S. L. Penfield — Stereographic Projection. 



123 



located on the meridian 8° 15' W., and by means of protractor 

 No. I, at 51° 50' N. In a similar manner, New York is located. 



22 



8'I5 



90° 



7 4-° Rio de Janeiro^ 

 23°$> 



Rio de Janeiro being south of the equator falls beyond the 

 engraved circle on the meridian 43° W., but can be easily 

 located by means of scale No. 3, figure 3. Instead of locating 

 Rio de Janeiro, however, beyond the engraved circle, its anti- 

 podal point i? can be located on the same meridian, at 23° N. of 

 the equator. Using now protractor No. IY, the points P and 

 P f , and S and S' are located, where the great circles passing 

 through Queenstown and New York, and Queenstown and Rio 

 de Janeiro cut the equator ; then using protractor No. II the 

 distances are measured. From Queenstown to New York the 

 distance, as plotted, was found to be 45° 23', calculated 45° ll 7 . 

 From Queenstown to R the distance as plotted was 99° 20' ; 

 hence to Rio de Janeiro is the supplement of this value, 80° 

 40'; while by calculation it is 80° 47' '. The data for the calcu- 

 lations were the longitudes and latitudes as previously given. 



An advantage is gained by using a meridian rather than an 

 equatorial projection, since the method of measuring is simpler, 

 and the plotting is done near the periphery of the divided 

 circle, where the distances between the stereographically pro- 

 jected degrees are largest. Figure 23 illustrates this method. 

 The divided circle represents the meridian passing through 

 Queenstown, and a mark at 51° 50' locates the place. On the 

 stereographically projected equator, the intersections of the 

 meridians of New York and Rio de Janeiro are plotted by 

 means of the graduation on the base line of protractor No. I. 

 The two meridians 74° and 43° West of Greenwich are respec- 



