Theory of Cryjialllfathn. *8y 



To form an idea then of the effect of the intermediary 

 law, combined with the preceding, and which gives rife to 

 the lateral trapeziums, let us fuppofe that cbpr {Jig. 49) 

 reprefents the fame fquare as fig. 46, fubdivided into fmall 

 fquares, which are the external faces of as many moleculse. 

 If we take thefe moleculae by pairs, fo that they form rectan- 

 gular parallelopipedons, having for bafes the oblong fquares 

 bn g b, hgm G, &c. and if we imagine that the fubtractions 

 are made by two ranges of thefe double moleculae, the edges 

 of the laminae of fuperpofition will be fucceffively ranged in 

 lines, as P G, XL, R/>, S/>, k z, yz, &c. and the fum 

 of all thefe edges will produce two faces which, departing 

 from the angles b 3 r t will converge, the one towards the 

 other, and will unite themfelves on a common ridge, fituated 

 above the diagonal cp, but inclined to that diagonal. We 

 fhall then have twelve faces as the complete refult of the 

 decrement; and calculation fhews, that the fix fuperior faces, 

 beicg prolonged to the point where they meet the fix lower 

 faces, will form with them the furface of a dod. caedron, 

 compofed of two right pyramids united at their baf-:6 Thefe 

 pyramids are here incomplete by the effect of the firit law, 

 which gives the hexagon abc.dru {fig. 4B) and its op- 

 pofite *. 



5. Mixed Decrements- 

 In other cryftals the decrements, either on the edges or on 

 •the angles, vary according to laws, the proportion of v.hich 

 cannot be expreffed but by the fraction \ or i. It may 

 happen, for example, that each lamina exceeds the following 

 by two ranges parallel to the edges, and that it may at the 

 fame time have an altitude triple that of a fimple molecula. 

 Figure 54 reprefents a vertical geometrical fection of one of 

 the kinds of pyramids which would refult from this decre- 

 ment ; the effect of which may be readily conceived by con- 



* The term (ynlaclic denotes the combination of decrements, one of 

 Which takes place by a finale range of fimpie molecule, and the other by 

 two ranges of double molecula;. 



Vol. I. U fidering 



