THEORY OF POLYCONIC PROJECTIONS. 



173 



throughout this publication these values are given by the 

 expressions 



X = pn cot ip sin (X sin ^) 



^ = Pn cot ip\\ — cos (X sin ^)] = 2pn cot (p sin^f — ^— ^ ) • 



In the tables as pubHshed in the International Map 

 Tables, the x coordinates were computed by use of the 

 erroneous formula 



a; = pn cot ip tan (X sm ^). 



The resulting error in the tables is not very great and is 

 practically almost negUgible. The tables as given below 

 are aU that are required for the construction of aU maps up 

 to 60° of latitude. This fact in itseK shows very clearly the 

 advantages of the use of this projection for the purpose in 

 hand. 



A discussion of the numerical properties of this map 

 system is given by M. Ch. LaJlemand in the Comptes 

 Rendus, tome 153, page 559. He finds that the maximmn 

 error of scale of a meridian is 1 part in 1270, which 

 corresponds to 0.35 mm. in the height, 0.44 m., of the sheet. 

 The maximum error of scale of a parallel is 1 part in 

 3200, and the greatest alteration of azimuth is 6 minutes 

 of arc. These errors are much smaller than those occa- 

 sioned by the expansion and contraction of the sheet due 

 to atmospheric conditions. 



TABLES FOR THE PROJECTION OF THE SHEETS OF THE 

 INTERNATIONAL MAP OF THE WORLD. 



[Scale 1: 1 000 000. Assumed figtue of the earth: 0=6378.24 km. ; 6=6356.56 km.] 



Table 1. — Corrected lengths on the central meridian, in millimeters 



