A new system of Crystallographic Symbols. 257 
ted between P’, a and e is lettered ae,, An intermediary may in- 
cline from an edge toits opposite. No dash below is then required. 
Each plane being lettered, there yet remains to be added, nume- 
rals expressive of the rate of decrement* that may be considered to 
have taken place in the formation of the new plane. This may be 
done by attaching in the form ofan algebraical index a fraction whose 
numerator consists of figures indicative of the rate of decrement 
along the edges of the plane on which the secondary inclines, and 
a denominator expressing the decrement in the direction of the other 
edge or edges. If a secondary plane is on an edge, decrement has 
taken place on but one edge of the plane on which it inclines. Con- 
sequently the numerator will consist of but one figure. ‘Thus we 
say e?. ‘The denominator of the index, and the index itself may be 
dropped when a unit. Hence we write e? instead of ef, e instead 
of e'. If the secondary is on an angle, an equal decrement has ta- 
ken place on each of the edges of the plane on which the secondary 
inclines, only that on one, need be expressed, the other being im- 
plied in the letter a; thus a® instead of a**. For intermediary 
planes the decrement in each direction must be stated, it differing in 
Ag) 18) 
each; as for example, 23, @’ (the denominator 1, is here to be 
understood.) ‘The right hand figure in the numerator must be that 
which expresses the decrement along the edge to the right, suppos- 
ing the edge, the rate of decrement in whose direction, forms the de- 
nominator, to be directly before the observer. It is not very im- 
portant on which plane we suppose an intermediary to incline. But 
in general, it is best to select the one, in the direction of whose edges, 
the greatest decrement has taken place. Of these two edges, that 
on which the decrementis the greatest, should give its letter to form 
the compound symbol of the intermediary. ‘Thus if the decrement 
(see fig. 1) is the least in the direction qj e, supposing the plane on 
angle a, it inclines on P, and if the greatest decrement is in the di- 
4.3 
rection of e, the symbol will be (supposing an index of 2, in which 
4,3 
2 expresses the rate of decrement along e, and 4 along é,) e'2. If 
4 expresses the rate of decrement along é, the symbol will become 
* It must not be understood that it is supposed that a decrement really takes 
place in the formation of secondary planes. The word decrement may be consid- 
ered to refer rather to the rate of decrease according to which the secondary planes 
might be formed on the primitive solids. 
Vou. XXVITL—No. 2. 33 
