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An -arm log-spiral antenna may be excited in orthogonal modes of -tuple input. A rigorous solution to the spiral antenna of more than two arms is obtained by numerical solution of the integral equations. Results for a four-arm spiral, including current distribution, half-power beamwidth, beam orientation, and gain and phase centers, are presented. The propagation constant of the current waves along each spiral arm is found to be approximately the speed of light. An approximate diagram is given which may be used to estimate the size of the antenna for each mode of operation.