6 CURVE OF 



But nU = nn'' -^Ln'' - 2Ln' . « r =:«n'2 - 2 W./n; 

 because L n' is very small when compared 

 with n nf: also ps^ =. 'pn'-sn'f zn pn'^ ^2pn' ,s n'= 

 pn''^ — 2»n'. -^it— Ln': because the triangles 



"^ An' 



L?»'* andAn'iy, are similar. 



Therefore ^(n . nU •{• m . ps^)'=z 



/ , / Dn 



n . TO r 4" ^ • P^ •-» — 



for ^z= — ^> nearly, when w is at a finite dis- 



A w A 7i' 



tance from A : and only two terms of the series 



are necessary, because L n' is infinitely smaller 



than n ri or jp v! . Hence 



^/(n. AD— w. An) "" 



n . n ?•' +w. ./^n 



^ (n . n n''^ + w . /? n'2 j ^ ^ j^ ^ ^ J) __ ^ _^ „) 



In the same manner 



