
EQUILIBRIUM OF ELASTIC SOLIDS. 103 
P being the extending force, 4 the length of the rod, s the sectional area, and 
Oa the elongation, which may be determined by the deflection of a wire, as in the 
apparatus of S’ GRAVESANDE, or by direct measurement. 
Case IV. 
The only known direct method of finding the compressibility of liquids is 
that employed by Canton, Cirstep, Perxins, Aims, &c. 
The liquid is confined in a vessel with a narrow neck, then pressure is applied, 
and the descent of the liquid in the tube is observed, so that the difference between 
the change of volume of the liquid and the change of internal capacity of the vessel 
may be determined. 
Now, since the substance of which the vessel is formed is compressible, a 
change of the internal capacity is possible. Ifthe pressure be applied only to the _ 
contained liquid, it is evident that the vessel will be distended, and the compressi- 
bility of the liquid will appear too great. The pressure, therefore, is commonly 
applied externally and internally at the same time, by means of a hydrostatic 
pressure produced by water compressed either in a strong vessel or in the depths 
of the sea. : 
As it does not necessarily follow, from the equality of the external and inter- 
nal pressures, that the capacity does not change, the equilibrium of the vessel must 
be determined theoretically. Cirsrep, therefore, obtained from Poisson his 
solution of the problem, and applied it to the case of a vessel of lead. To find the 
cubical elasticity of lead, he applied the theory of Poisson to the numerical 
results of TrReEpGoLtp. As the compressibility of lead thus found was greater than 
that of water, @irsTep expected that the apparent compressibility of water in a 
lead vessel would be negative. On making the experiment the apparent compres- 
sibility was greater in lead than in glass. The quantity found by TREDGOLD from 
the extension of rods was that denoted by E, and the value of u deduced from E 
alone by the formule of Poisson cannot be true, unless — = and as F for lead 
is probably more than 3, the calculated compressibility is much too great. 
A similar experiment was made by Professor Fores, who used a vessel of 
caoutchouc. As in this case the apparent compressibility vanishes, it appears that 
_the cubical compressibility of caoutchouc is equal to that of water. 
Some who reject the mathematical theories as unsatisfactory, have conjec- 
tured that if the sides of the vessel be sufficiently thin, the pressure on both sides 
being equal, the compressibility of the vessel will not affect the result. The fol- 
lowing calculations shew that the apparent compressibility of the liquid depends 
on the compressibility of the vessel, and is independent of the thickness when the 
pressures are equal. 
A hollow sphere, whose external and internal radii are a, and a, is acted on 
VOL. XX. PART I. 25 
