to designate the Planes of Crystals. 437 
deficient in simplicity and symmetry; but this will be considered 
hereafter. 
Removing then these objections; placing the indices in the 
simplest manner, namely, before and after the letter; altering 
the first index so that the same Jaw shall obtain for principal 
and subordinate series of forms; indicating each of the four 
systems of crystallization by a distinct letter, and pursuing 
this in all the derived forms; we have the above system of 
notation. 
13. We shall notice some of the properties which appear to 
recommend the preceding system of notation, by their sim- 
plicity and . uniformity. 
The fundamental forms are four. These are in our method 
designated by the successive letters O, P, Q, R, which appear 
in each of the derivatives of these respective systems, and thus 
indicate to which class each derived form belongs. These may 
be called fundamental letters. 
Every derivative is represented by the letter designating the 
fundamental form, attended by two indices, or numbers, one of 
which is always written before and one after the letter. 
In those cases in which we have only one number or index, 
as mP, 2R, Q3, the other index is 1, and may be so written, if 
convenient, for the sake of analogy. Thus, 
0O is 001, Q is 1Q1, &e. 
The index which is written before the fundamental letter al- 
ways. designates the same law of derivation in all the systems; 
namely, the derivation of one pyramid from another, by changing 
the axis in the ratio of the index. 
The index which is written after the fundamental letter also 
designates a law of derivation, which is the same in all the 
systems. 
