1887.] A. Mukhopadhyay — Memoir on Plane Analytic Geometry. 33 3 



If m = 2, Z;2 = a^ + h^^ we see that the reciprocal polar of the evolute 

 of the conic 



^2 y^ _ 



with regard to the circle described on the line joining the foci as diameter, 

 is the curve 



7^4-' ^'''^ 



which, when the hyperbola is equilateral, becomes 



xi>~y^"a^ ^^^^^ 



Again, if m = -|, /& = 1, we see that the reciprocal polar of the evolute 

 of the hypocycloid 



3 



1 



is the curve 



Q*®- 



€.*$)'(S;fS- • ■•■■■ (■"' 



the radius of the circle of inversion being unity ; if a = /?, the polar 

 equation of the reciprocal polar becomes 



r = asec2^ (125) 



Again, since the evolute of the conic 



a^'^h^~ 



IS 



where 



(o'^(?y='' 





a ' ' b ' 



we see, by putting m = f, ^2 — ^^ _ i%^ that the reciprocal polar of the 

 evolute of the evolute of the conic 



a^^h^~ ' 

 with respect to the circle described on the line joining the foci as 

 diameter, is the curve 



3 



(S+p)=(«^*-*W' (126) 



Again, by putting m = — 2, and attending to equation (122), it is 

 clear that the reciprocal polar of the evolute of the reciprocal polar of the 



