THE PRESIDENTIAL ADDRESS. 9 
present gradient, and would even be far more than sufficient unless the 
amount of radioactive material concerned were strictly limited. Assuming 
an average distribution of such material similar to what is found near the 
surface, a stratum of some 16 kilometres in thickness would provide all 
that is wanted. Radioactive speculation has gone further. A comparison 
of the amounts of uranium, and of the end-products associated with it, 
has led to estimates of the time that has elapsed since the final consolidation 
of the earth’s crust. The conclusion is, that it must lie definitely between 
10° and 10” years. The figure is necessarily vague owing to the rough 
value of some of the data, but even the lower of these limits is one which 
geologists and biologists are, I believe, willing to accept, as giving ample 
scope for the drama of evolution. We may say that physics has at length 
amply atoned for the grudging allowance of time which it was once dis- 
posed to accord for the processes of geological and biological change. The 
radioactive arguments on which these estimates are based are apparently 
irrefutable ; but from the physical point of view, there are reasons why 
one would welcome an extension even of the upper limit of 10” years, 
if this could possibly be stretched. For if this barrier be immovable, we 
are led to conclusions as to the present internal temperature of the earth 
which are not quite easy to reconcile with the evidence as to rigidity to be 
referred to in a moment. In the space of time I have mentioned, enormous 
as it is, the great mass of the earth could hardly have cooled very much 
from the temperature when it was in a state of fusion. The central portion, 
whatever its nature, and however high its thermal conductivity, is enclosed 
by a thick envelope of feebly conducting material, just as a steam boiler, 
for instance, may be jacketed with a layer of asbestos. To take a calculable 
hypothesis, we may assume with Wiechert that we have a central core 
of three-fourths the earth’s radius, with an outer shell of rock. We may 
give the core any degree of conductivity we like ; for mathematical sim- 
plicity we may even regard it as infinite. Then, if the outer layer consists 
of material having some such conductivity as the surface rocks, the internal 
temperature would take to fall to one-half its original value a period of at 
least ten times the limit I have named. It is obvious that the details of 
the assumption may be greatly varied without affecting the general 
conclusion of a very high internal temperature. 
The question as to the degree of rigidity of the earth has so often been 
dealt with, that a brief recapitulation will suffice. It was about the year 
1862 that Kelvin first pointed out that if the earth as a whole were only 
as rigid as a globe of glass or even steel, it would yield so much to the 
