432 Mr. Wuewe tt on the Selection of a Notation 
2. This principal series 
R-—2, RAR SRYS INR Pa 
and, P=2, .PiALA\P; 25 4,-P $2. 
in another system, aré, by Mohs, indicated by the same notation, 
though they are derived in different ways. In the first series 
the axis is doubled, and the base turned through 180°. In the 
second, or oblong-pyramidal system, the axis is doubled simply. 
In the square-pyramidal system, the base is turned through 45°, 
and the axis increased in the ratio 1: V2. 
The principle on’ which these series are constructed by Mohs 
is, that each member of the principal series shall truncate the 
preceding member. But in the oblong-pyramidal system this 
analogy is violated by omitting the alternate members. 
3. The subordinate series, cr forms whose axes do not agree 
with terms in the principal series, are represented thus, mR+n, 
which is used to indicate that the axis is m times that of the form 
Rin. It is manifest that since the m thus refers to the whole 
Rin, the symbol ought to be m.R+n, or rather, as has been 
said, mR,, or m.,R. But, even with this alteration, it would 
follow that m and n, indicating operations of the same kind, 
viz. an alteration of the axis, are different in their mode of 
writing, and in their effect in calculation; m indicating an in- 
crease of the axis in the ratio 1: m; while » indicates an 
increase in the ratio 1 : 2". 
It is a principle to be adopted in notation, that symbols, 
which are identical in their meaning, should appear to be so 
by the application of the rules of algebraical operation; thus, 
2.2R and 2°.R are the same in our notation. But, in Mohs’ 
notation, we have expressions 2°R+1 and R+3, which are 
identical without the identity appearing in the form of the ex- 
pression. Vice versd, we have, in the same rhombohedral system, 
