This relation is to be expected, since the decay and recovery curves of the emanation are determined by exactly the same conditions as the decay and recovery curves of Ur X and Th X. In both cases there is: (1) A supply of fresh radio-active particles produced at a constant rate. (2) A loss of activity of the particles following an exponential law with the time. In the case of Ur X and Th X, the active matter produced manifests its activity in the position in which it is formed; in this new phenomenon, a proportion of the active matter in the form of the emanation escapes into the surrounding gas. The activity of the emanation, due to a thorium compound kept in a closed vessel, thus reaches a maximum when the rate of supply of fresh emanation particles from the compound is balanced by the rate of change of those already present. The time for recovery of half the final activity is about 1 minute, the same as the time taken for the emanation, when left to itself, to lose half its activity. If _q₀_ is the number of emanation particles escaping into the gas per second, and _N₀_ the final number when radio-active equilibrium is reached, then (section 133), _q₀_ = λ_N₀_. Since the activity of the emanation falls to half value in 1 minute λ = ¹⁄₈₇, and _N₀_ = 87_q₀_, or the number of emanation particles present when a steady state is reached is 87 times the number produced per second. Radium Emanation. =144. Discovery of the emanation.= Shortly after the discovery of the thorium emanation, Dorn[236] repeated the results, and, in addition, showed that radium compounds also gave off radio-active emanations, and that the amount given off was much increased by heating the compound. The radium emanation differs from the thorium emanation in the rate at which it loses its activity. It decays far more slowly, but in other respects the emanations of thorium and radium have much the same properties. Both emanations ionize the gas with which they are mixed, and affect a photographic plate. Both diffuse readily through porous substances but are unable to pass through a thin plate of mica; both behave like a temporarily radio-active gas, mixed in minute quantity with the air or other gas in which they are conveyed. =145. Decay of activity of the emanation.= Very little emanation escapes from radium chloride in the solid state, but the amount is largely increased by heating, or by dissolving the compound in water. By bubbling air through a radium chloride solution, or passing air over a heated radium compound, a large amount of emanation may be obtained which can be collected, mixed with air, in a suitable vessel.