THEORY OF POLYCONIC PROJECTIONS. 33 



In order to take into consideration the ellipsoidal shape 

 of the earth, we proceed in the following way. If we 

 denote the element of length upon the ellipsoid by cZS, 

 we have 



L(l — e^ sinV)^ 1 — €^ sinVJ 



1 — e^ sinV L^osV (1 — ^ smV) J 



In this case 



dff — ^- — ■ 



cos <p (1 — €^ sinV) 



1 — e^ S>VD?(p — ^ COJ 



COS <p (1 — €^ sir 



dip ^ COS (p d(p 

 cos <p 1 — e^ sinV 



(1 — e^ sinV — €^ cos^<^) dip 

 ~ cos (p (1 — €^ sin^^) 



dip 

 "2 



_ dip € / € COS (p dip e cos <p dip \ 



(~ tT" \~2V1 — €sin^ l+€sin<zj/ 



2 + V 



[cos^Q + |) + sin^Q-f|)].Z. 



2sin(^+|)cosQ.-|) 



€ / e cos ip dip e cos y? (Z<p \ 

 2\1 — €sin<jj> l + €sin^/ 



"^ J-(M)' J-(M) 



£ r € cos (p dip e_ C e cos ip dip 

 ~2J 1 — €sin^ ~"2j l+€sin<^ 



<7 = l0ge sin (|+|)-l0ge COS (f + |) + ^ loge (1 - € sin ip) 



-^loge (1 + 6 sin v?) 



991943 O - 52 - 3 



