30 TJ. S. COAST AND GEODETIC SUKVET. 



DERIVATION OF STEREOGRAPRXC MERIDIAN PROJECTION 

 BY FUNCTIONS OF A COMPLEX VARIABLE « 



The element of length upon the sphere is given in the 

 form 



dS^ = a" {dcp" + d\^ cos V) = ^' cos V C^- + ^^') 

 If we set 



cos (p 



dS becomes 



dS^'^a' cos2 ^ (d(T^ + d\^). 



Any conformal projection may then be expressed as a 

 functio n eit her of o- + '^ X or of a — i\, in which i denotes as 



usual V— 1- 



Jd(p _ /* dip 

 cos <^~ I . /tt , \ 



j2sing + |)cosg+|)" 



cr= + loge sin (j + |)-ioge cos (^ + |) 

 (r=logetan ('^+|J» 



2 



a See General Theory of the Lambert Conformal Conic Projection, Special Publication 

 No. 53, U. S. Coast and Geodetic Survey. 



