94 U. S. COAST AND GEODETIC SURVEY. 



The limiting value of this is seen to be 



71=0 L-l +2m cos nX+m^J 



cn=2a 



=lim [c(m^-l)] 

 ri=0 4 



m=l 



= -r lim 

 4 



n=0 



en— 2a 



a T 

 =^lim 



71=0 



p-K(M)-in 



r tan-nQ+|)-l1 



71=0 



The value of this expression at the limit is 



2/ = aloge tan^^ + lj. 



We have thus arrived at the Mercator projection as a 

 special case of Lagrange's^ projection. Although it is 

 not a polyconic projection in the accepted sense, yet it 

 appears as a special case of one of the important projections 

 of the polyconic class. Lambert s conformal conic pro- 

 jection can also be obtained as a special case by letting 

 B become equal to zero in the equations containing the 

 A and B constants. 



*j Since ^ a^=a^ loge o I 



