84 
THE HON. J. W. STRUTT ON THE THEORY OF RESONANCE. 
When, however, the separate passages are sufficiently far apart, the constant c for the 
system, considered as a single communication between the interior of the resonator and 
the external air, is the simple sum of the values belonging to them when taken sepa- 
rately, which would not otherwise he the case. This is a point to which we shall return 
later, but in the mean time, by addition of equations (7), we find 
so that 
^i+X 2 -f ^ (c, + c 2 )(X,-f X. 2 ) - 0, 

( 9 ) 
If there be any number of necks for which the values of c are c t , c 2 , c 3 , . . . ., and no 
two of which are near enough to interfere, the same method is applicable, and gives 
n 
C \ “t c <2 + C 3 + • • 
( 9 ) 
when there are two similar necks c 2 =c 1} and 
V2 x yj 
fi- 
The note is accordingly higher than if there were only one neck in the ratio of */2 : 1, 
a fact observed by Sondhauss and proved theoretically by Helmholtz for the case of 
openings which are mere holes in the sides of the reservoir. 
Double Besonance. 
Fiff. 1 . 
Suppose that there are two reservoirs, S, S', com- 
municating with each other and with the external 
air by narrow passages or necks. If we were to 
consider S S' as a single reservoir and to apply equa- 
tion (9), we should be led to an erroneous result; 
for the reasoning on which (9) is founded proceeds on the assumption that, within the 
reservoir, the inertia of the air may be left out of account, whereas it is evident that the 
vis viva of the motion through the connecting passage may be as great as through the 
two others. However, an investigation on the same general plan as before meets the 
case perfectly. Denoting by X n X 2 , X 3 the total flows through the three necks, we have 
for the vis viva the expression 
T=b 15+5+xJl 
~ ( C 1 C 2 C 3 ) 
V = -/i 0 a 2 
x.-xp 2 , (X 3 -X 2 ) 2 
S "*■ b' 
and for the potential energy 
