in Cheinical Comlinationi. - 111 



lore, from the junction of two octahedrons. The hexahedral 

 prism will not be straight, unless so far as we shall have removed 

 the two first triangles in a direction perpendicular to their plan, 

 and it will have for its base a regular hexagon only in the case 

 Avhere those two triangles are equilateral. We may rem.ark, that 

 in the hexahedral prism formed in this way with two regular wc- 

 tahedrons, the height is to the sides of the bases as v^ 2 : 1 . 



In general, the examination of the circumstances which re- - 

 suit from the regularity or irregularity of the particles which 

 are united to each other, as two tetrahedrons are in order to pro- 

 duce a parallelopipedon, and two octahedrons in order to give 

 birth to a hexahedral prism, requires very complex considerations, 

 which are of no use to the explanation of the theory which I am 

 describing, while we are merely occupied with the number of 

 the molecules of each particle, and cannot have an application. 

 But when we study under this point of view the prinntive forms 

 'of the crystals given by observation, I shall put them out of 

 consideration in this extract ; and as it will only be necessary to 

 speak of the number of the molecules of which the particles 

 formed by the union of other particles already known are com- 

 posed, 1 shall consider as regular all the tetrahedrons and octa- 

 hedrons, the various combinations of which I shall examine. 

 It will be easy, by the help of a few reflections, to form an idea 

 of the modifications which the results of this examination will 

 undergo in cases where these polyhedrons are irregular. 



It is evitlent, that by placing at the same point the centres 

 of gravity of two tetrahedrons and an octahedron, so as that 

 the two former should make a cube, and the situation and di- 

 mensions of the octahedron are such that the ridges of this cube 

 and those of the octahedron mutually cut each other at right 

 angles into two equal parts, the polyhedron with 14 summits 

 which will result from their junction will be the dodecahedron, 

 the last of the primitive forms given i)y the mechanical division of 

 the crystals ; for we ought not to reckon among these forms the 

 double pyramid with hexagonal bases, admitted at first in order 

 to explain the crystallization of quartz, and brought back after- 

 wards to a parallelopipedon. 



It appears from what we have said, that when particles are 

 xmjted into a single particle, it is by placing themselves in such 

 a way that, the centres of gravity of the coni])onent particles 

 being at the same points^ the summits of the one are placed in 

 the intervals left by the sununits of the others, and t'ice versa. 

 It is in this way that -I consider chemical combination; and here 

 it differs from the aggregation of similar particles, which takes 

 place by simple juxtaposition, as is seen in that elegant theory 

 of tryslallizatiou which the sciences owe to .M. Haiiy. It is 



also 



