40 



YOS, BADE AND JEHLE 



advantageously generalize this approach by studying the discrimination which 

 an arbitrary molecule in the manifold exhibits in its interactions with the other 

 members of the manifold. In that case one forms averages of the type 

 ((Wsi — Wsn)-)Av where I and II are chosen at random from the manifold. Or, 

 equivalently, one can form averages ((Ws — (Ws)av)^)av from the distribution 

 of 'Ws which are of the same order of magnitude as the preceding averages. 



A given manifold of molecular types can be characterized by its (Ws)^^ 

 distribution. To simplify the discussion, one may forget about the subscripts 

 fjLP referring to the fact that (Ws)^^ are tensors in ordinary three-dimensional 

 space. Then one may simply talk about a distribution in the vector space 

 W. = (Wo , W_i , Wi , W_2 , Wo ••••)• 



One can illustrate the W^ as function of « for two extremely simplified mole- 

 cules, one of which has appreciable polarizabilities only in a narrow region in 

 the ultraviolet Si ^ 78, the other only in the classical region si '^ 0. 



N 



•W. = 2R-' 2 «'/(! + ^'A''), 



Sl 



= hwi/lirkT 



(14a) 



1=1 



If one had a molecule with some polarizabilities in both the indicated spectral 

 regions, its Ws as function of s, (14a), would be a weighted sum of these ultra- 

 violet and classical Ws , plotted in figure 3. For a special manifold of mole- 

 cules with polarizabilities distributed only over the two indicated regions (e.g. 

 with ultraviolet polarizabilities = some percentages of that of figure 3, and 

 classical polarizabilities = some percentages of that of figure 3) the W^ as 

 functions of 5 would again be weighted superpositions of the two functions 

 illustrated in figure 3. Such a molecular manifold may be said to depend on 

 the two parameters ^^a^ in the ultraviolet and 2_1"^' i^ ^^^ classical region. 



-"W. 



for a small molecule 

 -1.5^ classical s^wO, la, « 100 -10"^^ 



-0.2 



-0.1 



ultraviolet s, «78, Ia,w7.5-I0 



-24 



-10 10 20 30 40 50 60 70 80 90 s 



Fig. 3 



