52b' Dr. F. A. Lindemann and Dr. F. W. Aston on the 

 This is only true over a finite range of z, if 



7 M i 7 Mj 



w= ^j- a„, » n -i= jf °»-i etc - 



On the other hand, if this is so, 



and 



I r r n 4- 1 n 



Therefore if <j> (z) is an analytical function, both A arid v™ 

 cannot be identical and the isotopes must be separable under 

 appropriate conditions. 



It is of course true that the separation may be minute. 

 If, for instance, M only varies by 1 per cent, as in the case 

 of lead, the percentage difference of pressure at the boiling- 

 point would probably not exceed 1 per cent, and might be 

 very much less if the first-order terms cancel one another. 



A similar argument applies to the chemical separation of 

 isotopes. For 



T T JT f* T 

 A = U -TJ J£J $c p dT + %i, 



so that complete identity of the affinity A implies the 

 identity of U and c p over a finite range of values of r. It is 

 almost inconceivable that the values of U should be identical 

 unless the values of \ are identical, for U is made up of the 

 heat of reaction of one atom of the isotope with one or more 

 atoms in the gaseous state plus the algebraic sum of the 

 latent heats of the combination and of the reacting sub- 

 stances at the absolute zero. The possibility that there is a 

 difference between different isotopes in the heat of com- 

 bination of one atom with one or more atoms of some other 

 substance which exactly balances the difference in %X seems 

 sufficiently remote to be ruled out without further discussion. 

 But if one may conclude that the values of X are identical 

 the same difficulty arises in assuming the values v m to be 



identical as was experienced above. Since the values of ^~ 



