102 On Crystallography . 



to the first sections, it will happen that ot) one hand the 

 surfaces of the bases will always become narrower, while on 

 the other hand the altitudes of the panes will decrease ; and 

 at the term at which the bases have disappeared, the prism 

 will be changed into a dodecahedron (fig. 3,) with penta- 

 gonal races, six of which, such as o o i O e, o I A i i, &c., will 

 be the residues of the panes of the prism ; and the six others 

 E A I 00, O A'K//, &c. will be the iniraediate result of the 

 mechanical division*. 



Beyond this same term, the extreme faces will preserve 

 their figure and dimensions, while the lateral faces will inces- 

 santly diminish in height, until the points o, k, of the pen- 

 tagon 1 k ii, coming to be confounded with the points i, ?', 

 and so on with the other points similarly situated, each penta- 

 gon will be reduced to a simple triangle, as we see in fig. 4.t 



Lastly, when new sections have obliterated these triangles, 

 so that no vestige of the surface of (he prism remains, (fig. ),) 

 you will have the nucleus or the primitive form, which wilj 

 be an obiuse rhoitiboid J, (fig. 5,) the grand angle of which 

 EAI or EOI is 101°32' 13"§. 



The observation I have detailed is that which served for 

 developing my ideas on the structure of crystals, and has 

 been the key of the theory : it occurred to me on the oc- 

 casion of a crystal being presented to me by citizen De- 

 franee from his mineralogical collectiron. The prism had 

 a single fracture at the place of one of the edges situated 

 around the base, by which it had adhered to the remains of 

 the group. Insiead of placing it in my collection, I tried 

 to divide it in other directions; and 1 succeeded after some 



* We have contiuued to represent, the hexahedral prism circumscribed by 

 the solid from which we extract it, by dividing it, in order that the progress 

 of the operation may l)C more easily conceived. 



f The poinrs which are cdnfcmided, two and two, upon t!iis figure are each 

 narked with the two letters which served to designate them wiienthey were 

 separated, as in fig. 3. 



\ I denominate as ji r/irtw/'onZ a paralielopipedon, terminated by six equal 

 and similar rliombuses. Two of the solid angles, such as A, A', opposed to 

 each other, are formed by the union of three equal plane angles. Each of the 

 six others is formed b\' a plane angle equal to tlie preceding ones, and by two 

 angles which are sipplements to them. The points A, A', are the summits, 

 and the line which proceeds from the one to the other is the axis. We always 

 jupncse the rhomboid situated so as to make its axis vertical. In any single 

 face, such as A E O I, the line drawn from E to I is the horizontal diagonal, 

 and that from A to O is the oblique diagon.il. The rl'.omhoid is obtuse or acute, 

 accordingly as the angle contiguous lo the summit is itself obtuse or acute. 



§ I have observed that each trapezium, such as/)/; no (fig. 2,) uncovered 

 by th* first sections, was very sensibly inclined from the same quantity, as 

 veil upon the residue pp del: m ot the base, as upon thp residue uKif'L' of 

 the adjacent pane. Setting out from tin's equality of inclinations, we deduce 

 from it by calculation the value of the angles with the precision of minutes 

 iipd seconds, which mechanical raeasurcmcnts are not capable of attaining. 



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