Geographical Mays and Sailing Charts. 349 



dashed line gives 86° 15', and a point a trifle less than half 

 way between them determines a point on the desired meridian, 

 86° 6', which is then transferred to the map by puncturing 

 with a needle point. Through the point thus found a short 

 line is drawn parallel to the meridians, and over it the sliding 

 scale is again adjusted so that its outer lines cover the nearest 

 parallels, 39° and 41°, when the desired latitude 39° 47', is 

 located on the meridian 86° 6' by puncturing through the scale 

 just above the dashed line indicating 45'. Using the method 

 just described, it is probable that places were located on the 

 map within two miles of their true position, the chances being 

 that the average error was less than a mile. 



Any straight line drawn through the center of the map, 

 39° N. 97° W., figure 21, accurately represents the track of a 

 great circle, and the map corresponds to so small a portion of a 



22 



hemisphere, figure 20, that even near the periphery, where dis- 

 tortion is greatest, a great circle does not differ much from a 

 straight line ; this may be tested by applying a straight edge to 

 one of the outer meridians, which show the greatest curvature. 

 Moreover, distortion on the map is so slight that very satis- 

 factory measurements may be made with a scale of miles, and, 

 because of the evident importance of this simple method of 

 making measurements, this property of the map has been very 

 thoroughly tested. The examples chosen include distances over 

 all sections of the map, and they are sufficiently numerous to 

 give a satisfactory average idea of what may be accomplished 

 by such methods of measuring. The adoption of a scale of 

 miles suitable for a given map is a matter deserving special 

 consideration. Taking distortion into account, it is evi- 

 dent that a scale of miles adapted to the center of a stereo- 

 graphic map, figure 21, would be too short when used near the 

 periphery, and vice versa. As, on the other hand, the distor- 

 tion over the whole extent of the map is not very great, it was 

 assumed that a scale of miles could be found which would give, 

 on the average, satisfactory results when applied to any part 

 of the map. Accordingly the distance from the center of the 

 map, 39° K, 97° W., to a point near the periphery, 37° E"., 

 69° W., was selected as the basis of a scale of miles. The dis- 

 tance measured 35'08 cm on the map, and was found by calcula- 



