and Mineralogy. 165 
dary pyramid ; and the transverse section of a ternary when to 
a ternary pyramid. The rhomboid, with its axis infinitely 
great, that is to say, the regular six-sided prism constituting the 
limit of the rhomboidal series, has thus dependent on it three 
scalene six-sided pyramids, also with axes infinitely great, of 
which one is a primary, the next a secondary, the last a ter- 
nary; and which, therefore, assume the appearance of irregular 
twelve-sided prisms, each dependent on its appropriate trans- 
verse section. These prisms are the limits of the scalene six- 
sided pyramids. It is observable that the regular six-sided 
prisms, which form the limits of the isosceles pyramids (29.), have 
no twelve- sided prisms of this sort : hence these prisms appear 
in combinations, only in one and the same position. 
40. Examples of' the Limits. — These prisms which, like all 
forms having one of their dimensions unlimited, can only appear 
in combinations, are exemplified by nature, in tourmaline., in 
emerald', some of their faces are found even in calcareous- 
spar. In tourmaline, the prism, which depends on the secon- 
dary pyramid, is designated by h, the general expression for 
these prisms is ( p )% where m as above (35.), signifies the 
characters ', ", 
41. Mathematical basis cf the symmetry of Combinations. — On 
glancing back over the ground we have passed, one is astonished at 
the multitude and variety of forms which, with an extremely small 
expence of mathematics, may be deduced from a given rhomboid, 
and submitted to very simple laws ; yet the whole compass of 
this subject is still far from exhausted, and many remarkable 
phenomena relating to it have been omitted for want of room 
(37.) N,ature combines these forms in crystalline figures. 
From their dependance upon each other, and from the propor- 
tions in which they mutually stand, we may comprehend 
that all such combinations must possess the highest degree of 
regularity admitted by their simple figures, and therfore be 
completely symmetrical (3.) At the present stage of the in- 
quiry, nothing is better calculated for giving a palpable repre- 
sentation of this symmetry, than to study the crystallizations of 
calcareous-spar; and nothing for exciting a greater interest 
about that study, than to consider how simple the proportions 
are on which nature has founded that symmetry. 
