eral attains a value
no higher than 270 deg. C. is hardly tenable. We conclude, then, that
some other source of heat exists beneath. This may be radioactive
in origin and may be easily accounted for if the radioactive
materials are more sparsely distributed at the base of the upper
crust. Or, again, the heat may be primeval or original heat,
still escaping from a cooling world. For our present purpose it
does not much matter which view

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we adopt. But we must recognise that the calculated depth of 19
kilometres of crust, possessing the average radioactivity of the
surface, is excessive; for, in fact, we are compelled by the
facts to recognise that some other source of heat exists
beneath.

If the observed surface gradient of temperature persisted
uniformly downwards, at some 35 kilometres beneath the surface
there would exist temperatures (of about 1000 deg. C.) adequate to
soften basic rocks. It is probable, however, that the gradient
diminishes downwards, and that the level at which such
temperatures exist lies rather deeper than this. It is,
doubtless, somewhat variable according to local conditions; nor
can we at all approximate closely to an estimate of the depth at
which the fusion temperatures will be reached, for, in fact, the
existence of the radioactive layer very much complicates our
estimates. In what follows we assume the depth of softening to
lie at about 40 kilometres beneath the surface of the normal
crust; that is 25 miles down. It is to be observed that Prestwich
and other eminent geologists, from a study of the facts of
crust-folding, etc., have arrived at similar estimates.[1] As a
further assumption we are probably not far wrong if we assign to
the radioactive part of this crust a thickness of about 10 or 12
kilometres; _i.e._ six or seven miles. This is necessarily a
rough approximation only; but the conclusions at which

[1] Prestwich, _Proc. Royal Soc._, xii., p. 158 _et seq._

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we shall arrive are reached in their essential features allowing
a wide latitude in our choice of data. We shall speak of this
part of the crust as the normal radioactive layer.

An important fact is evolved from the mathematical investigation
of the temperature conditions arising from the presence of such a
radioactive layer. It is found that the greatest temperature, due
to the radioactive heat everywhere evolved in the layer--_i.e._
the temperature at its base--is proportional to the square of the