674 RICE 



ART. L 



pages requiring any special explanation, except perhaps the 

 remark in the footnote on page 325, that the value of the poten- 

 tial in the liquid which is necessary for the growth of the crystal 

 will generally be greatest for the growth at that face for which 

 a is least. The reader will note that if formation of solid 

 material is taking place on this face, it is the faces with larger 

 values of a which are increasing in size, and therefore the crystal 

 is receiving greater increments of energy per unit increase of 

 area than would be the case if growth took place on one of the 

 sides of low a. 



It should be mentioned that attempts have been made, 

 especially in recent years, to measure the free surface energy 

 and total surface energy of solids, but with very doubtful 

 success owing to the inherent difficulties of the situation. 

 Owing to the absence of mobility the usual methods applicable 

 to liquids fail. However, one can resort to a method which 

 treats the solubility of small particles as varying with size in the 

 same way as the vapor pressure of small drops of liquid. The 

 method is theoretically sound but there are unavoidable errors 

 in its application. It is known that the vapor pressure, p, of a 

 liquid above a plane surface and p', the vapor pressure in 

 equilibrium with a spherical drop of radius r, are connected by 

 the relation 



Rt v' 2(r 

 — log — = — ' 

 M p rp 



where M is the molecular weight of the vapor and p the density 

 of the liquid. The solubilities of a solid in large bulk, and in 

 the form of small spherical particles, are related in a similar 

 manner. However, there are considerable difficulties in grind- 

 ing suitable particles, or in preparing them by rapid condensa- 

 tion from vapor or by deposition from solution. It is not prob- 

 able that the surface atoms in such small portions will have the 

 same regular arrangement as in a plane surface. The reader 

 should consult the following papers for details: 



Ostwald: Z. physik. Chem., 34, 495 (1900). 

 Hulett: Z. physik. Chem., 37, 385 (1901). 



