radio-element. The radioactivity of these products is not permanent, but decays according to an exponential law with the time. The activity I at any time t is given by , where I is the initial activity and A a constant. Each radioactive product has a definite change constant which distinguishes it from all other products. These products do not arise simultaneously, but in consequence of a succession of changes in the radio-elements; for example, thorium in breaking up gives rise to Th X, which behaves as a solid substance soluble in ammonia. This in turn breaks up and gives rise to a gaseous product, the thorium emanation. The emanation is again unstable and gives rise to another type of matter which behaves as a solid and is deposited on the surface of the vessel containing the emanation. It was found that the results would be quantitatively explained on the assumption that the activity of any product at any time is the measure of the rate of production of the next product. This is to be expected since the activity of any substance is proportional to the number of atoms which break up per second, and, since each atom in breaking up gives rise to one atom of the next product together with α or β particles, or both, the activity of the parent is a measure of the rate of production of the succeeding product.
Of these radioactive products, the radium emanation has been very closely studied on account of its existence in the gaseous state. It has been shown to be produced by radium at a constant rate. The amount of emanation stored up in a given mass of radium reaches a maximum value when the rate of supply of fresh emanation balances the rate of change of the emanation present.
If q be the number of atoms of emanation produced per second by the radium, and N the maximum number present when radioactive equilibrium is reached, then , where λ is the constant of change of the emanation. This relation has been verified experimentally. The emanation is found to diffuse through air like gas of heavy molecular weight. It is unattacked by chemical reagents and in that respect resembles the inert gases of the argon family. It condenses at a definite temperature —150° C. Its constant of change is unaffected between the limits of temperature of 450° C and —180° C. Since the emanation changes into a non-volatile type of matter which is deposited on the surface of vessels, it was to be expected that the volume of the emanation would decrease according to the same law as it lost its activity. These deductions based on the theory have been confirmed in a striking manner by the experiments of Ramsay and Soddy. The radium emanation was chemically isolated and found to be a gas which obeys Boyle's law. The volume of the emanation observed was of the same order as had been predicted before its separation. The volume was found to decrease with the time according to
