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The detection of weak thermal radiation and similar noise-like signals is often limited by the internal noise of the receiving apparatus. Dicke has described a method of detecting such signals. It employs a mechanical modulator at the input of a wide-band superheterodyne receiver. The detected output of the receiver is multiplied by a voltage of the same frequency as that which actuates the modulator, and filtered to produce a dc voltage when an external signal is present. Another method has been proposed which uses two independent receivers. The undetected output voltages are cross-correlated, and the correlator yields a dc voltage when a signal is applied to both receivers. Each method can be used to measure the intensity of signals small in amplitude compared to the noise of the receiver. A mathematical model of each of the circuits is presented, using, insofar as possible, the same assumptions; and equations derived for the least detectable signal power of each. The two-receiver method has, under the assumptions made, somewhat greater sensitivity. Engineering problems associated with each of the radiometers are discussed.