1915] THE THEORY OF THE HELMHOLTZ RESONATOR
Thus in general by (18)
____'__ ;____= _ ^ _ 1 (2n + 1} c2
Xn-i/Xn ~n — I n
while for n — 1
—2 = - 2 + I - f c2 + terms in c3,
in accordance with (21). When n = 0
Vn
• = — 1 + c2 4- ic + terms in c3.
Using these values in (15), we see that, so far as c2 inclusive, 2 (outside) =(-l + c2 + w)P0
r. 1 5C2
-f P0
- a
In like manner for the form of %n appropriate to the inside
, }==__________
Xn(C) 1.3.5...
so that in general
Zn + J.
j + 3
and
This suffices for n = I and onwards. When n = 0 %° ___2 h _£l__-cll
r^;~ c^j1 15 525} •••
Accordingly, so far as c2 inclusive,
$ (inside) = 2 {P0 (/i) + Px (/*) + ...+ Pn (/*)}
369
ri/Xn-n-1 +n + l (?i + l)a(2n-l)'.........^
.(22)
.(23)
.(24)
.(25)
.(26) .(27)
.(28)
R. VI.
.(29) 24
9!