[ 2l8 ] 



Prop, i. The centripetal force varying inverfely as the 

 fquare of tlie difiance to determine the orbit when it has two 

 apfids. 



Solution. Let the greateft diftance S A = i -4-r 

 and the leaft diftance S B = i — e. Any diftance 

 S P = X, the perp. S Y let fall on the tang. - />, the F, 

 angle ASP=:^^ and the diftance S Z from which X^^^ 

 a body aded upon by the centripetal force muft 

 fall to acquire the velocity at A = 2r. 



Then (Cor. i. Prop. i. Sed. i. and Cor. 2. 40 Prop. 8 Sed. 

 I Lib. Ncwtoni Prin.) 



whence is = 2 



I _f. e : I Cj :. ^ — ^ z i-\-e z 



I II I X 



and V f: i + ^f ^ j':^ ~ T '' V~ T°''^'= 2"^=^'^ '"~^' 



S_PXSY_ — ; 



Nowa=ASP= pYxSP xCx'^ 



' r 



"- X u-2— 5f _,A~ ^'i^ — I 



For finding the 



I— f 



^4^^ - 7 



I — e 



fluent of this fluxion let v = j^^ "" ^ ^ " ~f/£__^^ ^ 



I — e' 



whence 



