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various important subjects in Mineralogy. 
of the Natural History of the mineral kingdom. These ideas are 
now so generally known, that we may dispense with treating 
them more at large in this place. We shall only observe, that 
they depend upon the equality of the relation between forms of 
the same kind, which produce series, and therefore upon these 
series themselves ; and that it is possible to recognise and to de- 
monstrate the internal connection between these forms, only upon 
the supposition of the existence of such series. It is impossible 
to do without these series in any system of crystallography, cal- 
culated to supply the wants of Natural History ; and this in par- 
ticular becomes evident, from the circumstance, that even the 
idea of the natural-historical species depends entirely upon the 
existence of these series. 
The simple forms, capable of appearing in the individuals of 
one and the same species, or which may produce combinations 
with one another, are found by a particular process, called De- 
rivation. This derivation, however, does not yield a number 
of forms undetermined in regard to the relative dimensions, one 
form being given ; but by means of it we obtain such as are 
perfectly determined in respect to these relations. From one 
rhombohedron there will not result every other form of the same 
kind, but only those which are capable from their dimensions to 
form combinations, — or, which is the same thing, to appear in 
the individuals of one and the same natural-historical species. 
Crystallography, therefore, is not merely to be understood as the 
science that ascertains the relative position of the planes which 
form the limits of crystals ; it must also be calculated to bring 
into connection the regular forms of minerals, together with their 
other natural-historical properties ; and this is effected by means 
of the series arising from derivation, and the idea of the spe- 
cies dependent upon their existence. Their derivation at least 
should be the foundation of the method of providing each of 
the simple forms obtained with crystallographic signs, — a matter 
of great advantage in Natural History, for avoiding the long and 
tedious descriptions of minerals, which do not elucidate the sub- 
ject, nor prepare us for applying calculations. The crystallo- 
graphic designation should, on that account, not only denote the 
kind and relations of the simple forms, but also their origin, in 
representing the series of forms capable of combining with each 
