102 TERMINOLOGY. . 103 



already been stated, P o? and P + cc. Since in the latter 

 case it is impossible to argue from the exponent upon the 

 position of the form, it is necessary to express this difference 

 of the two four-sided prisms, by some other contrivance in the 

 designation. The prism in the parallel position receives the 

 sign as it has been employed above, the sign of that in the 

 diagonal position is inclosed in crotchets, and the designa- 

 tion of the series of isosceles four-sided pyramids between 

 its limits is therefore as follows : 



P_...P + n...{^^ 



Five members of this series have been observed in pyra- 

 midal Garnet, four of them being consecutive, in the same 

 species also the limits on both sides of the series. Four 

 consecutive members are known in pyramidal Copper- 

 pyrites, three in pyramidal Lead-baryte, pyramidal Tin- 

 ore, pyramidal Titanium-ore. The limits of the series 

 occur still more frequently, even in those species, which 

 exhibit fewer members of finite dimensions. 



. 103. DERIVATION OF SCALENE EIGHT-SIDED 

 PYRAMIDS. 



From every member of the series . 101., seve- 

 ral scalene eight-sided pyramids may be derived. 



This derivation is effected according to the second method 

 (. 81.), and it is applied after a preparation of the form, as 

 described in . 92. 



The faces of the isosceles four-sided pyramids being iso- 

 sceles triangles, the figures BAC'A', C'AB'A", &c., Fig. 40., 

 will be rhombs, and the points A', A", &c., X', X", &c. will 

 be situated in the angles of two squares, whose planes, like 

 those of the rectangular figures, . 92., are perpendicular to 

 the axis in the terminal points A and X. These squares 

 A'A"A'"A"" and X'X"X'"X"" are equal and parallel to 

 the square circumscribed about the base BCB'C'. 



Draw now from the points A', A", &c. towards the upper, 

 from the points X', X", &c. towards the lower terminal 



