Dr. Brewster on the laws of polarisation , &c. 259 
coincident with some prominent line, either in the primitive or 
secondary forms.* 
The same coincidence ought therefore to be expected in the 
case of the cubical, octohedral, and rhomboido-dodecahedral 
crystals ; and it is a singular fact, that the cube, the octo- 
hedron, and the rhomboidal dodecahedron, are the only regular 
geometrical solids in crystallography, in which neither more 
nor less than three equal rectangular axes can be placed sym- 
metrically. In the cube, for example, each of three axes is 
perpendicular to the three pair of square surfaces by which 
the solid is contained. In the regular octohedron each of them 
coincides with the line which joins the six solid angles of the 
figure ; and in the rhomboidal dodecahedron, each of the rec- 
tangular axes passes through the six solid angles, each of 
which is contained by four acute angles of the rhomboidal 
planes 
Sect. VI. On the artificial imitation of all the classes of doubly 
refracting crystals by means of plates of glass . 
In the Philosophical Transactions for 1816, I have given 
a full account of the very remarkable phenomena which are 
* Malus seems to have believed that the axis of extraordinary refraction was ne- 
cessarily coincident with some prominent line in the primitive form. We quote the 
following passage in confirmation of our general views, though there can be no 
doubt that the generalisation which it implies is premature. “ Dans le rhomboide, 
l’axe de refraction se confond avec l’axe du crystal ; mais dans les autres formes on 
n’a pas de donnees suffisantes pour le determiner a priori. Cependant le nombre des 
directions entre lesquelles on peut balancer est toujours tres-borne. Dans Poctaedre 
a triangle scalene, par exemple, on est assure d’avance que P axe de refraction est un 
des trois axes rectangulaires de la forme primitive.” Tbiorie de la Double Re- 
fraction, p. 177. 
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