174 Journal of the Asiatic Society of Bengal. [April, 1908. 


eo 
Then OPi gpa) 
2 
a pm {[(iny)-p(X-0)-} 
But a by (30, 31) 
OP! PM2 (1+ pd). 819° 
A3(1+ p*) 

_ (¥—-y)—p (X~2)} A— 99°? 
81q® 
and A a I a 8 
CD* VK*' CD? PM?" CDs 
— 29°79 + (pr —3q*)8} {(Y-y)r— (X—2)(pr—- 39%) }* 
A¥, 81q° s 1 
{19 + (pr — 3q)9}99%(1 + p*). 5 
by (28, 81, 23, 29) 


(1 + p*) 

_A{(¥—y)r— (X—#) (pr — 398) 3*, 
at 81g 
Therefore 
Be Oe cele ve stm n et Coca care a 
or A{(Y-y) a Geom. ge mA es eng alg pr —3q*)}* 
18q°{(Y¥—y)—p(X—«)} (85). 
which is the general equation of any conic of the system. 
If A=0, ee ola. 
- Nga + +P") + 7? + (pr—3q*)? = 0, it is an equilateral hyperbola. 
conic of hon contact has evi idently for its centre 
the ke common between two consecutive lines of centres. Let 
X, Y be the co-ordinates of its centre, so that 
Xa, aan Sie) 
where A has to be determined. 
dX dY 
Then we must have —-=0 and —=0, as the two centres cor- 
dz dz 
responding to a, y, A and #+da, y+dy, A+dA must be identical. 
H dX i a+ 79) = dd 
Bi Sagigen so Seapee az 
dY_ —_3( pr* + pgs—8q*7) “apler 30 9 
de * x y de : dz ; 
=0 

