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The currents and charges induced in a pair of electrically thin crossed wires by a normally incident plane electromagnetic wave are derived by analytical methods. The boundary conditions at the ends and at the junction are explained. The solution of a new integro-differential equation for the currents is obtained in terms of trigonometric and integral-trigonometric functions. Depending on the electrical lengths of the crossed elements and location of their junction a variety of quite different distributions of current and charge obtain. These determine the scattered near and far fields. Graphs of computed currents and charges per unit length on the four arms of several important cases are displayed. The accurate determination of the induced currents and charges on a mathematically tractable structure-the thin-wire cross-is an early step in a study that will proceed to electrically thick cylinders, wide strips, and their junctions in crossed configurations in an effort to gain a meaningful approximate understanding of the currents and charges induced on an aircraft by an electromagnetic pulse.