. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 246 PEINCIPLES OF CRYSTALLOGRAPHY. now, C,D are the points of section of the zone with the main circle, we draw the diameter O D and a perpendicular to it, E F, and it is clear that the pole sought for must lie in the zone E F. Since, now, it must be 90° distant from every point of the zone, and therefore also from R, while the pole of the zone E F is one of the lioints 0 or D, we draw the straight line C E r and 0 Pjp, so that the a
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 246 PEINCIPLES OF CRYSTALLOGRAPHY. now, C,D are the points of section of the zone with the main circle, we draw the diameter O D and a perpendicular to it, E F, and it is clear that the pole sought for must lie in the zone E F. Since, now, it must be 90° distant from every point of the zone, and therefore also from R, while the pole of the zone E F is one of the lioints 0 or D, we draw the straight line C E r and 0 Pjp, so that the arc r i^ = 90°, and thus find the pole p of the zone CRD. Thus, all the expedients are given which are necessary for the construction and use of the projection; in general, the sim- plest of these are sufficient, especially c while in this method of projection we do not aim at the greatest exactitude attainable, but only a presentable representation of the arrangement of the faces. As a close of this section we shall give some special modes of the laws of zones, and an example of a complete development of them. 1. Zone passing through two i)inacoids— 100 100 010 010. — — ; — 0 0 1 [0 01] is the symbol of the third pinacoid. If a face, Ji 1c I, lies in this zone, so must— /i. 0 + A:. 0 4- L 1 = 0 also, I = 1, the general symbol of a face lying in the zone 10 [0 01] is k h 0. 2. Zone passing through a pinacoid and any face: U h I lilil 100 100 —',—', — o I % If a third face, J??y-, lies in the zone [o fk], so must— X .0 + y .l—1c .z = 0 7 7 y Tc yl = lcz^ - = r or If. therefore, a zone passes through a pinacoid, the relation of those two indices, which, in the symbol of the pinacoid, are o, is constant for all the faces of this Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may
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