17Ö 

 happens to be as small as possible. Hence the quantity : 



k =^ cos (f -{- sin ff' (3) 



plays the part of the capillarity factor in our scheme. 



It is seen that : 



A. the capillarity factor k is here a continuous function of the 

 orientation of the element of the apparent edge, which is the subject 

 in view here. (To get a graphical repi'esentation, k should be con- 

 sidered as function of the direction of tiie normals to the edge 

 element, and distances should be projected from a point W in all 

 directions, which are proportional with the values of k for this 

 direction of the normals. We obtain the curve dotted in figure (2), 

 which is composed of 4 arcs of a circle. 



Fig. 2. 



B. Yet the "equilibrium form" corresponding to it is a square. 

 This is immediately to be seen by the aid of the construction men- 

 tioned in § 1. See fig. 2: W is Wulff's point: WN is proportional 

 to k for this direction of the normal. If the straight line AE is 

 constructed for all directions WN, they envelop conjointly the 

 square drawn in fig. 2. ') 



C. The occurrence of "vicinal -planes" involves in our scheme no 

 deviation morth mentioning from the minimum of energy. For our 

 k depends continuously on the orientation, and the vicinal planes 

 are only exceedingly little rotated with respect to the planes of the 

 form of equilibrium. Here the contrast with Sohnke and Wulff's 

 supposition stands out very clearly. 



D. Strictly speaking the form of equilibrium can do loithout vicinal 



1) liy slight changes in the definition of the scheme another dependence of k 

 on the orientation can be obtained, hence other equilibrium polygons. 



