^ = ^2g4^'. 



88 U. 8. COAST AND GEODETIC SURVEY. 



If we eliminate X, we get 



(52+^ + ^ j -^ {x^ + y2)2 



Developing and arranging, we get 



Dividing by x^+y^, since this can only vanish for a;=0, 



y = 0, we get U^g^^cr _ ^2) (^2 _^ ^2) _ 2By = 1 



or 



or 



^^V A^e^'^-B'J ~ {A'e'^'-B'y 

 This is a circle with center at the point 



and with radius 



Since we know that the projection is conformal, it is 

 kaown that the magnification is the same at any point 

 in all directions. We can determine its value along a 

 parallel and in that way determine its value in all 

 directions. 



bx 2A^ cos 2/3X {A'e^'+B^e-^'') + ^A^B^ 

 d\ ~ {A'e^^' + 2AB cos 2^\ + B'e-^^'^Y 



by 2A^ sin 2^X U V^ + ^e-^^*^) - 4^^l8e-2/3<^ sin 2^X 

 dX ~ U^e^^' + 2AB cos 2|8X + B^e-'^^^Y 



4^232 



/dS\/bx\\/byV 



\d\J "Vdxy '^\b\J ~{A'e^^- + 



2 AB cos 2^\+B^e-^^-y 



