244 Journal of the Asiatic Society of Bengal. { April, 1908. 
’ 
a’ 
~ ym 
qa ba £5 
similarl og ont 
y ge om” m 
: ye 
*, the locus of 2, y, z is m* =2% ia = =m 
or 
So that, each of the two conicoids 
ay 
52045- hey 
y* ee: 
54% Ps 
is the locus of ne centres of polar planes with respect to the 
$ 
surface eat 52h+5 + == =] of points lying on the other. 
10. From what has gone before, it is clear that the idea of 
inverse points may be generalised and the inverse of a point may 
be defined to be the point where the line joining it to the origin 
meets its ag line (or plane) with respect to a curve (or surface) 
of the second gee inverse curves (or surfaces) being the loci 
of inverse poin 
In fact the rdinary definition of inverse curves is included in 
this as a partic 

R Thus, if O be the centre 
of a circle and P a point 
in its pine and @Q the 
i | point where OP meets the 
0 P polar of P, we have 
° OP.OQ=R* 
(where & = the radius). 
If O be taken as origin P and Q are inverse points. 
If x, y and 2’, y’ be the ee of the points P and Q, 
equation (4) of Art. 7 becomes in this ca 
(a8 + y2) (w+ y’?) = ~ RY —R = Be 
