CHAPTER XI. Review of the Evidence

REVIEW OF THE EVIDENCE

The discrepancy between the geological and radioactive methods of estimating time—Uniformity of the rate of decay of uranium—Joly’s criticism—Comparison of the two time-scales—Doubtful assumptions made in the geological arguments—Possibility of reconciliation no longer hopeless.

Of the various methods which have been devised to solve the problem of the earth’s age, only two, the geological and the radioactive, have successfully withstood the force of destructive criticism. The other arguments may be dismissed without further discussion, as in every case their cogency has been vitiated by the detection of a fundamental error. From the mists of controversy which for half a century have hung over the subject, the two hour-glass methods alone emerge, and the final issue must be fought out between them. In the one the world itself is the hour-glass, and the accumulating materials are salt, the sedimentary rocks and calcium carbonate. Three concordant sets of results may be drawn from this triple scheme of measurement, but it must not be supposed that they are altogether independent. Each set of data is intimately related to the others and all stand or fall together. In the other case the accumulating materials are helium and lead, and the hour-glass is constituted by the minerals in which they collect. Provided that the field-evidence is clear and convincing and that the relative geological age of a mineral specimen can be determined, the construction of an exact and precise time-scale is a task which can be dealt with successfully in the laboratory. The problem has advanced from the qualitative to the quantitative stage, and for the first time in historical geology accurate measurement founded on delicate experimental work has become possible.

It is a matter for regret that confidence in this pioneer work has been shaken by the advocates of the geological methods of attack. The surprises which radioactivity had in store for us have not always been received as hospitably as they deserved. With the advent of radium geologists were put under a great obligation, for the old controversy was settled overwhelmingly in their favour. But the pendulum has swung too far, and many geologists feel it impossible to accept what they consider the excessive periods of time which seem to be inferred. That there exists a serious discrepancy obviously points to a flaw in the underlying assumptions of one or the other or both of the methods. Evidently we are at the parting of the ways. The fundamental assumptions on which the arguments are based cannot both be right. One of them must be rejected. Which is it to be? Let us consider each in turn, and discuss the consequences of the two possible forms of reconciliation.

The only assumption which can reasonably be called into question is that of uniformity, and it is involved equally in both calculations. It is here, at the root of the problem, that the discrepancy really lies. If we favour the uniformity of geological processes—a well-worn doctrine which has done good service—then we must reject uniformity of radioactive disintegration. Joly has drawn attention to the latter possibility. He asks: Is it assured that the parent substance, uranium, has always in the past disintegrated at the rate determined by its present average life period? As far as we know, the rate of decay for substances of rapid transformation is constant, and independent of temperature and pressure changes. On the grounds that a large number of radioactive bodies decay at a constant rate, it is believed that this constancy is a definite attribute of all the radioactive elements. In the case of uranium this assumption cannot be proved for periods commensurate with its half-life period. On analogy with the behaviour of the shorter lived elements, it is probable that had we lived in Cambrian times and experimented with Archean uranium-bearing minerals just as has been done during the last decade, the half-life period would then have been exactly the same as we now find it—about 5400 million years. In the case of radium emanation there can be no doubt that experiments in Cambrian times would have given results concordant with ours. It would be as unphilosophic to doubt this as to believe that the laws of physics and chemistry vary with time. The difference between uranium and its daughter elements, the difference which suggests to Joly a possible distinction, is simply one of origin. We are in complete ignorance of the genesis of uranium. It is not impossible that, owing its origin to some process other than atomic transformation, the particular distribution of intrinsic energy among its atoms may not be such as to maintain a constant rate of decay. At the moment of its birth every radioactive atom has a definite expectancy of life, and when a sufficiently large number of atoms is under observation a definite fraction disintegrates every second. There is this difference in the case of parent elements. As they become aged with reference to the time of their origin, they are not reinforced by the addition of fresh, newly-born atoms, as are the other members of each series. Joly’s supposition seems to be that in the absence of this reinforcement the uranium in its early stages may possibly disintegrate more rapidly than it does now. However, it is not found that the younger atoms of the short-lived elements are, on an average, more prone to rapid decay than are their older companions. Whether an element is in equilibrium with the higher members of its family, or whether it is separated from them, its transformation proceeds with unaffected regularity.

It is very improbable that reconciliation will be found in the supposition of a progressive retardation of the rate of decay of uranium. There are three possibilities. Uranium may have disintegrated in the past exactly as it now does; or it may have decayed more slowly or more rapidly. The latter two alternatives do not favourably commend themselves. There is no evidence which can be cited in their support. On the other hand, the hypothesis of constant change is deduced from a well-established series of experimental facts, and is remarkably in accordance with the general phenomena of radioactivity. Uranium, in other respects, does not present any anomaly, and with regard to the mechanism of its decay physicists are not likely to regard it as an exceptional case without very definite reasons for doing so. The discordance between the time estimates drawn from the rates of geological and radioactive changes cannot be held to constitute a sufficient reason for rejecting current opinions unless it is conclusively demonstrated that the geological estimates are beyond question. In the future the case for uranium may be established more securely, when the dynamics of atomic disintegration, and the conditions upon which the distribution of unstable atoms depends, becomes more intimately understood. At present there is only one means of testing the constancy of uranium decay, but unfortunately it affords only negative evidence. The range of α-particles from a radioactive element is connected in some way with its rate of decay. If then, uranium in the past disintegrated more rapidly, the radius of its particular pleochroic halo ought to record the difference. It is improbable that any variation—assuming for the moment that there were a variation—could be detected even in the most favourable cases.

We now turn with a double interest to the geological estimates. If it can be shown that they ought to be largely increased, as Chamberlin and a few other geologists believe, then not only is a reconciliation at once made possible, but, in turn, the constancy of uranium decay is placed beyond doubt. Little need be added to the discussion in Chapter VI. It was there indicated that one factor previously over-looked—the average height of the continents in geological time—very largely controls the rate of denudation and therefore of sedimentation. Let us make an attempt to discover how past rates must be related to those of the present to make possible a complete reconciliation. In Fig. 17 the discrepancy is illustrated graphically by comparing the respective time scales from the close of the Archean (gneiss and granite phase) to the present day. All the sediments of which relics have remained to us are in this way taken into consideration. Lying buried in the Archean, the base of the record is obscured beyond recognition by the prevalence of metamorphic and plutonic igneous rocks. The extent to which the earliest sediments have been lost in the evolution of the earth’s crust, and the part they have played in the genesis of granites and gneisses are questions which betray our ignorance and offer food merely for wild speculations. These possibilities, however, do not touch the immediate point at issue, for in their time relations they lie outside the limits to which this discussion is restricted.

The curve A is plotted strictly against the maximum observed thickness of sediments, and corresponding to it is the sedimentation line A′ to which is granted 300 million years. According to these two graphs the greatest error lies beyond the Cambrian. The average rate of denudation and of sediment accumulation must now be nine times that of the pre-Cambrian periods, but if post-Cambrian is compared with present the ratio is reduced to two-and-a-half. In the B series, the lead ratios are plotted in a straight line and the stratigraphical column is extended in accordance with the palæontological evidence that pre-Cambrian time is at least as long as that which has elapsed since the beginning of the Cambrian. On this basis present rates are four times the average for post-Archean time.

Geological Time Scales.]

Assuming that the true time-scale lies somewhere between the extremes of A and B, we are led to two conclusions which, if accepted, greatly lessen the severity of the discordance between A and A′ and B and B′. From A and A′ it appears that pre-Cambrian denudation took place much more slowly than has since been typical. This proposition is in complete accordance with the view that the pre-Cambrian continents, when viewed in the light of the reconstructed geographies of the later periods, were of limited area and restricted elevation. From B and B′ the broad time conception of palæontology gains further support, and the existence of great gaps in the pre-Cambrian succession is suggested. It is well known that the most important unconformities of the whole geological record are to be found in the imperfect succession of the earliest formations. It is impossible to do more than guess at the duration of time periods which are without their sedimentary equivalents. On the most extreme assumption, the Algonkian sediments should be represented not by 82,000 feet, but by more than 300,000 feet. Unwilling though we may be to consider the record imperfect to this incredible degree, it is of importance to point out that had such an immense thickness existed in successive periods of time, the sodium content of the ocean would not necessarily be in any way different from what it is. The same amount of primary rock material may have been broken up, but instead of a reassorting of the materials to form three successive sets of sediments (on a rough average) we would be obliged to postulate six or more repetitions of the sorting process. The question need not be pursued farther. The suggestion here put forward is, that in the limitations of pre-Cambrian geography and in the imperfection of the sedimentary relics of those remote times, the discrepancy which is peculiar to the pre-Cambrian finds an adequate explanation.

If this be allowed, all that remains is to decide whether it is inconsistent with geological principles to assert that the modern hour-glass is running at two-and-a-half to four times its average rate. The decision depends largely on the broad point of view from which geological interpretation proceeds. From the standpoint of Catastrophism little progress was made. Uniformity proved a great advance, but in detail it is apt to lead us astray if applied too dogmatically. Modern interpretation is based on the more philosophic conception of Evolution, and in place of the earlier idea which was insisted upon by the older physicists—that changes have been such as would accompany a gradual running down of the earth’s internal kinetic energy—the form of development now favoured is that of cycles of phenomena, recurring in their broad features again and again and not necessarily hampered in their activity by any progressive diminution in the store of available energy. Igneous action, deposition of sediments, marine transgression and recession, are all rhymic phenomena and the factor common to each one, whether as cause or effect, is earth-movement.

The conditions of the present day cannot then be accepted as representing average conditions, unless it were by a happy accident. Amidst all the details of earthquakes and volcanic eruptions some great cycle is now running its course, and only in relation to the particular phase of the cycle under which we happen to pursue our investigations will our conclusions be strictly tenable. Although we cannot hope to judge the exact place which the present takes in the larger scheme of terrestrial activity, yet in comparison with the past, the present epoch would seem to approach just those extremes most favourable to a high rate of denudation, and to a rapid accumulation of sediments. Marine recession, brought about by deepening of the ocean basins, and raising of the land areas have together brought about continental expansion and elevation. The vulcanism of the present day, whether regarded as a closing phase of a period of igneous action, or as the initiation of a new cycle, probably affords an example of more than average intensity and violence. The weathering capacity of rain must be enhanced in proportion to its content of dissolved acid gases, and this in turn is conditioned by the prevalence of vulcanism. Still another factor leading to higher rates, though of a different category, is due to recent glaciation. Over wide areas easily eroded deposits are exposed, the areas being generally those which would resist denudation most successfully. In Fennoscandia, for example, four-fifths of the pre-Cambrian shield is buried beneath a thin covering of moraine.

It is not suggested that present rates have never before been reached, but only that they are characteristic of the more intense phases of denudation rather than of average conditions. If this be granted, reconciliation of the rival time estimates is no longer hopeless. There can be no doubt that agreement will never be brought about by the more convincing testimony of experimental demonstration. It must be almost entirely a question of interpretation. An attempt has been made to show that in the geological evidence there is nothing impossibly at variance with the dictates of the radioactive minerals. With the acceptance of a reliable time-scale, geology will have gained an invaluable key to further discovery. In every branch of the science its mission will be to unify and correlate, and with its help a fresh light will be thrown on the more fascinating problems of the Earth and its Past.

APPENDIX A

(a) Kinetic Energy of α-particles

1 gram of radium in equilibrium with emanation, Ra. A B and C generates heat at the rate of =132 calories per hour= (85% due to α-particles).

e = charge on α-particle = 9·3 × 10⁻¹⁰ E.S. units. = 3·1 x 10⁻²⁰ E.M. ”

m = mass of α-particle } v = velocity of α-particle } see Table below.

N = number of α-particles liberated from 1 gram of radium = 3·4 × 10¹⁰ per second.

Energy E transformed per second is given by—

Nmv² E = ½∑ ——— × e e

Ne mv² = —— ∑ —— 2 e

+---------------+---------------+----------------+ | | v | mv²/e | | Element. | Cms. per sec. | E.M. Units. | +---------------+---------------+----------------+ | Radium | 1·56 × 10⁹ | 4·78 × 10¹⁴ | | Ra. emanation | 1·70 × 10⁹ | 5·65 × 10¹⁴ | | Ra. A | 1·77 × 10⁹ | 6·12 × 10¹⁴ | | Ra. C | 2·06 × 10⁹ | 8·37 × 10¹⁴ | +---------------+---------------+----------------+

Substituting these values, we have—

Ne = 3·4 × 10¹⁰ × 3·1 × 10⁻²⁰ = 10·5 × 10⁻¹⁰ E.M. units.

mv² ∑ —— = 10¹⁴(4·78 + 5·65 + 6·12 + 8·37) e = 24·9 × 10¹⁴ E.M. units;

whence E = 13·1 × 10⁵ ergs per second

= 4·73 × 10⁹ ergs per hour.

Now 4·19 × 10⁷ ergs = 1 gram-calorie. ∴ E = 113 calories per hour.

(b) Production of helium from Uranium and Thorium in equilibrium with all their disintegration products.

Uranium—

N = number of helium atoms liberated from 1 gram of radium alone = 3·4 × 10¹⁰ per second. (Rutherford and Geiger, 1908).

The equilibrium ratio of radium to uranium is 3·4 × 10⁻⁷. Hence for each gram of uranium in equilibrium the number of atoms produced amounts to—

3·4 × 10¹⁰ × 3·4 × 10⁻⁷ × 8 per second = 29·1 × 10¹¹ per year.

Now the number of helium molecules, and therefore of atoms, in 1 cc. of the gas at N.P.T. is 2·72 × 10¹⁹.

The annual production of helium must consequently be

29·1 × 10¹¹ ———————————— ccs., 2·72 × 10¹⁹

i.e. 10·7 × 10⁻⁸ ccs., or 1·88 × 10⁻¹¹ grs. per gram of uranium.

An experimental determination gave 10·6 × 10⁻⁸ ccs. (Strutt, 1910).

Thorium—

The ionising power, or the energy of the α-particles from 1 gram of thorium, is 0·325 of that from 1 gram of uranium, each element being in complete equilibrium.

Average range of α-particles from thorium and its products = 5·4 cms.

Average range of α-particles from uranium and its products = 4·3 cms.

The average thorium α-particle is therefore 1·25 times as energetic as the average uranium α-particle.

Hence the actual production of α-particles or helium atoms from thorium is only 0·325/1·25 = 0·26 of that of uranium.

Experimental determinations 0·23 (Strutt, 1910), 0·27 (Rutherford and Geiger, 1910).

(c) Half-life Period of Radium.

(1) The number of α-particles emitted from 1 gram of radium per second (n = 3·4 × 10¹⁰) is equal to the number of atoms disintegrating per second.

If N is the number of atoms in 1 gr. radium, then λ, the fraction which transforms per second, is given by—

n λ = ——. N

The number of atoms in 1 gr. hydrogen is 6·24 × 10²³, and as the atomic weight of radium is 226 times that of hydrogen,

N = 2·76 × 10²¹. ∴ λ = 1·25 × 10⁻¹¹ gr. per sec. = 3·94 × 10⁻⁴ gr. per year.

=Half-Life period= = 0·69315/λ = =1760 years=.

(2) 1 gr. of radium is in radioactive equilibrium with 0·58 cubic millimetre, or 5·7 × 10⁻⁶ grs. of emanation (atomic wt. = 222).

If λ₁ = 2·085 × 10⁻⁶ is the fraction of emanation transforming per second, we have—

λ = 5·7 × 10⁻⁶ × λ₁ = 1·19 × 10¹¹ gr. per sec.;

whence—=Half-Life period = 1850 years.=

The earlier values given for the half-life period were 1760 and 2000 years, but the lower figure seems most accurate, with 1850 years as a probable value.

The half-life of uranium would then be—

1850 —————————— = =5400 million years=. 3·4 × 10⁻⁷

(d) Time-Average of Uranium

Uₜ = Quantity of uranium remaining after a time t. Uₒ = Quantity of uranium originally present (t = o). Uₘ = Time-average of uranium during time t. λ = Disintegration constant of uranium. Pbₜ = Lead accumulated during time t. Heₜ = Helium ” ” time t.

Graph I represents the rate of decay of uranium—according to the exponential law—

( -λₜ) Uₜ = Uₒ ( e ).

There is one rate of decay which, if it remained constant throughout the time t, would have a total effect equivalent to that produced by the actual slowly decreasing rate of decay. This average rate is represented by some point on the curve, and the corresponding quantity of uranium, Uₘ, is the time-average. Equating the amount of uranium transformed in each case, we have—

Uₒ - Uₗ = λUₘt

Uₒ - Uₜ whence Uₘ = ———————— (a). λt

For periods less than 2000 million years, the time-average is nearly equal to the arithmetic mean of Uₒ and Uₗ.

Uₒ + Uₗ Uₘ = ———————— (b). 2

The value of Uₘ for 2000 million years is,

according to equation (a), equal to 0·874 Uₒ and ” ” ” (b) ” “ 0·879 Uₒ.

The ages of minerals rarely exceed 1500 million years, and therefore the error involved by using equation (a) in preference to (b) is quite negligible.

In Graph II the ratio Uₘ/Uₜ, i.e. the factor by which the present uranium content of a mineral must be multiplied in order to obtain the true time-average, is plotted against time.

An approximation to the age, t, of a mineral is afforded by the ratio Pbₜ/Uₜ. From the graph the factor corresponding to this time can be obtained, and thence the time-average. This in turn can be utilised to give the more correct age represented by Pbₜ/Uₘ.

A more straightforward method of correction is as follows:

Uₒ can be determined from known quantities according to the following equation:

Uₔ = Uₜ + Pbₜ + Heₜ = Uₜ + 1·15 Pbₜ; whence, =Uₘ = Uₗ + 0·575 Pbₜ=.

The age of the mineral is then given by the ratio =Pbₜ/Uₘ=, or directly from Graph II.

(e) Analyses made by the Author of Radium in Igneous Rocks

(cited on p. 130)

Acid Rocks— Ra. per gram of rock

Granite, Mozambique 5·84 × 10⁻¹² grs. ” ” 2·61 ” ” ” 1·77 ” ” N. Nigeria 3·09 ” ” Rhodesia 2·43 ” ” Transvaal 2·12 ” ” South Africa 1·81 ” ” ” ” 2·73 ”

Basic Rocks—

Basalt, Mozambique 0·94 × 10⁻¹² grs. Dolerite ” 0·85 ” Gabbro ” 1·07 ” Norite ” 0·54 ”

Ultrabasic Rocks—

Composite analysis of 10 specimens from Scotland, New Zealand, Africa, and Canada 0·51 × 10⁻¹² grs.

APPENDIX B

BIBLIOGRAPHY