to designate the Planes of Crystals. 433 
(P+n)', which is not the same form as P +n, to which the 
symbol is algebraically equal. It is this principle of identity of 
meaning, corresponding with identity of numerical value, which 
mainly assists us in employing symbols as instruments of rea- 
soning. The algebraical reductions which we make, represent. 
then different ways of considering the same form. 
4. Forms derived from R+ 2 in a certain manner (namely, 
by the law of scalene derivatives,) are, by Mohs, represented by 
(R+n), (Pin), &e. 
It may be observed, first, that there is no sufficient reason 
in this case for altering the fundamental letter R into P. Mohs 
does this because the Rhombohedron becomes a six-sided Py- 
ramid, which change is marked by adopting the new initial 
letter: but it would have been more important to mark that 
this derivation was from the rhombohedron; and to leave it to 
be recollected that its form was a pyramid. The expressions 
would then be 
(Rin), (R+n), &e. 
5. But, in this notation, the exponents 2, 3, are used merely 
as indices: and there is no propriety in writing them in such 
a manner as to represent the powers of the symbols R+n. To 
refer again to the principle in the third observation, this would 
have been proper, if, by this means, reduction had given us 
different but identical symbols: if, for instance, (2 R)’ had been 
the same as 2°(R)*; but this is not at all the case. These in- 
dices, therefore, ought to be written where they have no alge- 
braical meaning, and, therefore, cannot give wrong coincidences. 
If we write both these numbers and those mentioned in Obser- 
vation 1. as indices before and after the foot of the letter, we 
shall have for 
3K 2 
