176 



cited papers by F. Sohnke and G. Wulff '). Botli these authors 

 namely assume that the capi/larit;/ constant of a crystal plane (apart 

 from a factor which continuously changes with the orientation) is 

 in inrcrsc ratio to the net den.siti/ of the plane in question '). 



This net density, however, is, as is known, a very discontinuous 

 function of the orientation : thus for irrationally orientated planes, 

 which have been rotated however little with respect to the plane 

 (1,1,1), the net density would still be infinitely small in proportion 

 to that of the plane (1,1,1). Here the exceptional function of the 

 planes with the smallest indices is at once seen. 



In spite of this appeal to the relation with the net density the 

 supposition that the capillarity constant depends discontinuously on 

 the orientation, will yet be thought very uncommon, if not quite 

 paradoxical ! Besides it involves a great difficulty for the frequent 

 occurrence of the so-called "vicinal planes". ') 



For according to Sohnke and Wulff these planes with particularly 

 large indices (which are practically irrationally orientated) would 

 possess extraordinarily large surface energy. Of course we are willing 

 to admit deviations from the theoretical equilibrium figure, taking 

 into consideration the small disturbances which are never entiiely 

 to be excluded (fluctuations of temperature, disturbances in the con- 

 centration etc.) But yet totally unexplained and even paradoxical it 

 remains when these slight disturbances give rise exactly to those planes 

 with extremely large surface energy, and particularly those which lie 

 very near to the planes with particularly small surface-energy *). 



') P. Sohnke. Zeitsclir. f. Krystallogr. 13 (1888) p. 221 ; G. Wulff. Zeitsclir. f. 

 Krystallogi'. 4 (1901) p. 526. Gibbs and Gurie do not give any further indication 

 on the continuous or discontinuous character of the dependence. 



2) Wulff gives this formula and characterises the gist of Sohnke's conception, 

 partly in Sohnke's own words in the following way : 'Nach Sohnke muss ein 

 Zusammenhang zwischen der Oberfliichenergie einer Kristallflache und ilirer Flachen- 

 dichliglieit bestehen. iN'amlich fur eine Fliiche von dichtester Besetzung können die 

 Molekularkriifte keine Arbeit mehr leisten, weil die Theilchen einander nicht welter 

 genahert werden können: die potentielle Energie einer solchen Fldche muss also 

 ein Minimum sein. In dem Masse, als die Flachendichtigkeiten der verschiedenen 

 Krystallllachen geringere sind, mussen die Oberftachenergieen (Gapillarconstanlen) 

 grosser sein .... 



^) By "vicinal planes" we understand planes which differ exceedingly little in 

 situation from the planes with small indices. 



1) H. Miers, Rep. of the Brit. Assoc. 1894 p. 654; Z. f. Kr. 9 (l'J04) p. 220 

 has demonstrated experimentally through accurate goniometric measurements during 

 the growth of alumn crystals, that the planes with small indices in this case (1, 1, 1), 

 practically never occur, but nearly always vicinal planes. Gf. also G. Viola, Z. f. 

 Kr. 35 p. 332. 



