170 TERMINOLOGY. . 



if n.or n' should become infinite and negative, whatever 

 may be the value of m and m'. 



4. But let m' be = m, and n' or n = -f co : the combi- 

 nation therefore (P + co). (P + n') m or (P + n) m . 

 ( P + co ) n . The edges of combination between, those faces 

 of the two forms, which are contiguous to the same apex, 

 must here likewise be horizontal, because the unequiangu- 

 lar twelve-sided prism is the limit of the series of pyramids, 

 and as such contains an identical transverse section (. 115.). 

 Ex. (P)* () and (P + os)* (c) in rhombohedral Fluor-ha- 

 loide. Vol. II. Fig. 148. The intersections of the faces from 

 two different apices, however, assume an inclined situation, 

 dependent upon the dimensions of the simple forms (i. 4.). 

 The inferences drawn in 2. extend also to the present case. 



5. In the series of scalene six-sided pyramids, 



... (P + n) 5 , (P + n + 1), (P + n + 2), (P + n + 1)*... 

 the law of progression is evident. Instead of n any whole 

 number, positive or negative, may be substituted, and the 

 series arbitrarily continued on either side. If now from 

 the above mentioned series we select a combination of any 

 two subsequent members, as (P + n) s and (P + n + I) 3 , 

 or (P + n + I) 3 and (P + n + 2) 2 , &c. ; the' obtuse ter- 

 minal edges of every more obtuse pyramid appear in the 

 place of the acute terminal edges of the more acute mem- 

 ber, the edges of combination being parallel to each 

 other, and to the mentioned terminal edges of the two py- 

 ramids. Examples occur in rhombohedral Lime-haloide, 

 between (P) 3 (r) and (P + I) 2 (#), &c. 



The situation of the edges is a consequence of the trans- 

 verse position of every two subsequent members of the 

 above mentioned series, and of its peculiar property, that 

 the more obtuse terminal edge of every lower member is 

 inclined to the axis at the same angle as the more acute 

 one of the higher member. We have in Fig. 47. 

 sin. 3BQ = __ (Sjnj^-.a __ 

 VI(3ra + iy. 2. a' + 36]' 



rin. 3CP = 



,/ ((3 ra' I) 2 . 2"'. a + 36] 



