17S 
and Mineralogy. 
pyramid^ o?' can be derived from any of' these figures. And 
since the rhomboid, the four-sided square-based pyramid, and 
the four-sided oblique-based pyramid, are forms which cannot 
by any means be derived from each other ; the Jour groups 
of simple forms as well as their combinations, must each be al- 
together distinct from the rest ; and hence arises a correct and 
natural division of all possible crystallizations, which promises 
to be of great utility in such pursuits. 
57. Fundamental forms and systems of Crystallisations . — AV e 
call every simple form, from which other simple forms are de- 
rived, a fundamental form ; and the class of figures derived 
from that fundamental form, a system of crystallisations. Hence^ 
in the mineral kingdom, there ai'e four fundamental forms, and 
four systems of crystallisations. 
58. Their Denominations . — Those systems of crystallisations 
might acquire their denominations from the fundamental forms 
on which they are grounded. Upon that principle, they would be 
named the rhomboidal^ the quadrato-pyramidal, the rhomboid- 
pyramidal, and the hexahedral. It is more convenient, how- 
ever, as well as more proper, to alter the denominations of the 
^ last three, and to call the first of them pyramidal, the second 
prismatic, because it contains so great a multitude of those fi- 
gures, and the third tessular. 
59. Constant and Variable Dimensions of the Fundamental 
Forms. Series of Crystallisations . — Three of our fundamental 
forms are indeterminate in their dimensions; the fourth, 
the hexahedron, is constant in its dimensions. The dimen^- 
sions of all derived forms depend upon those of the fun- 
damental forms ; the variations of which they follow tu their 
limits, in the rhomboidal and pyramidal systems ; and in 
the prismatic system, to the rectangular four-sided prism, 
which remains always the same, how different soever the di- 
mensions of the fundamental forms may become. In any of 
these three systems, if the dimensions of the fundamental form 
are determined, we obtain from it, by derivation, a train of forms 
having determinate dimensions, among which the general pro- 
portions of the system are observed. Whenever the dimensions 
of the fundamental form are altered, the dimensions of all such 
forms as result from it are altered likewise, without, however. 
