Theory of. Cr\Jhilli/alioTi. l5l 



he parallel to it ; and as there are fix rhombufes that undergo 

 like decrements on the primitive form, the faces produced 

 will be twelve in number. But in virtue of the law of de- 

 creafe by one range, the two faces which have the fame 

 angle, h,j\ g, Sec. (Jig. 4), for the point of departure, will 

 be in the fame plane, which reduces the twelve faces to fix, 

 and transforms the fecoodary cryflal into an acute rhomboid 



This rhomboid, from what has been faid, has its edges, 

 p z, py, p u, fituated each as the oblique diagonals of the 

 nucleus, or thofe which would be drawn from a to d, from 

 a to x, from a to c, &c. (Jig. 4). 



The edges of .the laminae . of fuperpoiition experience, in the 

 parts to which the decrement does not extend, auxiliary va- 

 riations, in virtue of which they are prolonged to envelop the 

 nucleus towards thefe parts, as in the regular octaedron, the 

 ftructure of which has been already explained. Moreover, 

 while the laminre decreafe, for example on the angles aj\{, 

 afx, (Jig. 4), they undergo alfo towards the adjacent angle 

 dfx, variations which intervene in a fubfidiary manner to aid 

 the effect of the principal decrement. The variations here are 

 alfo decrements by a fimple range on the inferior angles. But 

 in cafe the principal decrement fhould proceed by two ranges, 

 three ranges, or a much greater number, thefe variations 

 would become decrements of a particular nature, and which 

 would not be parallel to the diagonals. 



In fhort, we might apply here what we have already faid 

 in regard to the firft variations confidered otl the regular 

 oftaedron, and obferve, that the principal decrement alone 

 determines the form of the fecondary crvftal; fo that this de- 

 crement being well comprehended, nothing is then neceflary 

 but to fuppofe its effect prolonged, in order that the faces to 

 which it gives birth may interfecl: each other in fuch a 

 manner as to circumfcribe entirely the fpace to which they 

 correfpond. 



M, Bournon has difcovcred beautiful cryftals of this 

 M4 variety 



