3i6 On the FIGURE of the EARTH. 



a 



X 



"/a' + c" 



= _ = 



a: Va' + c' 



b =— = s^a' + c^ 



X 



Put z = the length of the elliptic arch AL 

 V = that of BL 



53 = — v/ 1-^ 1 by the nature of the curve : 



a ^ a" — x' ^ 



put a' — c = a then z = — v/ — i r- = — x 



■s/a" — d' x'^ X a* — d' x''^ , n r X 



— — ==— = — X ■ . z = the riuent or _ x 



\/a — X a a — x ^ a 



a' — d\x'^ 



Z I -I. 



a — X - 



, d'x' d^x* d'x' s^"^' o 



2 a S a 16 a izSa 



,. x' X* x' jx" 



e — x-^=:a -3-^ -r—r n~7' '^'^* 



The former of which feries being divided by the lat- 

 ter, the quotient is c + — — j + 0—7 x 3 «' + d^' + -7-77 x 



&c. which multiplied by — becomes 



c'x'x 



X + + -Q-x X 3 ^ + i + 7— -TT X 3« + 2.. ^/ + ^ 



2 a^ a 1 -r/ 



> 8 

 C X X 



+ — ^r-Td X 35^'*+ li'^^^^ + Q^'^'^ + i A ^c. the 



120 t2 



fluent of which is 



