﻿196 Mr. N. McCleland on the Absorption Spectra oj 



The frequency equation is 



(hp 2 -c 1 )(l 2 p 2 — c 2 )=7n 1i p\ . . . (v.) 



and, as is well known, the roots of this, i.e. the frequencies, 

 lie outside those of the simple vibrations of each centre, i. e. y 

 the bands are forced apart. 



The characteristic equation for the X vibration centre is 



^Khf-r^p-c^ikp 2 — r 2 vp— c 2 ) — my] 



= — E [(l 2 — m)p 2 — r 2 ip — c 2 ] • . (vi.) 



This is much too complicated to deal with conveniently, 

 but in the symmetrical case we easily find the frequencies 



p 2 = r. and the characteristic equation becomes 



' l±m 



X[(l + m)p 2 -np-c]=-E. . . . (vii.) 



When p 2 =-j — ■ — we see the actual value of X is—, 

 / + m pr 



and if p' 2 = ^ we find the actual value is 



6— 7ft pr 



where tan ?? = . From which it appears that the two 



2pm rr 



bands in such spectra may be looked on as derived from the 

 vibrations governed by 



(I + m) x + rx + ex = Ee*#, (I — m)x' + r cosec rjii + ex = Ee'^. 



Of these, the former represents a band on the near side of, 

 and sharper than that of the single vibration centre, while 

 the latter represents a diffuse band in the more remote 

 regions. 



The former band will therefore tend to break up into 

 lines. 



It must, however, be noticed that if m is small, the bands 

 will probably coalesce to form a single wide band. 



We assume that in asymmetrical cases, provided the 

 asymmetry is not too marked, a similar kind of result will 

 be obtained as to the relative sharpness of the bands ; the 

 experimental evidence in favour of this is abundant. 



Substances belonging to the above type are fairly 

 numerous: the ketones 3 - 13 ' 19 and ethylene 6 derivatives 

 may be quoted, The two bands demanded by theory 

 are found, but the more remote band is beyond A200. 



