Reciprocity in Electromagnetic, Mechanical, Acoustical, and Interconnected Systems

Recent criticism by Carson of the statement of the reciprocal relations in a radio communication system given by Sommerfeld is supported by a simple example showing the incorrectness of this statement. Carson's proof of the extention of Rayleigh's reciprocity theorem to a general electromagnetic system was limited to u= 1 and to sources consisting of ponderomotive forces on the electricity. A new proof is given under more general conditions, I, YJ, cr being merely restricted to be scalars and the impressed forces are of the electric type introduced by Heaviside and Abraham. These may be regarded as impressed charges and currents, including ether displacement current. The theorem is finally stated in terms of volume and surface integrals, and thus combines the viewpoints of both Lorentz and Carson. The reciprocity relations in a mechanical system are reviewed. The interconnection of electrical and mechanical systems is next considered and a "transduction coefficient" is defined. This concept is useful in formulating mechanical problems in electric-circuit form. An example of symmetrical transductance(copper coil in steady magnetic field) is given. The subject of units is taken up and it is proposed that in order to bring the mechanical quantities into agreement with the electrical ones when the latter are expressed in "practical" units, the mechanical quantities be expressed in "mechanical-volts," amperes, etc., i.e., in "practical-electric units of the mechanical quantities." A table for converting the principal mechanical quantities from c.g.s. to practical-electrical units is given.