The fundamental wavelength of a spherical resonator with a circular aperture is calculated. The result,λ/2π = R(2πR/3a)12(1−0.14324a/R+0.08455(a/R)2), whereadenotes the aperture andRthe sphere radius, is the correct form of an expansion as far as terms of relative order (a/R)2, inclusive. A procedure for approximating to the wavelength of a resonator with arbitrary shape is also described.