speaking generally of the active matter, which causes excited activity, without regard to its constituents, I have used the term "active deposit." The scheme of nomenclature employed in this book is clearly shown below:—
Radium Thorium Uranium Actinium
[v] [v] [v] [v]
Radium emanation Th X Ur X Actinium X
[v] [v] [v] [v]
Radium A } Thorium emanation Final product Actinium emanation
[v] } [v] [v]
Radium B } Thorium A } Actinium A }
[v] } Active [v] } [v] }
Radium C } deposit Thorium B } Active Actinium B } Active
[v] } [v] } deposit [v] } deposit
Radium D } Thorium C } Actinium C }
[v] } (final product) } (final product) }
&c.
Each product on this scheme is the parent of the product below it. Since only two products have been observed in the active deposit of thorium and actinium, thorium C and actinium C respectively refer to their final inactive products. It will be shown in the next chapter that, as in the case of thorium, an intermediate product exists between actinium and its emanation. From analogy to the products Th X and Ur X, this substance is termed "actinium X."
196. Theory of Successive Changes. Before considering
the evidence from which these changes are deduced, the general
theory of successive changes of radio-active matter will be considered.
It is supposed that the matter A changes into B,
B into C, C into D, and so on.
Each of these changes is supposed to take place according to the same law as a monomolecular change in chemistry, i.e., the number N of particles unchanged after a time t is given by N = N_{0}e^{-λt}, where N_{0} is the initial number and λ the constant of the change.
Since dN/dt = -λN, the rate of change at any time is always proportional to the amount of matter unchanged. It has previously been pointed out that this law of decay of the activity of the radio-active products is an expression of the fact that the change is of the same type as a monomolecular chemical change.
