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In switching problems, the efficiency of the switching circuits is often of considerable importance. In the past the basic switching mechanism has been actuated by pulses of simple functions of voltage, current, or force, and efforts to obtain increased efficiency have led to the use of transistors, development of better relays, and the improvement of other components. This paper considers, as an alternative or complementary approach to the problem, the optimization of the function of time which is used for triggering so as to minimize the energy required of the triggering signal. The general problem of determining the optimum triggering signal for a lumped-constant, linear circuit is considered. The optimum signal is defined as that which produces a given current through, or a voltage across, a resistive output element at time t = T while at the same time requiring a minimum of energy from the generator driving the circuit. The output resistance is considered as characterizing the input terminals of a monostable or bistable element such as a thyratron, multivibrator, or a magnetic relay. An equation characterizing the optimum signal is derived, and the conditions under which the equation is valid are noted. There are two types of circuits for which a characteristic equation is not obtained. However, both of these types of circuits are unrealistic in the practical sense because they do not allow for generator internal resistance or stray capacitance across the input terminals. For equivalent circuits of practical importance the characteristic equation is always valid.