S. L. Penfield — Stereographic Projection. 133 



protractor also would have to be increased in like proportion. 

 On such a scale the first degree of the protractor would be 

 g.gmm ( near ]y a centimeter) from the center, and if the small 

 circles of the protractor indicated tenths of a degree (6'), the 

 graduation would be far coarser than that of protractor No. 

 II, plate I. If the small circle graduation of the protractor 

 indicated every fourth minute, the first line would be distant 

 0'652 mm from the center, while the first-degree line of protractor 

 No. II, plate I, is 0*611 mm from the center. It will be at once 

 evident to any one accustomed to reading scales, that, with 

 divisions 0*65 mm apart, one quarter of the distance between 

 such divisions may be easily estimated, and with care, perhaps, 

 one eighth, which would be equivalent to half a mile on a map 

 of corresponding scale. By making use of a dividing engine, it is 

 possible to construct protractors of any size ; and used in con- 

 nection with carefully plotted maps, geodetic measurements 

 can be made with almost any desired degree of accuracy. 



For purposes of navigation of the North Atlantic, for exam- 

 ple, it would seem that nothing could be simpler than a stereo- 

 graphic chart with 35° W., 45° N., at the center. On such a 

 chart, 18 inches or more in diameter, all ports and lighthouses 

 could be accurately located. If a navigator can determine his 

 longitude and latitude correctly, which under favorable con- 

 ditions he is supposed to do within a minute (nautical mile), all 

 that remains to be done to find the distance from any desired 

 point would be to locate his own position on the chart, shift a 

 stereographic protractor so as to bring the two points on the 

 same great circle, and note the position of the two points with 

 reference to the small circles. The great circle, which it would 

 not be necessary to draw upon the chart, would indicate the 

 sailing direction. Compass bearings could be determined by 

 means of an ordinary protractor, as indicated on page 19, 

 figure 12. Calculations involving the use of tables and for- 

 mulas would not be necessary. An 18-inch chart would 

 probably be quite large enough for practical purposes. At all 

 events, the errors in determining longitude and latitude would 

 probably be as great as those resulting from locating the points 

 on the chart and reading the protractor. The position of a 

 ship from day to day being noted on a stereographic chart, the 

 daily runs could be determined directly by means of a stereo- 

 graphic protractor. Without doubt, vessels have frequently 

 been wrecked because of failure of the commanding office^ to 

 make his calculations correctly, but if ships were provided with 

 suitable stereographic charts and protractors such accidents 

 might be avoided. A navigator may make a mistake in locat- 

 ing his position, but, that having been correctly determined 

 and located on a suitable chart, • a stereographic protractor 



