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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 thickness of the layer.  This fact has a direct bearing on the influence of radioactivity upon mountain elevation; as we shall now find.

The normal radioactive layer of the Earth is composed of rocks extending—­as we assume—­approximately to a depth of 12 kilometres (7.5 miles).  The temperature at the base of this layer due to the heat being continually evolved in it, is, say, t1 deg..  Now, let us suppose, in the trough of the geosyncline, and upon the top of the normal layer, a deposit of, say, 10 kilometres (6.2 miles) of sediments is formed during a long period of continental denudation.  What is the effect of this on the temperature at the base of the normal layer depressed beneath this load?  The total thickness of radioactive rocks is now 22 kilometres.  Accordingly we find the new temperature t2 deg., by the proportion t1 deg. :  t2 deg. ::  12 deg. :  22 deg.  That is, as 144 to 484.  In fact, the temperature is more than trebled.  It is true we here assume the radioactivity of the sediments