. 145. OF COMBINATIONS. 161 



an accidental irregularity (. 31.). In general, and suppos- 

 ing, for the sake of brevity, only one series of rhombo- 

 hedrons, the binary combinations of this system are 

 i. 11 + n. R + n', 



ii. R + n. (P 4- n') m/ , 



iii. R + n. P 4- n', 



iv. (P 4- n)<". (P + n') m/ , 



v. (P 4- n) m . P + n', 



vi. P + n. P 4- n'. 



Some of the most common and remarkable of these com- 

 binations may be shortly noticed. 



i. R + n. R + n'. 



1. Let n' be = n + 1. The two forms are consecutive 

 members of the series . 110., and as such in a transverse 

 position to each other. The edges of combination which they 

 produce are parallel among themselves, and at the same 

 time also to the terminal edges of the more acute rhombohe- 

 dron, and to the inclined diagonals of the more obtuse one. 

 Example, R 1 (n) and R (P), or R (P) and R 4- 1 (r) 

 in rhombohedral Kouphone-spar. Vol. II. Fig. 120. 

 We may also argue inversely : when two rhombohe- 

 drons join in a transverse position, and produce edges 

 of combination of the above mentioned kind, that is to 

 say, parallel to each other, parallel to the terminal edges of 

 the more acute rhombohedron, and parallel also to the in- 

 clined diagonals of the more obtuse rhombohedron, the re- 

 lations between the two forms must be the same as those 

 between two consecutive members of the series . 110. 

 This is a direct consequence from the derivation of those 

 forms (. 108.). 



2. Let n' be = n + 2 r, where r may be any whole 

 number. In this case an odd number of members of the 

 series . 110. is wanting between the two combined forms, 

 the forms therefore are in a parallel position, and the edges 

 of combination produced are horizontal. Example, R (P) 

 and R 4- 2 (m) in rhombohedral Lime-haloide. Vol. II. 

 Fig. 115. A similar result is obtained from rhombohedrons 



VOL. i. L 



