Refractivity and Atomic Interaction. 127 



Returning to our chief subject, we have for the squared 

 frequencies of the free vibrations in the molecular plane, by 

 (48) and (45), 



4B „ 4B 



7 =Vo- W , 7 =^+3^3, 



7"'=7o+!(l+ V13) -^(double), 



7 iY =7o-|(v / l3-l)^fdouble), 



. . (50) 



besides the " normal" free frequency, \Zry 0y vvhich belongs 

 to each of the atoms. In all, therefore, we have five different 

 free frequencies, of which two are " double " *. Thus, a sub- 

 stance composed of regular triatomic molecules would show 

 five distinct absorption bands, or, speaking rigorously, seven 

 bands, of which four would coincide in pairs. 



Notice in passing that, by (50), the sum of the squares of 

 the six new frequencies in the molecular plane is again 

 equal to that of the old ones, i. e. 



7' + 7" + 27"' + 27 iv =b7o, 



as might have been expected. 



Let Yo be in the remote ultraviolet. Then y" and y'" will 

 be still more remote, and therefore inaccessible. But the 

 remaining two absorption bands, 7' and 7 iv , will always be 

 more accessible than 70? an d may well fall into the visible or 

 even the infra-red region of the spectrum, provided that the 

 size of the molecule, i. e. the distance R between its atoms, 

 is small enough. 



The longest wave corresponds, by (50), to the new fre- 

 quency Vy' . As long as this is real, all others are real. 

 Thus, the critical distance R = R c , marking the limit of 

 absolute optical stability, will, in the present case, be 

 given by 



4B, 



E 3 = 



7o 



or, in terms of X 



VB = V >£ V .... (51) 



* And as such would be split by a magnetic field into doublets 

 (inverse Zeeman-efFect): But this by the way only. 



