The theory of Brownian motion is applied to the problem of determination of the limiting sensitivity of seismic detectors. It is shown that a certain minimum suspended mass is requird for the recording of small ground motions. Electromagnetic geophones are studied in detail, and it is shown how spontaneous thermal fluctuations in voltage limit the performance of these instruments. Under certain conditions, a geophone may be treated as a power generator, and the necessary suspended mass is then determined by the power requirements of the recording apparatus.