227 
ga; + a, = 
a,t+-qa,+a, a 
a, +qa,+ 4, are ale) 
On—2 +4 @n-1 + a, = 0 
ny +g On: = 0 
In order to obtain a possible solution, the determinant of these 
equations must be equal to zero: 
Le OL Da va OD ON 
Bie bal 0 
[Ord sl «| 
Se fB ANSO BEAT 
0 Lg 1| 
ORNE a be Bad og 
Putting: 
g= 2 cos 
we find for the determinant *) 
__ sin (aT) 
ery commas wee, Set C 
er e 
sin 0 
This equation can be fulfilled by 
ka ig 
Ses aia (5a) 
where 
eae ee eh. oe ee 
the roots of (4) thus appearing to be 
nr 
HRO a 
= 2 zi 
Je — EE 
9 Sat 
q, = 2 cos —— 
: Hel Nees rena dave! ee 
ae ka 
Ln tE 
nT 
Qn == ICB —— 
n+l 
1) Comp. RAYLEIGH, The theory of sound, Vol. J, p. 172. The expression (5) 
for ‘An can be obtained from goniometric formulae, and also from continuous 
fractions. 
15* 
