J. W. Glbhs — Equilibrium of Heterogeneous Substances. 375 



It will not be necessary to discuss equation (443) at length, as the 

 case is entirely analogous to that which has just been treated. [It 

 must be remembered that ;/v,, in the discussion of (443) will take the 

 place everywhere of the temperature in the discussion of (444).] If 

 we denote by V and R' the elasticity of volume and t\\e rigidity^ 

 botli determined under the condition of constant entropy., (i. e., of no 

 trans))iission of heat^) and for states of vanishing sti-ess, we sliall 

 have the equations : 



F'=-|^ + f/>o, (458) 



i^' = 2 e' + 4/'r„2^ (459) 



2 e' + 4/' ?■„ 2 + h' r^ — 0. (460) 



Whence 



R' - .3 r„ F' ^, _ R' +_3 r^JT' ^^ _ _ ^' 



e'=^-^-'^^ / = ---t_?4._!:^, A'=-i-'. (461) 



In these equations r„, it', and V are to be regarded as functions of 

 the quantity ijx,. 



If we wish to change from one state of reference to another (also 

 isotropic), the changes required in the fundamental equation are 

 easily made. If a denotes the length of any line of the solid in the 

 second state of reference divided by its length in the first, it is evi- 

 dent that Avhen we change from the first state of refei'ence to the 

 second the values of the symbols fy, , 7/v, , //v*, H are divided by a^, 

 that of E by a^, and that of E by «*. In making the change of the 

 state of reference, we must therefore substitute in the fundamental 

 equation of the form (444) a^tl\,, a^E, a^F, a^H for y-,,, E, F, 

 and H., respectively. In the fundamental equation of the form (443), 

 we must make the analogous substitutions, and also substitute a'^7/v, 

 for l]^,,. [It will be remembered that i\ e\f\ and h' represent func- 

 tions of 7/v», and that it is only when their values in terms of i]^, are 

 substituted, that equation (443) becomes a fundamental equation.] 



(Joncernhig Solids which absorb Fluids. 



Tliere are certain bodies which are solid with respect to some of 

 their components, while they have other components which are fluid. 

 In the following discussion, we shall suppose both the solidity and 

 the fluidity to be perfect, so far as any properties are concerned 

 which can affect the conditions of equilibrium, — i. e., we shall sup- 

 pose that the solid matter of the body is entirely free from plasticity, 

 and that there are no passive resistances to the motion of the fluid 



Trans. Conn. Acad., Vol. III. 48 June, 1877, 



