222 C. Davison—Secular Straining of the Earth. 
temperature. The state of temperature may then on the same scale 
be represented by the curve ace. The temperature corresponding 
to the depth an is now represented by the line nq instead of NP, so 
_that the amount of heat lost in the interval is represented by the 
length of the line ap. If we now suppose the line nap to start from 
Ap and to move downwards, keeping parallel to itself, the part op, 
at first zero increases for a certain distance, until it becomes a 
maximum, and then it decreases until the line nap reaches the 
position BEC, where it is practically again zero. Since the rate of 
cooling is proportional to the amount of heat lost in a given time, it 
follows that this rate is zero at the surface, that it increases as the 
depth from the surface of the earth increases, until it is a maximum, 
after which it decreases, becoming insensible at a depth of two or 
three hundred miles. Ifthe time since the earth solidified be 100 
million years, Prof. G. H. Darwin has shown! that the depth at 
which the rate of cooling is greatest is about 53 miles. He has 
shown also that this depth increases in proportion to the square root 
of the time, that is, at four hundred million years the depth will be 
twice as great as this, three times as great at nine hundred million 
years, and soon. At the initial epoch, it coincided with the surface 
of the earth. 
If a sphere, having the same centre as the earth, pass through the 
point at which the rate of cooling ceases to be sensible, it will 
include within it the whole mass of the earth which has not yet 
begun to lose its heat, the ‘uncooled nucleus,” as it has been called 
above. The rest of the earth, constituting the ‘“ cooling layer,” 
may be supposed to be divided up into a very great number of very 
thin shells by spherical surfaces all having the same centre as the 
earth. Hach shell must be imagined so thin that the rate of cooling 
varies by an infinitely small amount between the inner and outer 
surfaces of the shell. 
Let us now consider the consequences of the method of cooling 
described above; and, first, in the lowest shell of the cooling layer, 
that next to, and surrounding, the uncooled nucleus. In a given 
time, this shell loses a definite, though small, amount of heat, in 
consequence of which it must contract in volume. If the shell were 
isolated, it would also contract in radius, by an amount proportional 
to the loss of heat. But this is prevented by the presence of the 
nucleus within. The contraction can therefore be accomplished 
only by the shell stretching over the nucleus, at the same time 
diminishing in thickness. 
The next succeeding shell is stretched in a similar manner. If 
the loss of heat were the same as in the first shell, both shells 
would be stretched by very nearly the same amount. But it loses 
more heat in the same time, for the rate of cooling at first increases 
from the nucleus outwards. The second shell is therefore stretched 
more than the first. In like manner, the third is stretched more 
than the second; and this is the case with every shell to very nearly 
as far as the surface where the rate of cooling is greatest. 
1 Nature, vol. xix. p. 313. 
