The data obtained from the counting experiments allow us to calculate simply the magnitude of a number of important radioactive quantities. It was found that the calculated values of the life of radium, of the volume of the emanation, and of the heating effect of radium were in excellent agreement with the values found experimentally. A test of the correctness of these methods of calculation was forthcoming shortly after the publication of these results. Rutherford and Geiger calculated, on the assumption that the α-particle was a helium atom, that one gram of radium in equilibrium should produce a volume of 158 cubic millimetres of helium per year. Sir James Dewar in 1908 carried out a long experimental investigation on the rate of production of helium by radium, and showed that one gram of radium in equilibrium produced about 134 cubic millimetres per year. Considering the difficulty of the investigation, the agreement between the experimental and calculated values is very good and is strong evidence in support of the identity of the α-particle with a helium atom. While the whole train of evidence we have considered indicates with little room for doubt that the α-particle is a projected helium atom, there was still wanting a decisive and incontrovertible proof of the relationship. It might be argued, for example, that the helium atom appeared as a result of the disintegration of the radium atom in the same way as the atom of the emanation and had no direct connection with the α-particle. If one helium atom were liberated at the same time that an α-particle was expelled, experiment and calculation might still agree and yet the α-particle might be an atom of hydrogen or of some unknown substance. In order to remove this possible objection, it is necessary to show that the α-particles, collected quite independently of the active matter from which they are expelled, give rise to helium. With this purpose in view some experiments were recently (1908) made by Rutherford and Royds. A large quantity of emanation was forced into a glass tube which had walls so thin that the α-particles were fired right through them, though the walls were impervious to the emanation itself. The α-particles were projected into the glass walls of an outer sealed vessel and were gradually released into the exhausted space between the emanation tube and the outer vessel. After some days a bright spectrum of helium was observed in the outer vessel. There is, however, one objection to this experiment. It might be possible that the helium observed had diffused through the thin glass walls from the emanation. This objection was removed by showing that no trace of helium appeared, when the emanation was replaced by a larger volume of helium itself. We may thus confidently conclude that the α-particles themselves give rise to helium, and are atoms of helium. Further experiments showed that when the α-particles were fired through the