THEORY OF POLYCONIC PROJECTIONS. 143 



Also 



Bm^=— I ^ (^+s)-4j 



, sec <p r/ TT . \ <^s , "I 



ORDINAR7, OR AMERICAN, POLYCONIC PROJECTION. 



This is the projection that is generally referred to in this 

 country as thepolyconic projection; but we have attempted 

 to show that the polyconic projection class is an exceed- 

 ingly broad one and that it contains examples of almost 

 every kind of projections. The name Amencan polyconic 



Erojection has been given to it by European writers chiefly 

 ecause it has been extensively used by the United States 

 Coast and Geodetic Survey; in fact, the projection seems 

 to have been devised by Supt. F. R. Hassler to meet the 

 requirements in the charting of the coast of the United 

 States. 



For convenience of reference we shall give again the dif- 

 ferential formulas developed on pages 10-13 : 



Krn^ 



ds . dp 

 •j- cos B—-T~ 

 (Up (JUp 



(l-e^sinV)'^'/(^ ^ dp' 



-e^sinV)'V (^ . dp\ 



a(i-e^) U^^"^ 5?;^^^ 



^ _ p(l-6^sinV)^ d^ 

 P a cos ^ dX 



^^ p (1 - e^ sinV)^ /^ ^ 003 g ^^\ ^^- 

 a^ (1 — e^) COS <p \d<p dip) dX* 



The characteristics of this projection are that each par- 

 allel is the developed base of the cone tangent along the 

 parallel in question; that the parallels are spaced along the 

 central rnendian in proportion to their true distances apart 

 along this meridian; and, finally, that the scale is main- 

 tain^ constant along the parallels. 



