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ZntroductionIn view of the difficulty of obtaining exact solutions of Maxwell's equations under given initial and boundary conditions and the difficulty of obtaining practically useful solutions even where exact, explicit solutions are known the potentialities of asymptotic solutions warrant investigation. This paper derives a form of asymptotic expansion suited to initial and boundary conditions shortly to be specified and then shows how it is at least theoretically possible to determine the successive coefficients of 6he expansion through t3he solution of ordinary difTerent,ial equations.'A somewhat more specific discussion of the material of this paper follows. Through a form of Duhamel's principle we can relate the electromagnetic field due to an arbitrary electric charge distribution with harmonic time behavior to the field created by the same charge suddenly placed in space at time t = 0.The latter field, denoted by E, , H,, , is to be called the pulse solution of Maxwell's equations. Both fields are required to satisfy the initial condition of being zero for t < 0 and both are required to satisfy Maxwell's equations for the same electromagnetic parameters t, p , and u, the latter being assumed to be sectionally continuous functions of z, y, and z, thereby allowing for abrupt ~ ~~

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