E 



266 DEVELOPMENT of a certain 



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



the femi-tranfverfe axis = 1, the femi- conjugate axis — " ~ ■ ' 



b 

 and excentricity = -• 



Let k denote 3.14159, &c. 



Then, A = {a + b ^ a _ by • £ 



id 2 E' 



B — y A — ^o* — b 1 } * v 



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

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

 then another ellipfe, 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'. 



a. Compute e — — ■— - and £ zz -^p- ; then e~ and c~ will de- 



° I + v 1 + e J 



.note the excentricity and femi-conjugate axis of an ellipfe more 

 excentric than either E' or E. 



4. Or, compute t" — *T% 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 x 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 = e% 



T 



Si 



J 2 +C * 3 +C 



I. I 4- e' l+e' 





+ 



14. There 



