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



The annual production of helium by uranium is 

 10*4 x 10~ 8 c.c. *, and therefore the amount (x) o£ 

 radium Gr generated in the same time is 1'19 X 10~ 10 gram. 



Hence the rate of production o£ thorium lead is *- (i.e. 0*4) 



that of uranium lead. In the case of a mineral in which 

 the present amounts of the parent elements are represented 

 by XJi and Th*, and the time-average t amounts by U TO and 

 Th m respectively, the amount of accumulated lead isotopes- 

 (Pb*) in the time t will be 



Pb,=*(ffU™+#Th M )t, 



whence 



Pb, 



t vears 



*(U.+ *Th.)" 



lb 

 __ Pb* 



,,(U Wi + 0-4Th m j * ears ' 



Pb* oeio . . Tr 



^tL^^4TK ; X8 ' 230milll °^ 



In the analyses which follow, the ratios have been calcu- 

 lated using the time-average values for uranium and thorium,, 

 though in the case of the above expression this is not 

 absolutely necessary §. 



If, then, thorium lead should be stable, the age factor 

 Pb 

 rTT 4-0-4-TM ought to be constant for minerals of the same 



* Calculated from data given in Le Radium, xi. pp. 4-5 (1914). 



t Lawson, Proc. Durham Phil. Soc. v. (1) p. 26 (1913). 



X The part played by actinium in the production of an isotope of 

 lead is here omitted as being of negligible importance. 



§ The above expression for the age, t, of a mineral can readily be 

 expressed in the following form : — 



Pb; 



~ IfTMQ^TUi Pb;(0-58U,+O09Th,) l/ 

 a ) (U f +0 4Th,)+- - Vt+Q ^ Tht) -j 



The more approximate expression 



Pb; 



t= 



4U*+0-4Tli4 



gives results slightly in excess of the exact values ; e. g., for minerals of 

 Devonian age the error is about 2 per cent., being greater for minerals 

 rich in uranium, and less for those in which thorium predominates. 



