The effects of fuel burnup, fission product poisoning, and hydrogen moderator density variation on reactivity in the AGN-201 reactor are considered. A modified one-group perturbation theory is developed and applied to changes in parameters resulting from a change in hydrogen moderator density. An equation for the reactivity change is obtained for three models: a bare cylindrical core, a bare core using extrapolated dimensions, and a reflected core. These three equations are then used to predict values of the reactivity increase resulting from interchanging in a new 3/4 inch thick fuel disk with comparable fuel disks presently in the core. The results obtained by a digital computer solution of the reactivity equations reveal that the increase in reactivity varies from 0.4392 to 0.7707%, depending upon the core model and position of the old disk within the core. Because the license of the Naval Postgraduate School does not permit a value of excess reactivity above 0.40%, it is concluded that a simple interchange of disks in this manner would produce too large a value of excess reactivity.