262 Penfield — Use of the Stereographic Projection ft 



or 



New "York is located on the outer circle, which is taken as 

 its meridian, at 40° 43' N. The longitudes of the remaining 

 places with reference to New York are obtained by subtract- 

 ing the longitude of New York from them, as indicated above, 

 and they are then located at their given latitudes. A few 

 great circles have been drawn on the plate, from New York 

 through Denver, Honolulu, Buffalo and Manila, but for the 

 sake of measurement it was not necessary to construct them. 

 After locating the places, a celluloid protractor* was placed 

 over the plate and a photograph taken from which figure 12 

 has been made. Only small circles are printed on the pro- 

 tractor, and, as they fall close together, the scheme was adopted 

 of representing every tenth degree by a heavy line, the inter- 

 mediate even degrees by full, and odd by dashed lines. The 

 dots within the circles represent the locations of the several 

 places. By careful inspection of the figure it may be seen 

 that, starting from New York, Buffalo is a little over 4°, Chi- 

 cago a little over 10°, Denver about 23§°, San Francisco a little 

 more than 37°, Honolulu just short of 72° and Manila just 

 over 123°. The results of the readings of the protractor as 

 stated above, and of still another plotting of this same prob- 

 lem, together with the calculated values, are given below : 



Distances 

 from New York. 



Buffalo. 



Chicago. 



Denver. 



San 

 Francisco. 



Honolulu. 



Manila. 



Calculated 

 Measured 



4° 18' 

 {4 5 

 *{4 20 



10° 16' 

 10 10 

 10 5 



23° 34' 

 23 40 

 23 40 



37° 9' 

 37 10 

 37 10 



71° 49' 

 71 55 

 71 45 



123° 2' 

 123 5 

 123 5 



It may be said of this and of every similar example cited in 

 this article that measurements with the protractors have been 

 made without knowledge of the calculated values. The superi- 

 ority of the stereographic projection is evident from the results 

 of the example just cited, where the maximum error from two 

 independent solutions of the problem was but 13' (15 statute 

 miles) and the average error but a trifle over 5 ; . It is further 

 to be taken into consideration that in this example a whole 

 hemisphere was projected within a circle of 14 cm , 5-J inches, 

 diameter. It is of course evident that by increasing the size 

 still greater accuracy would be attained. To locate places 

 with accuracy on a plate with only ten degree spacing of the 

 parallels and meridians requires some experience. In the 

 example just cited places were located by means of the graph- 

 ical methods described by the writer in a previous article. To 

 gain an idea of how accurately measurements may be made on 

 an engraved plate, 14 cm diameter, using no other guide than 

 the eye in interpolating places between the ten degree spaces, 



* Designated by the writer in an earlier paper as No. II. Loc. cit., p. 17. 



