EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES, 215 



Concerning Solids which absorb Fluids. 



There 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 suppose 

 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 

 components except such as vanish with the velocity of the motion, 

 leaving it to be determined by experiment how far and in what cases 

 these suppositions are realized. 



It is evident that equation (356) must hold true with regard to 

 such a body, when the quantities of the fluid components contained 

 in a given element of the solid remain constant. Let IV, IV, etc., 

 denote the quantities of the several fluid components contained in an 

 element of the body divided by the volume of the element in the 

 state of reference, or, in other words, let these symbols denote the 

 densities which the several fluid components would have, if the body 

 should be brought to the state of reference while the matter con- 

 tained in each element remained unchanged. We may then say that 

 equation (356) will hold true, when iy, IV, etc., are constant. The 

 complete value of the differential of e V ' will therefore be given by an 

 equation of the form 



de, = 



a ' + L b dT b ' + etc. (462) 



Now when the body is in a state of hydrostatic stress, the term in 

 this equation containing the signs of summation will reduce to 

 pdv v . (V T denoting, as elsewhere, the volume of the element 

 divided by its volume in the state of reference). For in this case 



x x , 



,dx 



J^y_dz__d?_^\ 

 p \dy dz' dy'dz'J' 



(463) 



dz 



(464) 



