GEODESY. 



lui 



^2 



a — r^: 

 r-i — r^z 



V 3 15 35 / 



- TrSk ^' - • • •). 



a (I 



I ^'" — sVff 



^ ae^ (i -\- -^ e^ -\- . . . ) = 0.00113 ^) about. 



^ ac* -j- . . . = 0.00000 1 a, about. 



II. Co-ordinates for the Polyconic Projection of Maps. 



In the polyconic system of map projection every parallel of latitude appears on 

 the map as the developed circumference of the 

 base of a right cone tangent to the spheroid along 

 that parallel. Thus the parallel EJ^ (Fig. 2) 

 will appear in projection as the arc of a circle 

 EOF (Fig. 3) whose radius OG ^= I is equal 

 to the slant height of the tangent cone EFG 

 (Fig. 2). Evidently one meridian and only one 

 will appear as a straight line. This meridian is 

 generally made the central meridian of the area 

 to be projected. The distances along this cen- 

 tral meridian between consecutive parallels are 

 made equal (on the scale of the map) to the real a\ 

 distances along the surface of the spheroid. The 

 circles in which the parallels are developed are 

 not concentric, but their centres all lie on the 

 central meridian. The meridians are concave 

 toward the central meridian, and, except near the corners of maps showing large 



areas, they cross the paral- 

 lels at angles differing little 

 from right angles. 



In the practical work of 

 map making, the meridians 

 and parallels are most ad- 

 vantageously defined by the 

 co-ordinates of their points 

 of intersection. These co- 

 ordinates may be expressed 

 in the following manner : 

 For any parallel, as EOF 

 (Fig. 3), take the origin O 

 at the intersection with the 

 central meridian, and let the rectangular axes of Y (OG) and X (OQ) be re- 

 spectively coincident with and perpendicular to this meridian. Call the interval 

 in longitude between the central meridian and the next adjacent one AA, and ■ 

 denote the angle at the centre G subtended by the developed arc OFhy a. 



