PHYSICS: A, G. WEBSTER 
279 
A = 
Mi, m 
Ui, Vi 
U2, V2 
U2, v'l 
, A = 
«1, Ui 
A = 
, A = 
U2, V2 
Wi, Ui 
1^2 
(22) 
which satisfy the relation, 
we may determine the constants A, Bin terms of any two out of pi, qi, p2, q2, 
so that we obtain 
p2 = (piD, + ^qiD,)/Di, ^q2 = (~piDe + ^q^Dz)/D,, (23) 
^ = {pzDz - (3q2D,)/D2, ^qi = (^A + ^q2D,)/D2. 
As it is more convenient to deal with the volumes Xi = criqi, X2 = (T2q2 we shall 
have in general 
(24) 
where 
and for the impedances belonging to the ends of the tube 
criA 
cZi + 
2i 
+ a 
(25) 
so that the impedance at either end of the tube is a linear fractional function 
of the other. According to the apparatus attached to an end the impedance 
attached to that end is known. A tube for which a, b, c, d are given may 
be replaced by any other tube having the same constants. 
Examples. — Cylindrical tube, a constant. Put X2 — = Zi, 
(fp 
dx^ 
2 + k'p = 0, 
u = cos kXf r — sin kx, 
A = A = l, A 
sin kx, 
cos kx, (26) 
= cos kl, = = sin kl, (27) 
d = cos kL 
Z> = - sin kl, 
Z2 = 
Zi cos kl - sin kl 
^ — Zi sin kl -{- - cos kl. 
c = — - sin kl, 
Zo cos kl — - sin kL 
^ Z2 sin kl + - cos 
(28) 
