MEASUREMENT OF AN ARC 



refpeaive latitudes are 4 4 4 '^c. Then it is knowa that if that 



aieddian of theearth be an ellipfe, 



X - X 



(1) m Jl) 



3 X (Sin.* i ~ SiB.» /) 



will exprers th( 



compreffion^ iec the ratio of the polar to the equatorial diameter be 



what It % 



m in 



X ~ X 



f) (2) (•) 



5 X (Sin.2 ; — Sja.2 /) 



isalfo equal the fame com- 



(3) f'J 



X — X 



X ~ X 



fi) (^1 (M c) m m 



(!> (1> Cl> Vm.' l^S-uJt 



.Sin.* I — SiQ,» I 



If® 



(1) 



m m (i) \Sin.* i -Sin.*/ 



: X + (X « X) 



SIho^ I — Sin.* i 



(5) (1) 



!) '\Si-'.* I -- Sin.* / 

 X ^ X + (X =. X) , < — >^u 



m v)( 



Sin.* I «- Siuo* J 



n) (I)" 



(fj) (1| (?) CS) \Siii.* I — Sin,* / 



X = X Hh C^ -^ ^>' 



^JDo^ i ~- SiB.* I J > 



mg X s X + (X ~ x>. ,< ..^ : -A = X 4- (X -^ x> ; 



(2) (OC 



^S|n.« i — SiD * I J .^ 



O) («) en CO \Su..« / - Sin.M f O) 



"' X + (X - X) . ^ .— — ^> = X 4- • 



(2) (0^ 



Sdu.* < — S,u.« I 



