172 TERMINOLOGY. . 145. 



the isosceles pyramid to the axis, is equal to the inclination 

 of the more obtuse terminal edges of the scalene pyramid 

 to that line. For the latter we have (iv. 5.) 



sin. 2BQ = (3j*Jl2l.t__ . 



V [(3m+ I) 2 . 2 2 . a 2 + 36]' 

 and for the former 



sin.2lBQ,= m/ - 2n/ ' a . 



^/(m' 2 . 2 2n . a 2 + 4)' 



two values which become equal, if in that for the scalene 

 pyramid we substitute 5 instead of m, and in that for the 

 isosceles pyramid the expressions, | instead of m, and 

 n 4- 3 instead of n'. Examples occur in (P 2) s and 

 P 4- 1 (n) of rhombohedral Iron-ore. 



2. Let m be = 3, n' = n 4- 2 ; the combination will be 

 (P 4- n) 3 . P + n 4- 3. In this case, similar to the pre- 

 ceding, the faces of the isosceles pyramid appear in the 

 place of the more acute terminal edges of the scalene one ; 

 the edges of combination being parallel among each other, 

 and to the above mentioned terminal edges, from the same 

 reason as in 1., because the inclinations of the terminal 

 edges to the axis are equal in these two pyramids. This 

 may be shewn by effecting the necessary substitutions in 

 the values of sin. <3CP, which here takes the place of 

 sin. 3BQ. 



3. For n or n' = co all the edges of combination be- 

 come horizontal (i. 3.). 



4. Let n' be = 4- cs. The combination is(P 4- n) m . P + os. 

 The edges of combination are parallel to the lateral edges 

 of the pyramids. Ex. (P) 3 (h) and P 4- co () in rhombo- 

 hedral Ruby-blende. Vol. II. Fig. 126. The situation of 

 the edges distinguishes P 4- oo from R + co in ii. 3. 



vi. P + n. P 4- n'. 



1. The edges of combination are always horizontal, what- 

 ever may be the value of n or n', even though this be 4- 03 

 or os. Ex. P + 1 (r) and P 4- 2 (ft) in rhombohedral 

 Corundum. Vol. II. Fig. 122. 



