The following discussion of the curves r1r2 = crn, where r1, r2, r are the distances of a point from the “foci” ±α, 0 and the origin, c a positive constant and n rational (integral or fractional, positive or negative), provides a good example of extensive knowledge of general curves obtained by elementary-considerations. The attention of the author was first drawn to these curves by the remark of a colleague, Mr. N Davy, M.Sc., that the curves r1r2=cr⅓ appeared in the design of the pole-pieces of certain electromagnets.