352 Pen field — Use of the Stereographic Projection for 



close measurements may be made with a scale of miles, mak- 

 ing no correction, or allowance for distortion. Except in the 

 case of long stretches on the Atlantic or Pacific coasts, for 

 which a reduction of one or two miles per hundred should be 

 made, no uncorrected measurement between places accurately 

 located should give an error of over ten miles. By applying 

 very simple corrections, as indicated, it may be assumed that 

 measurements made on any part of the map are probably cor- 

 rect within three miles. The error of the corrected measure- 

 ments exceeds six miles in only one case, that being from St. 

 John, N. B., which lies considerably beyond circle III, to Key 

 West. Excepting the last two measurements of Group III, 

 the errors of the corrected measurements amount to four miles 

 in only two cases, and the average error is less than two miles. 

 It is doubtful whether there is any other method of projection 

 which will give an equally good map of so large a country as 

 the United States, and one upon which better results of meas- 

 urement may be obtained by means of a scale of miles, than 

 those recorded in the foregoing tables. For a country con- 

 taining as many square miles as the United States, but more 

 symmetrical in shape, a better scale of miles could be adopted 

 than the one used in making the measurements recorded on 

 pages 350 and 351. 



On the original map, from which the measurements referred 

 to on pages 350 and 351 were made, one mile equals 0'23 mm or 

 0*009 inch; the scale of the map being practically 111 miles 

 to the inch. A scale of miles based on the average of aU the 

 recorded measurements was found to be 229*53 mm equal 1000 

 miles, a most satisfactory agreement with the one adopted, 

 229*68 mm , which, as explained on page 349, was based upon 

 the distance from the center of the map to 37° N., 69° W,, 

 near the periphery. 



No stereographic protractor has been made to accompany 

 the map of the United States, but to make one graduated to 

 either miles or degrees would involve no difficulties. By 

 means of a protractor the results would be exact, considering 

 of course the limitations of making a map and reading scales 

 exactly. Certainly the errors would seldom amount to more 

 than two miles, and it may also be said that it would be almost, 

 or perhaps quite, as easy to make measurements with a pro- 

 tractor as with a scale of miles. 



Stereographic Map of New York State. — It may be a matter 

 of some interest to know whether it would be worth while to 

 apply the principles of the stereographic projection to an area 

 as small, for example, as New York State. Numerous methods 

 of projection may be applied to so small an area, with results 



