This paper describes a family of oval curves first studied by Maxwell and which may be called generalized ellipses. Their equation may be written as follows:aS + bS′ = K, whereaandbare certain integral values,Kany value constant, andSandS′the distances of a current point from the two foci. The simplest oval results froma = 1,b = 2. Other values ofaandbgenerate similar ovals which are described. If in certain of these ovals the inside and outside regions are filled with material of a definite refractive index, then light proceeding from one focus to the other, will refract stigmatically at the oval surface.