84 Prof. Liveing, On Solution [May 26, 



May 26, 1890. 



Mr J. W. Clark, President, in the Chair. 



The following Communications were made to the Society : 



(1) On Solution and Crystallization. III. Rhombohedral and 

 Hexagonal Crystals. By Prof. Liveing. 



(Abstract.) 



In a former communication (Trans. Vol. XIV.) the author had 

 suggested, in order to account for hexagonal crystals, an arrange- 

 ment of molecules defined by supposing space to be divided by 

 planes into right triangular prisms, and a molecule placed at each 

 corner of the prisms. No mechanical reason, however, was forth- 

 coming to account for the molecules assuming such an arrange- 

 ment. On the other hand if we suppose the excursions of the 

 parts of the molecule to be comprised within an ellipsoid of definite 

 dimensions for each kind of matter, and suppose that in passing 

 into the crystalline state these ellipsoids pack themselves as 

 closely as possible (which they will do if they attract each other 

 according to any law), the surfaces of minimum tension will be 

 certain planes having the symmetry observed in crystals. That 

 symmetry depends on the dimensions of the ellipsoids. If they be 

 spheroids, and if oblate have their axes in any ratio except 2:1, 

 and if the orientation of the axes be such that each spheroid is 

 touched by six others in points lying in a plane perpendicular to 

 the axis of symmetry, the arrangement will be the same as if space 

 were divided into equal rhombohedra and a molecule placed at 

 every corner. In this case the surfaces of minimum tension will 

 be planes having a rhombohedral symmetry. But in arranging 

 the spheroids so as to place the greatest number in a given space 

 there are two arrangements with the centres in planes perpendi- 

 cular to the axis of symmetry which give the same number of 

 spheroids per unit of volume, and are therefore so far equally 

 probable. These two arrangements correspond to twin crystals 

 when the twin axis is the axis of symmetry. A crystal formed of 

 such molecules may therefore, so far as the packing of the mole- 

 cules determines its structure, be built up of alternate layers, of 

 no particular thickness, of twin crystals. If the external form be 

 rhombohedral such alternations will in general give ridged faces, 

 for which the surface tension will not be the minimum. But if 

 the external form be any one (or more) of those known as hexago- 

 nal, it will be identical for the two individuals of the twin, and 

 this circumstance will determine the growth of hexagonal forms in 

 cases in which the surface tension of the hexagonal forms is not 

 much greater than that of rhombohedral forms. At the same time 



