164 TERMINOLOGY. . 145. 



4. Let n' be = n 1, and m' = 3. The combination 

 is = R + n. (P 4- n I) 3 . Under these circumstances, 

 the forms are in a transverse position, because R + n 1, 

 the rhombohedron from which the pyramid is derived, is 

 itself in a transverse position towards R 4- n. The faces 

 of R + n have the situation of the more acute terminal 

 edges of the pyramid ; and the edges of combination are pa- 

 rallel to each other, to the above mentioned acute terminal 

 edges, and to the inclined diagonals of the rhombohedron 

 Ex. R _ 1 (z) and (P _ 2) 3 (i) in rhombohedral Ruby- 

 blende. Vol. II. Fig. 126. Inversely from the situation 

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

 the given position, we may infer the above mentioned re- 

 lation to exist between the two combined forms. 



In order to demonstrate this, let ABXC, Fig. 47., be 

 the principal section of the rhombohedron, from which the 

 pyramid is derived, AX its axis, and M3L half the axis of 

 the pyramid : 3LC becomes its acute terminal edge, and at 

 the same time the inclined diagonal of the rhombohe- 

 dron, whose plane touches the pyramid in this termi- 

 nal edge, if the horizontal projections of the two forms are 

 equal. Let now a = AX, be the axis of that rhombohe- 

 dron, from which the pyramid is derived ; and a' the axis 

 of the rhombohedron sought ; it follows in respect to the 

 pyramid, that 



ar = 3m '-- J a , 



6 



in respect to the rhombohedron, that 



aP=.a'; 

 and on account of the equality of both expressions, that 



3m' 1 , , 



-y- 



and a = . a'. 



3m' 1 

 If now we suppose m' = 3, 



a becomes = . a', or a' = 2. a. 

 and n' = 11 1. 



But, let m' be = 2 ; the result, obtained in the same 

 way, will be 



