Periods of time much less than, and very inconsistent with, these were also found. The lower results are, however, easily explained if we a.s.sume that the helium--which is a gas under prevailing conditions--escapes in many cases slowly from the mineral.

Another product of radioactive origin is lead. The suggestion that this substance might be made available to determine the age of the Earth also originated with Rutherford. We are at least a.s.sured that this element cannot escape by gaseous diffusion from the minerals. Boltwood's results on the amount of lead contained in minerals of various ages, taken in conjunction with the amount of uranium or parent substance present, afforded ages rising to 1,640 millions of years for archaean and 1,200 millions for Algonkian time. Becker, applying the same method, obtained results rising to quite incredible periods: from 1,671 to 11,470 millions of years. Becker maintained that original lead rendered the determinations indefinite. The more recent results of Mr. A.

Holmes support the conclusion that "original" lead may be present and may completely falsify results derived

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from minerals of low radioactivity in which the derived lead would be small in amount. By rejecting such results as appeared to be of this character, he arrives at 370 millions of years as the age of the Devonian.

I must now describe a very recent method of estimating the age of the Earth. There are, in certain rock-forming minerals, colour-changes set up by radioactive causes. The minute and curious marks so produced are known as haloes; for they surround, in ringlike forms, minute particles of included substances which contain radioactive elements. It is now well known how these haloes are formed. The particle in the centre of the halo contains uranium or thorium, and, necessarily, along with the parent substance, the various elements derived from it. In the process of transformation giving rise to these several derived substances, atoms of helium--the alpha rays--projected with great velocity into the surrounding mineral, occasion the colour changes referred to. These changes are limited to the distance to which the alpha rays penetrate; hence the halo is a spherical volume surrounding the central substance.[1]

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.

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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 quant.i.ty 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 a.s.sumption 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.

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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 a.s.sumption overestimate the age.

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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 a.n.a.logy with the constant rate of decay observed in the derived radioactive bodies. If uranium and thorium are really primary elements, however, the a.n.a.logy 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 a.s.sumed that uranium alone of the elements in radioactive minerals is ultimately transformed to lead by radioactive changes. We must consider this a.s.sumption.

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] See Soddy's _Chemistry of the Radioactive Elements_ (Longmans, Green & Co.).

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thing there is sometimes, along with very large amounts of thorium, an almost entire absence of lead in thorianites and thorites. And in some urano--thorites the lead may be noticed to follow the uranium in approximate proportionality, notwithstanding the presence of large amounts of thorium.[1] This is in favour of the a.s.sumption that all the lead present is derived from the uranium. The actinium is present in negligibly small amounts.

On the other hand, there is evidence arising from the atomic weight of lead which seems to involve some other parent than uranium. Soddy, in the work referred to, points this out. The atomic weight of radium is well known, and uranium in its descent has to change to this element. The loss of ma.s.s between radium and uranium-derived lead can be accurately estimated by the number of alpha rays given off. From this we get the atomic weight of uranium-derived lead as closely 206. Now the best determinations of the atomic weight of normal lead a.s.sign to this element an atomic weight of closely

[1] It seems very difficult at present to suggest an end product for thorium, unless we a.s.sume that, by loss of electrons, thorium E, or thorium-lead, reverts to a substance chemically identical with thorium itself. Such a change--whether considered from the point of view of the periodic law or of the radioactive theory would involve many interesting consequences. It is, of course, quite possible that the nature of the conditions attending the deposition of the uranium ores, many of which are comparatively recent, are responsible for the difficulties observed. The thorium and uranium ores are, again, specially p.r.o.ne to alteration.

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207. By a somewhat similar calculation it is deduced that thorium-derived lead would possess the atomic weight of 208. Thus normal lead might be an admixture of uranium- and thorium-derived lead. However, as we have seen, the view that thorium gives rise to stable lead is beset with some difficulties.

If we are going upon reliable facts and figures, we must, then, a.s.sume: (a) That some other element than uranium, and genetically connected with it (probably as parent substance), gives rise, or formerly gave rise, to lead of heavier atomic weight than normal lead. It may be observed respecting this theory that there is some support for the view that a parent substance both to uranium and thorium has existed or possibly exists. The evidence is found in the proportionality frequently observed between the amounts of thorium and uranium in the primary rocks.[1] Or: (b) We may meet the difficulties in a simpler way, which may be stated as follows: If we a.s.sume that all stable lead is derived from uranium, and at the same time recognise that lead is not perfectly h.o.m.ogeneous in atomic weight, we must, of necessity, ascribe to uranium a similar want of h.o.m.ogeneity; heavy atoms of uranium giving rise to heavy

[1] Compare results for the thorium content of such rocks (appearing in a paper by the author Cong. Int. _de Radiologie et d'Electricite_, vol. i., 1910, p. 373), and those for the radium content, as collected in _Phil. Mag._, October, 1912, p. 697.

Also A. L. Fletcher, _Phil. Mag._, July, 1910; January, 1911, and June, 1911. J. H. J. Poole, _Phil. Mag._, April, 1915

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atoms of lead and light atoms of uranium generating light atoms of lead. This a.s.sumption seems to be involved in the figures upon, which we are going. Still relying on these figures, we find, however, that existing uranium cannot give rise to lead of normal atomic weight. We can only conclude that the heavier atoms of uranium have decayed more rapidly than the lighter ones. In this connection it is of interest to note the complexity of uranium as recently established by Geiger, although in this case it is a.s.sumed that the shorter-lived isotope bears the relation of offspring to the longer-lived and largely preponderating const.i.tuent. However, there does not seem to be any direct proof of this as yet.

From these considerations it would seem that unless the atomic weight of lead in uraninites, etc., is 206, the former complexity and more accelerated decay of uranium are indicated in the data respecting the atomic weights of radium and lead[1]. As an alternative view, we may a.s.sume, as in our first hypothesis, that some elementally different but genetically connected substance, decaying along branching lines of descent at a rate sufficient to practically remove the whole of it during geological time, formerly existed. Whichever hypothesis we adopt

[1] Later investigation has shown that the atomic weight of lead in uranium-bearing ores is about 206.6 (see Richards and Lembert, _Journ. of Am. Claem. Soc._, July, 1914). This result gives support to the view expressed above.

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we are confronted by probabilities which invalidate time-measurements based on the lead and helium ratio in minerals.

We have, in short, grave reason to question the measure of uniformitarianism postulated in finding the age by any of the known radioactive methods.

That we have much to learn respecting our a.s.sumptions, whether we pursue the geological or the radioactive methods of approaching the age of our era, is, indeed, probable. Whatever the issue it is certain that the reconciling facts will leave us with much more light than we at present possess either as respects the Earth's history or the history of the radioactive elements. With this necessary admission we leave our study of the Birth-Time of the World.

It has led us a long way from Lucretius. We do not ask if other Iliads have perished; or if poets before Homer have vainly sung, becoming a prey to all-consuming time. We move in a greater history, the landmarks of which are not the birth and death of kings and poets, but of species, genera, orders. And we set out these organic events not according to the pa.s.sing generations of man, but over scores or hundreds of millions of years.

How much Lucretius has lost, and how much we have gained, is bound up with the question of the intrinsic value of knowledge and great ideas. Let us appraise knowledge as we would the Homeric poems, as some-

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thing which enn.o.bles life and makes it happier. Well, then, we are, as I think, in possession today of some of those lost Iliads and Odysseys for which Lucretius looked in vain.[1]

[1] The duration in the past of Solar heat is necessarily bound up with the geological age. There is no known means (outside speculative science) of accounting for more than about 30 million years of the existing solar temperature in the past. In this direction the age seems certainly limited to 100 million years.

See a review of the question by Dr. Lindemann in Nature, April 5th, 1915.

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DENUDATION

THE subject of denudation is at once one of the most interesting and one of the most complicated with which the geologist has to deal. While its great results are apparent even to the most casual observer, the factors which have led to these results are in many cases so indeterminate, and in some cases apparently so variable in influence, that thoughtful writers have even claimed precisely opposite effects as originating from, the same cause.