It is not proposed to discuss these schemes in detail or to consider at any length certain minor points involved to which exception might be taken. It is, however, difficult to understand just what is implied by the dual transformation with the expulsion of a-particles in both cases which is suggested for UI. in the first scheme and for U II. in the second. It would appear that the loss of an a-particle in each case. should lead to the production of one and the same kind of matter, namely, to a single product and not to two different products to be designated as U X, and U Y in one example and as Io and U Y in the other. The main point under consideration is, however, whether either of these schemes gives us a clue to the explanation of the relative activities of uranium and radium as they have been found in our experiments, and it may be stated that they do not, since the first scheme would suggest a ratio of 1/55 for the relative activities of the uranium and the radium, while the second scheme would imply a ratio of 1/53 for the same quantities.

In order that Scheme I. might satisfactorily apply to the ratio as found by experiment it would be necessary to assume that about 26 out of every 100 atoms of U I. were transformed in the mode leading to the production of actinium. This in turn is contradicted by the relative activity of the actinium products in an equilibrium mixture.

In order to fulfil the conditions involved in Scheme II. it would be necessary for 14 out of every 100 atoms of

uranium to be transformed in the mode leading to the production of actinium. Nor is there any apparent advantage gained by assuming that the transformation of either UI. or U II. into the first member of the side series is accompanied by the expulsion of a B-particle instead of an a-particle.

It might, however, be assumed that the branching of the series takes place at some other point, as at radium, for example, and that 86 per cent. of the radium atoms disintegrate with the emission of a-rays to form the emanation, etc., while 14 per cent. disintegrate (emitting B-rays) to form actinium. Direct evidence of the emission of B-rays by a specimen of radium has been obtained by Hahn and Meitner*. Under these conditions the a-ray activity of ionium would be proportional to the uranium radiation and would equal 0.53. The activity of the actinium series would equal 0.56 and the activity of the radium + emanation → radium A, C, and F would be 3:01 (the sum of the values given in Table V.). The sum of all of these together with uranium is 5·10 for the total activity of the uranium series (as in uraninite). There are, however, serious objections to the assumption that the side branch arises at radium, aside from the fact that the values mentioned are widely different from those found in Boltwood's experiments and the value found in the present experiments for the total activity of the uranium products.

The most significant objection is presented by the agreement of the value found for the disintegration constant cr radium by Rutherford and Geigert and the value of this constant found by Miss Gleditsch‡. The Rutherford and Geiger estimate was based on the number of a-particles emitted per second by the radium C in equilibrium with one gram of radium. If only eighty-six out of every hundred of the radium atoms disintegrate to form radium C, then this estimate would be 14 per cent. too low. The method employed by Miss Gleditsch depended on the production of radium from the ionium in equilibrium with a known amount of radium, and was measured in terms of the fraction of the total equilibrium amount which was produced in a known period of time. This would have given the true value for the disintegration constant irrespective of the mode of

Phil. Mag. S. 6. Vol. 40. No. 235. July 1920.

F

disintegration. These two methods would therefore have given different and not similar values if the collateral series had originated at radium.

Among other objections may be mentioned the experiment. made by Soddy*, who examined a specimen of radium salt containing 13.2 mgs. of radium which had been sealed for a period of ten years. No evidence of the presence of actinium was obtained. Paneth and Fajans† examined a specimen containing 180 mgs. of radium which had been sealed for six years, but were unable to detect the presence of any actinium products. We may therefore dismiss the possibility of the side chain splitting off at radium as highly improbable in the light of our present knowledge.

The possibility that the collateral series originates at ionium may also be considered. The fact that the experimental evidence is all opposed to the emission of a B-radiation by ionium is in itself a decided objection to this view. Moreover, it would require (uranium taken as unity) an activity of 0.56 for the actinium products, an activity of 0.46 for ionium, and an activity of 3.01 for radium and its products, with a total activity of 5·02. Paneth and Fajans‡ have directly attacked this problem by seeking for the presence of actinium in a strong preparation of ioniumthorium which had been undisturbed for four years. They were unable to discover the presence of any actinium products. Lacking any support, therefore, the supposition that the collateral series arises at ionium is untenable at present.

These circumstances compel a return to a consideration of the earlier members of the series, to U I. and U II., in the hope of being able to find there an explanation of the conditions indicated by our experiments. At first sight it might seem that the conditions would be satisfied by assuming that what we now call uranium consists of three radioelements, a parent element and two isotopic products in equilibrium, all emitting a-rays. But if these are present in relative amounts of the same approximate order of magnitude (i. e., 100, 92, 92, etc.), then the a-rays emitted by at least one of them would have to be of exceedingly short range and small ionizing power and the rate of change of this substance would be excessively slow. It is not impossible, but it does not seem probable, that ordinary uranium may consist of what we know as U I. and U II., both radioelements in the main line of descent, and a third isotope * 'Nature,' xci. p. 634 (1913).

† Wien. Ber. cxxiii. IIa, p. 1627 (1914).
Wien. Ber. cxxiii. IIa, p. 1627 (1914).

which is a product in the collateral actinium series. But the difficulties here are not inconsiderable aside from the fact that the existence of such an isotope is somewhat difficult to imagine. If present in amounts proportional to the actinium this product would have to emit comparatively long range (7·2 cm.) a-particles and would therefore have a very short life period. Such a conclusion does not seem at all probable in the light of our present knowledge.

It is not impossible that the values accepted for the ranges of the a-particles from uranium are considerably in error and that this is the reason for the lack of agreement between theory and experiment. But until some more definite data have been obtained there seems to be little justification for abstruse speculation on the genetic relationship in the earlier stages of the uranium series.

Summary.

The relation of the activity of radium to the activity of the uranium with which it is in radioactive equilibrium has been redetermined. The results obtained indicate that if the activity of uranium is taken as unity the activity of the radium is equal to approximately 0·49.

The total activity of uranium mixed with equilibrium quantities of its disintegration products has been compared with the activity of the uraniuin alone, and the former has been found to be 4.73 times the latter.

A critical examination has been made of the various theories which have been proposed to explain the genesis of radium and actinium from uranium. None of these theories appears to satisfy the necessary requirements.

CONS

V. The Bearing of Rotation on Relativity.
By Prof. R. A. SAMPSON, F.R.S.*

YONSIDER two concentric spheres with a very small space between them so that we need not distinguish between their radii. An observer A is placed on the outer surface of the inner sphere and an observer B on the inner surface of the outer. All phenomena are supposed to pass in the space between the two spheres.

Regard this system and its changes first from a purely geometrical point of view. A and B will possess in common a natural unit of length, being the circumference of their * Communicated by the Author.

sphere. Let the arc AB as it exists at any moment be determined as a fraction of this unit. Let it be determined again in the same way at a later moment. If the two do not agree, we can say that a relative rotation of the two spheres must have occurred, through a definite angle, about an axis perpendicular to the plane of the great circle AB. Whether any relative rotation about an axis in the plane AB has taken place, or whether both spheres have executed in common any other rotation about any axis whatever, the observers at A and B will be unable to say. We may express this position by saying that A and B are under circumstances of complete geometrical relativity.

The whole description is, however, an abstraction. It is the abstraction which lies at the basis of geometry; it eliminates time from consideration and supposes figures to exist with definite distances between the points. But in reality any distance assigned requires time for its determination, and the standard case would be this: A and B. each have hold of a graduated measure, allowing it to slip through their hands, and as they watch its successive readings they signal them to one another; each will then only be aware of the other's reading, that is to say, of the other's distance at any moment, as complicated by the time of transmission of the signals. This aberrational allowance is an inevitable attendant upon actual physical measures. It is inseparable from motion. It would not be surprising if the ideas of motion required a complete surrender of the scheme of abstract geometrical relativity defined above.

How much the physical theory of motion affects our notions of absolute and relative is very well known. Let the sphere A be the Earth and the sphere B a complete opaque sheet of cloud rotating with it. A Foucault pendulum set up at the north pole would of itself change its plane of oscillation with respect to the meridians, pointing out an absolute direction in space, and an absolute rate of rotation, of which the observer would be unaware without this, or other similar, appeal to dynamics. A similar pendulum set up at the equator would show no change of azimuth at all. By no conceivable explanation can this familiar experiment be made consistent with complete geometrical relativity of the system, geometrically self-contained, within the bounds of which it occurs. Other cases could easily be mentioned. But my purpose at the moment is to pursue a little further the aberrational considerations introduced above.

In 1893 and 1897 Sir Oliver Lodge, considering the Michelson-Morley experiment, then not infrequently taken