m MEASUREMENT OF AN ARC 



to each focceffive degree will be m . Sin. 2 latilode of the 

 , point of that degree, fo that 

 (I) (0 



X rz X.4" ^^^ latitude ..{iU'4- o) ^ 



(2) (!) 



X = X + »|- m , Slu. 2 (L i- o) 



(3) (0 «'■ 

 X:=: X + o -f. j?j . Sio. 2(L .f 0) -?at . Sla. 2- (L .+ .5) 



O) (0 



Xi=z X 4- -f wj . Sin. 2 (L -i- o) ~ OT . Siu.0 2<L -f-J) 4K . Sin. i.-(L S) 



(0 (i) ■ o 



Thfiiis X =: X + o for lat, (L. -h o) 



m 0) o 



J^z:: X -f-m (Sin. 2-(L -f. o) 



X::=X+m5;-^(^^-^«')i 

 •{Sin. 2 (L T 1>] 



(4) 0) ISi-nl' + O) I 



I Sin. 2 (L 4- 0) I 



= X+Ksiu. 2(L + 1) >^ 

 I 



L Sin. 2 ( L + 2) J 



c. 



r 



" Sin. 2 (L 4-0) 



j Sin.2(L 4-2) &c. I 



UoSin, 2(L + (« — 2)J 



(1) (?■) (3) (4) (n) 



Put X -f X + X + X . . . -o X.= ^ 



(1) 



'Then ^ = ?i X + 7?2 \72 — i . Sin» :s (L + o) .4- -ra — 2 .,Sin. s (Z-f r 



(I) 



J ~,n X 



^72 —.3 . Sin. a ,(I + 2) + ?^ — 4 Sin. 2 (L 4» 3) &c. 

 imd W2 == - — -=-- — 



72 — 1 . Sin. 2 ( L + o) + n — 2 . Sin. 2(^4 l)x n ~~ S . Sin. 2 ( L + 3),^i%c. 



Now 771 being determined, it will be eafy to compute the fucceCi\/e 



^egi-ees^ for from the above arrangemsnt it appears that 



