274: Penfield — Solution of Problems in Crystallography 



the following intersections with the horizontal axes, as deter- 

 mined bj scale IN'o. 4 of the printed sheets, 0-573<r^ : a : —0-365^. 

 The foregoing figures, which indicate a parameter relation, are 

 not easily interpreted, but their reciprocal values (1*746 : 1 : 

 — 2'740), which are equivalent to the indices, make it clear 

 what the relation is, namely. If : 1 : — 2f. The distance 0001 

 to 'Wj, measured with the stereographic scale, was found to be 

 72" 35' (theory 72° 30'), and the intercept on the vertical axis, 

 plotted in the same manner as, for example, v in figure 21, 

 was found to be almost exactly fc, the reciprocal (index) 

 being f . The indices expressed as fractions are therefore 

 If-l' — 2f'|-, or, cleared of fractions, 7'4-ll'3. 



Orthorhojsibic System. 



The example chosen for illustrating this system is a crystal 

 of anglesite from Eureka, Utah, selected from a suite of beauti- 

 ful specimens sent to the present writer by Mr. Maynard Bixby 

 of Salt Lake City. In figure 22 the crystal is shown both in 

 orthographic and clinographic projection, the figure having been 

 drawn by Mr. W. E. Ford of the Sheffield Laboratory. The 

 method employed in plotting is indicated by figure 23. The 

 positions of the poles of the prism m, 110, and brachydome o, 

 Oil, were first jocated from the fundamental measurements, 

 mAm, 110AllO = 76° 16' and oAo, Oil AOll = 104° 24'. 

 These measurements are especially favorable for determining 

 the lengths of the a and c axes, which are the tangents, re- 

 spectively, of r and t:, figures 6 and 8, or the tangents of one- 

 half the given angles ; hence it is only necessary to draw two 

 chords from h, intersecting the graduated circle at 76° 16' and 

 104° 24', measured from 010, figure 23. Thus the lengths of 

 a and c, measured on the respective radii by scale IN'o. 4, were 

 found to be 0-786 and 1-289, calculated 0*786 and 1-289. The 

 slope of the brachydome, cAo=52° 12' (f of ^A^), may also 

 be plotted in the upper left-hand quadrant, and the_ length of 

 the G axis measured on a perpendicular erected at 010, as indi- 

 cated. The macrodomes d and I will be considered next. 

 These were located on the vertical diameter by means of the 

 angles cAd^Sd" 23' and cAl=22° 19', and lines plotted at 

 these angles in the upper left-hand quadrant intei'sect the per- 

 pendicular from a' {c a' equals the length of the a axis) at dis- 

 tances equal respectively to \ and J the length of the c axis, 

 thus determining the symbols <:Z=102 and Z=104. The posi- 

 tion of the pyramid^ is determined by the intersections of the 

 zones a : o and c : m. Thus plotted, the slope of j9, measured 

 with the stereographic scale, was found to be 64° 30', calculated 

 64° 24', and a line drawn at this angle from the center meets 



