Refractivity and Atomic Interaction. 525 



gas. Then the molecular refractivity o£ the diatomic gas, 



that is, by (5a) arid (5t), and writing % for the sum, and 

 II for the product of the two atomic refractivities Ni, i\ 2 , 



N 



_ 1 t + 2,TL s-«n 



-3 !_, 2n +3 1 _ i ,2 I i W 



This is the required formula, valid for any diatomic gas. 



The free frequencies belonging to the molecule will be 

 obtained by equalling to zero the determinant of the equa- 

 tions (4 a) and that of (4tf). The former gives for the 

 squared free frequencies y a , corresponding to axial oscilla- 

 tions, as in I., 



y:,7 a "H(yi + Y 2 m[(7i-Y 2 ) 2 + -^PV] , (6a) 



and the latter gives for y t , corresponding to transversal 

 oscillations, on simply replacing s by — -Js, 



rb, - 1/2 



Vt 



',7 ( " = i(7i + 7 2 ))+i[(7i-7 2 ) 2 +^P« 2 ].' • (6 



Thus, none of the original frequencies, and therefore, of the 

 atomic bauds, will remain in the absorption spectrum of the 

 compound. The dispersion curve will be entirely modified 

 by atomic interaction, to an extent depending on the value 

 of V ' B^Bi/'B?. Yet, the sum of the squared new frequencies 

 will be equal to that of the original or atomic ones. In fact, 

 as has already been remarked in I., 7 a ' + 7a" = 7i + 72 j and 

 so also, by (6 t), y t ' + 7/' = 71 + 72* Remembering that each 

 of the y t counts for two (inasmuch as it belongs to two 

 mutually perpendicular transversal oscillations), and denot- 

 ing the new frequencies summarily by y f , we can express 

 the said conservation of the sum of squared frequencies by 

 writing 



%y = tyi = 3 (7! + 72) (7) 



This invariance with respect to mutual action is a general 

 property, valid for any number of interacting atoms. The 

 proof is easily obtained by examining the determinant of the 

 corresponding system of linear equations. 



