Cyo On Ctysiallography. 



same solid angle O (fig. 20), the three faces produced were 

 alw'AVa on a level, and that in this case we might confine 

 ourselves to the consideration of the cffLCt of the decre- 

 ments with respect lo one of the plane angles, w^hich con- 

 curred to the forniation of tlie solid angle, by supposing 

 this efiect to be prolonged above the adjacent faces. In 

 this case the decrements which take place on these latter 

 faces are reckoned as intervening in a subsidiary manner, 

 in order to favour the action of the principal decrement. 



In general, whenever a solid angle of the primitive 

 form undergoes decrements which tend to give rise to 

 a facet in its place, whatever be the law of that to which 

 we refer the production of this facet, there are always auxi- 

 liary decrements, the concurrence of which is necessary in 

 order that the facet m question may be properly prolonged. 



Now, when this decrement, which we consider in pre- 

 ference, takes place by two or more ranges, the auxiliary 

 decrements which form a continuity with it follow a law 

 entirely peculiar, the consideration of which is the objeet 

 of this article. 



Let A A' (fig. 32) be, any given parallelopipcdon which 

 undergoes a decrement by two ranges on the angle EOI, 

 of its base A EO I. It is evident that the edges of the 

 laminse of superposition will have directions be, rs,* 

 parallel to the diagonal which goci from E to I, and situated 

 in such a manner that there will be on the edges O E, 01, 

 two ridges {arefes) of molecules comprised either between 

 the term of departure Oand /' c, or between I'C and rs. But, 

 as we have said, the laminte applied on the adjacent faces 

 lOA'K, EO.VH, also undergo variations or auxiliary 

 decrements, which continue the eflTecl of the decrement on 

 the angle EOI. Now, sucti are the variations in this case, 

 that the edges of the laminae piled upon the face I O A'K, 

 have directions c g, s t, and that those of the lamin:e which 

 rise on the face EO A'H arc lineally disposed like b g, r i. 

 Foe, since the lower edge of the first lamina .iiiphcd on 

 AEOI coincides wiih be, and as the height of this 

 I unina ansu ers to a ridge of a molecule, we may, with a 

 little attention, conceive that the plane beg, which, in 

 one part also coincides with b c, and ia another is re- 



* We must conceive that tlie subtractions which are here represeoted on 

 the quatiril;^ter A E O I take place successively on the dilTerent lamina; of 

 superposition. The distances between each of these iamin.-E and the suc- 

 ceeding one beings the same witli that which exists between the lijies /> c, rs, 

 i.nd a'l the rest similarly situated, we may, for the sake of greater coiive- 

 jiiuace, refer the whole, as we do in the present instance, lo tiio quadrilater 

 A E 01, as a kind of scale which gives the measurements of the iiibtractious 

 ovfrat^fl 'jy t^s decrtment on the corresponding; lamina;. 



moved 



