The theoretical problem of determining the Cˇerenkov radiation from an electron traveling in a circle through a medium has been advanced and the fields and resultant radiation from such a geometry have been determined. A solution is achieved by a transformation of the fields as determined by Frank and Tamm in their original article on Cˇerenkov radiation. This transformation results in a solution as a summation of eigenfrequencies each separated by the frequency of the periodic motion of the electron. The radiation expression derived by this transformation method approaches the Frank and Tamm radiation expression in the limit.