planes only in particular cases. Indeed: if the number of molecules 

 happens to be the square of a whole number, then the form of 

 equilibrium is exactly a square. When however successively more 

 molecules are added, they must adjust themselves somewhere against 

 the square to get maximum saturation, which leads to vicinal planes. 

 (In the formulae of § 1 this circumstance remains concealed, 

 because there it is considered that the minimum must be determined 

 with respect to infinitesimal changes of form. Here we realize, 

 however, that it is a question of addition or displacement of a • 

 vihole number of molecules). 



§ 4. Observations. A. If a certain number of molecules is originally 

 grouped in the form of two squares of different sizes, potential 

 energy may be still diminished by the removal of a row of molecules 

 from the small square, which are then laid against the large square. 

 Decrease of energy also takes place when a rectangular grouping 

 is changed into a square one. Until we take the temperature motion 

 into consideration and consider the process of solution and sublima- 

 tion, we can of course not ascertain whether in our molecular 

 scheme these transitions will take place spontaneously. A somewhat 

 trustworthy treatment of this question seems difficult to me, because 

 for this the unevennesses of the edge are to be considered, i.e. those 

 molecules which at a given moment are only bound singly or doubly, 

 and not threefold. 



B. It has been experimentally proved that for crystal powder e.g. 

 of gypsum with a radius of about one micron the saturation concen- 

 tration of the solution around it still appreciably depends on the 

 radius. But for a radius of some microns this dependence already 

 loses its significance with respect to disturbances of various nature. 

 In virtue of this doubts will rise as to whetlier the changes discussed 

 under A will appear spontaneously, and whether the actually occurring 

 crystalline forms really agree with a minimum of surface energy '). 

 Shortly ago Vai.eton") defined this view in the following way: 



"For microscopic and submicroscopic crystals the surfa?e energy 

 has a measurable influence on the solubility. Such crystals can be 

 in equilibrium with a solution only when their form corresponds 

 with the minimum of surface energy. Kor macroscopic crystals this 



1) A. Berthoud, Journ. de Chim. Phys. 10 (1012) p. 62-i. — G. Friedel, Journ. 

 de Chim. Phys. 11 (1913) p. 478. 



2) I.e. p. 42. Compare there the fuller lepoit of Hulett's experiments. Z. f. pliys 

 Cl'em 37 (1901) 385 with crystal powder of gypsym and barium sulphate. 



