130 S. L. Penfield — Stereographic Projection. 



method of applying a scale of miles in a straight-away direc- 

 tion across a map. For the sake of demonstration, the distance 

 between New York, 74° W., 40° 40' N., and New Orleans, 

 90° 7 W., 29° 55' N., was chosen. Making use of atlases, only 

 those maps can be employed on which both New York and 

 New Orleans appear on the same sheet, therefore maps of 

 the whole United States must generally be used. On a 

 number of such maps, varying in width from 14 to 26 inches, 

 and accompanied in each case bv a scale of miles, the following 

 results were obtained: 1170, "ll80, 1185, 1190, 1200, and 

 1210 statute miles. On all the maps, the position of the two 

 places with reference to the meridians and parallels corre- 

 sponded closely with the longitudes and latitudes as already 

 given. By calculation from the longitudes and latitudes as 

 given, the distance was found to be 16° 52', or 1166^ statute 

 miles. By plotting in equatorial projection, and measuring 

 with protractor No. II, the distance was found to be 16° 53' 

 (figure 22 shows both New York and New Orleans in equato- 

 rial projection). By plotting four different times in meridian 

 projection, using the method shown in figure 23, page 124, the 

 distance as measured by protractor No. II was found to be 

 16° 53', 16° 53', 16° 53V and 16° 58'. It should be explained 

 that in three cases (a zero point of the protractor being at New 

 York) New Orleans fell just short of coincidence with the 17° 

 line of the protractor; hence the position was recorded as 16° 

 55'. In one case it was on the 17° line. From these readings 

 2' were deducted to allow for the shrinkage of the celluloid 

 protractor. It is in part accidental that four of these deter- 

 minations, 16° 53', came so close to the calculated value, 

 16° 52'; still it is seldom that an error of 6' is made in plot- 

 ting and measuring on a meridian projection, and the 

 average of measurements of a similar nature which the writer 

 has made would be not over 4 r , probably not over 3', from the 

 truth. Consider for a moment the discrepancies between 

 measurements as made on ordinary maps and those made by 

 means of the stereographic projection. On maps including the 

 United States alone, and varying in width from 14 to 26 

 inches, the measurements ranged from 1170 to 1210 miles, a 

 maximum error of 44 miles ; while on a stereographic projection 

 of 14 centimeters (5-J- inches) diameter, comprising a whole 

 hemisphere, the greatest error was less than seven miles, the 

 average error being but two miles. To appreciate better the 

 discrepancies of the two methods, compare the size of the 

 whole North American continent, as shown on the stereo- 

 graphic map, plate IY, with an ordinary map of the United 

 States. It seems to the writer that this example furnishes a 

 strong argument for discarding the defective methods of map 

 representation now in general use. 





