^6-2 On Cnjstallo^rnpliy. 



For ihe straight prioiii with square bases, that of fig. 57, 

 PI. VJI. 



Fina'lv, for the cube, that of fig. 5S. Here \vp have only 

 flesigualed the superior base by letters, because we may 

 a;M">lv to t-he one any of the other faces, which takes place 

 wiih respect to that base. 



Wc sliall follo'v, with respect to all these chfTerent pri- 

 initive forms, a method of cyphering analogous with that 

 which we have adopted for the oblique-angled parallelo- 

 gram of fiii'. 48, by dispensing with a repciition of the let- 

 ters of the same word cyphered in the same manner. 



An example will show this method. Fig. 59. represents 

 the most common varietv of the cvmophane, the nucleus 

 of which is a rectangled parallelopipedon as wc see it in fig. 

 55, The sign of the secondary crystal will be M T -G G^ 



1 , , M 'I' J 



B A"-A. I have named ibis variety onimlar cymophane. 



That we may better seize the course vi'hich has led us t(> 

 the foresioing expression, we shall indicate all the angles by 

 as many particular letters, as if the parallelopipedon wa^ 

 an oblique angle. See fig. 60. The sign will becon)e MT 



*GH'BFE-''0. But on comparing fig. 60. with fig. 55. 

 we find that H = G, F=B, = A, &c. ^By thus substitut- 

 ing, instead of the first letters, their values, we shall have 



MT ^GG'- BB A''A, which returns to the expression 



indicated above, suppressing the useless repetition of B. 



It results from the above, that we must avoid confound- 

 ing, for instance "^GG^ with G^ 'G. The first sign indi- 

 cates decrements which take place on the face T (lig. 55) 

 and upon that which is opposite to it, going irom the 

 ridges G towards those corresponding with then) behind 

 the parallelopipedon ; the second designates decrements 

 which take place on the face M going to the mectine: of 

 both. If the two decrements took place simultaneously, 

 their representative sign would be -G-. 



In the foregoing signs, everv letter, such as "GorG-, can 

 only be applied to a single ridge, situated like this letter it- 

 self, to the ri'-.hlor the left. But 'G~ is applied indifferently 

 to both ridges ; it is therefore of no use to repeat this letter. 



We shall give a new example drawn from the distich to- 

 paz (fig. 61). If we suppose that fig. 5i3. represents the 

 primitive form, which is a straight prism with rhombic 

 bases, we shall have for the •■ign of the varietv in qMCstioii 



5G' MB BEE P. 



m tA r I -i u r 



