z66 DEVELOPMENT of a certain 



2. Also, find E' half the perimeter of another ellipfe, o f which 

 the femi-tranfverfe axis = i, the femi- conjugate axis — ^^ ~ ■ * 

 and excentncity = y 



Let «• denote 3.14159, &c. 



Then, A rz , — , ■>. ^„ — jst-Z' 



^ — b ^ — bi<i^—b^yii- 



If either of the ellipfes E, E', were judged to be of fuch a 

 form, as that the feries for its redification converged too flowly, 

 then another eUipfe, either more or lefs excentric, might be fub- 

 ftituted for it thus : 



Let e and c denote the excentricity and femi-conjugate axis 

 of the ellipfe E, and e' and c' the fame things of the ellipfe E'. 



3. Compute (?' rz \~, and d ■=. ^-^ ; then e- and c' will de- 



jiote the excentricity and femi-conjugate axis of an ellipfe more 

 excentric than either E' or E. 



4. Or, compute e" — ^TJi and c" — '^~-. ; then e'^ and c* will 



denote the excentricity and femi-conjugate axis of an ellipfe lefs 

 excentric than either of the fame ellipfes. 



5. Compute E' half the perimeter of the ellipfe, of which the 

 excentricity is e\ 



6. Or, Compute E"half the perimeter of the ellipfe, having 

 its excentricity zz e% 



— i±i F^ a. £(l±f) p' 



— 2+C^ "*■ 3 +C ^' 



— lif' V,' <^'(t + O £// 



1 +e' I + e' 



= 7^^E--^,E\ 



2 + e' ' a + c 



14. There 



Then, E < 



'! 



