80 
THE HON. J. W. STRUTT ON THE THEORY OF RESONANCE. 
which is only applicable, however, when the necks are so long that the corrections at the 
ends may be neglected — a condition not likely to be fulfilled. This consideration suffi- 
ciently explains the discordance. Being anxious to give the formulae of Parts I. and II. 
a fair trial, I investigated experimentally the resonance of a considerable number of 
vessels which were of such a form that the theoretical pitch could be calculated with 
tolerable accuracy. The result of the comparison is detailed in Part III., and appears 
on the whole very satisfactory ; but it is not necessary that I should describe it more 
minutely here. I will only mention, as perhaps a novelty, that the experimental deter- 
mination of the pitch was not made by causing the resonators to speak by a stream of 
air blown over their mouths. The grounds of my dissatisfaction with this method are 
explained in the proper place. 
[Since this paper was written there has appeared another memoir by Dr. Sondiiauss* 
on the subject of resonance. An empirical formula is obtained bearing resemblance 
to the results of Parts I. and II., and agreeing fairly well with observation. No attempt 
is made to connect it with the fundamental principles of mechanics. In the Philoso- 
phical Magazine for September 1870, I have discussed the differences between Dr. 
Soxdiiauss’s formula and my own from the experimental side, and shall not therefore 
go any further into the matter on the present occasion.] 
PART I. 
The class of resonators to which attention will chiefly be given in this paper are those 
where a mass of air confined almost all round by rigid walls communicates with the 
external atmosphere by one or more narrow passages. For the present it may be sup- 
posed that the boundary of the principal mass of air is part of an oval surface, nowhere 
contracted into any thing like a narrow neck, although some cases not coming under 
this description will be considered later. In its general character the fundamental 
vibration of such an air-space is sufficiently simple, consisting of a periodical rush of 
air through the narrow channel (if there is only one) into and out of the confined space, 
which acts the part of a reservoir. The channel spoken of may be either a mere hole 
of any shape in the side of the vessel, or may consist of a more or less elongated tube- 
like passage. 
If the linear dimension of the reservoir be small as compared to the wave-length of 
the vibration considered, or, as perhaps it ought rather to be said, the quarter wave- 
length, the motion is remarkably amenable to deductive treatment. Vibration in general 
may be considered as a periodic transformation of energy from the potential to the 
kinetic, and from the kinetic to the potential forms. In our case the kinetic energy is 
that of the air in the neighbourhood of the opening as it rushes backwards or forwards. 
It may be easily seen that relatively to this the energy of the motion inside the reservoir 
is, under the restriction specified, very small. A formal proof would require the assistance 
of the general equations to the motion of an elastic fluid, whose use I wish to avoid in 
* Fogg. Ann. 1870. 
