242 ON THE USE OF SYMBOLS. 



2. Those which are partially modified, or on which 



the same modification does not occur on all 

 the similar edges or angles ; as in modification 

 g, h, i, A:, of the cube. 



These may be termed defective modifications, 

 and they may be again subdivided into two 

 portions. 



a. Those in which an edge or angle is replaced 



by only half the number of planes which the 

 law of symmetry would require. 



b. Those in which only one of two similar edges 



or angles is modified, while the other remains 

 entire. 



3. Those in which two or more similar edges or 



angles are affected by different laws of decrement. 

 And the symbols, to be perfect, ought to represent 

 each of these divisions clearly and perspicuously. 



In the table subjoined to this section, which will 

 point out the relation of the theory of decrements to 

 the different classes of modifications, the various 

 modes of adopting the symbols to particular cases will 

 be fully explained. Whence it will not be necessary 

 here to give more than an outline of the general 

 principle which will regulate their application. 



To represent the secondary forms belonging to the 

 first of these divisions, it may not appear strictly 

 necessary to do more than indicate the character of a 

 single plane belonging to any set of similar planes 

 occurring upon the same crystal ; but it may tend to 

 prevent ambiguity if we construct our symbol so as 

 to indicate that the secondary planes occur sym- 

 metrically on certain edges or angles of the crystal. 



We may here remark, that the sets of planes which, 

 in the tables of modifications, replace the solid angles 



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