188 TERMINOLOGY. . 149. 



member of the second subordinate series which belongs to 

 P + n' + 3. 



6. Let n' be = n 3, m' = 3, the combination there- 

 fore P -f n. (P + n 3) 3 . The forms again are in a dia- 

 gonal position, and the more acute terminal edges of the 

 eight-sided pyramid, therefore, fall into the same vertical 

 plane, which passes through the terminal edges of the four- 

 sided pyramid. The edges of combination, arising between 

 the faces of the two forms, become parallel among them- 

 selves, and to the above-mentioned terminal edges of the 

 pyramids. Ex. P + 2 (5) and (P I) 3 (2) or P + 4 (r) 

 and (P + I) 3 (e) in pyramidal Garnet. Vol. II. Fig. 96. 



For, the rest being as in the other example, let A'C, 

 Fig. 69., represent the terminal edge of the four-sided py- 

 ramid : it will follow that 



MA = 2^. a = m ^- 1 - 2~^~. a. 



If now, according to the supposition, m' be = 3; we 

 have 



n = n' + 3, and n' = n 3. 



But if m' is = 4 ; P + n becomes = | P -f n 7 + 3, or 

 that member of the second subordinate series, which be- 

 longs to P + n' + 3 ; if m' is = 5, the pyramid becomes 

 -= ^ + n' + 4, or that member of the first subordinate 

 series, which belongs to P -f n' + 4. 



7- Let n' be = n 4, m' = 4, or the combination 

 P + n. (P + n 4) 4 . The forms are in a parallel posi- 

 tion ; the more obtuse terminal edges of the eight-sided 

 pyramid coincide with the terminal edges of the four-sided 

 pyramid. In this situation of the faces, the edges of com- 

 bination between the two forms are parallel to each other, 

 and to both the mentioned terminal edges. Ex. P + 4 (r) 

 and (P) 4 (x) in pyramidal Garnet. Vol. II. Fig. 96. 



For we have 



% 

 MA = 2?. a = m'. 2'. a, 



from which, 4 being substituted for m', we obtain 



