﻿200 Mr. N. McCl eland on the Absorption Spectra of 



The equations o£ motion are : 

 Yxx + mje % + m m x 3 + ?» p .r 4 + m m :r 5 + m iv G + rx A + c.i\ =s E^, &c. 



The frequency equation is 



lp 2 —c, »t p 2 , m m p?, &c. —0 



»w. jt> 2 , lp 2 —c, 



&c. . . (xi.) 



and from this the squares of the frequencies are : 

 («) r: r4=^=, (ft 



/ + m p -f 2??i + ??i TO ' / + m — m TO + m, 



(y)rr — -, (*) 



l + mp—m + m m l—m p —2m —m m 



The second and third of these represent coincident roots of 

 the equation. This cannot mean more than the coincidence 

 of two bands, i. e. a very deep band. 



Since m will clearly be greater than m m or m p , the above 

 are in order of magnitude. 



The four bands will be called the a, /3, 7, 8 bands 

 respectively. 



Characteristic equation. 

 This de Generates into 



X[(l + m p + 2m + m m )p 2 -rip-c~] = -E. . (xii.) 



From this we see that the least refrangible band may be 

 derived from the equation 



(I + mp + 2m + m m )px + rk + ex = Ee'i }t (a) 

 and the others from 



L.r + r cosec 77 + ex = Jhe' pt , 



where 



4- m._ — )>) ... — ni_l f 11 n -n = 



L = (Z + wi»— w TO — wip), tan 9/== ^ § ti ; - - for /3 band. 



r 



= (l—m —m m + m p ), = -— — -— „ 7 „ 



p' K dm + 5m m ) 



= (l-2m o + 2m m -m p ) = r „ g „ 



' />( k 4»j +2m p ) 



