THECmY OF POLYCONIC PROJECTIONS. 87 



shall have the equation of the X meridian and, by the 

 elimination of X, we may obtain the equation of the 

 parallel of latitude «p. 



,_ A^ + 2ABe-^^'' cos 2^\+B^e-^' 

 ^'^y U2g2^a ^ 2AB cos 2^X + B^e-^^y 



-2/3<r 



Therefore 



A'e^^' + 2AB cos 2^\+B^e-^^' 



^2^2= - (A^^' cos 2/3X+5) 

 ^ ,=^e2^''sin 2i8X. 



From these, by the elimination of cr, we obtain 



X 



or 



x^+y^ + ^y+'gc cot 2i8X = 0. 



/ . cot 2^X V , / , ly 1 



y "^ ~^B^J '^y^2B)~~^^ sin^ 2^X' 



This is a circle, the center being at the point 



cot 2i3X 

 ^0"" 2B 



_ J_ 



^0" 2B 



and its radius being 



1 

 ^« 2j5sin2/3X* 



This equation is identically satisfied by the values x = 0, 



^ = 0, and by a: = 0, i/=— ^J since all meridians pass 



through these points, they represent the two poles; the 

 Y axis is the central meridian. 



