. 145. OF COMBINATIONS. 163 



of the combination, and vice versa. Ex. R (P) and II -f oo (c) 

 in rkomboliedral Lime-haloide. Vol. II. Fig. 114. The co- 

 sine of the angle at the horizontal edge, is equal to double 

 the cosine of the angle at the inclined edge of combination. 

 From the horizontal edges of combination between a rhom- 

 bohedron and a regular six-sided prism, we may infer that 

 the latter is R + oo and not P + OD (. 118.). The demon- 

 stration of this depends upon . 111. 



ii. R + n. (P + n') m '. 



1. Let n' be = n. Upon this supposition the forms be- 

 come co-ordinate (. 112.). The edges of combination 

 which they produce are parallel to the edges of the rhom- 

 bohedron, and to the lateral edges of the pyramid, whatever 

 be the value of m'. The figure of the faces of the rhom- 

 bohedron remains a rhomb, and they appear contiguous to, or 

 in the place of the apices of tbje pyramid. Ex. R (P) and 

 (P) 3 (r), or It (P) and (P) 5 (y) in rhombohedral Lime-ha- 

 loide. Vol. II. Fig. 116. From the rhombic figure of the 

 faces, which is a consequence of the situation of the edges 

 of combination, follow the relations of the combined forms, 

 as is immediately evident from the derivation (. 112.). 



2. Let n or n' be = 03. One of the forms becomes 

 = R 03, and the edges of combination are horizontal 

 (i. 3.). 



3. Let nbe = +oo;R + n therefore = R + eo. The 

 figure which the faces of this prism assume in the combi- 

 nation with a pyramid, is that of an irregular tetragon, 

 which may be divided by a horizontal line into two isosceles 

 triangles. The relative heights of these triangles are to 

 each other in the ratio of m' 1 : m' -f 1. The more ob- 

 tuse triangle is produced by the intersection of the faces of 

 R + 03 with the upper faces of (P 4- n') m ', while the more 

 acute one results from the intersection of the same faces of 

 R -f oo with the lower ones of (P + n^'. Ex. R + 03 (c) 

 and (P) 5 (y) in rhombohedral Lime-haloide. Vol. II. 

 Fig. 116. The figure of the faces of the regular six-sided 

 prism c at once indicates it to be R -I- oo, and not P + so. 



