iSi On Crystalhgrnphy, 



I shall give the name of suhtractivb molecules to thosi 

 parallelopipednns coinposed of tetfahedrons, or of triansiular 

 prisms, and whose ranges measure the quantity of the de- 

 crement which the laminsE of snperpiositiort undergo when 

 applied on the faces of the priihitive form. 



We find from wliat precedes, that, to speak pfetisely, 

 theory would not admit of our proceeding towards its prin- 

 cipal object, on stopping at the parallelopipedons given in 

 the first place by the mechanical division of crystals; and 

 the kind of anatomical dissection afterwards nndergont; by 

 these parallelopipedons, when we try fo ascend to the true 

 form of the integral molecule, is an ulterior step, vvithout 

 which, observation, rather than theory, would leave some- 

 thing untinished. The paralleloplpedon here represents 

 unity, at which all the results of the theory end ; and frac- 

 tions formed of its subdivisions beyond this unity arc of no 

 consequence. 



We see at the same time, that by means of this con- 

 formity between the results given by the various forms of 

 intccral molecules, theory has the advantage of gene- 

 ralizing its object by chaining to a single fact the multitude 

 of facts, which from their diversity seem little susceptible 

 of concurring in one common point. 



regularity which the other has not, and whicli consists in the equality and 

 iimilitude of its lateral faces. 



Here a consideration presents itself which we ought not to omit. I^et 

 A B C D (fig. 1-) be the upper hast of one of tlic prisms we have mentioned. 

 Let us suppose for a moment that this prism cannot be sulidivideJ except 

 parallel to its four panes and to its two bases. The arrangement of the small 

 rhombuses situated on both sides of tlic rliombus A B C D will reprcient tlie 

 effect of a decrement by one range on the two longitudinal ridyes terminated 

 by the points A and C; and it is visible tliat this decrement will produce for 

 the secoudary form, a hexahedral prism, whose base is represented by C'i 

 7/i D' r It. 



Now if we conceive that the rhomboidal prism which has for its bast) 

 ABCD, may be subdivided in the direction oi the diagonal BD into two 

 triangular prisms, all the small rhomboidal prisms of which it is the assem- 

 btagf brtng susceptible of the same division, we shall suppose that ihc 

 small vacuums which existed between / and m on one hand, and between 

 h and r on the other, in the hypothesis of the decrement, are tilled up by 

 triangular prisms, in which case the hexahedral prism will be immediately 

 given without .iny decrement. Nevertheless we cannot admit of considering 

 the faces which will be in this case as being produced in virtue of a decre- 

 ment by one rang?, because then the form of the secondary crystal is merely 

 composed of small rhomboidal prisms similar to the primitive form, as would 

 have taken place if tlie decrement was produced by two or more ranges ; so 

 that here it is only a particular case which should seem to have been assimi- 

 lated with all the others for the sake of uniformity in the laws of structure. 

 The same reasoningapplies to primitive forms different from the parallelopi- 

 pedon, as wc shall iiud in the course of this work. 



m^ 



erenee 



