the Separation of the Isotopes of Mercury. 43 



and the ratio between the initial volume and that remaining 

 after distillation by 



Vi 



v r 2 — (?ij + ?i 2 ) 



W 



we obtain 



m= l + 0h -m)- 2 - (5) 



or 



l-n 1 = - 1 + 



M 



A 

 / i_Mr\ 



1 ~^=- 1 jr-^J. J 



(«) 



Introducing the two latter equations into (2), and denoting 



the ratio of the element weights ~, which is equal to 



the corresponding densities, by d r — the meaning of this 

 magnitude being nothing but the density of the remaining 

 part expressed in terms of that of the standard substance — 

 we obtain 



= 1 + A, 



v r l — d r 

 in t — 



v t A 



or, transformed, 



1 ~ clr = JTA ]n ^ (7) 



By means of this equation from the known ratio — and 



the relative density of the residue d r , A and thus the 

 molecular weight (atomic weight) of both the pure elements 

 can be calculated. The validity of *the above equation can 

 be tested by proving that it can be satisfied for all corre- 

 sponding d r and - values by a single A value. This is 

 v r 



possible when calculating the density of our mercury 

 residue (d r ) from equation (7), on the assumption that 

 A has the constant value 0*0070. 



The results of this calculation, as well as the densities 

 experimentally determined, are shown in Table IV. 



