a number of possible "excited" states of the atom as a consequence of the previous disintegrations. This satellite theory is useful in another connection. It has been suggested that possibly the high frequency _γ_ rays from a radioactive atom may arise not from the movement of the electrons as ordinarily supposed, but from the transfer of _α_ particles from one level to another. In such a case, the difference in energies between the various groups of _α_ particles from radium C and thorium C should be connected by the quantum relation with the frequencies of prominent _γ_ rays. The evidence at present available is not definite enough to give a final decision on this problem, but points to the need of very accurate measurements of the energies of the various groups of _α_ particles. On account of the relatively small number of particles in some of the groups, this is difficult of accomplishment. In considering the satellite theory in connection with the radioactive bodies, it is at first sight natural to suppose, since the end product of both the radium and thorium series is an isotope of lead, that one of the isotopes of lead forms the central core. It may, however, well be that the radioactive processes cease when there are still a number of satellites remaining. If this be so, the core may be of smaller nuclear charge and mass than that of lead. From some considerations, described later, this core may correspond to an element near platinum of number 77 and mass 192. FREQUENCY OF VIBRATION OF THE NUCLEUS