﻿Organic, Substances and the Electron Theory. 197 



III. Two similar vibration centres with a third the 

 frequency of which is great. The coefficients of 

 induction are as follows : 





X 



y 



t 



X 



I 



m 



f 



y 



m 



I 



9 



i 



f 



9 



h 



It is easy to see that the frequencies are given by 



lp* — c, 



mp 2 , 



fP 



mp 2 , 



lp 2 -c, 



w 



fp\ 



9P 2 



hf- 



= 



and c x is by supposition large compared with /, g, l x . 

 The equation reduces to 



(c 1 -li P 2 ){(¥-cy-my}+p i {(f + g*Xlp°-c)-2f 9 mp*} = 0. 

 It is easy to see that if j > j— — two values of p 2 are 



approximately 7^(1-*^ fs)) 



The bands are therefore both shifted towards the visible 

 region by the introduction of the new vibration centre. 

 The effect is also seen to be equivalent to a diminution of c. 

 Therefore, in examining the effect of say a methyl group, 

 we will not look on it as a separate vibration centre, but will 

 diminish the value of c for the atom to which it is attached. 



IV. Four centres placed parti// symmetrically. 



x and y correspond, so do f and 77, so that (a?, f) is a 

 group of the kind considered above, and (//, 77) is an identical 

 group : 



e.g. 



HC = 



I I 

 HC = 



v y 



