Lord Rayleigh and reciprocity in physics

The reciprocal theorem of mathematical physics was not originated by Rayleigh. However, the theorem is presented, in several forms, with elegant clarity in his Theory of Sound. Since its publication his book has influenced generations of physicists, particularly those working in acoustics. When combined with the parallel reciprocal theorem of electric‐circuit theory, it has proved to be invaluable to the subject of electroacoustics, on which is based the modern technology of acoustical measurements. In the ensuing 100 years since publication of his book, physicists have found the reciprocity principle to be valid in many areas of physics. However, the principle is not universally valid; we describe physical systems to which an antireciprocal theorem applies. Kelvin–Tait had, in effect, developed an antireciprocal theorem (for gyroscopic forces proportional to velocities) in a nonconservative mechanical system. The results in their 1879 book were introduced by Rayleigh in his second edition (1894), but without identification of an antireciprocal theorem. Particularly in the electroacoustics of transducers—microphones and loudspeakers—application of the reciprocal and antireciprocal theorems are of comparable usefulness. The latter theorem may be said to date from Faraday’s discovery of electromagnetic induction in 1831; the electrocmechanical action of an electromagnetic motor–generator satisfies an antireciprocal theorem.