. 149- OF COMBINATIONS. 189 



n = n' 4- 4, or n' = n 4 ; 

 m' = 3 gives P + n = L_P + n'-f 3, the member of 



2 V'2 



the first subordinate series belonging to P + n' + 3 ; 

 m = 5 gives P + n = \ P + n' + 4, or that member of 

 the second subordinate series which belongs to P + n' + 4. 



iii. (P + n)". (P + n') m/ . 



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

 (P + n) m '; the forms are co-ordinate pyramids, and as 

 such in a parallel position. The situation of the edges in 

 which the faces of the two pyramids intersect each other, 

 do not depend upon m or m' (ii. 1.). The situation of the 

 edges produced between any one of those pyramids, and the 

 four-sided one from which they are derived, is such that 

 the faces of the latter become rhombs, or the edges of 

 combination are parallel to their terminal edges. The 

 edges of combination between two such co-ordinate scalene 

 eight-sided pyramids, will therefore likewise be parallel to 

 the edges of that isosceles four-sided pyramid to which 

 they belong ; and if more than two appear in one and the 

 same compound form, the above mentioned parallelism will 

 be observable in the edges of combination between them all. 

 Ex. The pyramids a 1 , ?/, and 2, already mentioned in pyra- 

 midal Zircon. Vol. II. Fig. 99. From the observed pa- 

 rallelism, we may decide inversely whether the pyramids 

 are co-ordinate forms or not, and whether or not they are 

 derived from that isosceles four-sided pyramid, with which 

 they enter into combination. 



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

 (P 4- n') m . If, moreover, the forms are in a parallel position, 

 the edges produced by the intersection of their faces be- 

 come horizontal. Ex. (P I) 3 (z) and (P 4- I) 3 (e) in 

 pyramidal Garnet. Vol. II. Fig. 96. The transverse sec- 

 tions of the two forms are similar to each other, since these 

 forms are members of one and the same series (. 105.). 

 The observations in respect to scalene six-sided pyramids 

 in . 145. iv. 2. extend likewise to this case. 



3. If one of the combined forms, by n becoming ~ +_ co 



