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Two identical linear circuits are excited by generators furnishing equal and opposite voltages. Homologous portions of the two circuits are interchanged at random times with, on the average, r interchanges per unit time. Because of these interchanges, the currents in the remaining portions are irregular. A theorem is derived that permits one to calculate the statistical averages of these currents. It states that one may disregard the interchanging; instead, one merely replaces the complex frequency s by s+2r in the circuit functions [e.g., the impedances Z(s)] of the portions that were being interchanged. On the basis of this theorem one may design counting rate meters with nonlinear (e.g., logarithmic) scale, useful in reactor instrumentation, and function generators for functions of practical importance, such as the logarithmic and exponential functions, and powers with arbitrary exponent. The nature of the function depends only on linear passive circuit elements, such as resistors and capacitors.