4 Mr Whewell on the use of Notation 



bohedral system, in which it is required to obtain the law of 

 derivation of each of the faces. 



If we had the faces c only, the others being suppressed, and 

 then produced, they would form at the upper extremity a 

 three-sided pyramid. In the same manner, the faces a, d, e 9 re- 

 spectively, would form three-sided pyramids, but transverse to 

 the former, and therefore derived from R/. Let pR, //R', 

 p // R\ p"R\ represent the pyramids. 



The facesyby themselves would form a 6-sided pyramid. 

 In the same manner, the faces b would form a 6-sided pyra- 

 mid. Let qRm 9 q'Rm' represent these pyramids. 



The faces g are manifestly parallel to the axis, and agree 

 with the faces of a rhombohedron, of which the axis is infinite. 

 Hence they are represented by the symbol oo R. 



Therefore we have the symbols corresponding to the faces 

 thus, 



pR 9 //R', fW, pf«B/ 9 oo R, qRm y q'Rm'. 

 c a e d g f b 



and we have to determine p, p* 9 q> m, &c. 



To find p. We may assume one of the rhombohedrons 

 which occur to be the primitive form ; and it will be conve- 

 nient to take for this the one of which the faces are c. Hence 

 pR is R, and p — 1 . 



To find pi. If we had only the faces c and a, (suppressing &,) 

 it is evident that the faces a would truncate the edges of the 

 rhombohedron with faces c. Hence the latter rhombohedron 

 being R, the faces a belong to \ R 7 (A.) Therefore ^R', is 

 J R', andy = \. 



Tofindp // . If we suppose the faces c increased, till they 

 intersect the faces e, * it will be found that the intersections . 

 will be parallel to the inclined diagonal of the rhomb c ; and 

 consequently the faces c will then be bounded by two parallel 

 lines, and will truncate the edges of the rhombohedron, of 

 which the faces are e. Hence c being R, e is 2R' (A.) 

 Therefore j/'R' is 2R' and p"= 2. 



(A.) In combinations of forms pJ\, 2pR', or pR', 2/>R the first trun- 

 cates the edges of the second. 



• In such a case as that of carbonate of lime the faces e may be enlarged 

 by cleavage. 



