362 Pen field — Use of the Stereographic Projection for 



the stereographic, irregular curves on the polyconic map. The 

 thirty-ninth parallel is the same for both projections ; while in 

 the polyconic the twenty-seventh has a larger, and the forty- 

 seventh a shorter, radius than the corresponding parallels of 

 the stereographic projection. Based upon a sphere of 1*8 

 meters diameter, the radii for describing the three parallels 

 mentioned are as follows : 



Parallels 27° K 39° N. 47° N. 



Stereographic 148'05 cm lll*14 cm 90*22 cm 



Polyconic 176-63 111*14 83'93 



By examination of figure 27 it may be seen that near the 

 center the two projections are nearly alike, while near the 

 periphery there are decided differences, the stereographic 

 showing less distortion than the polyconic. Take, for example, 

 Key West and St. John. Their positions are indicated by 

 dots in the stereographic, and by circles in the polyconic pro- 

 jection ; hence it is evident that when measured with a scale 

 of miles, their distance apart must be considerably greater in 

 the polyconic than in the stereographic projection. Moreover, 

 owing to distortion, the distance measured with a scale of 

 miles on the stereographic map, page 351, is already too great. 

 As regards the measurements made with the scale of miles 

 accompanying the polyconic map of the survey, it should be 

 stated in all fairness that the errors given on pages 350 and 

 351 are to some extent misleading, for undoubtedly exactly 

 the same data were not used for locating places on the poly- 

 conic map as were employed by the writer. For the purpose, 

 however, of illustrating that the stereographic projection is 

 better than the polyconic, the comparison is a perfectly fair 

 one. There is one noticeable feature of the measurements 

 made on the polyconic map ; namely, with two exceptions, 

 the measured distances are too great, hence it is evident that 

 a somewhat better scale of miles might have been chosen than 

 the one published with the map. No scale of miles, how- 

 ever, would give such satisfactory results as were obtained 

 from the stereographic map and given on pages 350 and 351. 



In a publication issued by the IT. S. Coast and Geodetic Sur- 

 vey,* entitled, " Methods and Results. A review of various 

 Projections for Charts in connection with the Polyconic Pro- 

 jection used in the Coast and Geodetic Survey" a brief 

 summary of the principal methods of map projection is given. 

 Referring briefly to the more common projections, including 

 the orthographic, stereographic, gnomonic or central, and some 

 modifications of the globular, the following statements are 

 made : 



* Report for 1880, Appendix No. 15. 



