Let _d_ be the thickness of the metal plate, ρ its density compared with air. Consider a point _P_ close to the upper side of the plate. The range of the particles moving from a point, when the path makes an angle θ with the normal at _P_, is _a_ − ρ_d_ sec θ, where _a_ is the range in air. The rays coming from points such that the paths make an angle with the normal greater than $$ \cos^{−1} \frac {\rho d} {a} $$ will thus be absorbed in the plate. By integrating over the circular area under the point _P_, it is easy to show that the total ionization in the vessel is proportional to $$ \int₀^{\cos^{−1} \frac {\rho d} {a}} 2 \pi \sin \theta \cos \theta (a − \rho d \sec \theta) d\theta = \frac {\pi (a − \rho d)^2} {a} $$ . The curves showing the relation between current and distance of metal traversed should thus be parabolic with respect to _d_. This is approximately the case for a simple substance like radio-tellurium. The curve for a thick layer of radium would be difficult to calculate on account of the complexity of the rays, but we know from experiment that it is approximately exponential. An account of some recent investigations made to determine the range of velocity over which the α particle is able to ionize the gas is given in Appendix A. The results there given strongly support the theory of absorption of the α rays discussed above. PART IV. The γ or very penetrating Rays. =105.= In addition to the α and β rays, the three active substances, uranium, thorium, and radium, all give out a radiation of an extraordinarily penetrating character. These γ rays are considerably more penetrating than the X rays produced in a “hard” vacuum tube. Their presence can readily be observed for an active substance like radium, but is difficult to detect for uranium and thorium unless a large quantity of active material is used. Villard[167], using the photographic method, first drew attention to the fact that radium gave out these very penetrating rays, and found that they were non-deviable by a magnetic field. This result was confirmed by Becquerel[168]. Using a few milligrams of radium bromide, the γ rays can be detected in a dark room by the luminosity they excite in the mineral willemite or a screen of platinocyanide of barium. The α and β rays are completely absorbed by placing a thickness of 1 centimetre of lead over the radium, and the rays which then pass through the lead consist entirely of γ rays. The very great penetrating power of these rays is easily observed by noting the slight diminution of the luminosity of the screen when plates of metal several centimetres thick are placed between the radium and the screen. These rays also produce ionization in gases and are best investigated by the electrical method. The presence of the γ rays from 30 mgrs. of radium bromide can be observed in an electroscope after passing through 30 cms. of iron.