On Crystallography. 45T 



angles T, E, each of these angles is, relative to crystalhz;\- 

 tion, as it were, indepentleiu of that which corresponds 

 with it diagonally. Fuially, the ridges C and D, B and F, 

 G and H^ (fig. 48) compared wiih each other, are no 

 lonp-er in (he same siination, becanse the two planes which 

 unite npon one do net form between them the same angle 

 witli those which have the other for the hne of jinictiou. 

 It is between these same ridges and those which are dianie- 

 tricallv opposite to them ; for instance, between A I and p .9, 

 (fig. 30) between A E and p u, &.c., tlial there is a perfect 

 equal ilv. 



By this we see why the four polid angles round the upper 

 base, as well as the four edges of this l)asc and the two lon- 

 gitudinal edges v\hich are 'jKCsented in front, are each of 

 them marked with a particular letter. But as the laws eF 

 decrement act with the greatest possible symmetry, at least 

 in general, every tiling which takes place on one of the 

 solfd arigles or of the edges designated, is repeated on the 

 angle or the ed^e diametrically opposite, among those which 

 have remained In vacuo, i^ccording lu this, it uas only 

 necessary to designate the number of solid angles, or of 

 ridges which undergo decrements really distinct, because 

 these decrements contain implicitly those which take place 

 on the angles or the analogous edges. 



We are nevertheless sometimes obliged to indicate also 

 these last angles or these last edges. Then we shall make use 

 of small letters which bear the s^ame names with the capital 

 letters employed ii> fig. 48: for example, p (lig. 50) will be 

 designated by o, spbyc, puhyb, &c. But it will be 

 rarely necessary to make these small letters on the figure ; 

 it will be sulKcient to make them enter into the sign of the 

 crystal, because in imagination we can easily reier each to 

 its proper place. 



To indicate the elTects of decrements by one, two, three, 

 or more ranges, in breadih, wc shall employ the cyphers 

 1, 2, 3, 4, See, in the way to be immediately explained; 

 and in order to indicate the effects of dL^cremiiits by two 

 and three ranges in height, we shall use the fractions 

 i.', ^&c. 



The three letters P, M, 1, will serve to dcsigr.ate either 

 the form of the nucleus without any modification, when 

 4hey will compose of themselves the sign of the crystal, or 

 the faces which would be parallel to those of the nucleus, 

 in the case of the decrements not attaining ihiir limits, and 

 then these leltlers will be combined, m the sign of the 



crystal. 



