. 145. OF COMBINATIONS. 16*9 



bination therefore II + es. P + os ; the result is an equian- 

 gular, and if the faces are of equal extent, it is a regular 

 twelve-sided prism ; because the faces of one of the six- 

 sided prisms appear under equal inclinations in the place of 

 the edges of the other prism, their edges of combination being 

 parallel to each other and to the axis. Ex. B, + os (e) and 

 P + os (M) in rhombohedral Fluor-haloide. Vol. II. Fig. 149. 

 Hence the twelve-sided prism is a compound form, and not 

 a simple one. Also this combination depends upon the dif- 

 ferent situations of the two prisms. 



iv. (P 4- n) m . (P 4- n') ra '. 



1. Let n' be = n. The combination is (P 4- n) m . 

 (P 4- n) m/ ; the forms will be co-ordinate scalene six-sided 

 pyramids. The faces of the more acute pyramid are situ- 

 ated in the place of the lateral edges of the more obtuse 

 one. The edges of combination are parallel to each other and 

 to the lateral edges of both the pyramids. Ex. (P) 3 (r) and 

 (P) 5 (y) in rhombohedral Lime-haloide. Vol. II. Fig. 11G. 

 If, on the contrary, the edges assume the mentioned po- 

 sition, we may infer that n is = n', which is exactly what 

 follows from their derivation. 



2. Let m' be = m, the combination will be (P + n) m . 

 (P + n') m . Suppose at the same time the forms to be in a 

 parallel position, or n' = n + 2 r (i. 2.). Under these cir- 

 cumstances, the edges of combination which they produce 

 become horizontal. For the transverse section of one of 

 these pyramids is similar to the transverse section of the 

 other (. 113.), and therefore a plane passing through 

 those edges in which the faces of the two forms meet, will 

 be perpendicular to their axis. Ex. (P 2) 3 (t) and (P) 3 (r) 

 in rhombohedral Lime-haloide. Vol. II. Fig. 129. This 

 situation of the edges cannot take place, if the scalene six- 

 sided pyramids are in a transverse position. From such ho- 

 rizontal edges, therefore, we infer not only the parallel 

 position of the two forms, but also that they are derived 

 according to the same m, or that m' is = m. 



3. The horizontal situation of those edges is not altered, 



