In this Paper I have developed a method of dealing with questions connected with Anchor Rings. If r, θ, ϕ be the coordinates of any point outside an anchor ring, whose central circle is of radius c , then ∫ π0 dϕ/√(r 2 +c 2 - 2cr sinθ cosϕ ) is a solution of Laplace’s equation, finite at all external points and vanishing at infinity. Let this be called I. Then dI/dz is another solution; and two sets of solutions may be found by differentiating I and d I/ d z any number of times with respect to c . These solutions are symmetrical with respect to the axis of the ring. In the first set z is involved only in even powers; in the second set in odd powers.