Refractivity and Atomic Interaction. 117 



of diamond *, and therefore, possibly, to that of the isolated 

 carbon atom. If this is taken for \ , then, no matter what 

 length R c is itself, formula (31) gives the following interesting 

 table :— 



E/Rc= oo 5 2 1-5 1-2 1-10 105 l'OlO 1-005 1-002 1-001 1 

 \'=720 723 770 858 1109 1444 1951 4199 5908 9318 13,159 oo 



For R = 1'5R C the line \ r becomes accessible to the vacuum 

 spectrograph, and for 1*05 for the ordinary quartz spectro- 

 graph ; when R is just above 1'OlOi^ the visible region of 

 the spectrum is reached, and before it falls to l'0022? c , 

 V plunges into the infra-red. 



"With regard to the absolute length of the critical distance 

 itself, it could be determined with precision, if the true atomic 

 dispersive curve and therefore A and B were known, quite 

 apart from the electrical significance of B. We may return 

 later to this aspect of the question. Here, however, let us 

 remark that if the second form of (32) is used, R c can be 

 put into an interesting form. In fact, if the mass m of the 

 dispersive particle (not necessarily an electron) is of purely 

 electromagnectic origin, and if, to fix the ideas, the charge 

 is assumed to be uniformly distributed through its volume, 

 a sphere of radius a, then 



= e 2 /'c 2 

 57ra' 



and the above expression of the critical distance becomes 



* In fact, I find that Martens's observations of the refractive index n 

 of diamond (Land. -Born., 1905, p. 631) extending over X = '313 to 

 '643 micr., can be fairly well represented by 



N ^?+2'^=X^x7' wlth> o = /199A - U - ' ' ' <°> 



Having determined the two constants from /u 3l3 and /z 4 4i, I obtain 

 from (C) 



(\ = -313) (-346) (-441) (-508) (-643) 



Ncaic. - 2-195 2-172 2-135 2-121 2-105, 



and, from Martens's observations, 



Nobs. = 2-195 2-172 2-135 2-122 2-106. 



The agreement is, for the present purpose, more than sufficient. 



