1000 Mr. Gr. H. Livens on a Theory of the 



Although the equations for q 1 and q 2 could be solved abso- 

 lutely this process appears unnecessary, as the restrictions 

 imposed by the fundamental assumptions are probably such 

 as could not stand the test of absolute accuracy. Besides the 

 approximation obtained by treating ft as small is a very good 

 one, and would be sufficiently justified in most cases. The 

 equations are 



(9*-l)(«±?)=l, 



and if we expand q in powers of ft we get 



q J- qo± 2c^ +Al3 ^'" J 



so that ftn 



to a very good approximation if ft is small. Substituting 

 the values for a and ft we find 



/V beVm \/x e 2 /™ \ 



c . N \^ n r 2 -rinnr' — n 2 /\n r 2 + innr' — n <2 ) 



/ _ s ae 2 t in y 



\ ^ n/ + inn r —iv J 



and this is the general formula from which all the circum- 

 stances of the phenomena are obtained. 



In regions of the spectrum where there is no appreciable 

 absorption, the imaginary parts of these formulae are negli- 

 gibly small, and then the difference ^(^1 — 92) represents 



the rate of rotation of the plane of polarization in the sub- 

 stance, usually called a>, so that under these circumstances 



;<ra> 



/y be'/m \(s? be 2 /m\ 



n 2 / 1 "sr* ae 2 /m 



/ ^ ae'/m V 



a formula which can be adopted into an explanation of most 

 of the apparent anomalies in the polarimetric behaviour of 

 solutions when their aggregate constitution is varied. It 

 leads for instance, under the usual assumptions that 



^~* e 1 11% 



Zi~^ 2 ^ a ken per unit volume for any definite set of 



electrons is proportional to the partial density of the sub- 

 stauce with whose molecules they are associated, to a formula 



