Refractivity and Atomic Interaction. 527 



e' = e/ s/±ir for the charge in ordinary (irrational) electro- 

 static units, 



, 1-008 e'/ce'Jc ,„ , 



k =— ,3- -- - (11a) 



Substituting (12) in (8), developing ;md rejecting the 

 second and the higher powers o£ g u, we have, for the mole- 

 cular refractivity of the diatomic gas, 



N = &.+ #w, (13> 



/0 (i-M(i + l^;' 



where — 2b Q 



y (i4> 



l-b s + % b V 

 ^« (l-6 ,)(l-lV^) j 



These are the refraction- and the dispersion coefficient of the 

 gas in terms of the atomic coefficients b , g and the inter- 

 atomic distance involved in 5. Writing, analogously to k , 



k = b 2 jg, 

 we have, from (11), 



°l-b s+H 



2,2> 



4 l 



whence _. _ ,-— r7T 



,6 = 2 A=*±iVfcil). . . . ( i5) 



This is the correct formula to be employed instead of 

 formula (12) in a previous Note (Phil. Mag., Feb. 1917, 

 p. 218). Asjin that Note, let e be the value of the right- 

 hand member of (11 a) which would correspond to an electron 

 proper, i. e. 



€ = 0-107 . 1-77 . 10 7 . 9650 --=1-83 . 10 10 — , . (16) 



gr. 



and let us assume again that any atomic k is an exact 

 multiple of the electronic value, 



*<, = «*, (17) 



n being the smallest integer compatible with the conditions 

 of the problem. Now, notwithstanding the above correction 

 of the transversal part of the interaction, the expression under 

 the radical in (15) has remained exactly as before. Thus, 

 k being essentially positive and sb real, n will again be the 

 smallest integer satisfying the inequality 



k = ne>ik (18) 



The condition of stability, is by (10), in terms of b , 



*h<i, . (19) 



1 27rR c 3 



the critical distance R c being given bv - = — = b . 



& ° - s c a. 



