26, On some Reciprocal Relations of Curves and Surfaces. 
By Manenpranati Dp, M.A., B.Sc., Bengal 
National College, Calcutta. 
1. The following theorem is given by Dr. Asutosh Mukho- 
padhyaya in ‘A Memoir on Plane ney ia Geometry’ in thé 
Journal of oe pearcag Society of Bacal for 1887. 
“Tf from any point P two tangents be drawn to the conic 
= S+t- 1 and P is constrained to move on any curve F(a, y) =0, 
ig locus of the middle point of the chord of contact is 
RP ( a®*htz, a®hy —0.” 
He adds that this résult is an immediate consequence of a 
new method which he proposes to call the Method of Elliptic 
Inversion. 
-That method does not faci to have been published since, and 
the object of this paper is to give a very simple method of estab- 
lishing this and similar results and their space- rin ne: and to 
point out a remarkable relation between the two loc 
2. If x’, y’ be the co-ordinates of any point P in the plane of 
the curve =; a =1; X, Y the co-ordinates of the middle point 
ee’ yy’ ae , that 
of the chord of contact > i a 1, it is easily seen tha 
a 
a’ es ; 
x= oe eee Y= Seer 
ME 72 
a Me RR. 
[.: it is well known that the diameter phasing through 2’, y 
contains the point X, Y. 
a 
Se FH ws ain See 
cai Can ee 
at at ~~ bf 
’ xX Y 
‘=a i" mT 
saree a tie pth 
