On Crystallography. 30i 



very Umited action. These subtractions are most frequently 

 iornied by one or two ranges of molecules. I have found 

 none which went beyond six ranges*; but such is the fer- 

 tility which is united with this simphcity, that, by confinmg 

 ourselves to decrements by one, two, three, and tour 

 range's, and abstracting those which are mixed or inter- 

 mediate, we find that the rhomboid is susceptible of eighty 

 millions three hundred and eighty-eight thousand six hun- 

 dred and four varieties of crystallization. Without doubt, 

 amonw the circumstances which can determine all these 

 varietfes, there are many which are not met with m nature. 

 But there is reason to think that discoveries of this kind 

 will continue to be multiplied for some time to come, m 

 proportion as a taste for mineralogy continues to be diffused, 

 since we have hardly as yet observed 48 distuict varieties in 

 the species of carbonated lime, which is the richest of all 

 in crystalline forms, at least if we may judge from the pre- 

 sent state of our knowledge. . . , c 

 In order to have a still more accurate idea of the power of 

 crystallization, we must add to this facility of producing so 

 many difterent forms, in commencing with a single figure, 

 that of attaining one and the same form by different struc- 

 tures. The rhomboidal dodecahedron, for instance, which 

 we obtained by combining cubical molecules, exists m 

 the garnet, with a structure composed of small tetrahe- 

 drons with triangular isoscele faces, as we shall find under 

 the head of this mineral substance ; and I have found it m 

 a -pecics of fiuated lime, where it is also an assemblage 

 of tetrahedrons, but regular, and the laces of which 

 are equilateral triangles. But besides all this, it is possible" 

 Tiiat similar molecules, subjected to- a variation ot laws, 

 present identically the same result. Thus the regular hexa- 

 hedral prism, which in carbonated lime generally exists m 

 viitue of a decrement on the inferior angle, sometimes pro- 



» We meet Mihough very rarelv, with mixed decrements, which take 

 place according to ratio* sucli as 4 i's to 9, or 3 to 8, one of the two terms 

 Jesiifnalin- ll.c number ot ranges subtracted in breadth, and the other the 

 number ot"rangtssub.ractcd in height ; and such are hitherto the ratios of 

 this description, that it issultlcient to increase or dunmi.-h by a unit one of 

 the two terms, that the decrement may enter into the most common cases. 

 For example, if in the first of the ratios which has been quoted we retrench 

 a unit trom i), and if we add one to tlir(?e in the second, each ratio will be- 

 come ' or I It rcuhs that the absoKite measuremerw ot the decrements ui 

 question does not exceed that ol lU ordinary decrements. I'or instance, 

 1 aud ; are both of them less thui ',, which expresses a simple decrement. 

 Now it seems to me that a decrement ought to be estmiatcd according to 

 tiic absiiiutc value of the ratio which represents it, and not according to the 

 terms of thi? ratio considered indcpeudcntly of each otlier. 



ceeds 



