CRYSTALLOGRAPHY. 



D, jjg.6^ we mufl. fuppofe the faces of the cryftals 



7 



reverfed. Hence, d will exprefs a decrement by two 



ranges upon the other bafe p, juft as D exprefles a 

 fimilar decrement on the bafe P. For the fame reafon, c 



3 



will exprefs a decrement by three ranges proceeding from 

 r B, to E O. 



If the fame folid angle, or the fame edge, undergo feveral 

 fucceffive decrements on the fame fide, or different decre- 

 ments which take place on different fides, the letter pointing 

 out the angle or edge is repeated as often as the decrements, 

 varying the figure each time, to make it correfpond with the 



particular decrements denoted. Thus, D, D, will denote 



3 



two decrements upon the edge D, one of two ranges on the 

 bafe P, and another of three ranges upon the face M ; and 

 " H, H *, will denominate two decrements, one by two 

 ranges on the left, the other by four on the right of the 

 edge H. 



Mixed decrements are marked according to the fam.e 

 principles, employing the fractions f , |, which reprefent 

 them ; the numerator referring to decrements in breadth, and 

 the denominator to decrements in height. 



The intermediate decrements are thus defcribed. Let 

 A E, I O, [PlateY.f?. 67.) be the fame face as mfg. 66, 

 but divided into rows or ranges ; let us fuppofe a decrement 

 by one range of double molecules, according to the lines 

 parallel X.o x y ; io that O y meafures the double length of a 

 molecule, and O x that of a fingle molecule. 



This kind of decrement is thus expreffed, (O, D % F ^,) 

 the parenthefis indicates that the decrement is intermediate ; 



O, that it takes place by one range on the folid angle marked 

 by that letter in Jig. 64; D', that there is one length of a 

 molecule taken away along the edge D ; and F -, that two 

 kngths are taken away along the edge F. 



The written language to denote the fymbols, that they 

 may be eafily expreffed when diftated, would be thus: for 



O % ^ O, read, O two on the right, O three on the left; O, O, 



rem", O iirder tivo, O above four. Andthefymbol (O, D ', 

 F ',) read. In a parenthefis, O under one, D one, Y two. 



The order in which thefe letters muft be placed to denote 

 a fecondary cryftal remains to be explained. If the alpha- 

 betical order were adopted, there would refult a degree of 

 confufion in the pifture which the formula prefents. It is 

 more natural to conform to the order that would direft an 

 obferver in the defcription of the cryftal ; that is, to begin 

 with the prifm or middle part, and to Indicate its different 

 faces as they prefent themfelves lucceffively to the eye ; 

 then to pafs to the faces of the fummit or the pyramid. 



Suppofe [PlaleVl.flg. 68.) that variety of felfpar which 

 Haiiy calls bibinary, -viz. where there are two decrements 

 by two rows each. The primitive form is reprefented 

 Jigt. 64 and 66. In this form of the cryftal, the face / 

 refults from a decrement by two ranges on the edge G, 

 Jg. 64, going towards H ; the face M,fg. 68. correfponds 

 with M,fg. 64 ; the face T,Jg. 68, is parallel to T,Jlg. 64; 

 the pentagon x comes by a decrement of two ranges on the 

 angle, correfponding with the angle I, fg. 64. and paraUel 

 to the diagonal A O. As this decrement does not reach 

 its limit, the fummit exhibits a fecond pentagon P, parallel 

 to the bafe P, fg. 64. All this defcription may be exhi- 

 bittd by five letters in fymbolic langi-.age: thas 'G M T 



I 



I P denoting a decrement by two ranges on the edge G, 

 and a decrement by two ranges on the angle I, fg. 64. 



It is cuftomary, in order to prevent any ambiguity, to 

 place under the dififerent letters that compofe the fymbol 

 thofe that correfpond to them in the figure. Thus in the 



bibinary {e\[pzT,fg. 68. 



G MT I P ,, , . , ,. 



/ M T .V P' letters m the Une 



below thofe of the fymbol enable us to compare the fymbol 

 vnth the figure, and thus to decypher the meaning with 

 facility, however complicated it may be. 



Where the primitive form has great fimplicity, as in the 

 cube and rectangular prifm, when the oppofite angles are 

 equal, one letter will denote them both, and when the (fppo- 

 fite edges are equiangular, the fame letter mil denote cither ; 

 for ever)- thing that denotes one of them, takes place alfo in 

 the other. If, for inftancc, we fuppofe _^^. 64. to become 

 more fymmetrical, and that certain folid angles which were 

 before unequal are become equal, they fhould be marked 

 with the fame letter. If, for inftance, the primitive form be 

 a reftangular prifm, which has oblique-angled parallel- 

 ograms for its bafes, one fide of which is longer than the 

 other, fg. 69 ; in this cafe, we have the angle O = A, 

 I = E ; we may fubftitute in each cafe the fecond letter for 

 the firft, as is done fg. 69. 



If we renew the different kinds of parallelograms we 

 fhall find them acquire different degrees of fimplicity, which 

 occafions new equalities in the angles and edges, and new 

 fubftitutions of letters. The oblique prifm with rhomboidal 

 bafes is repreler-tcd ^^. 70. The reftangular prifm with 

 reftangular bafes fg. 71. The rectangular pHfm with 

 rhomboidal faces fg. 72. The reftangular prifm with 

 fquare bales ^^. 73. 



The cube is reprefented fg. 74 ; here only the fuperior 

 bafe is marked, becaufe what takes place with refped to 

 this may be applied indifferently to any of the other faces. 



The fame mode is employed in writing the fymbols for 

 thefe regular forms, only the letters that have the fame name 

 and the ume figure are not repeated. An example will render 

 this method evident. Fig. 75. reprefents the mo ft common 

 variety of the chryfoberj-l, orcymophane,(feeCHRYSOBER\i,) 

 the nucleus of which is a rectangular parallelopiped, fuch as 

 reprefented^. 71. The fymbol of the fecondary cr^llal, 



.„,_ MT'GG'BA^^A t,,- - . 

 fg. IS, will be j^j ^ ^ ; ^ . This vanety is 



called by Haviy annular cymophane. 



To underftand this exprelfion better, let us mark each 

 angle and edge with a particular letter, as vifg. 76. In this 



cafe, the fymbol would become M T '- G H ', B F E^ ^O ; 

 but if we compare jf^. 71. with 76, we fhall fee that H = G, 

 F = B, O = A : hence if we fubftitute inftead of their firil 



1 r 77 



letters their equal values, we get MT'G G* BBA^ '^A, 

 which becomes the fame as the one before given, when the 



ufelefs repetition of B is fuppreffed. 



From the preceding ftatement, it is evident that we muft 

 not confound fuch fymbols as " G G " with C '^ G ; the 

 firft fymbol indicates the decrements which take place on 

 the face T,fg.']\. and on the edge oppofite to it, going 

 from the edges G towards thofe that correfpond with them 

 behind the parallelopiped. The fecond fymbol indicates 

 the decrements which take place upon the face M, and 

 which meet each other in the middle of that face. If thefe 

 two decrements took place fimultancoufly, thefe fymbcls 



would be ' G '• , 



In 



