The Brownian Motion of the Resonance Radiometer

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Abstract
A completely analytical treatment is given of the effect of Brownian motion on the useful sensitivity of the resonance radiometer; the assumption of particular values for the constants is not necessary, as heretofore. Care is taken that the assumption regarding what is to be considered a detectable e.m.f. shall be equivalent to the corresponding assumption for the critically‐damped galvanometer. On this basis it is found that a resonance radiometer with the same resistance and time of observation as a given critically‐damped galvanometer would be limited by its Brownian motion to the measurement of e.m.f.'s approximately three times as large as for the latter, but attention is called to the much greater suitability of the resonance radiometer for operation with a long time of observation and correspondingly greater sensitivity. The treatment is further generalized to include the case of differently‐damped galvanometers, and it is found that no advantage is to be gained (from the Brownian‐motion standpoint) by departing from the original conditions of equal damping. The same analysis permits of the calculation of the Brownian‐motion limitation for the usual arrangement of two critically‐damped galvanometers coupled by a Moll thermorelay; the result is the same as that already given by Ising for one galvanometer alone. A proof of the fact that the magnetic coupling does not affect the mean‐square Brownian‐motion deflection of a galvanometer coil is also indicated; this proof is independent of the damping conditions.

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