592 
MR. G. H. DARWIN ON PROBLEMS CONNECTED 
shows that by far the larger part of the heat is generated in the central parts, and 
calculation shows that about one-third of the whole heat is generated within the central 
one-eighth of the volume, whilst in a spheroid of the size of the earth only one-tenth 
is generated within 500 miles of the surface. 
In the paper on “ Precession ” the changes in the system of the sun, moon, and 
earth were traced backwards from the present lengths of day and month back to a 
common length of day and month of 5 hours 36 minutes, and it was found that in 
such a change heat enough must have been generated within the earth to raise its 
whole mass 3000° Fahr. if applied all at once, supposing the earth to have the specific 
heat of iron. It appeared to me at that time that, unless these changes took place at 
a time very long antecedent to geological history, then this enormous amount of in¬ 
ternal heat generated would serve in part to explain the increase of temperature in 
mines and borings. Sir William Thomson, however, pointed out to me that the 
distribution of heat-generation would probably be such as to prevent the realisation of 
my expectations. I accordingly made the further calculations, connected with the 
secular cooling of the earth, comprised in the latter portion of Part II. 
It is first shown that, taking certain average values for the increase of underground 
temperature and for the conductivity of the earth, then the earth (considered homo¬ 
geneous) must be losing by conduction outwards an amount of energy equal to its 
present kinetic energy of rotation in about 262 million years. 
It is next shown that in the passage of the system from a day of 5 hours 40 minutes 
to one of 24 hours, there is lost to the system an amount of energy equal to 13^- times 
the present kinetic energy of rotation of the earth. Thus it appears that, at the 
present rate of loss, the internal friction gives a supply of beat for 3,560 million years. 
So far it would seem that internal friction might be a powerful factor in the secular 
cooling of the earth, and the next investigation is directly concerned with that question. 
In the case of the tidally-distorted sphere the distribution of heat-generation 
depends on latitude as well as depth from the surface, but the average law of heat- 
generation, as dependent on depth alone, may easily be found. Suppose, then, that 
we imagine an infinite slab of rock 8,000 miles thick, and that we liken the medial 
plane to the earth’s centre and suppose the heat to be generated uniformly in time, 
according to the average law above referred to. Then conceive the two faces of the 
slab to be always kept at the same constant temperature, and that initially, when 
the heat-generation begins, the whole slab is at this same temperature. The problem 
then is, to find the rate of increase of temperature going inwards from either face of 
the slab after any time. 
This problem is solved, and by certain considerations (for which the reader is referred 
back) is made to give results which must agree pretty closely with the temperature 
gradient at the surface of an earth in which 13^ times the present kinetic energy of 
earth’s rotation, estimated as heat, is uniformly generated in time, with the average 
space distribution referred to. It appears that at the end of the heat-generation the 
