in the Analysis of Crystalline Forms. 5 



To find q. If we suppose all the faces suppressed besides 

 € and f, we shall have a 6-sided pyramid, terminated by a 

 3-sided pyramid, and the faces c of the 3-sided pyramid 

 will be rhombs, in consequence of the parallelism of the lines 

 which bound its faces. Hence, c being R,yis Rm (B ;) and 

 q = 1, m being still undetermined. 



To find m. The faces e manifestly truncate the alternate 

 edges of the pyramid whose faces are/, (namely, the more acute 

 edges.) Hence e being 2R', and / being Rm, we have the 



relation — j— r = % (C.) Therefore m = 3, and qRm, which 



designates/, is R3. 



To find m 1 . The faces b intersect the faces^ in Jines which 

 are horizontal, (the axis being vertical.) Hence f being R8, 

 b is ^R3, (D,) and m! = 3, q' being still undetermined. 



To find q[. The faces a manifestly truncate the alternate 

 edges of the pyramid of which the faces are b 9 (the more acute 

 edges .) Hence a being JR', and b being q / KS i we have the 



relation '-^— — a* 'ss \- (C,) and q' = J. Therefore qfRm', 



which designates 6, is £R3. 



To find p f ". If we suppose all the faces to be suppressed 



besides b and d 9 since the intersection of b and d is parallel to 



the intersection of b and b, it is manifest that the edges of the 



rhombohedron whose faces are d, are replaced by the pairs of 



faces of the pyramid b, (namely, the pairs which meet at the 



more obtuse angles.) Hence b being J R3, pf tf R, which is d, 



3.34-1 1 6 



will be determined by the relation -^ — . - = p" = - (E.) 



And d will be | R'. 



(B.) In combinations of forms, pR, pRm, the faces of pR are rhombs, 

 terminating the pairs of faces of pRm. 



(C.) In combinations of forms pR', gRm } the former will truncate the 



acute terminal edges of the latter, if p = — -r~q> 



(D.) In combinations of forms gRm, g'Rm, (m being the same in both,) 

 the edges of combination are horizontal. 



(E.) In combinations of forms pR', and glim, the other terminal edges 

 of the latter, in pairs, replace the edges of the rhombohedron pR' if 



37»+l 



