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An analysis of the scattering effect of a thin dielectric ring on an electromagnetic field is developed under two assumptions: the incident field is the free space field of the source, and the scattered field tends asymptotically to zero as the radial thickness of the ring approaches zero. When an integral equation of Barrar and Dolph, derived directly from Maxwell's equations, is employed, a formal expansion of the field in powers of the thickness is obtained, and then it is proved that the linear approximation obtained from it is indeed asymptotically equal to the total field. The sufficiency of this approximation is justified by experimental evidence. The far-zone pattern function of the ring is next obtained, and the resulting formulas are applied to the situation where the incident field is generated by a dipole antenna coaxial with the ring for which experimental comparisons are possible.