Homographic three-body motions with positive and negative masses

This note describes some homographic solutions of the N-body problem with positive or negative masses. Some of them are natural generalizations of the solutions of the two-body problem with vanishing total mass. The configurations which generate these motions are described in the case: N = 3. A case of integrability of the collinear three-body problem with vanishing total mass is shown. A similar case of integrability was known for four vortices satisfying Helmholtz's equations [(5)].