54 THE EQUILIBRIUM OF ELASTIC SOLIDS. 



3. When A, = 0, 



o/\ 

 f ' 



87 A, fa,' , .a,' 



, , ., 



17-= -- 1 +f 

 F '-' * 



m 



M. Lamd's equations differ from these only in assuming that p. = ^m. If 

 this assumption be correct, then the coefficients p., m, and fi,, 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 fi is supposed 

 independent of m. In Equations (39), the quantities which may be varied at 

 pleasure are A, and h t , and the quantities which may be deduced from the 

 apparent compressions are, 



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 JA,, 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 



1 1 2 

 rod, and - = - + . 



We have here five quantities, which may be determined by experiment. 



(43) 1. c,= (- + ^ j by external pressure 



on sphere. 



A 1\ 

 (42) 2. c,= ( ---- J equal pressures. 



\r" fa/ 



(31) 3. = + ) bv elon gation of a rod. 



(17) 4. m by twisting the rod. 



5. /t, the elasticity of the liquid. 



