Simple series solutions of dirichlet field problems with symmetrical circular boundaries

The problem of determining a harmonic potential function in a plane region bounded internally and externally by circles on each of which the function is a stipulated constant, has been solved, in principle though not necessarily in practice, in a number of ways by several authors. The solutions are general and inuvitably abstruse. The object of the paper is to show how comparatively simple solutions can be found for both the potential and the stream functions when the system is geometrically, though not necessarily physically, symmetrical.