454 On Ci'ystallographi/, 



their sides. Thus, upon the hypothesis that the cube per- 

 forming the function of the primitive form undergoes a 

 decrement by a simple range around its eight sohd angks, 

 it may happen that the effect of tlie decrement remains m- 

 terrupted, at the term at which all the faces which it pro- 

 duces are eq\iilateral triangles far enough removed from 

 the centre to avoid meeting, and then the faces parallel to 

 those of the primitive cube will be octagons. If, on the 

 contrary, the same faces come in contact, the primitive 

 planes will preserve the form of the square : finally, if they 

 intersect each other, they will be changed into hexagons, 

 without the primitive faces ceasing to be squares, and these 

 variations might pass through an infinity of degrees which 

 will be as many approximations, with respect to the form 

 of the complete octahedron, which is the object towards 

 which the law of decrement tends. 



But amid all these diversities of positions, the mutual in- 

 cidences of the faces of the crystal are constant. This 

 truth, which has been placed beyond all question by the 

 numerous observations of Rome de I 'Isle, is a necessary 

 consequence of the integrant molecule being itself invari- 

 able in its form, and also from the law of decrement in its 

 turn having a constant progress, which is only arrested 

 more or less far from its limit in the different crystals re- 

 lative to one and the same variety. 



A second cause of variations is that which disturbs the 

 symmetry and regularity of the crystalline form, and the 

 effect of which is to destroy the equality of the analogous 

 faces, in such a way that some take a very visible extension, 

 while otherg almost entirely escape the eye. The ifieory 

 ought to make an abstraction of these variations, and re- 

 gard them as null : but they are visible enough to confuse 

 the mind of a person not much habituated to these exer» 

 cises, and who cannot easily distinguish the type from the 

 true form through the traits which disfigure it, and this is 

 the source pf the greatest difficulties which the study <>f 

 crystallography presents. The projections traced from re- 

 gular crystals, and the copies in relievo of these bodies, may 

 be of great use to the naturalist, in order to bring back the 

 rest, by an exercise of imagination, to the symmetry from 

 which they are separated. 



These imitations of the work of nature will serve to 

 obviate a difficulty of another kind, namely, that which 

 arises from the grouping of crystals partly concealed by 

 pach other, or from their slight projection above tiie mar 



