. 145. OF COMBINATION;?. 167 



a = f. a', or a' = f . a = .f. 2 1 . a 

 and R + n = f & 4- n' + 1. 



The number 5 substituted for m', gives 



a = i. a', or a' = 7- a = |. 2 2 . a, 

 and R 4- n = 1 11 + n' + 2. 



7. Let n' be = n 3, m' = 5. The combination is 

 R 4- n. (P 4- n 3) 5 . The forms are in a transverse posi- 

 tion. The more obtuse terminal edges of the pyramid are 

 parallel to the terminal edges of the rhombohedron, and at 

 the same time also to the edges of combination arising from 

 the intersection of their faces. 



Suppose the horizontal projections of the forms to be the 

 same ; the terminal edge of the rhombohedron will lie in 

 the more obtuse terminal edge of the pyramid. Hence 

 for the pyramid we have 



~~6~~~ 



for the rhombohedron 



&Q, = . a', 



and consequently IJ^-U. a = . a'. 



. 6 



For m' ;== 5 this expression gives 



a = $. a', or a' = 8. a = 2 3 . a, 

 and R 4- n = R 4- n' 4- 3 ; 

 for m' = 3, 



a = \. a', or a' = 5. a = . 2 2 . a, 

 and R 4- n = f R 4- n' 4- 2 ; 

 for m' = 2, 



a = f. a', or a' = . a = |. 2 1 . a, 

 and R 4- n = I R 4- n' 4- 1. 



iii. R 4- n. P 4- n ; . 



1. For n' = n, the combination is R + n. P 4- n. The 

 forms are co-ordinate, and the faces of the pyramid appear 

 in pairs in the place of the terminal edges of the rhombo- 

 hedron. The edges of combination are parallel to these, 

 to the alternating terminal edges of the pyramid, and 

 among each other. In a combination, which, besides these 



