the Separation oj the Isotopes of Mercury. 45 



and that of the first distillate, in so far as the distilled 

 amount is a small one : 



Ar N,1I, + N 3 V, . 



J> i ~r JN 2 



When we write i^-= a and " r = /3 2 , we find 

 Mi __ (a + /3)(<z/3 2 4-l) 



M d £(* + !) (*£+!)' 



(10) 



which, when the atomic weights M, and M 2 are not too 

 unlike, is practically identical with the following : 



where da denotes the density of the first distillate. The 

 value of d c i can either be directly determined from the 

 result of a single distillation, or with greater accuracy from 

 the A value with the aid of the equation : 



d d = VI- A 2 (12 



This expression inserted in equation (11) gives finally 



2* ' ,x, A 2 



^- 1 ) f =9lfAi. ■ • • • (13) 



(1 + a) 2 vr " 2 -A 2 



or for small values of A : 



If A is given, then in equation (14) to each value of a 

 there is only one single ft value — that is, when in addition 

 to the experimentally determined A the proportion in which 

 the pure elements are present in the mix-element is known, 

 the atomic weight of the pure elements can be determined*. 



* The equation (14) lends to the magnitude A (denned initially 

 as relating to the case where the mix-element contains the two pure 

 elements in equal amounts) a more general significance when interpreting 

 separation results. 



