The possible shapes of continuous critical loci for binary systems exhibiting a negative azeotrope which persists up to the critical region are reviewed and extensively discussed. Such a review made it possible to prove that the existence of an intersection point - in a (P, T) projection - between the critical line and one of the vaporization curves was a sufficient condition for a binary system to exhibit a critical azeotrope. The Bancroft's rule which until now stated that the existence of an intersection point between the two vaporization curves in a (P, T) plane was a sufficient condition to observe an azeotropic behavior was thus upgraded to take into account the crossing of the critical line and one of the vaporization curves. Such a point was logically called a Bancroft point of the second kind. In a second part, mixture critical points of the acetone + chloroform binary system were measured in order to determine if such a system exhibited a Bancroft point of the second kind and consequently if the negative azeotrope persisted up to the critical region. Along the critical line, the acetone mole fraction was varied between 0.06 and 0.92.