﻿674 Messrs. A. Holmes and R. W. Lawson on 



fortuitous choice of analyses would be useless for our purpose. 

 The effect of thorium lead must be sufficiently predominant 

 to exert a marked influence in spite of the unavoidable 

 presence of uranium lead. Moreover, it cannot be lightly 

 assumed that in all the minerals given in the above mentioned 

 table, the amount of original lead is the same; and in the 

 event of thorium lead being of relatively short life, it is 

 clear that negligence of this inequality would lead to indefinite 

 or even conflicting conclusions regarding the half-period of 

 thorium E. 



Careful consideration of the analyses made it clear that 

 the only results which could be used with confidence were 

 those of Nos. 3, 6, 7, and 12. The instability of thorium 

 lead, and the large percentage of uranium in mineral No. 12, 

 makes it certain that the effect of thorium E in affecting the 

 Pb/U ratio of this mineral must be very small and, practically 

 speaking, negligible. The value (0*041) for this mineral can 

 thus be taken with great probability as representative of 

 Devonian minerals. Also, since these four minerals are 

 similar in type, comparable in composition, and from the 

 same locality, it is possible that their contents of original 

 lead are not very different. Vogt * has given 0*000^ gram 

 as the average amount of lead in 100 grams of rock. If we 

 assume this value, and give x the value 5, the corrected Pb/U 

 ratios for those minerals poor in thorium show a better 

 agreement than previously. Complete agreement is not to 

 be expected from what has already been said, but the mag- 

 nitude of this value is evidently of the right order. The 

 value 0*0005 gram will thus be taken as the amount of 

 original lead in 100 grms. of the minerals used for the calcu- 

 lation of the half-period of thorium E by the first two of the 

 following three methods to be described. 



The total amount of experimentally found lead is evidently 

 equal to the sum of the following three constituents : — 

 (a) Original lead ; (b) Uranium lead ; (c) Thorium lead. 

 This statement can obviously be expressed in the following 



Pb, = Pb + /c.U, + m.Th„ 

 where Pb f , U$, and Th f are the present percentage contents 

 of the minerals in lead, uranium, and thorium respec- 

 tively. Pb is the quantity of original lead present per 

 100 grams of the mineral ; k is the amount (constant) of 

 uranium lead associated with one gram of uranium in these 

 Devonian minerals ; and m is the equilibrium amount of 

 thorium lead associated with one gram of thorium. 



(a) In the first method for the determination of the value 

 * Vogt, Zeit.fiir prakt. Geol 1898 ; Holmes, lac. cit. p. 253. 



