We have seen that the two emanations and the products Ur X, Th X lose their activity with the time according to a simple exponential law, and at a rate that is independent—as far as observation has gone—of the chemical and physical agents at our disposal. The time taken for each of these products to fall to half its value is thus a definite physical constant which serves to distinguish it from all other products.
On the other hand, the variation of the excited activity produced by these emanations does not even approximately obey such a law. The rate of decay depends not only on the time of exposure to the respective emanations, but also, in the case of radium, on the type of radiation which is used as a means of comparative measurement. It will be shown, in succeeding chapters, that the complexity of the decay is due to the fact that the matter in the active deposits undergoes several successive transformations, and that the peculiarities of the curves of decay, obtained under different conditions, can be explained completely on the assumption that two changes occur in the active deposit from both thorium and actinium and six in the active deposit from radium.
195. Nomenclature. The nomenclature to be applied to the numerous radio-active products is a question of great importance and also one of considerable difficulty. Since there are at least seven distinct substances produced from radium, and probably five from thorium and actinium, it is neither advisable nor convenient to give each a special name such as is applied to the parent elements. At the same time, it is becoming more and more necessary that each product should be labelled in such a way as to indicate its place in the succession of changes. This difficulty is especially felt in discussing the numerous changes in the active deposits from the different emanations. Many of the names attached to the products were given at the time of their discovery, before their position in the scheme of changes was understood. In this way the names Ur X, Th X were applied to the active residues obtained by chemical treatment of uranium and thorium. Since, in all probability, these substances are the first products of the two elements, it may be advisable to retain these names, which certainly have the advantage of brevity. The name “emanation” was originally given to the radio-active gas from thorium, and has since been applied to the similar gaseous products of radium and actinium.
Finding the name “radium emanation” somewhat long and clumsy, Sir William Ramsay[[294]] has recently suggested “ex-radio” as an equivalent. This name is certainly brief and is also suggestive of its origin; but at least six other ex-radios, whose parentage is as certain as that of the emanation, remain unnamed. A difficulty arises in applying the corresponding names ex-thorio, ex-actinio to the other gaseous products, for, unlike radium, the emanations of thorium and actinium are probably the second, not the first, disintegration product of the radio-elements in question. Another name thus has to be applied to the first product in these cases. It may be advisable to give a special name to the emanation, since it has been the product most investigated and was the first to be isolated chemically; but, on the other hand, the name “radium emanation” is historically interesting, and suggests a type of volatile or gaseous matter. Since the term “excited” or “induced” activity refers only to the radiations from the active body, a name is required for the radiating matter itself. The writer in the first edition of this book suggested the name “emanation X.”[[295]] This title was given from analogy to the names Ur X and Th X, to indicate that the active matter was product of the emanation. The name, however, is not very suitable, and, in addition, can only be applied to the initial product deposited, and not to the further products of its decomposition. It is very convenient in discussing mathematically the theory of successive changes to suppose that the deposited matter called A is changed into B, B into C, C into D, and so on. I have therefore discarded the name emanation X, and have used the terms radium A, radium B, and so on, to signify the successive products of the decomposition of the emanation of radium. A similar nomenclature is applied to thorium and actinium. This system of notation is elastic and simple, and I have found it of great convenience in the discussion of successive products. In 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 |
| Radium emanation | Th X | Ur X | Actinium X |
| Radium A (Active) | Thorium emanation | Final product | Actinium emanation |
| Radium B (Active) | Thorium A (Active) | Actinium A (Active) | |
| Radium C (Active) | Thorium B (Active) | Actinium B (Active) | |
| Radium D (Active) | Thorium C (final) | Actinium C (final) | |
| &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
where N₀ is the initial number and λ the constant of the change.