As is well known, a harmonic function φ(P), satisfying the Laplace's equation ▿2φ = 0 at any point P in a simply connected domain D bounded by a contour Γ, may be represented by: where q is a point on the contour Γ. On the boundary this equation attains the value φ(p) ≡ g(p) where the point on the boundary has been distinguished by small p. Hence to solve Dirichlet's problem, one must find the value of σ(q) from the equation: substitute it in equation (1) and find the value of φ(P) at any point P. This equation may be adopted to solve Neumann's problem, since: Hence given g′(p) on the boundary, one has to solve equation (3) in place of equation (2). Log |q − p|′ denotes the normal derivative of log |q − p| at p.