CRYSTALLOGRAPHY. 



jniy necellary to make fedtions cutting through the oblique 

 diagonals of the different faces of the fecondary rhomboid. 

 One of the fettions, for inftance, that which paffes through 

 the diagonals drawn from a to t, and from a to «,»and which 

 cuts off the fohd angle z, coincides with the face a b, d f, of 

 the nucleus. But there are fix lateral folid angles z, c, y, 

 and t, m, u. We^ have, therefore, fix feftions to make, 

 inclined three and three towards each fummit ; and becaufe 

 the upper fohd angles alternate with the inferior, the feftions 

 which cut them off preferve the. fame alternation, and crofs 

 in fuch a manner as to prefent the fix'rhomboidal faces of 

 the nucleus. 



To conceive the ftrufture of this fecondary rhomboid, let 

 us refer to the rhomboidal dodecahedron [Plate III.^^. 29.) 

 before defcribed. We have feen that by a decrement of one 

 range in breadth on all the edges, there refulted two trian- 

 gular faces on each edge, which being in the fame plane 

 formed a rhomb, the (hort diagonal of which is I O. 



Let us fuppofe, that the nucleus was the primitive rhomb 

 of carbonate of hme {a b, d f. Jig. 34.), and that the lamina 

 of fuperpofition decreafe by one range of little rhomboids 

 Cmilar to the nucleus ; but the decrements to take place only 

 on the edges a b, af, a n, which meet at the fummit a, and 

 on the oppofite edges, which 'meet at the oppoilte point a'. 

 Then inftead of twelve rhombs there will only be fix, of 

 which the fhorter diagonals will coincide with the edges 

 ab, af, a n'. Sec. The other parts of the lamins of fuper- 

 pofition, that is, thofe which are fituated near the lower 

 edges, bd, df,fx, &c. will not undergo any decrement, 

 but will fuffer variations that will tend to prolong the faces 

 produced by thefe decrements, until they interfeft each 

 other. From hence it refults, that the laminse, inftead of 

 preferving the figure of a rhomb, as would have been the 

 cafe if the' decrement had taken place on all the edges, will, 

 zl-, they are further and further removed from the nucleus, 

 pafs fucceffively from the figure of a pentagon to that of a 



triangle. 



Fig. 35. A, a*, i//, is the face ofthe fame nucleus or rhomb 



?.s in fg. 34, and what is faid of this face may eafily be 

 applied to the others. Suppofe this face divided mto 81 

 rhombs, which reprefent the faces of fo many molecules, or 

 729 in the whole. The firft lamina of fuperpofition, which 

 we apply to the face a b, df, will be B,/^. 35, in which U /, 

 Z' d, reprefent the upper face, and C U I h, XZ I h, the 

 facets of the two upper edges. We m.uft place this lamina in 

 fuch a manner on the face a b, df, that the point h' (hall unite 

 with the point h, the point A' with the point A, and the 

 point B' with the point B. We Ihall perceive immediately, 

 that the two upper ranges of the face a b, df,Jig. 35. A, 

 that is, thofe included between a b, Ah, on one fide, and 

 af, B h, on the other, will remain uncovered, the neceffary 

 refuk of a decrement by one range of molecules. The 

 lamina B is a pentagon refulting from the fubtraftion of the 

 three httle rhombs neceffary to complete the rhomb. This 

 fubtraaion was required, that the lamina by its figure 

 might aid the effe6t of the decrement, as wiU be afterwards 



explained. , r j r u v 



The two ranges of rhomboids on each iide ot the lines 

 D d', E d', are added, that the nucleus may be covered and 

 continue to increafe on the edges b d,fd, A, Jig. 35, which 

 correfpond with thefe lines. Thefe two ranges being 

 fufficient to fill up the void, it is not neceffary to add fimiJar 

 ranges towaids the adjacent edges of the larnins ot luper- 

 pofilion, apphed on the neighbouring faces. The operation 

 v/iU indicate of itfelf what is required m thefe kinds ot addi- 

 tions. . , 

 The Jg. C, 35. reprefents the fecond lamina oi luper- 



pofitioji, which is to be applied to the former in fuch a 

 manner, that the points /', D', E, d, fliall unite v/ith thofe 

 which are marked with the fame letters in fg. B. As the 

 cryftal will receive another increafe towards the edges, which 

 correfpond with F d', C d', we may conceive that inftead of 

 one range added on each fide D d', E d. Jig. B, it will be 

 neceffar)' to add two on each of the two lines E d', C d', 



M- c, 35. 



We muft place in the fame manner, in fuccellion, the two 

 laminx reprefented D and E, fig. 34 ; obferving that the 

 letters marked with an accent in each figure (hall coir.cide. 

 with the fame letters not accented in the preceding figure. 

 Beyond the feries which anfv^ers to Jg. E, the laminx of 

 fuperpofition ^vill ceafe to envelope the lower edges of the 

 cryftal, and will be reduced to fimple triangles, which may 

 be perceived on examining the figures E, F, G, H, whofe 

 pofition will be determined according to the conditions 

 before ftated. 



The number of rhomboids which compofe the laminx 

 being now progreffively decreafing, is reduced at laft to a 

 a fingle rhomboid d' {Jg. D, 35-), which being applied oa 

 that which is defignated by the fame letter in Jg. H, will 

 form the fummit of one of the lateral fohd angles of the 

 fecondary rhomboid. It will now be feen why the laminx 

 of fuperpofition take fucceffively pentagonal ajid triangular 

 faces as they recede from the nucleus. For example, every 

 lamina, detached from the crj-ftal [Jg. 34. ) by a feition which 

 paffes any where between the angle 2, and the middle of the 

 lines Z /, 7j u, is neceffarily triangular, and has the fame 

 ftrufture as P' / R',Jg. G, 35 ; namely, it is really furrowed 

 at its bafe, but the ridges are imperceptible on account of 

 their extreme minutenels. 



Decrcjncr.'s on the Angles. — To explain tlie formation of 

 fecondary crj-ftals, in m.my inftances it is neceffar}' to admit 

 that the decrements take place on the folid angles. The 

 formation of the regular otlahedron formed on the cube 13 

 reprefented Plate III. Jg. 36. Cryjallography, and an 

 account of it given under the article Crystal, but the 

 reference is erroneoufly to Plate I. Jg. 20. 



The effetl of decrement on the angles by one range of 

 molecules in breadth is explained in the article Crystal, and 

 a" reference made to Plate I. Jg. 21, for which fee Plate II. 

 Jg. 21, Mifcellany, O I, I' O'; where the face of a^ cubic 

 nucleus is reprefented as divided into a number of leffer 

 fquares ; and /^. 23, A, B, C, D, E, F, G, H, I, in the 

 fame plate, reprefent a fuccefCve feries of plates, or laminae, 

 placed on the cubic nucleus, each decreafing by one row on 

 the angles. Thefe are defcribed under the article Crystal, 

 but referred to Plate I-/^- 23 : by applying that defcription 

 to the proper figures as here given, the reader will be able 

 to comprehend this cafe of decrement, where a regular 

 oftahedron is formed on a cubic nucleus. The arrange- 

 ment of the integrant molecules on one of the triangular 

 faces of the oftahedron is reprefented Plate IV . Jg. H- 

 Cryflallography. 



If the decrements on the angles of a cube were to Itop 

 before they terminated in a point, there would remain faces 

 parallel with that, of the cube, which will be evident from 

 infpeaing Plate III. Jg. 36. The cryftal would then have 

 fourteen faces, eight thofe of the oftahcdron, and fix ihofe 

 of the cube. Nothing is more common than to find Inch 

 cn-ftals both in iron pyrites and in galena. 



As another example of decrements on t^e angles, let us 

 take the rhomboid {Plat: IV. Jg- 38.). v.hich differs fome- 

 what from the cube. If the plates applied fuccelSve y 

 upon all the faces of this rhomboid fuffer decrements crly 

 at the angles contiguous to the fummits A and O', andj^hat 



