50 IHE EQUILIBRIUM OF ELASTIC SOLIDS. 



The quantity E may be deduced from experiment on the extension of wires 

 or rods of the substance, and \L is given in terms of m and E by the equation, 



< 32 >> 



(33), 



P being the extending force, b the length of the rod, s the sectional area, 

 and Sx 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, (Ersted, Perkins, Aimd, &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 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. If the pressure be applied only to 

 the contained liquid, it is evident that the vessel will be distended, and the 

 compressibility 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 

 internal pressures, that the capacity does not change, the equilibrium of the 

 vessel must be determined theoretically. (Ersted, 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 Tredgold. As the compressibility of lead thus found was 

 greater than that of water, (Ersted expected that the apparent compressibility 

 of water in a lead vessel would be negative. On making the experiment the 

 apparent compressibility was greater in lead than in glass. The quantity found 



