42 Prof. J. N. Br^nsted and Prof. G. Revesy on 



The mercury used in the density determination was present 

 in the purest state. In each fraction examined we made sure 

 that any further vacuum-distillation made in the usual way 

 had no influence on the density of mercury within the limit 

 of our errors of measurement. 



5. Calculation of the separation. 



In the case of a mix-element composed of two isotopes, 

 to be separated into its components by means of the evapo- 

 ration method described, the change which the element weight 

 suffers through a single evaporation can be calculated in the 

 following way. If Ni and N 2 are the number of molecules 

 originally present, n x and n 2 are those of the evaporated 

 molecules of the first resp. second isotope, M, and M 2 the 

 corresponding molecular weights (atomic weights) ; then, 

 granted the above-mentioned ideal conditions (p. 33), the 

 differential equation fundamental to our calculation, 



dn 1 _ Ni — n x /M 2 

 dn 2 ~ N 2 -n 2 V Mi' 



(1) 



follows ; from which, by integration, we obtain 



No — no 





In the special case, which we will deal with first, where the 

 initial ratio of the two isotopes is equal to unity , we can put 



and further 



Mi = Mi(l- A), M 2 = M t -(l + A), 



where M» indicates the element weight of the mix-element 

 in its original state. We then obtain 



ln(l— m) _ /l-t-A 

 . ln(l-n 2 ) ~~ V 1^E> 



or with great approximation 



! n ^^=l + A (2) 



ln(l— n 2 ) v J 



Taking into consideration that the element weight of the 

 • .... 



fraction remaining after distillation is expressed by 



_ (1-» ! )M 1 + (1-^ 2 )M 2 , 



r ~~ 2-^ + nd ' ' ' * W 



