116 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Then 0 1 P 1 is given by 
and P x is the point 
P X R .*. has the equation 
oc/a + yly=l . 
7 a - d s 
d, y — 
a - d a , ns. 
y - y =-{x- d) 
a y 
or 
y 2 (a - d) - ayy + a 2 x - a 2 d = 0 
The equation to P 2 R is 
y 2 (b _ 3) _ lyy + -b 2 8 = 0 
Hence, on solving for y 2 and y, we have 
y 2 = Ax + B 
lx + m 
y= 
so that 
y 
y 2 { Ax + B) = (lx + m) s 
a cubic with double point at 
(-» 
Cor. 5. l v l 2 , l s parallel to C^Og. 
Take 0 any point in 0 1 0 2 as origin. 
Let O D 1 = d] OD = (5; OC = c; OO^a; 00 2 = 6. 
Let Q be the point (£ c). 
QO x has the equation 
y x - a 
c ( - a 
and P x is the point 
(a + -^-(£ - a), d'j. 
Thus P X R has the equation 
y — d — 
a) 
( 2 ) 
(3) 
(5) 
• ( 1 ) 
