A quantitative but simple theory of the control effect of a uniformly distributed set of thermal poison elements in a hydrogen-moderated bare reactor core has been developed. Starting with plane parallel poison sheets, a zero-flux boundary condition, in a slab core and applying Fourier analysis, it has been possible to generalize to any boundary condition, to orthogonally intersecting sets of poison sheets in an infinite rectangular core, to control crosses, and cylindrical rods in regular array, to finite rectangular cores, and to finite cylindrical cores. Each element of the control array is associated with a cross-sectional area Ac within the core and within this area is an easily determined effective “absorption area” C. To a rather good accuracy the critical k of the controlled core is greater than the k of the uncontrolled core by the ratio Ac/(Ac − C). In this the theoretically based conclusion substantiates the intuitionally based and empirically confirmed methods worked out by Greebler (1), and by Pearlstein, Ruane, and Storm (2), and furnishes correction terms.