CRYSTALLOGRAPHY. 



In the preceding fymboU, each letter, fuch as on G * or 

 ^ G, can only be applied to a fingle edge fituated to the 

 right or left, as the letter is itfelf; but ^ G" applies indif- 

 ferently to the one edge or the other : hence it is needlefs to 

 repeat the letter. 



If we take Plate VI. fg. 77. as another example, and fup- 

 pofe^^. 70. to reprefent its primitive form, we fhall have 

 for the fymbol of the variety of cryftal here reprelented, 



'G'M B B E E P 



M r J- z u P. 



In this fymbol, ' G ' indicates two diftinft faces formfed on 



each fide of each edge G, but it is not neceflary to place 



two letters under that fymbol, becaufe all the faces fituated 



in the fame manner being diftinguifhed by the fame letter 



in the figure; it is fufficient to point out that the fymbol 



^ G ' applies to the faces marked with the letter 0, and this 



requires only to write the letter under the fymbol. 



From the fame principles it follows, that the rhomboidal 



dodecahedron derived from the cube, Jig. 74. is exprcffed 



I 



by the fymbol B B. The oftahedron derived from the 



1 



I 



cube is thus exprefled A ' A '. 



The rhomboid, fuppofing it placed in the moft natural 

 afpeft, fo that the two folid angles, compofed of three 

 fimilar plane angles, are in the fame vertical line, has, pro- 

 perly fpeaking, no bafe, but merely fummits, which are the 

 extremities of its axis. Its angles and edges are marked as 

 in Plate VI. fg. 78. 



If all the lateral angles were indicated by letters, thofe 

 that are neareft the fummit A would have the letter E, and 

 thofe which are neareft the inferior fummit the letter e. 

 As the rhomboid has fix faces equal and fimilar, it is only 

 neceflary to confider the decrements relative to one of thefe 

 faces ; as, for example, that marked P, Jig. 78, becaufe all 

 the others are mere repetitions of this. The decrements 

 which fet out from the fuperior angle A, or the fuperior 

 edge B, will have thf figure indicating the number of 

 ranges placed below A and B. Thofe which fet out from 

 the lateral angles E, will have their figures fituated at the 

 fide and towards the top of the letter. Thofe decrements 

 which fet out from the inferior angle e, or the inferior edge 

 D, will have the figure placed above the letter <? or D. 



Suppofe, for example, that ^g. 79. reprefents the variety 

 of calcareous fpar, called analogic by Haiiy, its fymbol 



3 2 



would be , , the interpretation of which will be 



'^ >■ g 

 eafy. What has been faid of the rhomboid may be applied 

 to the other primitive forms, of which we (hall give exam- 

 ples i^g. 80. reprefents the oftahedron with fcalene triangles ; 

 Jig. 82. the regular oftahedron. In placing the figures that 

 accompany the letters in the fymbols in ^g. 80, the figure 

 denoting the decrement is placed below the letter A or B, 

 to reprefent decrements fetting out from the angle A, or 

 the edge B. The figure is placed above for thofe which fet 

 out from the edge D, and at the fide for thofe which fet out 

 from the angle E. 



If we want to denote a decrement by one range upon all 



the angles of the regular oftahedron, Jig. 82, we have only 

 1 



to write A ' A ' . To indicate a decrement by one range 



on all the edges we write B B. The firft of thefe decre- 



I 

 ments produces a cube, the fecond a rhomboidal dodecahe- 

 dron. In feme mineral fpecies, as in the nitrate of potafh, 

 the primitive octahedron, which is compofed of eight ifof- 



z 



celes triangles, fimilar four and four to each, ought to have 

 the pofition reprelented as in ^^.83, that the fecondary 

 cryftal may have the moft natural attitude. The edges 

 which join the two pyramids ought to have two of them a 

 vertical direftion, as F, F ; and two an horizontal direftion, as 

 B. By compmugjg. 83. with^^-. 84, in which the letters 

 are placed as if all the edges and angles had different func- 

 tions, it will be eafy to conceive the arrangement of the 

 letters adopted in Jig. 83 ; for in the prefcnt cafe we have 

 E=A, D = B, G = F. 



The tetrahedron being always regular when it bacomes 

 a primitive form, it will be exprefled as in Jig. 85, and the 

 decrements marked as in the oftahedron. 



In the regular fix-fided prifm, fig. 86, the figures are 

 written precifely in the manner already defcribed for the 

 four-fided prifm. But it happens fometimes, that three of 

 the folid angles taken alternately are replaced by faces, 

 whilft the intermediate angles remain untouched. In that 

 cafe, the prifm is diftinguifhed as in fig. 87. In the rhom- 

 boidal dodecahedron, fig. 88, each folid angle compofed of 

 three planes may be alTimilated to a fummit of the obtufe 

 rhomboid : hence it is only neceflary to give letters to one 

 face, as may be feen in the^^. A A, E E, B B, P. .Where 

 the parts of cryftals oppofite to thofe which undergo certain 

 decrements remain untouched, it is eafy to mark this pecu- 

 liarity by zeros. This cafe belongs chiefly to the tourma- 

 line. One variety of the tom-maline is reprefenled ^g. 90, 

 and the primitive form ^g. 89. The prifm, which is nine- 

 fided, has fix of its faces, namely s s, produced by tlie fub- 

 traftion of one range upon the edges D D,Jig. 89, and the 

 three others, as /, by the fubtraftion of two ranges only on 

 three angles e. The inferior fummit has fimply three faces 

 parallel to thofe of the nucleus ; while on the fuperior fummit 

 the three edges ^,Jig. 89, are replaced each by a facet n nrt, 

 ^g. 90, in confequence of a decrement which has not reached 

 its limit. This cryftal is reprefentcd by the following 

 fymbol : 



D 



1 .0 



E P B ^ 



P n 



E b indicate, the one that the angles E, Jig. 89, oppofate 



1 "o 



to e, undergo no decrement ; the other, that the edges 

 parallel to B remain alfo untouched. If thefe edges under- 

 went a different law of decrement, for inftance, that which 



produced a fubtraftion by two ranges, the fymbol would be, 



1 2 2.0 

 D e E P B ^ : hence it may be underilood, that the 



decrements reprefented by a capital letter, accompanied with 

 a figure, do not always include fimilar decrements repre- 

 fented by a fmall letter of the fame name. Thus B does 



not implicitly imply b, or vice "verfd ; it is only when the 



fecond letter is not introduced into the fymbol with a dif- 

 ferent figure, or a 7ero, that we imply that the fame decre- 

 ments take place on the analogous fides or angles. 

 • 32.0 

 In the fymbol D f E P B i, by B is implied a 



decrement by one range, which takes place only on the 

 edges contiguous to the fuperior fummit A, Jig. 89 : b in- 



dicates a decrement by two ranges, which only takes place 

 on the edges contiguous to the inferior fummit. The quan- 



2 3 



titles e and E indicate two ranges on the angles e only, 

 and that' no decrement whatever takes place upon the oppo- 

 fite angles E. 



The 



