Mr. FoRSTER on the Molecular Formation of Crystals. 493 



unexplained the different cleavages which are found ; — in fact, he took no notice 

 whatever of cleavage, except some unintelligible remarks, and did not even 

 perceive that this formation would give rise to the cubical cleavage, and no 

 other, — a fact which wc shall presently prove. 



Thus we have the two most successful systems, those of Hauy and Dana ; 

 the first founded on the phenomena of cleavage, an attempt which, as we have 

 seen, totally failed : the second altogether throwing aside the consideration of 

 what is the most important and remarkable of all the phenomena of crystalliza- 

 tion. The success of Hauy's theory of decrements depends solely on the fact, 

 that what he applied to cubes is equally applicable to spheres ; but it is to be 

 remarked, that it would have completely failed if he had attempted to apply it 

 to the other forms of molecules which he supposed to exist — in other words, 

 his own theory failed completely when applied to his own system. We can 

 only ascribe to a fortuitous circumstance the truth of a theory which has its 

 very foundation in error. 



Dana, however, was right so far as he went, and his theory will actually 

 go a little farther than even he took it, for the formation which he supposed to 

 exist will explain the cubical cleavage. The phenomenon of cleavage is a very 

 remarkable one, and it may be said that the existence of several directions in 

 which the crystal divides with less than the ordinary resistance is the origin of 

 this phenomenon. It is evident that in any crystal where the faces are plane, 

 and the molecules accordingly arranged in layers, the direction of that divi- 

 sion which will give the least resistance will be some plane, and that this plane 

 will be symmetrically situated with regard to the crystal, and that there will be 

 as many planes as there are corresponding parts of the crystal, provided the 

 poles of each molecule have the same attractive power. Thus, in the first sys- 

 tem, where all the poles are naturally of the same strength, the number of planes 

 of cleavage is either three, four, or six ; so, if a cube be divided by planes pa- 

 rallel to the faces, the number of different directions in which it will be divided 

 is evidently three : if it be divided by planes tangential to an edge, as the 

 edges are twelve in number, parallel two and two, the number of cleavage 

 planes will evidently be six ; and if by planes replacing the corners, since the 

 corners are eight in number, the cleavage planes are in number four. In order, 

 then, to ascertain what will be the cleavage in any formation, we must look for 



VOL. XXIII. 3 T 



