388 Reflections on some Miner alogicul Systems, 



octaedron as a primitive figure, give occasion for some 

 reflections which I shall here venture, although I feel by 

 their importance, and by the considerations necessary to 

 give I hem due illustration and support, that these points 

 merit being treated separately and at greater length. It is 

 possible that there bad been but one single form of mole- 

 cule in all nature, and that this form was a tetraedron. 

 In the octaedron the existence of this figure is inevitable, 

 since it results from sections parallel even to the faces of 

 the octaedron. It also occurs, and simultaneously with 

 other figures, from supersections made in the direction of 

 the diagonals of all the faces of a parallelopiped. The 

 triangular prism likewise affords it, but of different forms, 

 by supersections in the direction of the diagonals of the 

 lateral faces. As we must necessarily allow of vacuums 

 between the molecules of bodies, we may suppose that the 

 interstices are those portions of spaces, from which every 

 other figure (except * the tetraedral molecule of the body,) 

 would have disappeared. The form and the quantity of 

 these interstices, conjointly with the presence of a greater 

 number of the proper molecules of the body, will pro- 

 duce all the diversities of specific gravity which are known 

 in nature ; and when we consider that a portion of space 

 cannot be inclosed by less than four planes, we observe in 

 the tetraedron that mark of simplicity which nature im- 

 presses on all her works. 



*f All the molecules in nature are spherical," said a most 

 celebrated German, in showing me that with small balls of 

 ivory he produced all the figures which he wished. " The 

 English and the French have not yet advanced so far," he 

 added. " From reason," said I to myself. The proba- 

 bility that nature would have given the preference to such a 

 solid rather than to another for an universal molecule, every 

 thing otherwise being equal, would be inversely as the 

 number of planes which terminate them. Between the 

 sphere and the tetraedron it would be as four to infinity. 



Besides its being hitherto impossible to extend the system 

 of the integral -molecule to all minerals, there are naturalists 

 who reproach it with the difficulty of finding the directions 

 of the cleavage in many cases, the trouble of calculating 

 them, 8cc. We should no longer use the microscope, the 



* This exception enclosed in ( ) appears superfluous ; the author is 

 speaking of the presumed vacant spaces or vacuums between the molecules ; 

 but neither the figure nor the forms of these vacuums interest the practical 

 erystallographer, as tangible solids are quite sufficient to establish the va- 

 lidiiy of the general principle.— Trans. 



telescope, 



