476 RICE 



ART. K 



energy of sensible masses, or heat. This justifies the brief 

 statement of Gibbs on page 196 near the bottom: "This 

 quantity is necessarily positive except, etc." 



The remarks so far have been concerned with mechanical 

 equilibrium. Equation [388], rewritten for the three possible 

 pressures in [393], [394], [395] involves equilibrium as regards 

 solution of the sohd in the fluid, or crystallization on the solid 

 from the fluid. This amplification of Gibbs' treatment of the 

 mechanical relations will, it is hoped, render the task of master- 

 ing these pages easier for the reader; there appears to be noth- 

 ing of special difficulty in the deductions on page 197 concern- 

 ing the supersaturation of the fluid. 



It should be carefully borne in mind that the argument has 

 been confined to a homogeneous state of strain in the solid. 

 Gibbs remarks on page 197 that "within certain limits the 

 relations expressed by equations [393]-[395] must admit of 

 realization." But even if it were hardly practicable to make 

 the special arrangements conceived in these arguments, that 

 does not invalidate the conclusions. We are all thoroughly 

 familiar with "perfect engines," "perfectly smooth surfaces," 

 "perfect gases" and other conceptual devices of the physicist 

 and chemist which are the "stock in trade" of many mechan- 

 ical and thermodjTiamical arguments. Of course in any prac- 

 tical case, if a solid of any form immersed in a fluid were 

 subject to distorting surface forces the strain would be hetero- 

 geneous. Perhaps some readers, recalling equations (29) of 

 this article or [377] of Gibbs, might wonder how a hetero- 

 geneous state of strain can exist without body forces; for in 

 such a case the equations referred to would become 



dXx dXy dXz 



dYx dYr dYz _ 



dx ~^ dy ~^ dz ~ ^' 

 dZx dZr dZz 



ox dy dz 



(We are neglecting gravity.) One might rashly conclude from 



