ON A LOCUS DERIVED FROM TWO CONICS. [389 
A = y 1 ' T y there is still a sinuous oval as above, but the interior oval has 
(™ + IY 
V mj 
dwindled to a conjugate point at the centre. 
A > X m -±J0- 2 < m • a = m; A>m<^“^ ; there is no interior oval, but only a 
(ra + —^ 
V mj 
sinuous oval as above; which, as A increases, approaches continually nearer to the four 
sides of the square. For the critical value A = m, there is no change in the general 
form, but the curve has for this value of A, two conjugate points, one on each axis 
at infinity. 
A = ^ (m + l) 2 , the curve becomes the four lines. 
A > J (to + 1 ) 2 , the curve lies wholly in the four regions a and the four regions e, 
consisting thereof of four detached sinuous ovals. As A deviates less from the value 
\(m + l) 2 , each oval approaches more nearly to the infinite trilateral formed by the side 
and infinite line-portions which bound the regions d, e to which the oval belongs. 
And as A departs from the limit |(w+l) 2 , and approaches to oo, each sinuous oval 
approaches more nearly to the circular arc which separates the two regions d, e, which 
contains the sinuous oval. 
Finally, A = 0, the curve is the circle twice repeated.