The most striking cases of branching occur in the "C" products of radium, thorium and actinium, each of which breaks up in two or more distinct ways. In the case of radium C, a new substance called radium C" was obtained by recoil from a nickel plate coated with radium C. This product emitted only 0-rays and had a period of 1.4 minutes. Fajans estimated that the amount of the product was only of that of radium C. To account for these results the following scheme of transformation has been pro posed:— In the table T is the time-period of a product or the time re quired for the product to be half-transformed. It will be seen that the value of T, which is a measure of the relative stability of atoms, varies between 2.2X years (Thorium) and .002 second (Actinium A). The atomic weights and atomic numbers of uranium, radium, uranium-lead, thorium, thorium-lead have been directly determined by X-ray methods. The atomic weights and atomic numbers of the others are deduced on the assumption that the expulsion of an a-particle (helium atom) of charge 2 and mass 4 lowers the atomic number of the succeeding element by two units and the atomic weight by four. The expulsion of a 43-particle raises the atomic number by one unit, but it is not supposed to influence the atomic weight to a detectable where in the main branch a 0-particle is first expelled, giving rise to radium C', which emits an a-particle. The reverse process is assumed to take place in the other branch. Radium C', which emits a swift a-particle, has an exceedingly short period of trans formation, which has been measured approximately by Jacobsen, and found to be about seconds. It is uncertain whether the radium C" branch ends after the expulsion of a 0-particle. The resulting product is an isotope of lead like radium D in the main branch.
In the case of thorium C, two sets of a-particles are observed, one-third of the total number having a range of 4.8 cm. and the remainder 8.6 cm. Here, as in radium C, Marsden supposed that the main series goes by a 0-ray change to the C' product. In actinium C, which also shows a dual transformation, Marsden found that 99.84% of the C atoms change with the emission of an a-particle of 5.15 cm. range to the C" product, the remaining 0.16% going to C', which gives a-particles of 6.4 cm. range. Sub sequent research has shown that the modes of transformation of the C' bodies are even more complicated than was at first sup posed. Rutherford and Chadwick found two additional sets of a-particles which are emitted in very small numbers compared with the main group of particles. One group has a range in air of 9.3 cm. and the other i1.3 cm. Rutherford and Wood found in the thorium C a group of particles of a range r1.3 cm. while Meitner and Freitag found a small number of range 9.5 cm. No evidence has been obtained of the exact origin of these swift a-particles but they are probably due to different modes of disintegration of the C' bodies. It is quite possible that a close examination of radioactive substances may reveal other examples of such com , plex methods of transformation, for, after the violent explosion that occurs during the breaking-up of an atom, more than one state of temporary equilibrium may be possible for the residual atom.
Relation Between Range of a-Rays and Period of Trans formation.—We have seen that each a-ray product emits a-par ticles of characteristic velocity which have a definite range in air. It was early observed that there appeared to be a connection between the period of transformation of a product and the ve locity of the a-particles emitted. The shorter the period of transformation, the swifter is the velocity of expulsion of the a particle. This relation was brought out clearly by the measure ments of Geiger and Nuttall, where it was shown that if the logarithm of the range was plotted against the logarithm of X, the constant of transformation, all the points lay nearly on a straight line.
A similar result has been observed for the thorium and actinium products. This relation, when carefully tested by Geiger, appears to be only a rough approximation. It is still of great interest as indicating a possible relation between the stability of the radio active nucleus and the velocity of the expelled helium atom. This relation has proved very useful in forming estimates of the period of transformation of ionium and other substances before the re sults of more direct determinations were available. From this relation also the change which gives rise to the swift a-particle of radium C was believed to be exceedingly rapid. This has been confirmed by the detection of radium C' and measurement of its period. A similar conclusion is drawn for the product emitting the very swift a-particles from thorium C.