112 
THE HON. J. W. STRUTT OX THE THEORY OE RESONANCE. 
first undertone (the octave), or even the second (the twelfth), than when the actual note 
of the resonator was used. The explanation is, I believe, not so much that the overtones 
belonging to any note on the piano surpass in strength the fundamental tone, although 
that is quite possible *, as that the ear (or rather the attention) is more sensitive to an 
increase in the strength of an overtone than of the fundamental. However this may be, 
there is no doubt that a little practice greatly exalts the power of observation, many 
persons on the first trial being apparently incapable of noticing the loudest resonance. 
Another plan very convenient, though not to be used in measurements without caution, 
is to connect one end of a piece of india-rubber tubing f with the ear, while the other 
end is passed into the interior of the vessel. In this way the resonance of any wide- 
mouthed bottle, jar, lamp-globe, &c. may be approximately determined in a few seconds ; 
but it must not be forgotten that the tube in passing through the air-passage acts as an 
obstruction, and so lowers the pitch. In many cases, however, the effect is insignificant, 
and can be roughly allowed for without difficulty. For large resonators this method is 
satisfactory, but in other cases is no longer available. I have, however, found it possible 
to determine with considerable precision the pitch of small flasks with long necks by 
simply holding them rather close to the wires of the piano while the chromatic scale is 
sounded. The resonant note announces itself by a quivering of the body of the flask, 
easily perceptible by the fingers. Since it is not so easy by this method to divide the 
interval between consecutive notes, I rejected those flasks whose pitch neither exactly 
agreed with any note on the piano nor exactly halved the interval. In some cases it 
is advantageous to sing into the mouth, taking care not to obstruct the passage ; the 
resonant note is recognized partly by the tremor of the flask, and partly by a peculiar 
sensation in the throat or ear, hard to localize or describe. 
The precision obtainable in any of these ways may seem inferior to that reached by 
several experimenters who have used the method of causing the resonators or pipes 
to speak by a stream of air. That the apparent precision in the last case is greater I 
of course fully admit ; for any one by means of a monochord could estimate the pitch of 
a continuous sound within a smaller limit of error than a quarter of a semitone. But 
the question arises, what is it that is estimated 1 Is it the natural note of the resonator \ 
I have already given my reasons for doubting the affirmative answer ; and if the doubt 
is well grounded, the greater precision is only apparent and of no use theoretically. I 
may add, too, that many of the flasks that I used could not easily have been made to 
speak by blowing. If they sounded at all it was more likely to be the first overtone, 
which is the note rather of the neck than the flask: see equation (20). In carrying 
out the measurements of the quantities involved in the formula, the volume of the flask 
or reservoir was estimated by filling it with water halfway up the neck, which was then 
measured, or in some cases weighed. The measurements of the neck were made in two 
ways according to the length. Unless very short their capacity was measured by water, 
* In this respect pianos, even by the same maker, differ greatly. 
t The black French tubing, about y inch in external diameter, is the pleasantest to use. 
