228 
From this we find, with the help of (2) the m unequal roots 
of p,, Pp 
Ef Dis Pays ea 
Using formula (5) to calculate the determinants in the numera 
tors in the expressions for «,,@,...@,, we find, after some simple 
reductions : 
a, == Corin 0 
a, — — C sin 20 
a, — C sin 30 
an = (—1)"F1 C sin nd 
(’ being an arbitrary constant. 
Every « is a function of 6. Giving to 6 one of the values of the 
‘set (5a) we obtain the coefficients «7/, where the second index relates 
io the number of the root (@ = 4@,). For a, we have 
kl 
hl = ap = (—I)EH C sin k 0j= (— IH C sin RED 7 
n+ 
BE 
whereas we have from (2) and (6) 
am —r 
vj — - rates 
L—2M cos - ts 
n 
From this we obtain‘) for the general solutions of (1) 
1) The expressions obtained for the currents may also be found in the following way 
The general differential equations have the form 
Let us put 
ie == y sin kO 
where y is a function of the time. Substituting this we find 
dy dy. 
ry + L— | sinkO = — 2M— sin kO cos 0 
dt dt 
or 
d; 
p= (L + 2056) Te ae 
From this we have 
The form 
ip = C sin kO el 42M cos 4 
identically fulfils the first equation of the set (i. the mth from this set giving 
