On Crystallography, 465 



In order to indicate, for example, a decrement by three 



3 



ranges on all the edges, we shall take B B ; and in order to 



designate one by two rano;ei on all the angles, we shall take 

 A^A-, as in the ca?e of the regular ociaiiedroii. 

 * A single glance at fig. 70. will be sufficient to give an idea 

 of the designation of the regular hexahedral prism in or- 

 dinary cases ; and as to the manner of placing the cyphers, 

 we shall not detain our readers a moment, because it i? easily 

 deduced from tjiat which we have adopted with respect to 

 quadrangular prisms. 



But it sonK'tmies hap)->ens that three of the solid angles 

 taken alternaielv are replaced by facets, while the interme- 

 diate angles remain untouched. In this case the expres- 

 sion of the prism will be that which we see in fig. 7!» 



In the rhomboidal dodecahedron (fig. 72, Plate VIII.) 

 each solid angle comp'>sed of iliree planes mav be assimi- 

 lated to an obtuse rhomboidal sunnnit ; and thus w" shall 

 confine ourselves to decyphering a single face, as the figure 

 represents. 



Hitherto we have not been in the habit of employing the 

 sign of the dodecahedron with isosceles triangular planes 

 because it is more natural to substitute in its stead, as a 

 primitive form, the rhomboid from which it is derived, and 

 which gives still more simple laws of decrement. 



It remains to make known ihe method of representing a 

 particular circumstance which occurs in some crystals, in 

 which the parts opposite to those which undergo certain 

 laws of decrement remain untouched, or are modified by 

 different laws. This circunjstance particularly applies to 

 tourmalines, and it is then easy to indicate ihe difference by 

 means of zeros. For exaniple, in ine equidifferent loiir- 

 mahne represented in fig. 74., and of winch wc see the 

 rhomboidal nucleus (fig. 73.), the prism which is enncago- 

 iious has six of its panes,' viz. s, s (fi<r. 74.) produced by 

 subtractions of one range on the ridges D, D (fig. 73.) ; and 

 the three otliers, such as /, by subtractions of two rangrs 

 .solely on the three angles e. Moreover, the lower suumiit 

 has simply tliree faces pyrallel to those of the nucleus, 

 while on the upper summit the three ridges B are replaced 

 each by a facet «, « (fi:^. 74.) in virtue of a decrement 

 which does not attain its limit. The followins: is the re- 



1 -i so " 



presentative sign of this form. DeEPBi. The quanlif 



1" . I !• n 



ties ¥., h make known, the one of thenj, that the angles 

 Vol. 34. No. 140. Dec. 1803. Gg E 



