The disintegration theory, which was put forward in the first edition as an explanation of radio-active phenomena, has in these later researches proved to be a most powerful and valuable method of analysing the connection between the series of substances which arise from the transformation of the radio-elements. It has disclosed the origin of radium, of polonium and radio-tellurium, and of radio-lead, and now binds together in one coherent whole the large mass of apparently heterogeneous experimental facts in radio-activity which have been accumulating since 1896. The theory has received a remarkable measure of verification in the past year, and, in many cases, has offered a quantitative as well as a qualitative explanation of the connection between the various properties exhibited by the radio-active bodies. In the light of this evidence, radio-activity may claim to have assumed the position of an independent subject, though one with close affinities to physics on the one hand and to chemistry on the other. The present edition includes a large amount of new material relating to the nature and properties of the radiations and the emanations. In the limits of this book, it would have been found impossible, even had it been thought desirable, to include more than a brief sketch of the physiological effects of the rays. The literature on this subject is already large, and is increasing rapidly. For reasons of space, I have not been able to refer more than briefly to the mass of papers that have appeared dealing with the examination of various spring and well waters, sediments, and soils, for the presence of radio-active matter. In order to make the book more self-contained, a short account has been given in Chapter II of the magnetic field produced by an ion in motion, of the action of an external magnetic and electric field upon it, and of the determination of the velocity and mass of the particles constituting the cathode stream. Two appendices have been added, one giving an account of some work upon the α rays which was completed too late for inclusion in the subject matter of the book, and the other containing a brief summary of what is known in regard to the chemical constitution of the various radio-active minerals, the localities in which they are found, and their probable geologic age. For the preparation of the latter, I am indebted to my friend Dr Boltwood of New Haven, who, in the course of his researches, has had occasion to analyse most of these minerals in order to determine their content of uranium and radium. I hope that this account of radio-active minerals will prove of value to those who are endeavouring to elucidate the connection between the various radio-active substances and the inactive products which arise from their transformation.