WITH THE TIDES OF A VISCOUS SPHEROID. 
565 
throughout the whole earth, which we called H. Suppose that p times the present 
kinetic energy of the earth’s rotation is destroyed by friction in a time T, and suppose 
the generation of heat to be uniform in time, then the average heat generated through¬ 
out the whole earth per unit time is 
Therefore 
yJT ' 51V1(X 0 
earth’s volume. 
vsadn^ 
9 
4 
2 5 
P 
jrp wae 0 . 
Where e 0 is the ellipticity of figure of the homogeneous earth and is equal to \ ~"y, 
which I take as equal to 
Hence 
—9500 jT Wae <» 
and 
dp 16x85/7 r\3 w pe 0 t 
~dx~ 9500 \2/ 7 ~J~T* 
But y—sw, where s is specific heat. 
Therefore 
dp _ 1 707 t 3 pe 0 1 t 
dx 9500 s JT' 
The dimensions of J are those of work (in gravitation units) per mass and per scale 
of temperature, that is to say, length per scale of temperature ; p, <? 0 , and s have no 
dimensions, and therefore this expression is of proper dimensions. 
Now suppose the solution to run for the whole time embraced by the changes 
considered in “Precession,” then t—T, and as we have shown p-= 13*57. Suppose 
the specific heat to be that of iron, viz.: -g-. Then if we take J=772, so that the 
result will be given in degrees Falnenheit per foot, we have 
_dp_ 17tP 13-57 x 9 
~dx~ 950 X 232x772 
_ 1 
2650’ 
That is to say, at the end of the changes the temperature gradient would be 1° Fabr. 
per 2,650 feet, provided the whole operation did not take more than 1,000 million 
years. 
It might, however, be thought that if the tidal friction were to operate very slowly, 
