ALGEBRAIC FORMULA. 293 



4. Computation of eR t and thence of z the arch required. 



Logarithms. 



** a (l .*° fin 2?' = + .1075153 1.0314702 

 ^+ f0(l + g//) nn 4 /- — 0063127 5.8002164 



a.a.a. . a , a . a fm8( P =+-000°OI 7 6.2210236 



^R = .1012043 

 0P(i — ^QJ) = .9978042 



The elliptic arch % == 1.0990085 



It appears from the preceding calculation, that the length of 

 the elliptic arc would in this cafe have been found with nearly 

 the fame degree of accuracy, if inftead of computing the three 

 quantities e', e", <?"', alfo fin 2<p', fin 4<p // , and fin 8<p'", we had on- 

 ly computed two of each feries, viz. e and e" of the one, and 

 fin 2<p', fin 4<p // , of the other feries ; or, fuppofing all the three 

 quantities of each feries to have been computed to a fufficient 

 number of places of figures, it is evident that we might thence 

 have found the length of the arch to feveral more places of fi- 

 gures than we have here made ufe of. 



Vol. V.—P. II. Pp XIL 



