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A solution of Maxwell's equations is obtained for an antenna consisting of an infinite number of equally spaced wires in the form of coplanar equiangular spirals. Radiation amplitude patterns obtained from this solution agree closely with measurements on two-element spiral antennas. The phase pattern shows the approximate validity of a phase center at a distance behind the antenna which decreases with the tightness of the spiral. The current distribution clearly shows increased attenuation with increase in the tightness of the spiral, thus showing how the frequency-independent mode depends on the curvature. A remarkable feature of the solution is that the current consists of an inward traveling wave at infinity when the antenna is excited in that sense which produces an outward wave at the center.