106 Dr. L. Silberstein on Molecular 



Thus, in (^ as compared with o> s , the old free frequencies 

 \/7i> \/j2 (and, therefore, absorption bands) are replaced 

 by new ones, vV> v/V'? an d the old coefficients B l3 B 2 are 

 replaced by new ones, B', B". The forms of the corre- 

 sponding dispersion curves, with, say, 7 as abscissse and 

 a) s , (D a as ordinates, are entirely different; the first of them 

 only being a superposition of the atomic dispersion curves, 

 while the second is profoundly modified, to wit, not only in 

 its coefficients but also with respect to the position of its 

 singularities. As to these latter, y', 7" are the roots of 

 D = 0, i. e. by (15), 



y^ilTi + ^+iVCTi-^' + ieBA/R 6 . . (18) 



Thus, even if both y 1} y 2 are m the extreme ultraviolet, 

 7' may well be thrown into the accessible region of the 

 spectrum. Of this more will be said in the next section. 

 The formulae (16) and (17), with (18), complete the solution 

 of the problem in hand. If i is a unit vector along the axis, 

 the whole refractivity-operator can be written w=o) s + (o a i . i, 

 where i.i is a dyad. The corresponding permittivity- 

 operator will be K— K s + K a i . i. The resulting crystal will 

 have one optical axis coinciding with the parallel axes i of 

 the molecules. In common optical terminology, 



li s — *yiL s will be the ordinary, 

 and fM a =^/ 1 Ka the extraordinary refractive index of the 

 uniaxial crystal. And if M is the molecular weight and 

 d the density of the crystal, 



N.= 3 T *« N a=3T o, a , . . . (19) 



will be its ordinary and extraordinary molecular refractivity, 

 respectively. Thus (16) will read : the ordinary molecular 

 refractivity is additive, and the extraordinary non-additive or 

 u constitutive." 



Notice that, by (17) and (18), we have 



B ' + B " = Bl + H (20) 



and 7' + 7" =71 +72 J 



i. e. the sum of the dispersion coefficients, and the sum of the 

 squared free frequencies of the diatomic molecule have the 

 remarkable property of being invariant with respect to 



