Refractivity and Atomic Interaction. 523 



9^ = 2*76 . 10 19 cm.~ 3 , so that the average distance of neigh- 

 bouring molecules is of the order of X = 3*3 . 10~ 7 , while the 

 critical distance R c of the atomic centres within a molecule 

 is of the order 10 " 8 , and in some cases even smaller than 

 that. Thus the ratio RJL is a small fraction, like 1/40 or 

 1/50, and since all optical perturbations are brought about 

 essentially through the variation of the free frequencies, 

 the influence of neighbour molecules, being represented by 

 (R /jL) 3 ===10 -5 , will be practically evanescent. Under these 

 circumstances we have simply 



G = E, 



and the general system of equations (2) gives, for each 

 molecule, the two equations 



(yi-y)pi- 2^53 [3u(*p 2 ) -p 2 ]=B 1 e, 



(7s-7)P2- ^ 3 PuOPi) -Pi] =B 2 E. 



(4) 



Here R is the mutual distance of the two atomic centres 

 and u a unit vector coinciding in direction with the molecular 

 axis V2 or 21. 



Consider, first, the ideal case in which the axes of all 

 molecules are parallel to one another. Let a i be the axial 

 and t t the transversal component of p., and E a , E^ the 

 corresponding components of E, the electric vector in the 

 incident light. Then (1) will split into 



(yi-7K-2^K 8 =BlE « ; (72-7)«2-^^ 3 =B 2 E a , (4a) 

 and 



(7i -rX + sle = B ' K * : <*-7)«. + & = b,e, . (i 



At the same time we shall have P;=p,, and therefore, by (3), 

 (K-l)E=fSt(a l + a 3 ) ; (K ( -l)E f = 9?(t 1 + ; 2 ), . (3') 



where K a =//- a 2 , T£. t =fi f 2 ; /ji a , \x t being the corresponding re- 

 fractive indices. 



Now, the axial equations (4 d) are identical with those 

 2 02 



