 In the "n"-body problem, the study of the motions of point masses under Newton's law of universal gravitation, an important role is played by central configurations, solutions to the "n"-body problem in which all of the bodies rotate around some central point as if they were rigidly connected to each other.For instance, for three bodies, there are five solutions of this type, given by the five Lagrangian points.For four bodies, with two pairs of the bodies having equal masses (but with the ratio between the masses of the two pairs varying continuously), numerical evidence indicates that there exists a continuous family of central configurations, related to each other by the motion of an antiparallelogram linkage.