crust-stretching by lateral 
tension, and not any crust-folding by lateral pressure. 
But, as shown above in § (11), lateral pressure, brought into action by secular 
cooling, does produce folding in the Earth’s crust—to a limited depth, it is true, and 
in rock that may already once have been stretched by lateral tension. 
I maintain, therefore, that an argument built up on the virtual hypothesis of a 
sudden cooling of the globe, however favourable to the contraction theory the other 
data employed may be, loses its force when we consider the natural process of a 
continuous and gradual cooling. 
(19) Lastly, even if it were to be proved that the volume of rock folded by lateral 
pressure due to secular cooling is insufficient to produce the existing inequalities of 
land and ocean-basin, it would in no wise follow that the mountain-chains alone could 
not be so produced. And it should be remembered that this is all that is generally 
asserted by the advocates of the contraction theory. Mr. Fisher’s argument assumes 
that the Earth’s surface was initially spherical. But Professor B. Peirce # and 
Professor G. H. Darwin + have shown that vast wrinkles would be formed on the 
* “ The Contraction of the Earth,” ‘Nature,’ Feb. 16, 1871 (vol. 3, p. 315), reprinted from the 
‘ Proceedings of the American Academy of Arts and Sciences,’ vol. 8. 
t “Problems connected with the Tides of a Viscous Spheroid,” ‘Phil. Trans.,’ 1879 (Part 2), 
pp. 539-593. 
