1891.] 



on Crystallisation. 



379 



how this packing of the spheres will affect the external form. And 

 here I must bring in the surface tension. We are familiar with the 

 effects of this force in the case of liquids, and if we adopt the usual 

 theory of it we must have a surface tension at the boundary of a solid 

 as well as at the surface of a liquid. I know of no actual measures 

 of the surface tension of solids. But Quincke has given us the 

 surface tensions of a number of substances at temperatures near their 

 points of solidification. The surface tension of most of the solids are 

 probably greater than these, since surface tension usually diminishes 

 with increase of temperature. 



Table of Surface Tensions of Substances near their Temperatures of 

 SoUdification, in dynes per lineal centimetre, after Quincke. 



Platinum 1,658 



Gold 983 



Zinc 860 



Tin ' .. 587 



Mercury 577 



Lead 448 



Silver 419 



Bismuth 382 



Potassium 364 



Sodium 253 



Antimony 244 



Borax 212 



Sodium carbonate 206 



Sodium chloride 114 



Water 86-2 



Selenium 70*4 



Sulphur 41-3 



Phosphorus 41 '1 



Wax 33-4 



We have evidently to do here with an agency which we cannot 

 neglect. In all these cases the measured tension is at a surface 

 bounded by air, and is such as tends to contract the surface. We 

 have then at the boundary between a crystallising solid and a fluid, 

 gas or liquid, out of which it is solidifying, a certian amount of 

 potential energy ; and by the laws of energy the condition of 

 equilibrium is that this potential energy shall be a minimum. The 

 accepted theory of surface tension is that it arises from the mutual 

 attractions of the molecules. The energy will therefore be a mini- 

 mum for a surface in which the molecules are as closely set as 

 possible. 



Now if you draw any surface through a heap of spherical balls 

 arranged so that each is touched by twelve others, you will find that 

 the surfaces which have the greatest number of centres of the balls in 

 unit area are all plane surfaces ; and those for which the concentration 

 is greatest are the faces of a regular octahedron, next those of a 

 cube, next those of a rhombic dodecahedron, and so on for the other 

 planes which follow the crystallographic law of indices. Taking the 

 concentration in the faces of the cube as unity, those of other forms 

 will be 



It must not be supposed that these figures give the surface energies. 

 We have at present no means of determining the exact magnitudes of. 



