Refractivity and Atomic Interaction. 121 



refractivity N n = a> n /a8l will be simply 



N n = N 1 + N 2 +N 3 , (37) 



where N; = Bi/a(7; — 7), as before. The problem, therefore, 

 is reduced to finding the refractivity-operator JYp = co p /<xdl 

 for directions of E parallel to the molecular planes. The 

 molecular refractivity of an isotropic substance will then 

 easily be found by averaging. 



Let i, j, k be three unit vectors directed from 2 to 3> 

 from 3 to 0i, and from X to 2 respectively. Then 



1*1 = r 12 ) + r 13 k, 



and similarly for r 2 , r 3 . The equations of motion (9) for 

 the six displacement components 



^12- r n ; r 2s, r 21 ; r 31 , r S2 



will most conveniently be written in the Lagrangian form 



<*.73L\ 3<S> 1 



ttI^-J + s — = m 2 b 23 , etc. I 



j> , . . (do) 



( *;. ) + ^r= m 3 ( *M> etc - 



where w 2 Gr 23 , m^Gr^ are the generalized forces on r 23 , ?' 32 , 

 due to the external electric field E, determined by the right- 

 hand members of (9), and where " etc." means always two 

 more equations obtained by cyclic permutations of the suf- 

 fixes 1, 2, 3. The S3 mbols L and <I> are used for the relevant 

 kinetic and potential energy of the molecular system. These 

 latter functions are easily obtained. Using the abbreviations 



/9i== S7' ai = C0S ^' »=1.»» S. ' ' • (39) 



we have 



L = -^ OV + f 13 2 - 2a l r u r u ) + etc., 



(£> = m, I ^(r 12 2 + r u 2 — 2a 1 r 12 ri 3 ) — pi^'21^31 J + etc. 



}>. (40) 



