198 TERMINOLOGY. . 



other, and to the above mentioned terminal edges of the 

 pyramid, which is evident from the derivation. The same 

 takes place for (Pr + n) m . Pr + n', and if m be = 3, also 

 for (Pr + n)m. Pr -f n'; and it is therefore a very useful 

 and evident datum for the determination of forms. Ex. 

 P (P) and r (o) in diprismatic Olive-malachite. Vol. II. 

 Fig. 5. 



vii. P -f n. Pr -f n'. 



1. What has been said in vi. of the acute terminal edges 

 of P 4- n, applies here on the same supposition to the ob- 

 tuse ones, in the combination P + n. Pr + n, as well as in 

 those of (P + n) m . Pr + n, and, in the case of m = 3, also 

 to (Pr + n) m . Pr + n. Ex. P (o) and Pr (P) in diprisma- 

 tic Iron-ore. Vol. II. Fig. 4. 



2. Suppose now a triple combination, whose crystallo- 

 graphic sign is 



P -f n. Pr + n'. Pr + n", 



and in this n' = n, n" = n 1 ; the faces of Pr + n" will 

 assume a rhombic figure in the combination. 



Let AM, Fig. 71-5 represent part of the axis, MB one of 

 the diagonals, and BG part of that terminal edge of the pyra- 

 mid P + n, which is contiguous to BG ; FGHI, FGH'F 

 will be the faces of the horizontal prism Pr 4- n. 



The rhomb AQB'P is a face of the horizontal prism 

 Pr + n" ; AN is = NB', the triangle NB'N' therefore simi- 

 lar to the triangle AB'M', and equal and similar to the 

 triangle NGA. Hence N'N = NG = | N'G. 



The line N'B' is at the same time the diagonal of the 

 pyramid P + n, and of the pyramid P + n", to which the 

 horizontal prism Pr + n" belongs. N'G therefore repre- 

 sents the axis of the first, N'N that of the second pyramid, 

 and from the ratio of these = 2 : 1, we infer that n" is 

 n 1. 



3. If instead of P -f n, the triple combination contains 

 the vertical prism P + co, and n' is = n", the faces of all 

 the three forms become rhombs. The rhombic figure of the 

 faces of a horizontal prism, if produced by the intersection 



