78 TERMINOLOGY. . 92. 



of an infinitely small axis. The crystallographic signs for 

 these limits are P 4- co and P oo , and the series itself is 

 thus represented between its limits : 



P OS ... P + 11 ... P + CO. 



The algebraic expressions in the preceding . yield the 

 plane angles of the base of P, which is equal to the trans- 

 verse section of the prism of infinite axis, if n be supposed 

 SB + oo, as follows : 



b 2 c 2 



cos. y = " S. . 



b 2 + c 2 ' 



b 2 



. 



c 2 + b 2 



The value of cos. z = 1, indicates that one face of the 

 pyramid contiguous to the upper apex, and one contiguous 

 to the lower apex, coincide in a single plane parallel to the 

 axis, by which the lateral edge z becomes = 1 80. 



Several members of this series, together with their in- 

 termediate forms and limits, have been observed in nature. 

 Thus, prismatic Topaz, presents three consecutive mem- 

 bers, the intermediate form belonging to the most acute 

 of them, and both the limits of the series. Two consecu- 

 tive members, with their intermediate forms and limits, 

 are known in several species, as in prismatic Lime-haloide, 

 prismatic Lead-baryte, diprismatic Copper-glance, and 

 others. 



. 92. DERIVATION OF SCALENE FOUR-SIDED PYRA- 

 MIDS OF DISSIMILAR TRANSVERSE SECTIONS. 



The members of the series of . 90. serve as a 

 foundation to several other derivations. From every 

 one of them, several Pairs of scalene four-sided Py- 

 ramids may be derived, the bases of which are dissi- 

 milar to that of the fundamental form, and partly 

 also amongst themselves. 



The derivation is effected by the second process (. 81.); 



