4 
ON THE LOCUS OF THE FOCI OF THE CONICS &C. 
[417 
P.S. In general the curve \\ZA+g^/B + v\/C + 7r f JD = 0 has (exclusively of 
multiple points at infinity) six double points ; viz. these are situate at the intersections 
of the pairs of circles, 
(V4 + H* Vj5 = 0, yV(7 + 7rVZ) = 0), 
(\^A+v^/G — 0, / aV J S+7rVD=0), 
(\*fÄ + 7r*JD = 0, 'JB + v V(7 = 0). 
In the case of the curve of foci, the first, second, and third pairs of circles intersect 
respectively in the points (AB. CD), (AG.BD), (.AD.BG), which, as mentioned above, 
are double points on the curve; and they besides intersect in three other points, 
which are the other three double points mentioned above. 
Professor Sylvester reminds me that he mentioned to me in conversation that he 
had himself obtained the foregoing equation S ± (B, G, D) VA =0, for the locus of the 
foci of the conics which pass through the four points A, B, G, D. 
Cambridge, October 10, 1866.