Geographical Maps and Sailing Charts. 283 



the problem given above was twice plotted, and measured as 

 shown in figure 12, with the following results : 



Distances from 









San 







New York. 



Buffalo. 



Chicago. 



Denver. 



Francisco. 



Honolulu. 



Manila. 



Calculated 



4° 18' 



10° 16' 



23° 34' 



37° 9' 



71° 49' 



123 2 



Measured 



(3 50 



10 15 



23 50 



36 45 



72 00 



123 00 



"U io 



9 55 



23 40 



36 45 



71 50 



123 00 



The maximum error here amounts to 28', and the average is 

 12' : Hence an accurate plate and a protractor is all that is 

 needed for quickly solving problems with close approximation 

 to the truth. 



To locate places easily and at the same time accurately it is 

 recommended to use, in connection with an engine divided 

 plate as already described, a projection of the parallels and 

 meridians, figure 13, printed on tracing paper. When matched 

 over a plate of corresponding size, any place may be located 

 by puncturing with a needle point through the protractor to 

 the plate below. 



Figure 13 is a reproduction by photo-engraving of a stereo- 

 graphic projection 18 inches in diameter, published by Captain 

 C. D. Sigsbee, U. S. N., in an atlas folio entitled " Graphical 

 Methods for Navigators."* Captain Sigsbee's protractor is 

 practically identical with Chauvenet's Great Circle Protractor 

 and was perhaps printed from Chauvenet's original plate in 

 possession of the Hydrographic Office. It is circular, and 

 figure 13 represents only half of it, reduced to 14 cm diameter 

 to correspond with the engine divided plate described by the 

 present writer. A serious objection to the use of such a pro- 

 tractor when on a -small scale, is that the lines are so crowded 

 as to be confusing. This difficulty, however, is to a great ex- 

 tent obviated by using two protractors, one having only great 

 circles, the other on]y small circles, as shown in figures 11 

 and 12, respectively. 



An excellent summary of graphical methods applied to great 

 circle sailing, based upon the stereographic projection, may be 

 found in a publication by Mr. G. W. Littlehalesf of the IT. S. 

 Hydrographic Office, Washington. 



Stereographic Map of the World. Planisphere of the 

 Antipodes. — Figure 14 represents a combination of stereo - 

 graphic projections of the western and eastern hemispheres, 

 which it is believed would make a most useful kind of a map. 

 It is scarcely necessary to state that the northern and southern 

 hemispheres might be combined in a similar manner. The 

 important feature of the map is that any point on one of the 



* U. S. Hydrographic Office, Washington, 1896. 



f The Development of Great Circle Sailing. Washington : Government 

 Printing Office, 1399, p. 36. 



