CRYSTALLOGRAPHY. 



further application, the affemblage B, jff . 59, will be changed 

 into that of A, Jig. 59, where we have on each fide three 

 laminx of fuperpofition. Thefe different tranfitions, of which 

 vre may continue the feries as far as we pleafe, will convey 

 an idea of the manner in which fecondary cryftals may increafe 

 in magnitude and ft ill preferve their form, from which we may 

 judge that the ftrufture combines with this augmentation of 

 volume in fuch a inanner, that the law was already fketched 

 in the nafcent cryftal, according to which the lamina of fuper- 

 pofition fucceflively decreafe when the nucleus has attained 

 its grsateft dimenfions. 



The inllrument by which the angles of cryftals are mea- 

 fured is called a goniometer. For a defcription of Dr. 

 WoUafton's reflefting goniometer, fee Goniometer. A 

 more fimple inftrument was employed by Haiiy, ( See 

 F/ate Vl. Jig. g$. Cryjiallography.) It confifts of a femi- 

 circle of brafs divided into degrees. At the centre is fixed 

 a pin, upon which Aide the two arms A B, G F. The 

 lail of thefe, by means of a fcrew, may be fixed in any pofi- 

 tion, fo that the diftance between the end G and the centre 

 may correfpond with the face of the cryftal to be meafured. 

 The other arm A B is drawn up till the diftance between B 

 and the centre correfponds as nearly as poffible with the fize 

 of the other face of the cryftal. It is then turned round till 

 the angle of the cryftal to be meafured correfponds exactly 

 with the angle B c G ; the arm A B then cuts the femicircle 

 in the angle, which correfponds with that of the cryftal. 

 This inftrument is found to be not fufficiently accurate for 

 delicate obfervations, but it is truly furprifing that Haiiy was 

 enabled by it to approximate fo nearly to the correft admea- 

 furement of the various cryftals which he has defcribed. 

 The inftrument for determining the eleftricity of cryftals 

 [P/ate Yl.Jig. 92.) is defcribed in the article Mineralogy, 

 jiddenda. 



On the Notation of Cryjiah. — To facilitate and abridge 

 the defcription of the ftrudlure of fecondary cryftals, Haiiy 

 has invented fymbols which denote the particular laws of 

 decrement, that produce the various forms that may occur. 

 This mode of notation will be eafily undcrftood by a refer- 

 ence to the figures in Plates V. and VI. CryJlallography. 

 Let Plate V. Jig. 64. reprefent any oblique parallelepiped, 

 the faces of which have angles of different meafures ; let it be 

 the primitive form of fome mineral, as felfpar. The vowels 

 are to reprefent the folid angles. The four firft. A, E, I, O, 

 are placed at the four angles of the upper bafe, following 

 the order of the alphabet. The confonants are chofen to 

 defignate the edges. The fix firft are placed on the middle 

 of the edges of the upper bafe, and upon the two longi- 

 tudinal edges of the lateral faces, B C, D F, G H. The 

 letters P, M, T, which are the initials of the fyllables of the 

 Vfcrd Primitive, are placed in the middle of the upper bafe, 

 and of the two lateral planes or faces exhibited to view. 



Each of the folid angles, or of the fix edges marked by 

 letters, is fufceptible of undergoing particular laws of 

 decrement, on account of the irregular form of the parallele- 

 piped. For this reafon, they are marked each with a 

 different letter. But as the laws of decrement aft with the 

 greateft poffible fymmetry, every thing which takes place 

 with refpeft to the angles and edges that undergo dillinft 

 decrements, takes place alfo on the angles and edges that are 

 diametrically oppofite, and are perfeftly equal, but which 

 are not vifible, or are not marked. Thus mjig. 66. the edges 

 A I, ^ /, A E, and p u, and the fohd angle's I and .f, 

 O and r, are equal. It is, therefore, only neceffary to mark 

 the number of folid angles or edges that have diftinft decre- 

 ments, becaufe thefe are underftood to include all thofe 

 which take place on analogous edges or angles. 



In fome cafes, it is neceflary to indicate the .analogous 

 edges and angles ; this is done by fimilar fmall letters : the 

 angles analogous by A E, I O, are reprefented by a t, i 0, 

 and the fame with the edges. But it is feldom neceflary to 

 mark thefe fmall letters in the figure ; it is fufficient to 

 introduce them into the fymbol of the cryiial, becaufe the 

 place which every one ftiould occupy in the figure may 

 eafily be conceived. 



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

 or more ranges in breadth, the figures i, 2, 3, 4, &c. are 

 employed in a manner to be immediately explained ; and to 

 indicate the effefts of decrements by two, three, &c. ranges 

 in height, the fraftions i, j, -5, &c. are employed. 



The three letters P, M, T, ferve to diftinguilh either the 

 form of the nucleus without any modification when they 

 alone conftitute the fymbol of the cryftal, or the faces 

 parallel to thofe of the nucleus in the cafe where the decre- 

 ments do not reach their limit ; and then thefe letters are 

 combined in the fymbol of the cryftal with thofe which 

 relate to the angles or edges that have imdergone decre- 

 ments. 



I^et us fuppofe that one of the foUd angles O, Jig. 64. is 

 intercepted by a fingle additional face. The decrement 

 which produces this face may take place either on the 

 upper bafe P, or on the plane T, which is on the left of the 

 obferver, or on the face M, which is on the right. In the 

 firft place, the figure marking the decrement is placed above 

 the letter O ; in the fecond cafe, the figure is placed on the 

 left-hand, a little above the letter ; and in the third cafe, it is 



placed on the right-hand. Thus O denotes the efFe£l of a 

 decrement by two ranges in breadth, parallel to the diagonal 

 of the bafe P, that pafles tlirough I, E ; O' indicates the 

 efi^df of a decrement by three ranges in breadth, parallel to 

 the diagonal of the face M, which paffes through the angle 

 E ; and ■* O indicates the effeft of a decrement by four ranges 

 in breadth, parallel to the diagonal of the face T, that paffes 

 through the angle O. 



When the decrement takes place on one of the three other 

 folid angles I, A, E, the obferver is fuppofed to move round 

 the cryftal till he is oppofite to that angle, or to turn round 

 the cryftal till the folid angles E, A, I, are exaftly oppofite 

 to him ; and it is relative to that pofition that the decrement 

 is faid to take place to the right or the left. 



For example, if we are fpeaking of the folid angle A, the 

 fign ^A will reprefent a decrement by two ranges on the 

 furface A E, s r, Jig. 66. or oppofite to T ; and A ^ will 

 reprefent the effedt of a decrement by three ranges upon the 

 face A I n r, oppofite to M. 



As to the decrements on the edges, thofe which take 

 place towards the boundary of the upper bafe B, C, F, D, are 

 expreffed by a letter placed above or below the letter as the 

 effefts occur above or below the terminal edge, fuppofing 

 them to fet off from the edge to which they are referred, 

 whilft thofe which take place on the lateral edges are con- 

 dufted by an exponent placed on the right or the left of the 

 letter, according as they occur in one direftion or the other. 



s 



Thus D expreffes a decrement by two ranges proceeding 



3 

 from D towards C : C, a decrement by two ranges pro- 

 ceeding from C towards D : D, a decrement by two ranges 



z 



defcending upon the face M : H ', a decrement by three 

 ranges, proceeding from H towards G : and G ■*, a decre- 

 ment of four ranges proceeding from G towards the edge 

 oppofite to H, or A r,Jig. 66. When it is neceffary to denote 

 by a fm.iU letter, fuch as d, a decrement upon the edge a r. 

 Jig. 66. oppofite to the edge denoted by the capital letter 



