THEORY OF POLYCONIO PROJECTIONS. 135 



The condition that the areas should be preserved along 

 this line will then be 



or, by integration, 



^ J. + ^ tan2 — j tan "2 =X, 



no constant being added, since X and X' vanish simulta- 

 neously. 



There is an infinity of circular projections with oblique 

 angles that are atractozonic. If we suppose the meridian 

 of 90° of longitude represented by the circumference 

 described upon the hne of poles as diameter, these pro- 

 jections are furnished by the following equations: 



o / . • o / /I . o /\ 2€ — sin 2e 



2^ +sm 2^ —(1 +COS 2(p )-^ o~ = '"' sm (p 



i. — cos .Z€ 



2X^-sui2X^ _ 

 1-C0S2X' ~ 



The first leaves yet undetermined one of the two quantities 

 <p^ and € as a function oi (p; as to the second, it is incom- 

 patible with the condition of preservation of areas along 

 the Equator, which proves that no circular projection 

 with obUque angles can be equal-area in the complete 

 sense. 



PROJECTION OF NICOLOSI OR GLOBULAR PROJECTION. 



In this projection the Equator and the central meridian 

 are foimd developed in straight lines and with their true 

 lengths; the principal meridian is represented by the 

 circimiference described upon the line of poles of the 

 map as diameter; and, finally, the arcs of tnis meridian 

 and the corresponding arcs of the circumference are pro- 

 portional. We therefore have 



