350 Pen field — Use of the Stereographic Projection f< 



or 



tion to be equivalent to 22° 4', -or 1526 statute miles : hence 

 by simple proportion it was determined that 1000 miles were 

 equal to 22*986 cm . The scale of miles thus determined would 

 be a trifle too long for the central portion of the map, too 

 short for the outer portions, while there should be an inter- 

 mediate portion for which it is approximately correct. 

 Accordingly three circles were drawn about the center of the 

 map, rather empirically it is confessed, which may be regarded 

 as approximately defining certain zones to which the scale of 

 miles is applied. The results of the measurements will be 

 given in groups, according to the zones in which they are 

 made. For future comparison measurements made on the 

 poly conic map of the Geological Survey, referred to on page 

 273, are also given. 



Group I. 



Philadelphia to Trenton _ _ . 



New York to Buffalo 



New York to Chicago 



Buffalo to Duluth 



New York to New Orleans. 



Buffalo to Ealeigh : 



Nashville to Ealeigh 



Nashville to Lansing 



Baltimore to Columbus 



Indianapolis to Lansing _ _ . 



Calcu- 



Meas- 





Cor- 





Poly- 



lated. 



ured. 



Error. 



rected. 



Error. 



conic. 



28 



28 











34 



297 



298 



+1 



297 







290 



710 



711 



+1 



710 







711 



700 



700 











713 



1166 



1167 



+1 



1165 



-1 



1188 



491 



493 



+ 2 







512 



446 



449 



+ 3 







468 



474 



471 



-3 







479 



346 



349 



+ 3 







367 



223 



220 



-3 











230 



+ 6 



-7 

 + 1 

 + 13 



+ 22 

 + 21 

 + 22 

 + 5 

 + 21 

 + 7 



In the foregoing group the distances measured fell almost 

 wholly in the intermediate zone, between circles I and II, 

 figure 21, for which the scale of miles is approximately cor- 

 rect. Since New York lies slightly beyond circle II, slight 

 corrections, which will be explained later, have been made in 

 three cases, but they do not materially alter the results. The 

 maximum variation, =fc 3 miles, is scarcely greater than prob- 

 able errors of plotting and measuring. 



Group II. 



San Diego to Portland, Me. 



Duluth to St. Augustine 



Helena to Denver . 



Lincoln to Springfield, 111 



St. Paul to New Orleans 



St. Louis to Denver 



New York to Denver 



New York to San Francisco 



Portland, Ore. to New Orleans 



San Diego to Duluth 



Olympia to St. Augustine 



Calcu- 



Meas- 





Cor- 





Poly- 



lated. 



ured. 



Error. 



rected. 



Error. 



conic. 



2620 



2617 



-3 



2624 



+ 4 



2657; 



1311 



1307 



-4 



1313 



+ 2 



1344| 



587 



583 



-4 



585 



-2 



592 



394 



388 



-6 



392 



-2 



384| 



1048 



1040 



-8 



1048 







1062 ; 



794 



785 



-9 



793 



-1 



796 



1630 



1623 



-7 



1631 



+ 1 



1635 



2569 



2564 



-5 



2570 



+ 1 



2587i 



2056 



2048 



-8 



2055 



-1 



2093! 



1636 



1631 



-5 



1639 



+ 3 



1660; 



2514 



2507 



-7 



2515 



+ 1 



2546 ! 



+ 37 

 + 33 

 + 5 

 -10 

 + 14 

 + 2 

 + 5 

 + 18 

 + 37 

 + 24 

 + 32 



In the foregoing group all of the measurements are too low, 

 but it is noticeable that the variation in no case amounts to ten 



