638 Prof. E. C. C. Baly on 



The value of v is generally very large and lies in the 

 extreme ultra-violet region beyond the working limit o£ a 

 spectrograph in air. The value of v is therefore calculated 

 from the refractivities for two different values of v. Now if 

 each energy quantum hv absorbed is evolved as a whole 

 number of quanta of infra-red radiation, it is obvious that we 

 can replace v in the formula by some multiple of the frequency 

 of the infra-red absorption band. In doing this it must be 

 remembered that we are not dealing with substances which 

 have their closed force fields opened up by solvents or in 

 any other way. The infra-red absorption bands have been 

 observed with considerable accuracy in the case of many 

 substances, and recently Mr. and Mrs. Cuthbertson** have 

 published the refractivities of several gases for which the 

 wave-lengths of the infra-red absorption bands are known 

 fairly accurately. Calling the frequency of the infra-red 

 band v y , the value nv y , where n is a whole number, can be 

 substituted in Sellmeyer's formula, so that it reads 



N 



fi-± 



(nvf) 2 —v 



2_,,2' 



This should give a very accurate means of calculating the 

 refractivities. I have done this for the following substances 

 given by Mr. and Mrs. Cuthbertson : chlorine, hydrogen 

 chloride, water vapour, ammonia, nitric oxide, and nitrous 

 oxide; and the results of the calculation are given in the 

 following tables. 



The method of calculation is very simple, for it is only 

 necessary to find which multiple of v y gives the best values 

 of the constant N in the formula, making use of the ob- 

 served values of the refractivities. The mean value of the 

 constant N is then found and inserted in the formula, and 

 the refractivities calculated. The following values were 

 obtained : — 



Water Vapour. 

 X (infra-red bands) =2*95 /-tf, whence ^=1*017 x 10 u . 

 The following are the refractivities calculated from the 



* C. Cuthbertson and M. Cuthbertson, Phil. Trans, ccxiii. A. p. 1 

 (1913). 



t Coblentz, Carnegie Institution Publications No. 35, p. 56 (1905). 



