Mr. J. F. Daniell on Crystallization. 35 



talline substances, chose the tetrahedron with octohedral va- 

 cuities, rather than the octohedron with tetrahedral spaces, for 

 reasons which he has assigned. Now, if we refer to the figure 

 of the cube, constructed upon this principle, it will be observed 

 that, if ever there had been a power which could have thus 

 grouped together these particles, mechanical force would have 

 split the solid in directions parallel to the faces of the cube, 

 and not parallel to the faces of an octohedron ; for in such an 

 arrangement each particle is in contact with one other par- 

 ticle, while in the second each is engaged by three; so that 

 the force of attraction must be greater in the latter than in 

 the former. We thus, in fact, demolish the foundation upon 

 which the whole superstructure is founded. 



Dr. Wollaston * proposed to obviate the difficulty of the in- 

 tersticial vacuities in these tetrahedral and octohedral arrange- 

 ments, in a most ingenious manner. He suggested that the 

 whole difficulty would vanish, by considering the elementary 

 particles to be perfect spheres, and to assume that arrangement 

 which would bring them as near to each other as possible. 



The relative position of any number of equal balls in the 

 same plane when gently pressed together, forming equilateral 

 triangles with each other, is familiar to every one ; and it is 

 evident that if balls so placed were cemented together, and 

 the stratum thus formed were afterwards broken, the straight 

 lines in which they would be disposed to separate would form 

 angles of 60 with each other. 



If a single ball were placed at rest upon such stratum, it 

 would be in contact with three of the lower balls ; and the lines 

 joining the centres of four balls, so in contact, or the planes 

 touching their surfaces, would include a regular tetrahedron 

 having all its sides equilateral triangles. 



The construction of the acute rhombohedron and octohe- 

 dron, on the same principle's as simple as that of the tetrahe- 

 dron ; and the following figures will illustrate the simplicity and 

 stability of the arrangement, and its perfect harmony with 

 the known laws of attraction, both in its construction and the 

 directions in which it would be disposed to yield to mechanical 

 force. 



Phil. Trans. 1813. 



D2 



