CRYSTALLOGRAPHY. 



451 



Tlieflry. 



t'UTE 



ccxxin. 

 Fig. 8, a. 



into the 9ymbol of the crystal, because it is easy to con- 

 ceive the place which every one ought to occupy in 

 the Figure. 



To indicate the effects of decrements by one, two, 

 three, four, or more ranges in breadth, the figures 1 , 

 2, 3, 4, &c. are employed in the way to be immediate- 

 ly explained ; and, to indicate the effects of decre- 

 ments by 2, 3, &c. ranges in height, the fractions L §-, \, 

 &c. are employed. 



Tile three letters P, M, T, serve to distinguish ei- 

 ther the form of the nucleus, without any modifica- 

 tion, when they alone constitute the symbol of the 

 crystal, or the faces parallel to those of the nucleus, in 

 the case where the decrements do not reach their limit; 

 and then these letters are combined in the symbol of 

 the crystal with those which relate to the angles or 

 edges that have undergone decrements. 



Let us suppose at first, for the greater simplicity, that 

 one of the solid angles, such as O, is intercepted by a 

 single additional face. Tire decrement which produces 

 this face may take place either on the base P, or on the 

 face T, which is on the right of the observer ; or on 

 the face M, which is on the left In the first case, the 

 figure marking the decrement is placed above the letter 

 O ; in the second case, the figure is placed like an or- 

 dinary exponent ; in the third case, it is placed on the 

 left side, and somewhat above the letter. 



1 



Thus, O denotes the effect of a decrement by two 

 ranges in breadth, parallel to the diagonal of the base 

 P, which passes through the angle E. O 3 indicates 

 the effect of a decrement by three ranges in breadth, 

 parallel to the diagonal of the face T, which passes 

 through the angle I. 4 indicates the effect of a de- 

 crement by four ranges in breadth, parallel to the dia- 

 gonal of the face M that passes through the angle E. 



When the decrement relates to some one of the three 

 other solid angles I, A, E, the observer is conceived to 

 move round the crystal till he is opposite to that angle, 

 as he is naturally opposite to the angle O in the case 

 which we have been describing ,• or, which comes to 

 the same thing, he is conceived to turn round the crys- 

 tal till the solid angle that he is considering be exactly 

 opposite to him, and it is relative to that position that a 

 decrement is said to tak« place towards the right or to- 

 wards the left. 



For example, if we are speaking of the solid angle A, 

 the sign A 1 will represent the effect of a decrement by 

 two ranges on the surface AE s r (Fig. £).), or upon 

 that which is opposite to T (Fig. 8.) ; and 3 A will re- 

 present the effect of a decrement by three ranges upon 

 the face Alur (Fig. 9.), or upon that which is oppo- 

 site to M (Fig. 8.) 



As to the .decrements on the edges, those which take 

 place towards the boundary BCFD of the base, are ex- 

 pressed by a number placed above or below the letter, 

 according as their effect takes place in going up or go- 

 ing down, supposing them to set out from the edge to 

 which they are referred ; while those which take place 

 •on the longitudinal edges G, H, are indicated by an ex- 

 ponent placed on the right or the left of the letter, ac- 

 cording as they take place in one direction or the other. 



Thus D expresses a decrement by two ranges proceed- 

 ing from D towards C; Ca decrement by three ranges 

 going from C towards D; Da decrement by two 



ranges, descending upon the face M;=Ha decrement 

 by three ranges, proceeding from II towards G ; *G a 

 ■decrement by four ranges, proceeding from G towards 

 the edge opposite to H, &c. 



When it is necessary to denote by a small letter, such Theory, 

 as d, a decrement upon the edge u r (Fig. Q.), oppo- p *"^ 7 

 site to the edge denoted by the capital letter D (Fig 8.), CCXXIII. 

 we must suppose the crystal turned upside down. Hence Fig n, !). 



d will express a decrement by two ranges upon the base 



p, just as D expresses a similar decrement on the base 

 P. For the same reason, c will express a decrement by 



three ranges, proceeding from s p towards EO (Fig. 9.) 

 If the same solid angle, or the same edge, undergo 

 several successive decrements on the same side, or dif- 

 ferent decrements which take place on different sides, 

 in that case, the letter pointing out the angle or edge is 

 repeated as often as the decrements, varying the figure 

 each time, to make it correspond with the particular 



decrements pointed out. Thus D D will denote two 



3 

 decrements upon the edge D, one of two l-anges upon 

 the base P, another of three ranges upon the face M. 

 *H 4 H will denote two decrements, the one by twp 

 ranges, the other by four, on the left of the edge H. 



Mixed decrements are marked according to the same 

 principles, employing the fractions A, A, &c. which re- 

 present them; the numerator referring to the decree- 

 ments in breadth, and the denominator to decrements 

 in height. 



The method of describing the intermediate decre- 

 ments still remains to be explained. This will be best 

 done by an example. Let AEOI (Fig. 10.) be the Fig. s. 19. 

 same face as in Fig. 8. Let us suppose a decrement 

 by one range of double molecules, according to lines 

 parallel to xy, so that Oy measures the double length 

 of a molecule, and O x lines equal to that of a single 

 molecule. This kind of decrement is written in this 



manner, (OD- F z ). The parenthesis lets us know, 

 in the first place, that the decrement is intermediate ; 



O indicates that it takes place by one range upon the 

 angle marked by that lettter, and that it belongs to the 

 base AEOI (Fig. 8.) D 1 F 2 indicate that there is one 

 length of a molecule taken away along the edge D, and 

 two lengths along the edge F. 



It is useful to have a language to denote these sym- 

 bols, so that they may be easily written down when 

 dictated by another person. On that account, we shall 

 mention here the mode followed by Hauy for that pur- 

 pose. The symbols O 2 , s O, are thus read: O t:vo on 



the right, O three on the left, O, O thus, O wider two, 



A 



O above four. Finally, the symbol (O D 1 F 2 ) thus, in 

 a parenthesis, O under one, D one, F txw. 



We must now notice the order in which these letters 

 must be placed, in order to denote a secondary crystal. 

 If the alphabetical order were adopted, there would re- 

 sult a sort of confusion in the picture which the for- 

 mula presents. It is more natural to conform to the 

 order which would direct an observer in the descrip- 

 tion of the crystal ; that is to say, to begin with the 

 prism or the middle part, and to indicate its different 

 faces as they present themselves successively to the eye, 

 then to pass to the faces of the summit or the pyra- 

 mid- 

 Suppose, now, that Fig. 1 1. represents the variety of 

 felspar called bibinnire by Hauy, the primitive form of F 'S- & I 1 ' 

 wluch is seen in Fig. 8. In this variety, the face / 

 (Fig. 11.) results from a decrement by two ranges on 

 the edge G (Fig. 8. ) going towards H. The face M 

 (Fig. 1 1.) corresponds with that which is marked with 

 the same letter in Fig. 8. and which is only concealed 



