332 
SECOND REPORT— 1832 . 
derived all forms from the octahedron; the axis being, in the 
regular octahedron 720, and in the other cases greater or less. 
Particular questions of crystallometry (as the mathematical 
part of crystallography has been termed by some writers,) have 
been examined by various persons. Mr. Haidinger in the 
Edinburgh Journal of Science for 1824, gave an excellent series 
of papers on twin crystals ; in which he pointed out the various 
laws of combination, and analysed the resulting forms, in each 
of the systems of crystallization, and in the most important 
species. The general principle which governs these various 
combinations is, that the two parts of the twin crystal are such 
that one would come into the position of the other, by making 
a half-revolution round a certain axis; and this axis is always a 
real line in the series of crystalline forms belonging to the spe¬ 
cies which presents these phasnomena. This general law in 
particular cases gives rise to occurrences as curious and as per¬ 
plexing to the mineralogist as double and monstrous flowers 
are to the botanist. These are now for the most part under¬ 
stood. 
One of the most common and yet most curious of these cases, 
is that of the interposed films in calc spar. These films, which 
were early noticed as giving rise to remarkable optical proper¬ 
ties, were shown by Sir David Brewster to consist of crystalline 
plates of a thickness from T o o'o^ 1 an i nc ^ upwards, in a posi¬ 
tion transverse to that of the crystal. He proved this by an 
analysis of the optical properties, and also synthetically by imi¬ 
tating those properties by means of crystalline plates purposely 
interposed. 
A question has been raised whether the oblique prism and 
the forms referable to it should be considered as a peculiar sy¬ 
stem, or as a right prism with only one half the number of sides 
extant in one case (hemihedral), and one fourth in the other 
(tetartohedral). Thus the twin-crystallization of pyroxene and 
of wolfram appears to indicate that though they appear as ob¬ 
lique prisms, they have rectangular axes. Yet the more gene¬ 
ral opinion and evidence seem to be in favour of the existence 
of a monoklinohedral or hemiprismatic system. And thus 
wolfram may be an oblique prism of an angle of 90° 1', or 
90° O' V 1 . Naumann expresses nearly the same thing by saying 
that it is qualitatively monoklinohedral, quantitatively rhombic. 
The question must be decided by determining which mode of 
considering such crystals gives simple numbers and relations for 
the individual forms and twin crystals which really occur. 
The part of Hauy’s views w r bich most caught the popular 
attention w as the supposed exhibition of the real structure of 
crystals as built up of molecules of known shape, the crystalline 
