504 Journal of the Asiatic Society of Bengal. [November, 1908. 
If w be the angle between the normal and line of centres (66), 
called the angle of aberrancy, then Here 



3QQ,- RP 5 
tan y= 
ny= oS 
cos y= Sinn tae L (71) 
(9Q*+ ce eth 
sin y= 3QQ, — 
eS 7 u 
If a and b be the semi-axes of the conic (56), then, evidently, 
1 
3 2 3 2 3 
ait Bt ap OOPe— Rdx)* + \dx* + (3Qd*y — Rdy)? + Ady?} 
4 3 3 ry 
= papl9e + (83QQ, —BP)*+AP4} 
1 42 
BA Ba ga (8 Ode — Rd) +da®}{ (3Qd?y — Bdy)* + dy") 
— { (3Qd*z — Rdz)(3Qd*y — Rdy) +Adaxdy}*] 
(3Qd?y— Rdy)de — (3Qd*x— Rdx)dy}* 
»B 
O78Q8 
~ Bia, aun 
Therefore, a? + b= 19954 (30Q,— —RP)*+AP%}]_ (72) 
AP 
4 
i 
es 
If OD be the diameter conjugate to OP, then from (69) and (72) 
20 ap 5 
ODi=a9+18— OP? = 


OP? 9Q*+ (3QQ, —- RP)? 
Cl XP3 r (73) 

i 
CP {9Q*+(3QQ,-RP)*}2 : 
(7a), ie equation of the director circle, deduced from (68) and 
A{(X—w#)*+ (Y—y)?} -6Q{(X—2«)(3Qd%e~ Rdz) 
+ (Y¥~y)(3Qd?y — Rdy) + $QP}=0 (74) 

A Aalst Nag bs 
; Oe — ~y 



