CHAPTER X.
TRANSFORMATION PRODUCTS OF URANIUM, THORIUM, AND ACTINIUM.
205. In the last chapter the mathematical theory of successive changes has been considered. The results there obtained will now be applied to explain the radio-active phenomena observed with uranium, thorium, actinium, radium, and their products. Transformation products of Uranium.
It has been shown in sections 127 and 129 that a radio-active constituent Ur X can be separated from uranium by several different processes. The activity of the separated Ur X decays with the time, falling to half value in about 22 days. At the same time the uranium, from which the Ur X has been separated, gradually regains its lost activity. The laws of decay of Ur X and of the recovery of the lost activity of the uranium are expressed by the equations
I_{t}/I_{0} = e^{-λt}, and I_{t}/I_{0} = 1 - e^{-λt},
where λ is the radio-active constant of Ur X. The substance Ur X is produced from uranium at a constant rate, and the constant radio-activity observed in uranium represents a state of equilibrium, where the rate of production of new active matter is balanced by the rate of change of the Ur X already produced.
The radio-active processes occurring in uranium present several points of difference from the processes occurring in thorium and radium. In the first place, uranium does not give off an emanation, and in consequence does not produce any excited activity on bodies. So far only one active product Ur X has been observed in uranium. This active product Ur X differs from Th X and the emanations,
