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°. 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°, by the proportion t1° : t2° ::
12° : 22° 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.