Part 21

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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. 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

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

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and of the normal crust to be the same. The sediments are, however, less radioactive in the proportion of 4 to 3. Nevertheless the effects of the increased thickness will be considerable.

Now this remarkable increase in the temperature arises entirely from the condition attending the radioactive heating; and involves something additional to the temperature conditions determined by the mere depression and thickening of the crust as in the Babbage-Herschel theory. The latter theory only involves a shifting of the temperature levels (or geotherms) into the deposited materials. The radioactive theory involves an actual rise in the temperature at any distance from the surface; so that the level in the crust at which the rocks are softened is nearer to the surface in the geosynclines than it is elsewhere in the normal crust (Pl. XV, p. 118).

In this manner the rigid part of the crust is reduced in thickness where the great sedimentary deposits have collected. A ten-kilometre layer of sediment might result in reducing the effective thickness of the crust by 30 per cent.; a fourteen-kilometre layer might reduce it by nearly 50 per cent. Even a four-kilometre deposit might reduce the effective resistance of the crust to compressive forces, by 10 per cent.

Such results are, of course, approximate only. They show that as the sediments grow in depth there is a rising of the geotherm of plasticity--whatever its true temperature may be--gradually reducing the thickness of that part

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of the upper crust which is bearing the simultaneously increasing compressive stresses. Below this geotherm long-continued stress resolves itself into hydrostatic pressure; above it (there is, of course, no sharp line of demarcation) the crust accumulates elastic energy. The final yielding and flexure occur when the resistant cross-section has been sufficiently diminished. It is probable that there is also some outward hydrostaitic thrust over the area of rising temperature, which assists in determining the upward throw of the folds.

When yielding has begun in any geosyncline, and the materials are faulted and overthrust, there results a considerably increased thickness. As an instance, consider the piling up of sediments over the existing materials of the Alps, which resulted from the compressive force acting from south to north in the progress of Alpine upheaval. Schmidt of Basel has estimated that from 15 to 20 kilometres of rock covered the materials of the Simplon as now exposed, at the time when the orogenic forces were actively at work folding and shearing the beds, and injecting into their folds the plastic gneisses coming from beneath. The lateral compression of the area of deposition of the Laramide, already referred to, resulted in a great thickening of the deposits. Many other cases might be cited; the effect is always in some degree necessarily produced.

Schmidt, Ec. Geol. Helvelix, vol. ix., No. 4, p. 590

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If time be given for the heat to accumulate in the lower depths of the crushed-up sediments, here is an additional source of increased temperature. The piled-up masses of the Simplon might have occasioned a rise due to radioactive heating of one or two hundred degrees, or even more; and if this be added to the interior heat, a total of from 800 deg. to 1000 deg. might have prevailed in the rocks now exposed at the surface of the mountain. Even a lesser temperature, accompanied by the intense pressure conditions, might well occasion the appearances of thermal metamorphism described by Weinschenk, and for which, otherwise, there is difficulty in accounting.

This increase upon the primarily developed temperature conditions takes place concurrently with the progress of compression; and while it cannot be taken into account in estimating the conditions of initial yielding of the crust, it adds an element of instability, inasmuch as any progressive thickening by lateral compression results in an accelerated rise of the goetherms. It is probable that time sufficient for these effects to develop, if not to their final, yet to a considerable extent, is often available. The viscous movements of siliceous materials, and the out-pouring of igneous rocks which often attend mountain elevation, would find an explanation in such temperatures.

Weinschenk, Congres Geol. Internat., 1900, i., p. 332.

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There is no more striking feature of the part here played by radioactivity than the fact that the rhythmic occurrence of depression and upheaval succeeding each other after great intervals of time, and often shifting their position but little from the first scene of sedimentation, becomes accounted for. The source of thermal energy, as we have already remarked, is in fact transported with the sediments--that energy which determines the place of yielding and upheaval, and ordains that the mountain ranges shall stand around the continental borders. Sedimentation from this point of view is a convection of energy.

When the consolidated sediments are by these and by succeeding movements forced upwards into mountains, they are exposed to denudative effects greatly exceeding those which affect the plains. Witness the removal during late Tertiary times of the vast thickness of rock enveloping the Alps. Such great masses are hurried away by ice, rivers, and rain. The ocean receives them; and with infinite patience the world awaits the slow accumulation of the radioactive energy beginning afresh upon its work. The time for such events appears to us immense, for millions of years are required for the sediments to grow in thickness, and the geotherms to move upwards; but vast as it is, it is but a moment in the life of the parent radioactive substances, whose atoms, hardly diminished in numbers, pursue their changes while the mountains come and go, and the

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rudiments of life develop into its highest consummations.

To those unacquainted with the results of geological investigation the history of the mountains as deciphered in the rocks seems almost incredible.

The recently published sections of the Himalaya, due to H. H. Hayden and the many distinguished men who have contributed to the Geological Survey of India, show these great ranges to be essentially formed of folded sediments penetrated by vast masses of granite and other eruptives. Their geological history may be summarised as follows