258 A new system of Crystallographic Symbols. 
3.2 
Pe Still if the first example should be written 2/4 no mistake 
could be made in the situation of the plane. The dash below signi- 
fies that the intermediary is supposed to incline on P’, The nume- 
rator will of course express the rate of decrement along its edges, 
and if the edge é, whose rate of decrement is 4, be placed before the 
observer, 3 applies to the left edge, edge é, and 2 to the right, edge e. 
In the octohedra, the denominator of the index for intermediary 
planes, will consist of two figures, thus — unless the plane in- 
clines from an edge to its opposite, when an equal portion of two op- 
posite edges is cut off, and consequently the situation of the plane 
will be accurately indicated, by expressing merely the ratio of the 
n.m 
parts cut off from the two other edges. Thus wo instead of wn. 
Such are the principles of the proposed plan. An application of 
them will be found in the plate. Some particular observations re- 
specting the figures, and the arrangement of the symbols in a de- 
scription, will be made after offering a word or two concerning the 
advantages of the method. : 
A remark has already been made with regard to its conciseness. 
A few examples from Brooke’s Familiar Introduction to Crystallo- 
graphy, with their proposed substitutes, will exhibit the comparative 
merits of the two systems, in this particular. Brooke’s system may 
be taken as a specimen of all, as far as conciseness is concerned. 
The expressions that follow, are each for a single class of planes, as 
given in his work. : 
Brooke’s. : Proposed substitutes. 
Classa. ' A! a 
3.2 
Cube “ d. (B3 B’”’2 B’/1: BI B’’2 B’3) et 
. P 
«i, (B/qBp B’s) (B’qB’p Br) (Br B’pBq) = 
2 
Class a. 'A' a 
Right 1 . 
Pa ry. “ f. (Bp Dq D’q B’r) aer 
q 
“ d. (Bp B’q b’r bs : Bp B’r b’q br) ers 
Class b. PAP P 
Rhom- P : 
“ P-9 
ea d. (B’p Bg B’r : Bp B’q B’r) er 
ace © (D’p b’r Dq : D’q b’’r Dp) ae. 
