KKFKACTION AND Dlsl'KltSION OF T1IK HALOGENS, HALOGEN ACIDS, ETC. 3 



and confirmed by experiment. But it is desirable to emphasise the fact that the 

 calculation of the constants given in this paper from a formula containing only one 

 tt-nn on the right-hand side is only provisional, since the main conclusion of the 

 authors is that, Ixitli for i-lcim-iils and compounds, a single term is inadequate, except 

 in the case of monatomic gases. The simple form of the formula is, however, useful 

 for indicating at a glance the direction and magnitude of the changes in refractive 

 and dispersive power which take place when elements combine to form a compound. 



It' /<, n-, are the refractive indices of a substance for two wave-lengths for which the 

 frequencies an- //, H.J, we have 



I -Ma _ ni-nj ._ 



approximately, 



since / is usually small compared witli H {I J . The left side of the equation expresses 

 the dispersive power of the substance, which is thus seen to be inversely proportional 

 ion, 3 . 



Chiiniji-x <>f /f,'fi-'i<-/ir<- Power. Let yu A 1 = 3 A ' MB~! = IL ~l be the 



^0 A ft "' B ft 



formuko which express the refractivity of two gaseous elements in the region of the 

 visible spectrum, and let MAB 1 = 3 ** a express the refractivity of the compound 



~~ 



wliich they form. If the molecules of the two elements are diatomic, and one 

 molecule of the compound is formed of one atom of each, then the change of refractive 



jx>wer on combination is 



. f N A ( N B 1 N AB 

 ' In.^v-w 8 'B n*J WAB-W*' 



<>f />/.<./ /r/-.s//v I '< ,!<< r. If the additive law were strictly followed the 

 dispersive power of a compound, measured in a region remote from free frequencies, 

 would lie between the dispersive powens of its constituents, i.e., HO'AB would lie 

 Ix-tween nj^ and H^ B . For it can be shown that, for a short region of the spectrum, 

 it-mote from free frequencies, so that n a is large compared with ;t a and n*jn* can be 

 neglected, 



A n A "o 



and this expression lies between these limits. 



Hence, if the experimental value of /i u a AB differs from this value, the variation must 

 be due to the changes in one or more of the four qiiantities N A , N B , n/x, n^a 

 consequent on combination. It is evident that all four unknown quantities cannot 

 be determined from a knowledge of N AB> ft,i a AB , which is all we obtain from a deter- 

 mination of the dispersion of the compound. But two cases should IK' distinguished. 

 The value of MU'AB mav vary owing to changes in u/v and ti^ B consequent on 

 combination, i.e., to real modifications of the free periods of the vibrators ; or it may 



B 2 



