EQUILIBRIUM OF ELASTIC SOLIDS. 105 
OV _ a2 h,—a,% h 
2 h,—h, 1 
When r=a,5> = = 
A 
3 st 7p ip or Rs 3 
a>—a> pb 2 a,>—a,> m 
h, a> 3a, hoa (1 3 ) 
= +52) -- + 
a>—a,>\ um 2m a>—a,>\u 2m 
When the external and internal pressures are equal 
on Boh 


(39.) 

the change of internal capacity depends ited on the cubical elasticity of the 
vessel, and not on its thickness or its linear elasticity. 
When the external and internal pressures are inversely as the cubes of the 
radii of the surfaces on which they act, 
a’ la 
a,° hy=a,* hy, P=Fa'yIe— 278 3 
OV. visa? A, 
vT=-55 ene (315) 
when Eee 
In this case the change of capacity depends on the linear elasticity alone. 
M. Reenavtt, in his researches on the theory of the steam engine, has given 
an account of the experiments which he made in order to determine with accuracy 
the compressibility of mercury. 
He considers the mathematical formule very uncertain, because the theories 
of molecular forces from which they are deduced are probably far from the truth; 
and even were the equations free from error, there would be much uncertainty in 
the ordinary method by measuring the elongation of a rod of the substance, for it 
is difficult to ensure that the material of the rod is the same as that of the hollow 
sphere. 
He has, therefore, availed himself of the results of M. Lams for a hollow 
sphere in three different cases, in the first of which the pressure acts on the inte- 
rior and exterior surface at the same time, while in the other two cases the pres- 
sure is applied to the exterior or interior surface alone. Equation (39.) becomes 
in these cases,— 
1. When 2, =, ou =" and the compressibility of the enclosed liquid being 


B 
M,, and the apparent diminution of volume 0 vl = fhe (- i) a C9) 
2. When nao y= Sh ai et (4+ gS) ah ee (45) 
