282 Penfield — Solution of Problems in Crystallography 



y and r; compare figures 6 and 8. The angle a was measured 

 by means of the stereographic scale on the diameter 1 to 2, 

 figure 30, and found to ^be 93° 25', calculated 93° \^ . Sim- 

 ilarly /? was measured on the diameter 4 to 5, and found to be 

 116°, calculated 115° 56^ To measure y and r, a great circle 

 at 90° from, c was first constructed."^ The supplement of y^ 

 from 6 to T, was then determined as 88° 55^ by means of the 

 small circle protractor, giving as the value of y^ 91° 5', calcu- 

 lated 91° 12^ In like manner the arc from 7 to 8 was meas- 

 ured, giving 32° W as the value of r. On still a third sheet, 

 shown in figure 32, the angles «, /9 and y were plotted, and 

 also r, the latter determining the length of the brachy axis, 

 <^= 0*636, calculated 0'635. It is still necessary to make use of 

 the fifth fundamental measurement, from h to 6, in order to 

 determine the length of the vertical axis. By means of a small 

 circle about J, figure 30, the position of ^, on the great_ circle 

 &,<?, was located, and a great circle through 100, e and 100 de- 

 termines TT. The value of ;r, measured on the diameter from 

 2 to 3, was found to be 45° 45', and when plotted as shown in 

 figure 32, the length of 2c was found to be 1*095 ; hence 

 c= 0*5475, calculated 0*550. The value obtained directly from 

 Tz in this case is 2c, because the symbol of e is 021. 



Having located, as in figure 30, the poles 5, m, 100, M^ c 

 and ^5 and also^and z from figure 31, the remaining forms of 

 the crystal were easily identified by means of zonal relations 

 and the measurement of a few angles. The construction of 

 the zones shown in figure 30 would have proved a laborious 

 task had it not been for the great circle protractor. This was 

 used not only for determining the zones, but, far more impor- 

 tant, its graduation furnished the means of getting the radii of 

 the circular arcs from scale ]N^o. 1 of the sheets. 



Meas. Cal. Error. 



CA^t, 001/^201, 41° 30' 41° 28' -^ 2 



C/^q, 001 yx 34 45 34 46 — 1 



C/^x, 001/slOl, 51 40 51 26 +14 



C/sy, 001/s201, 81 30 81 14 -hl6 



c/^p, 001/slll, 33 10 33 17 — 7 



Cy^a, 001/slIl, 34 35 34 10 +25 



c/^m, 001/slll, 54 10 54 17 — 7 



c/^o, 001^111, 58 00 57 52 +8 



C/vW, 001/^221, 85 00 84 50 +10 



C/sK, 001/s061, 75 20 75 10 +10 



C/v7?, 001/s021, 47 00 46 46 +14 



C/^k, 001/s,- 18 55 18 38 +17 



V ^^X, 010/^ 52 20 52 11 +9 

 6'^7r, 010/^ . 34 10 ■ 34 20 —10 



V /^v, OIOa 38 05 38 16 —11 

 V /s^w, 010^ 38 55 38 42 +13 



* The Stereographic Projection and its Possibilities, loc. cit., p. 18. 



