THEORY OF POLTCONIC PROJECTIONS. 113 



n=V^+cosVm- 



Having thus found n, we would calculate ^'m by means of 

 the formula 



2 n 



Then we should have for the determination of po 



tan^ = tan^('cot^)^. 



For example, if the principal place was found on the 

 Equator, we should have 



<^m = 0, 7z,= V2, v?'m = 0, andpo = 2' 



The Equator woidd then be represented by a straight line 

 and the system of projection would be defined by the 

 equations 



tan " ' ' " '^^ 



l'=(*-i) 



A special case considered by Lagrange is given by the 

 values of definition 



s = cot K 



Hence 



or 



5==cot 2 



cosec <^' = cot ^ 

 cot X' = cot ^ 



^ -2 

 1 



tan I =(tan|) - 



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