CRYSTALLOGRAPHY. 



and the three Isft to the fuinmit A'. If we fuppofe a 

 decrement by two ranges of rhomboidal molecules on thefe 

 different angles, fix faces will be produced parallel to the 

 axis, as has been already obferved. . , , 



The plates of fuperpofition, at the fame time that they 

 undergo a decrement towards the inferior angles, will 

 extend by their fuperior parts, fo as to remain always con- 

 tiguous to the axis, the length of which wiU progreffively be 

 augmented. The fmall faces produced by the decrements 

 on the angles will gradually increafe till they touch each 

 other ; we Ihall then have the folid reprefented AA,Jig. 20, 

 where each of thefe fmall faces, as O 0, is marked with 

 the fame letters as the angle to wliich it belongs, and 

 which is now fituated in the middle of the triangle, becaufe 

 it conftitutes the- point from which the decrements fet out. 

 As new plates are applied, the points or line rife up, 

 ?.nd the point O finks down ; fo that at a certain period v.-e 

 fliall have the fohd reprefented Jig. 19, where the faces 

 produced by the decrements become pentagons ooi, O e. 



Let us now fuppofe a fecond decrement to concur with 

 the firft, and to take place by a fingle range upon the 

 fuperior angle E A I and the inferior angle H 'A K, 

 and alfo on the other faces of the rhomb which form the 

 folid angles A and A' ; the effeft of this will be to pro- 

 duce two faces perpendicular to the axis ; and when it has 

 reached the point at which thefe faces cut the fix faces 

 parallel to the axis which are produced by the firft decre- 

 ment, the fecondary folid will be completed, and will be a 

 regular fix-fided prifm. {Plate II. fg. 17.) It has been 

 already faid, that the refult is general, whatever be the 

 form of the primitive rhomboid. It may now be feen wliy, 

 in the mechanical divifion of the prifm, the fedtion pp, 0, 

 has the fides />/>, 00, parallel to each other, and to the 

 diagonal of the nucleus E ¥,Jig. 21. Since the two de- 

 crements taking place, one upon the angle E O I, the 

 other upon the angle E A I, the jJlates of fuperpofition 

 ought to have the edges formed by the decrements parallel 

 to the fame diagonal, or to E I. 



In the cafe we have been confidering, and which is the 

 moft common, the axis of the fecondary cryftal is longer 

 than that of the nucleus ; but if we fuppofe the two decre- 

 ments to commence at the fame time, then the axis of the 

 prifm being equal to that of the nucleus, both the lateral 

 angles and the fummits of the nucleus would touch the 

 prifm, the one on the fides, and the other the bafes. If the 

 decrement were to commence on the fuperior angles prior 

 to the lateral decrements, the fummits of the nucleus would 

 then be contiguous to the bafes of the prifm, whilft its 

 lateral angles would be wholly within the prifm, between 

 its planes and axis. This is the cafe with certain cryftals, 

 in which the prifm is very fliort, and rcfembles an hexa- 

 gonal plate. 



Another remarkable example is offered in that variety 

 of calcareous fpar, called by Haijy analogique. (See 

 Plate y^- fig-SS') ^^ '^ compofed of twenty -four trape- 

 zoidal faces, of which fix are vertical faces, as dab c, da' b c', 

 and twelve others, difpofed fix and fix, as c'pa, and c'pa"b, 

 &c. and fix terminal faces, as pap's. The vertical trape- 

 zoids refult from the fame law that produces the hexahe- 

 dral prifm {Plate II. _fig. 17.) ; the fecond refult from the 

 law which produces the metaflatic cryftal. Jig. 22. In 

 comparing Jig. S5 with ^g. 21, we may fee that the vertical 

 faces cut thofe of the metaftatic cryftal, fo as to intereft 

 the lateral fohd angles E O, I K, Scc.Jigs. 22 and 23 ; and, 

 laftly, the terminal faces refult from a decrement fimilar to 

 what produced the equiaxe cryftal. {Plate III. Jig. 34.) 

 Fig. ^^. A} B, C, D, reprefents the different trapezoidal faces 



of this cryftal. Variouo relations of proportion between 

 theii* fides and angles are given by Haiiy, Mineralogie, 

 tom. i. p. 85, 86. 



It is a character common to all the primitive forms to 

 be divifible, parallel to their faces. In the parallelepiped, 

 where this divifion is not joined with fome other in a dif- 

 ferent direftion, it leads us obvioufly fo the form of mole- 

 cule fimilar to that of the primitive cryftal. In the regular 

 fix-fided prifm, it gives us for a molecule the triangular 

 prifm, as has been before obferved, (See PlateV.fg. 56.) 

 In the oftaiiedrons, it appears to produce two kinds oi" 

 m.olecules, tetrahedrons and oftahedrons. Haiiy, in tliis 

 cafe, conceives that the tetrahedron is the integrant mole- 

 cule, and that the oftahedrons are empty fpaces between 

 them. The difficulty is removed, by conceiving the mole- 

 cules to be an affemblage of fpherical particles, as we have 

 before obferved. The dodecahedron, with ifofceles trian- 

 gular faces, cannot have molecules extrafted, without di- 

 viding it in direftions different from thofe which are parallel 

 to the face. The cutting-planes muft pafs through the 

 axis, and through the edges contiguous to the fummits, ' 

 from whence will refult irregular tetrahedrons. Some 

 other primitive forms divide alfo in directions which are 

 not parallel to the faces, as we have feen in the cafe of the 

 tourmaline. See Plate III. Jig. 26. 



Thus, befides parallelopipcds, there are two other forms 

 which integrant molecules alfume, namely, the tetrahedron 

 and the triangular ])rifm ; but it deferves particular attenr- 

 tion, that the tetrahedral and prifmatic molecules are always 

 Arranged in fuch a manner in the interior of cryftals, that, 

 taking them in groups of two, four, fix, or eight, they 

 compofe parallelojipcds, fo that the ranges fubtrafted by 

 decrements are no other than thefe parallelopipcds ; and 

 we may confider fuch decrements as taking place by one 

 or more ranges of rbomboidal molecules. If, for example, 

 we take the regular fix-fided prifm {Plate V. Jig. 56.), 

 fuppofe one bafe of this prifm divided by feftions parallel 

 to its fides into fmall triangles, which form the bafes of 

 the integrant molecule ; it is evident that any two adjoin- 

 ing triangles. Apt, A Of, compofe a rhomb, and by their 

 union the two little triangular prilms to which thsfe baft: 

 belong would form by their union a rhomboidal prifm or 

 parallelepiped. It is obvious, therefore, that we may 

 conceive the larger prifm to be compofed of fimilar rhomb::. 

 Now, if we conceive a feries of plates piled upon the 

 hexagon A, B, C, D, F, G, and which undergo, for exam- 

 ple, on their different edges, a fubtraft.on of one range 

 of thefe parallelepipeds, thefe edges will fucceflively cor- 

 refpond with the lines of the hexagon ilmnrhi, iiixyge, 

 &c. from which we fee that the quantity by v/hich each 

 plate decreafes is a fum of parallelepipeds, or prifms with 

 rhomboidal bafes ; and il the decrement attains its limit, 

 we fhall have a right fix-fided pyramid, which v.-ill have 

 for its bafe the hexagon A, B, C, D, F, G. Thefe parallele- 

 pipeds, compofed of tetrahedrons or triangular prifms, 

 are called by Haiiy JubtraBive molecules ; and as far as the 

 theory of cryftals is concerned, we may conceive all cryftals 

 to be compofed of parallelepipeds. 



Plate "^ .Jig. 58. refers to a particular cafe dcfcribed in a 

 note by Haiiy (tem. i. p. 96.), to explain the vacuities on 

 the edges h, c, I, m ; but being of lefs importance, we pro- 

 ceed to ftate the obfervations of M. Haiiy on fome apparent 

 anomalies in cryftallizatien. 



In common cryftals, the faces adjacent to each other 

 always form falient and never r«-entering angles ; but cer- 

 tain cryftalhne forms exift, which prefcnt the latter angle?. 

 Let B d, Plate V._/%-. 60. reprcfcnt an oblique prifm with 



rheniboiilal 



