One of the most interesting and important methods of throwing light on nuclear structure is the study of the very penetrating _γ_ rays expelled by some radioactive bodies. The _γ_ rays are identical in nature with X-rays, but the most penetrating type of rays consists of waves of much higher frequency than can be produced in an ordinary X-ray tube. The work of the last few years has indicated very clearly that the major part of the _γ_ radiation from bodies like radium B and C originates in the nucleus. A determination of the frequencies of the _γ_ rays thus gives us direct information on the modes of vibration of parts of the nuclear structure. The frequency of some of the softer _γ_ rays excited by radium B and radium C was measured by the crystal method by Rutherford and Andrade, but it is difficult, if not impossible, by this method to determine the frequencies of the very penetrating rays. Fortunately, due largely to the work of Ellis and Fräulein Meitner, a new and powerful method has been devised for this purpose. It is well known that the _β_ rays from radium B and radium C give a veritable spectrum in a magnetic field, showing the presence of a number of groups of _β_ rays each expelled with a definite speed. It is clear that each of the groups of _β_ rays arises from conversion of the energy of a _γ_ ray of definite frequency into a _β_ ray in one or other of the electronic levels in the outer atom. The energy ω required to move an electron from one of these levels to the outside of the atom is known from a study of X-ray absorption spectra. The frequency ν of the _γ_ ray is thus given by the quantum relation hν = E + ω, where E is the measured energy of the _β_ particle. Since each _γ_ ray may be converted in any one of the known electronic levels in the outer atom, a single _γ_ ray is responsible for the appearance of a number of groups of _β_ rays, corresponding to conversion in the K, L, M, etc., levels. In this way, an analysis of the _β_ ray spectrum allows us to fix the frequency of the more intense _γ_ rays which are emitted from the nucleus. The energy of the shortest wave measured in this way by Ellis corresponds to more than two million volts, while other evidence shows that probably still shorter waves are emitted in small quantity from radium C. Ellis and Skinner have shown that the energies of these rays show certain combination differences, such as are so characteristic of the energies of the X-rays arising from the outer electrons. A series of energy levels may thus be postulated in the nucleus similar in character to the electron levels of the outer atom, and the _γ_ rays have their origin in the fall either of an electron or of an _α_ particle between these levels. This is a significant and important result, indicating that the quantum dynamics can be applied to the nucleus as well as to the outer electronic structure.