460 Mr. S. S. Richardson on Magnetic Rotary 



Unless 7) varies more rapidly than the inverse square of 

 the dispersional period, « x , & . . . will be all less than unity. 

 Thus 



1— «o= 



e~ 



7rG 5 



■m^A 



*= 



Itt 

 e2 



/ e 2 > 



' V 7r(J 2 m / 



Hence 







(*> 



'-1 



-«o) 2 





S?) 





(«> 



7T 



In applying this formula we may note that * — 



(i.) N'>Nj. Hence the result will furnish an upper 

 limit to the number of electrons of the longest ultra- 

 violet period. 



(ii.) When \ 1? X 2 . . . are not widely separated, N' 

 approximates closely to (Ni-f-N 2 + N 3 + . . .), and the 

 result gives the total number of dispersional electrons 

 very nearly. 



(iii.) As a is known for very few substances, it must 

 usually be neglected and the result treated as an 

 augmented value of p. When condition (ii.) is satisfied, 

 the result will be a close approximation to the total 

 number of refractive electrons f. 



(iv.) In the case of unsaturated compounds, the value 

 of W will be influenced by the small values of a, /3, etc. 



Using equation (1) to find the number of electrons per 

 molecule, we have 



2 2' <f> 'd'e/h' ' ' W 



Denoting the specific rotation and molecular rotation 

 relative to water by p and B, w respectively, we obtain 



^ -01308 x -0002909 £ ° r X=B " 5898 A 



" J ^r^;K im <10) 



and (^-l-a ) 2 t M^ x . Q2285 



* See Note 1. 



+ Of. results for aliphcatic compounds, Table III. 



