108 TERMINOLOGY. . 108. 



sion of the co-efficient. If the co-efficients become powers 

 of the number 2, the members belong to the principal 

 series. The members of the subordinate series in particu- 

 lar are designated by m P + n, agreeably to the rules 



given in . 96. 



The position of the members of the subordinate series in 

 respect to those of the principal series, follows easily from 

 their derivation ; and the expressions of the cosines of their 



edges are found by substituting m+ . a instead of a in 



the formulae . 56. 



The values of the co-efficients hitherto ascertained by 

 observation are, ~-^ f , -^- 2 , and f . Members of the series 

 j-^P + n occur in pyramidal Zircon and pyramidal Cop- 

 per-pyrites ; of the series | P + n in pyramidal Tin-ore ; 

 of the series ^pP + n in pyramidal Lead-baryte, pyra- 

 midal Kouphone-spar, of the series f P + n in pyramidal 

 Kouphone-spar and pyramidal Titanium-ore. It may be 

 remarked here, that the two series, ^/^P + n and 

 P + n are obtained together with the principal series, 

 if, according to the first method of derivation, tangent 

 planes are applied to the terminal edges of those eight- 

 sided pyramids, which depend upon m = 3, m = 4, and 

 m = 5. 



3. DERIVATIONS FROM THE RHOMBOHEDRON. 

 . 108. DERIVATION OF HOMOGENEOUS FORMS. 



From every rhombohedron, another form of the 

 same kind, but more obtuse, may be derived. The 

 derived rhombohedron is in a transverse position to- 

 wards the fundamental form. 



The first method, . 81., is applied here without any 

 further preparation ; and it is evident that the form thus 



