254 Penfield — Use of the Stereographic Projection for 



The great circles shown, such as from Northern Luzon, Philip- 

 pine Islands, to San Francisco, Luzon to Honolulu, etc., were 

 drawn on the plate. The illustration also shows a celluloid 

 protractor, figure 3, over a portion of the plate in position 

 suitable for measuring the distance from Luzon to San Fran- 

 cisco. Starting from the upper zero of the protractor, Luzon 



Stereographic Protractor adjusted for measuring from Luzon to San Francisco 

 along trie arc of a great circle. See Note. 



is about 26° and San Francisco about 124° from the periphery, 

 and the difference, 98°, is the distance. Using a protractor with 

 finer graduation, such as shown in figure 12, the distance was 



Note. — Figure 6 and other similar half-tone illustrations have been made 

 from photographs of drawings over which stereographic scales, printed on 

 transparent celluloid, have been laid. The celluloid being of a yellowish 

 tone of color, those portions of the drawings covered by the protractors 

 appear darker in the photographs and half-tones, and thus may be easily 

 recognized. The lines on the original celluloid protractors are very fine, 

 and appear still finer in the reduced half-tones, but it is believed that they 

 are sufficiently distinct for purpose of illustration. 



