THEORY OF POLYCONIC PROJECTIONS. 81 



Let i denote as usual V~ 1 and assume the relations, 



x + iy=f2((T-i\), 



bhen/i and/2 are conjugate functions of a complex variable 

 that are only limited to beiDg analytical functions. From 

 these we find at once 



or, denoting /i(o' + '^X) by/j and/jCo- — iX) by/2, 



^ = j(/l+/3) 

 ^y=- 2^/1-/2) 



dX 2^^ ^^J ^^' 

 From these equations it follows that 



do" dX dX da 



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