128 On Molecular Refractivity and Atomic Interaction. 



and if the dispersive particles are pure spherical charges, o£ 

 radius a, 



R c 3 =-V«, (51a) 



as in the case o£ diatomic molecules, (33), the only differ- 

 ence being that -J is now replaced by 5. In short, the critical 

 distance for a regular triatomic molecule is 1'260 times 

 that for a diatomic molecule, composed of the same atoms. 

 The two infra-\ absorption bands can now be written 



V 2 VL R 3 J' x w "VL °" 4 R 3 J (5 ^ 



When R approaches R c (from above), the wave-length X' 

 tends to disappear in the remote infra-red, while X iv , moving- 

 more lazily, tends to become only 1*329 times X . Thus, for 

 example, if A =720 A.U., the greatest length of X iv , com- 

 patible with stability, is 957 A.U., still in the extreme 

 Lyman-region. But V may fall into any region of the 

 spectrum, from X to infinity, — precisely as our previous X' 

 in the case of a diatomic molecule. 



This settles the question of the free frequencies belonging 

 to a regular triatomic molecule. The refractivity of a sub- 

 stance composed of such molecules, as a function of the 

 frequency \/ y of the incident light, will contain seven terms 

 having in their denominators the expressions 



Yo-Y, Y'-Y ? Y"-Y, (y" -Y) 2 , Y'"-Y, (Y iY ~Y) 2 , Y iv -Y- 



The corresponding coefficients, as functions of the attributes 

 of the atoms and of their mutual distances, will be deter- 

 mined by means of (44) and (10). Further details con- 

 cerning triatomic and some of the more complex molecules 

 will be given in a later publication. 



I gladly take the opportunity of thanking my friend 

 Dr. A. G. Goldsobel for having directed my attention to 

 this subject and for furnishing many interesting chemical 

 data. 



November 14, 1916. 



