106 MR JAMES CLERK MAXWELL ON THE 
M. Lamz’s equations differ from these only in assuming that p = > mn. If this 
assumption be correct, then the coefficients py, m, and u,, may be found from two 
of these equations; but since one of these equations may be derived from the other 
two, the three coefficients cannot be found when p is supposed independent of m. 
In Equations (39.), the quantities which may be varied at pleasure are /, and h,, 
and the quantities which may be deduced from the apparent compressions are, 
il 3 1 1 
°= ce a) and (a = =¢, 
therefore some independent equation between these quantities must be found, and 
this cannot be done by means of the sphere alone; some other experiment must 
be made on the liquid, or on another portion of the substance of which the vessel 
is made. 
The value of ,, the elasticity of the liquid, may be previously known. 
The linear elasticity m of the vessel may be found by twisting a rod of the 
material of which it is made ; 
Or, the value of E may be found by the elongation or bending of the rod, and 
1 1 2 
EB 9p* 3m’ 
We have here five quantities, which may be determined by experiment. 
(43) elec — (= +50) by external pressure 
on sphere. 
(AD Ss 5 ta (=-=) equal pressures 
(81.) 3 = = (satan) by elongation of a rod. 
(17.) 4. m by twisting the rod. 
5. Py the elasticity of the liquid. 
When the elastic sphere is solid, the internal radius a, vanishes, and 4,=p=g, 
d éV_A, 
an Vv = - 
When the case becomes that of a spherical cavity in an infinite solid, the ex- 
ternal radius a, becomes infinite, and 
3 
poh, + (thy) 
ib ae 
q=h, -5 +o (hy —hy) 
(46.) 

