244 Prof. J. J. Thomsen on the 
or if 2p 1s proportional to e'%, 
a ae Ge aD ay ’) +2 Die. = 0; 
9 
ve" 
(Dia Pele 
-thus 
a Ge —D—my?) +2,D,+2;D.+...=0, 
g (ee + 21), epee 
Ue: LST Ser Ras Ps 
We sce that again being one of the nth roots of unity, the 
solution of equations C is 
<2= W<], £3 = WK9, K4= Wiz lvls 
9 
” 
au —D—m¢+ ol, +’D,+e"-D,_1=0. . % (4) 
: 2har . aka ee er 
Putting @= Cos —— +cesin Tone find, substituting the 
values for D given above, that 


Qkhawr Akar 6hor 
, cos = | cos cos 
9 Phan i's é hr n n 
wD,+@ D.+o D,1= Rap TT ah eee 
sin? — sin® sin? == 
n n n 
Denoting this by Pz and noticing that D= Py, we find that 
equation (4) becomes 
ve 
b? 
Putting in succession k=0,1,...n—1, we get nm values 
of g giving the n frequencies corresponding to the displace- 
ments at right angles to the plane of the undisturbed orbit. 
We shall now “proceed to calculate the frequencies for 
systems containing various numbers of corpuscles. The four 
quantities Lz, Mz, Nz, Pz which oceur in the frequency 
equation may be expressed in terms of three quantities Sz, 
Tx, Ux, where 
+P,—P)—m¢’=0. 
og 2m if 
i 8 ipa YSOF 
SU 
te 
S,= Es Ea: 

