82 
THE HON. J. W. STRUTT ON THE THEORY OF RESONANCE. 
The expression for the vis viva in terms of the rate or total flow is accordingly 
vis viva— (I) 
If S be the capacity of the reservoir, the condensation at any time inside it is given by 
x 
— , of which the mechanical value is 
S’ 
1; ,X S (e) s 
a denoting, as throughout the paper, the velocity of sound. 
The whole energy at any time, both actual and potential, is therefore 
7, Y2 7 ; V2 
HUN J fo /q\ 
and is constant. Differentiating with respect to time, we arrive at 
X + ^X=0 (4) 
as the equation to the motion, which indicates simple oscillations performed in a time 
Hence if n denote the number of vibrations per second in the resonant note, 
a f~c rr\ 
«=5V5 (°) 
The wave-length a, which is the quantity most immediately connected with the dimen- 
sions of the resonant space, is given by 
x =l= 2 *\/- c ( 6 ) 
A law of Savart, not nearly so well known as it ought to be, is in agreement with 
equations (5) and (6). It is an immediate consequence of the principle of dynamical 
similarity, of extreme generality, to the effect that similar vibrating bodies, whether they 
be gaseous, such as the air in organ-pipes or in the resonators here considered, or solid, 
such as tuning-forks, vibrate in a time which is directly as their linear dimensions. Of 
course the material must be the same in two cases that are to be compared, and the 
geometrical similarity must be complete, extending to the shape of the opening as well 
as to the other parts of the resonant vessel. Although the wave-length X is a function 
of the size and shape of the resonator only, n or the position of the note in the musical 
scale depends on the nature of the gas with which the resonator is filled. And it is 
important to notice that it is on the nature of the gas in and near the opening that the 
note depends, and not on the gas in the interior of the reservoir, whose inertia does not 
come into play during vibrations corresponding to the fundamental note. In fact we 
