THEORY OF POLYGON IC PROJECTIONS. 93 



The parallel circles whose latitudes are greater than — a 

 lie on the positive side of ^; those with latitudes less than 

 — a. lie on the negative side. 



In the expressions for the projection to which we have 

 arrived, c, a, and n are constants that we can determine to 

 fit such conditions as we may require the projection to 

 fulfill, these being limited, of course, to the conditions 

 that are possible in a conformal map. 



c determines the scale of the projection and it may be 

 any real constant, so that it only remains to determine a 

 and n. If q; = 0, then the straight line parallel represents 

 the equator and m becomes 



=KM)' 



m 

 so that ^ = 1 . 



SPECIAL CASES OF THE PROJECTION. 



If n converges to zero, and at the same time c converges 

 to 00 in such a way that cn = 2a, we obtain a projection 

 in which the parallels are represented by straight lines 

 perpendicular to the Y axis since their centers lie at 

 mfinity on the Y axis. In the same way the meridians 

 have infinite radii with centers at infinity on the X axis ; 

 consequently they are perpendicular to this axis. 



To determine the values we have 



_,. r 2cm sin n\ "1 

 n^O^ Ll + 2m cos n\ + m^J 



cn=2a 

 m=l 



I 2m en ( 

 a; = lim — , , ^^ 

 ^ = L 1+277 





■)■ 



+ 2m cos n\ 4- m^ 



cn = 2a 

 m=l 



