. 107. OF THE CONNEXION OF FORMS. 107 



Examples of (P 4- os) 3 we have in pyramidal Garnet, in 

 both positions ; also in pyramidal Copper-pyrites, pyra- 

 midal Tin-ore, &c. ; of (P + co) 5 in pyramidal Lead-baryte, 

 and pyramidal Tin-ore. 



. 107. SUBORDINATE SERIES. 



There are several Subordinate Series of isosceles 

 four-sided pyramids, belonging to that in . 103., 

 which, in reference to these, is termed the Princi- 

 pal Series. 



The derivation of the members of these subordinate se- 

 ries is exactly the same as that employed for the scalene 

 four-sided pyramids, . 96. ; only being here applied to 

 members of the series of isosceles four-sided pyramids, the 

 result will be the required subordinate series of isosceles 

 pyramids. The co-efficient thus obtained is likewise 



= m ; and the subordinate series themselves proceed 



according to the law of the principal one, and are bounded 

 by the same limits. 



The same members of the subordinate series may also be 

 obtained by laying tangent planes on the homologous termi- 

 nal edges of the scalene eight-sided pyramids, &c. The latter 

 process would be the same as that employed in . 116., for 

 the derivation of subordinate series of rhombohedrons from 

 the principal one. The results of this and of the preceding 

 process are identical. For if the tangent plane be laid on 

 the acute edges of the scalene eight-sided pyramid, the co- 

 rn 4- 1 

 efficient obtained will be j ; if it be laid on its obtuse 



edges, the co-efficient will be m . By substituting seve- 



v 2 



ral values instead of m, for instance, those which are most 

 commonly found in nature, we obtain members belonging to 

 the same subordinate series. It is therefore sufficient to 

 assume one of these terms as the general algebraic expres- 



