In this work a method is given for finding the position of ring singularities in a three-dimensional potential field having axial symmetry, by consideration of the very much easier case of a similar two-dimensional potential function. It is seen that the traces of these ring singularities on a plane through the axis of symmetry occur at points corresponding to those of the singularities existing in the two-dimensional plane when the axial velocity potential functions are the same. It is thought that this might be of value in the plotting of stream surfaces.