THE HOX. J. W. STRUTT OX THE THEORY OF RESOXAXCE. 
Ill 
to make the calculated value of n too great. On the other hand, two sources of error 
must he mentioned which would act in the opposite direction. The air in the vicinity 
of the opening must have been sensibly warmer than the external atmosphere, and we 
saw in Part I. how sensitive resonators of this sort must be to small changes in the phy- 
sical properties of the gas which occupy the air-passages. Indeed Savart long ago 
remarked on the instability of the pitch of short pipes, comparing them with ordinary 
organ-pipes. The second source of disturbance is of a more recondite character, but not, 
I think, less real. It is proved in works on hydrodynamics that in the steady motion of 
fluids, whether compressible or not, an increased velocity is always accompanied by a 
diminished pressure. In the case of a gas the diminished pressure entails a diminished 
density. There seems therefore every reason to expect a diminution of density in the 
stream of air which plays over the orifice of the resonator, which must cause a rise in 
the resonant note. But independently of these difficulties, the theory of pipes or other 
resonators made to speak by a stream of air directed against a sharp edge is not suffi- 
ciently understood to make this method of investigation satisfactory. For this reason I 
have entirely abandoned the method of causing the resonators to speak in my experi- 
ments, and have relied on other indications to fix the pitch. The only other experiments 
that I have met with on the subject of the present paper are also by Sondhauss, who has 
been very successful in unravelling the complications of these phenomena without much 
help from theory*. For flasks with long necks he found the formula 
72=46705 , 
L*S* 
as applicable when the necks are cylindrical and not too short, corresponding to the 
theoretical 
obtained by combining (5) and (21), or, in numbers with metrical units, 
n=Um~^~ x . 
L*S* 
The discrepancy is no doubt to be attributed (at least in great measure) to the omis- 
sion of the correction to the length of the neck. 
In the experiments about to be described the pitch of the resonator was determined 
in various ways. Some of the larger ones had short tubes fitted to them which could 
be inserted in the ear. By trial on the piano or organ the note of maximum resonance 
could be fixed without difficulty, probably to a quarter of a semitone. In most of the 
experiments a grand piano was used, whose middle c was in almost exact unison with a 
fork of 256 vibrations per second. Whenever practicable the harmonic undertones 
were also used as a check on any slight difference which might be possible in the quality 
of consecutive notes. Indeed the determination was generally easier by means of the 
* Pogg. Arm. t. lxxxi. 
Q 2 
