A mathematical analysis of the effects of perturbations upon the guide field of a circular alternating gradient synchrotron was made to determine the amount and type of perturbation which would make the horizontal motion unstable, but would not affect the vertical motion to the extent that it would become unstable. The purpose of the analysis was to determine if the technique of beam extraction developed by Hammer and Bureau for a conventional synchrotron would apply to an alternating gradient synchrotron.