100 Proceedings of the Royal Society of Edinburgh. [Sess. 
Case X. 
Let l be parallel to C^Og, V perpendicular to O^Og ; 0 1 PQ = ^-. 
Let0 2 A = <x; 0 2 B = 6; Ofi x = d. 
Then the equation to the locus of Q is 
y 3 - ay 2 + ^-^(vPy - dxy - cft.—^x'^ = 0. 
Case XVIII. 
Let 0 1 PQ = Q0 2 R = — (in Prop. V); l parallel to 0 1 0 2 , V perpendicular 
to 0 1 0 2 , 
If y = tx is the equation to 0 2 R, R is the point (b, tb), 0 1 PR has the 
equation 
y — bt(x - d)/(b - d) (1) 
and P is the point 
K-^«> 
Hence PQ has the equation 
. . . . m 
■ ( 3 ) 
while 0 2 Q is given by 
ty + x = 0 
