The time required to form a halo could be found if on the one
hand we could ascertain the number of alpha rays ejected from the
nucleus of the halo in, say, one year, and, on the other, if we
determined by experiment just how many alpha rays were required
to produce the same
[1] _Phil. Mag._, March, 1907 and February, 1910; also _Bedrock_,
January, 1913. See _Pleochroic Haloes_ in this volume.
21
amount of colour alteration as we perceive to extend around the
nucleus.
The latter estimate is fairly easily and surely made. But to know
the number of rays leaving the central particle in unit time we
require to know the quantity of radioactive material in the
nucleus. This cannot be directly determined. We can only, from
known results obtained with larger specimens of just such a
mineral substance as composes the nucleus, guess at the amount of
uranium, or it may be thorium, which may be present.
This method has been applied to the uranium haloes of the mica of
County Carlow.[1] Results for the age of the halo of from 20 to
400 millions of years have been obtained. This mica was probably
formed in the granite of Leinster in late Silurian or in Devonian
times.
The higher results are probably the least in error, upon the data
involved; for the assumption made as to the amount of uranium in
the nuclei of the haloes was such as to render the higher results
the more reliable.
This method is, of course, a radioactive method, and similar to
the method by helium storage, save that it is free of the risk of
error by escape of the helium, the effects of which are, as it
were, registered at the moment of its production, so that its
subsequent escape is of no moment.
[1] Joly and Rutherford, _Phil. Mag._, April, 1913.
22
REVIEW OF THE RESULTS
We shall now briefly review the results on the geological age of
the Earth.
By methods based on the approximate uniformity of denudative
effects in the past, a period of the order of 100 millions of
years has been obtained as the duration of our geological age;
and consistently whether we accept for measurement the sediments
or the dissolved sodium. We can give reasons why these
measurements might afford too great an age, but we can find
absolutely no good reason why they should give one much too low.
By measuring radioactive products ages have been found which,
while they vary widely among themselves, yet claim to possess
accuracy in their superior limits, and exceed those derived from
denudation from nine to fourteen times.
In this difficulty let us consider the claims of the radioactive
method in any of its forms. In order to be trustworthy it must be
true; (1) that the rate of transformation now shown by the parent
substance has obtained throughout the entire past, and (2) that
there were no other radioactive substances, either now or
formerly existing, except uranium, which gave rise to lead. As
regards methods based on the production of helium, what we have
to say will largely apply to it also. If some unknown source of
these elements exists we, of course, on our assumption
overestimate the age.
23
As regards the first point: In ascribing a constant rate of
change to the parent substance—which Becker (loc. cit.) describes
as "a simple though tremendous extrapolation"—we reason upon
analogy with the constant rate of decay observed in the derived
radioactive bodies. If uranium and thorium are really primary
elements, however, the analogy relied on may be misleading; at
least, it is obviously incomplete. It is incomplete in a
particular which may be very important: the mode of origin of
these parent bodies—whatever it may have been—is different to
that of the secondary elements with which we compare them. A
convergence in their rate of transformation is not impossible, or
even improbable, so far as we known.
As regards the second point: It is assumed that uranium alone of
the elements in radioactive minerals is ultimately transformed to
lead by radioactive changes. We must consider this assumption.
Recent advances in the chemistry of the radioactive elements has
brought out evidence that all three lines of radioactive descent
known to us—_i.e._ those beginning with uranium, with thorium,
and with actinium—alike converge to lead.[1] There are
difficulties in the way of believing that all the lead-like atoms
so produced ("isotopes" of lead, as Soddy proposes to call them)
actually remain as stable lead in the minerals. For one
[1]
