REPORT ON MINERALOGY. 335 
of their edges of combination, which are so useful, as we have 
already said. Moreover three coefficients are more than we 
need; for the ratios of one of the three to each of the others 
are all that we have occasion for. Accordingly Mohs uses tivo 
indices only, by which he indicates any plane; and so far his 
method has an advantage. But he has been most peculiarly 
unfortunate in the mode he has selected of combining the in¬ 
dices with his fundamental letter. It is quite inconceivable how 
a mathematician, having to annex the two indices 2 and 3 to 
the letter P, should, without any support whatever from mathe¬ 
matical analogy, choose to connect one index with the letter by 
the sign + so as to convert the symbol into a binomial P -j- 2, 
and then use the other index as the exponent of a power of this 
binomial, as (P+ 2) 3 . The violation of all mathematical signifi¬ 
cance, and the anomalous and useless complexity thus incurred, 
make such a system truly forbidding. Mr. Naumann has been 
more fortunate ; and indeed his notation is indisputably almost 
as simple as it is possible for a crystallometrical notation to be ; 
for two indices being necessary, and all that is necessary, he 
puts one before and one after his fundamental letter, and thus 
obtains a simple and convenient symbol. Moreover, the mode 
in which the laws of derivation are treated in his system is such 
as to bring very well into view the most important relations of 
the forms*: and as he has both published an excellent treatise 
on crystallography, and a compendious system of mineralogy, 
in which all the known forms of individual crystals are exhibited 
in this notation, we may hope that in time this system, or one 
resembling it, will supersede more complex and imperfect ones. 
It may be added that the systems of Weiss and of Naumann 
approach near to each other, and the notation of the one is 
very easily translated into the other. They predominate over 
a great part of Germany, and stamp the language of a great 
number of the best publications on the subject. 
3. Optical Properties. 
Malus examined many mineral substances in the course of 
his inquiries concerning double refraction ; but he does not ap- 
* In comparing, however, the notation of Naumann and of Weiss, it ought to 
he taken into the account, that Naumann’s two indices have often a more com¬ 
plicated appearance than Weiss’s three indices. Thus we may compare Nau- 
3 5 i5 i5 
mann’s symbols—P 3, —Pco,— O— with Weiss’s equivalent sym- 
J 2 2 ’ 7 11 
bols, (3 a, 16, 6c), (5a, 26, oo c), A-, 
