166 TERMINOLOGY". . 145. 



for the rhombohedron 



aQ=5- a'; 

 therefore 



6 3 m' + 1 



If now we suppose m' = 5, 



a becomes = . a', or a' = 4. a, 

 and n' = n 2. 



If here we suppose m' = 3, we find 



a = f. a'; a' = f. a = |. 2>. a, 



and R + n = f R + n' + 1, the meml)er of the first sub- 

 ordinate series belonging to II 4- n' + 1. 



For m' = 2, follows 



a = f . a' or a' = |. a = |. 2. a, 



and R + n as R + n', that member of the second sub- 

 ordinate series, which belongs to 11 + n'. 



6. Let n' be = n 2, m' = 3. The combination is 

 R 4- n. (P + n 2) 3 . The forms are in a parallel position ; 

 the more acute terminal edges of the pyramid coincide with 

 the terminal edges of the rhombohedron, and the edges 

 of combination are parallel as well among themselves as 

 also with both the mentioned terminal edges. Ex. R (P) 

 and (P 2) 3 (t) in rhombohedral Ruby-blende. Vol. II. 

 Fig. 126. From this situation and position we may in- 

 versely conclude, that the given relations really take place 

 among the forms. 



For let 2CC be the more acute terminal edge of the pyra- 

 mid, in which the terminal edge of the rhombohedron is 

 situated. We shall have for the pyramid 



for the rhombohedron 



a? = ^. a', 



and therefore 3 m ' "" 1 . a = . a'. 



6 

 Now m' being = 3, we obtain 



a == |. a', or a' = 4. a = 2 2 . a, 

 and 11 + n = R + n' + 2. 

 If m' is supposed = 2, we find 



