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Under transient excitation the energy transmitted by an antenna of finite size to a faraway receiver can decrease much more slowly than the usual R-2. Instead, by a suitable choice of excitation, this quantity can decrease as slowly as one wishes, under the physical restriction that the total energy radiated by the antenna is finite. Such cases of slow decrease are referred to as electromagnetic missiles. Another way of stating the result is that the product of the following two quantities can approach zero as slowly as one wishes: (1) the energy transmitted per unit area of receiver, and (2) the total area of the receiver. Examples are constructed when either one, but not both, of these quantities remains finite at infinite distance.