The Gnomonic Projection
Figures 38 and 39 show the gnomonic projections of the upper and lower ends respectively of the anorthite crystal discussed in the following paper by Professor Parsons, assuming that the same faces would be developed on the upper end as were found by measurement on the lower end. The two figures are similar, the differences being such as to be very puzzling unless the relations of the two are clearly in mind. The one may be obtained from the other by pricking the face-poles thru on to the back of the paper, and then turning the paper over in such a way that the right-and-left coordinate maintains its direction but with ends interchanged. Figure 38 is that which would be obtained by plotting the angles of the respective forms as given in the Winkeltabellen2 In figure 39 the forms have the same ρ values and the same φ values but measured in the opposite sense; the latter is also true of the angle v; and the y and q coördinates are measured in the reverse direction. Thus pq of figure 38 is equivalent to pq of figure 39. The latter is similar to Parsons’ figure 43, in which the forms are indicated by the face numbers used in the measurements; the horizontal coordinate of 38 is the direction-line of the two faces 15 and 18 of figure 43.