THEORY OF POLYCONIC PROJECTIONS. 91 



By performiiig the indicated operations, we obtain 



^ Z: tan^( j + ^ )-l a 



tan 7y= 7- — -X tan ^• 



(M)- 



The projection is thus found to be identical with the one 

 previously obtained by a different procedure. 



With these values the magnification (denoted by Ic' for 

 distinction) for the ellipsoid becomes 



, , 2ckn-yjl — e^ siriV 



a cos <p (^6^*^ + 2^ cos TiX + e-^"^)' 

 in which 



= tan^(:7 + g ) . ( q- r— ^ ) 



\4 2/ Vl+€sm<^/ 



If the parallel, the latitude of which is — a, is to be repre- 

 sented by the circle of infinite radius or by the straight 

 line, among the circles of parallels, which forms the perpen- 

 dicular bisector of the line joining the poles of the projec- 

 tion, then the radius of this parallel and the distance of its 

 center from the origin must become infinite. This wiU be 

 the case if 



Ptan^-(^^-|) 

 hence 



Ptan-(^-^)-l=0 

 or 



If, for the sake of abbreviation, we set 



the expression for the center of the parallel becomes 



c(w?-\-l) • 2cm 



iCo = 0, yo— 2_i y ^^^ the radms becomes Po= ^2_] 



