THE HON. J. W. STEUTT OH THE THEOEY OE EESOHAHCE. 
87 
pressed or rarefied as well as that inside the reservoir, though not to the same degree ; 
in fact the condensation must vary continuously between the interior of the resonator 
an,d the external air. This consideration shows that, at least in the case of necks which 
are tolerably symmetrical, about half the volume of the neck should be included in S. 
[In consequence of a suggestion made by Mr. Clerk Maxwell, who reported on this 
paper, I have been led to examine what kind of effect would be produced by a deficient 
rigidity in the envelope which contains the alternately compressed and rarefied air. 
Taking for simplicity the case of a sphere, let us suppose that the radius, instead of 
remaining constant at its normal value R, assumes the variable magnitude R+§. We 
have 
where m and (o are constants expressing the inertia and rigidity of the spherical shell. 
Hence, by Lagrange’s method, 
equations determining the periods of the two vibrations of which the system is capable. 
It might be imagined at first sight that a yielding of the sides of the vessel would neces- 
sarily lower the pitch of the resonant note ; but this depends on a tacit assumption that 
the capacity of the vessel is largest when the air inside is most compressed. But it may 
just as well happen that the opposite is true. Everything depends on the relative mag- 
nitudes of the periods of the two vibrations supposed for the moment independent of one 
another. If the note of the shell be very high compared to that of the air, the inertia 
of the shell may be neglected, and this part of the question treated statically. Putting 
in the equations m= 0, we see that the phases of X and % are opposed, and then X goes 
through its changes more slowly than before. On the other hand, if it be the note of 
the air- vibration, which is much the higher, we must put /3 = 0. which leads to 
47tR 2 A 0 X — cmg — 0, 
showing that the phases of X and § agree. Here the period of X is diminished by the 
yielding of the sides of the vessel, which indeed acts just in the same way as a second 
aperture would do. A determination of the actual note in any case of a spherical shell 
of given dimensions and material would probably be best obtained deductively. 
But in order to see what probability there might be that the results of Part III. on 
glass flasks were sensibly modified by a want of rigidity, I thought it best to make a 
direct experiment. To the neck of a flask was fitted a glass tube of rather small bore, 
and the whole filled with water so as to make a kind of water-thermometer. On 
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