WITH THE TIDES OF A VISCOUS SPHEROID. 
559 
This expression gives the rate of generation of heat at any point in terms of the 
average rate, and if we equate it to a constant we get the equation to the family of 
surfaces of equal heat-generation. 
We may observe that the heat generated at the centre is 3-Jy times the average, at 
the pole —■ of the average, and at the equator —^ of the average. 
The accompanying figure exhibits the curves of equal heat-generation; the dotted 
line shows that of ^ of the average, and the others those of 1, lijr, 2, 2\, and 3 times 
the average. It is thus obvious from inspection of the figure that by far the largest 
part of the heat is generated in the central regions. 
The next point to consider is the effect which the generation of heat will have 011 
underground temperature, and how far it may modify the investigation of the secular 
cooling of the earth. 
It has already been shown'" that the total amount of heat which might be generated 
is very large, and my impression was that it might, to a great extent, explain the 
increase of temperature underground, until a conversation with Sir W. Thomson led 
me to undertake the following calculations :— 
We will first calculate in what length of time the earth is losing by cooling an 
amount of energy equal to its present kinetic energy of rotation. 
The earth’s conductivity may be taken as about ‘004 according to the results given 
in Everett’s illustrations of the centimeter-gram-second system of units, and the 
temperature gradient at the surface as 1° C. in meters, which is the same as 
=>1° Fahr. in 50 feet—the rate used by Sir W. Thomson in his paper on the cooling of 
the earth.t 
This temperature gradient is — degrees C. per centimeter, and since there are 
31,557,000 seconds hr a year, therefore in centimeter-gram-second units, 
* “ Precession,” Section 15, Table IV., and Section 16. 
f Thomson and Tait’s ‘Nat. Phil.,’ Appendix D. 
4 O 
MDCCCLXXIX. 
