80 TERMINOLOGY. . 92. 



are not homologous with each other ; and the form conse- 

 quently is not a simple one. 



It is the intermediate or auxiliary form, mentioned in 

 .81. This compound form can be resolved, or the simple 

 forms, contained in it, can be extracted, as follows : Produce 

 first the lines C'S, and CS", to their intersection in OB ; 

 C'S' and CS'" to their intersection in 113', and draw OB& 

 and OB'a : MC', C'BOB', &c. will be faces, BCB'C' the 

 base of the pyramid aBCB'C% which is one of those 

 sought for. On the other hand, produce the lines BS" and 

 B'S"' to their intersection in C ; BS and B'S' to their intersec- 

 tion in C', and draw CSJ and C'SL : BEC', C'SB', &c. will 

 be faces, BC'B'C the base of aBC'B'C, &c. which is the 

 other pyramid contained in the compound form. The 

 transverse sections of this pair of derived pyramids are 

 dissimilar, or differ from each other, as well as from that of 

 the fundamental form. 



The former of these two pyramids has the same short 

 diagonal CC', the latter the same long diagonal BB', as the 

 fundamental form. The latter is therefore said to apper- 

 tain or to refer to the long diagonal, while the other is said 

 to appertain or to refer to the short diagonal of the funda- 

 mental form. 



The axis 2l, common to these pyramids, may be con- 

 sidered as being = m. AX, a product of the axis AX of 

 the fundamental form, and a certain number m, which is 

 called the Number of Derivation. This number must be 

 positive, and greater than 1, either whole or fractionary. 

 The values of this number most commonly, though not 

 exclusively, occurring in nature, are 3, 4, and 5. The crys- 

 tallographic signs of the pyramids thus obtained, are com- 

 posed of the sign of that fundamental or derived member 

 of the series (. 90.), upon which they depend, which is in- 

 cluded in a parenthesis, and of the number of derivation m, 

 added to it in the form of an exponent. The signs o and -, 

 placed above the letter referring to the fundamental form, 

 denote the diagonal to which the derived pyramids belong. 

 The first indicates the long, the second the short diagonal 

 of the fundamental form. Thus, 



