ON THE USE OF SYMBOLS. 249 



crystals, we have supposed those forms to have been 

 strictly symmetrical, or to have resulted from similar 

 modifications on all the similar edges or angles of the 

 primary form. 



It remains now to point out the methods of dis- 

 tinguishing by appropriate symbols, those secondary 

 forms in which similar planes do not occur on all the 

 similar primary edges and angles. 



1st. Let us consider the case where an angle or 

 edge is only partially modified. See cube, fig. 303, 

 p. 243. 



In class i of the modifications of the cube, the solid 

 angles are replaced by only three planes, which are 

 found to correspond with the alternate planes of 

 class d. 



But the symbol representing class c?, is such as to 

 imply that there are three pairs of planes on each 

 solid angle. We should therefore construct the sym- 

 bol which is to represent class ?", so as to indicate the 

 existence of only three single planes on each solid 

 angle ; and it should denote the relative positions of 

 the analagous planes on the solid angles at A', and 

 at A. 



The three planes at A' may be represented by the 

 following symbol, in which q is supposed to be 

 greater than r ; 



(B'q Bp B"r)(B"q B'p Br)(B'r B"p Bq). 



And the three planes at A by the following ; 



(Bq B"'p B'r)(B'"q B'p Br)(B'q Bp B'"r). 



If these symbols be attentively regarded, they will 

 be observed to express the relative positions of the 

 corresponding planes on each of the solid angles. 

 And by substituting in them b and b' for B and B', 

 the planes on the lower solid angles might also be 

 represented, and thus the entire figure would be 

 implied. 



2 i 



