A theoretical derivation of the convolution integral produced by N. S. Boulton's originally empirical ‘delayed yield’ theory shows that it describes the vertical velocity at the base of a water table aquitard having negligible compressibility. The derivation requires that fluid compressibility be neglected and that water be obtained from storage by instantaneous desaturation (or saturation) with a declining (or rising) water table. An expression for the ‘delay index’ shows that it is a function of hydraulic conductivity, specific yield, and thickness of the aquitard. To evaluate the effect that gradual desaturation may have on flow in a water table aquitard, flow in the unsaturated zone was approximated by an analytical solution of Richards' equation assuming time invariant power law functions for change of both capillary conductivity and moisture content in the vertical. An equation was derived that shows that the length of time for which gradual desaturation could influence flow in the saturated zone is a function of the hydraulic conductivity and specific yield of the aquitard and the thickness of the capillary fringe. To investigate the effect that delayed yield could have on flow in the aquifer, analytical solutions were made for flow to a well pumping at a constant rate in a compressible aquifer overlain by a compressible water table aquitard. Comparison of results that consider delayed yield effects with those that do not suggests that the unsaturated zone has little effect on flow in the aquifer, and comparison of these solutions with numerical solutions that treat the unsaturated zone explicitly conforms with this result.

A mathematical expression relating the economic worth of ground-water mining to the remaining worth of a basin after it has been partially depleted permits establishment of an optimal, one-time storage reserve that may justifiably be exploited. With water-level position selected as the denominator common to both the ground-water basin and its economic worth, the extreme conditions of perennial use of natural replenishment and depletion of the entire reserve emerge as special cases of the general model. This is reflected through an expression for optimal mining yield, a one-time volume of nonrenewable water •hat may take on values ranging from zero to the maximum amount of usable water in storage. The maximizing conditions are expressed in terms of verbal decision rules and give new interpretation to the concept of overdevelopment generally associated with exceeding safe yield. A criterion is thus provided by which the economic state of development can be tested at any time. (

Equations are developed that allow the transmissivity and storage coefficient of an aquifer to be determined from recovery data taken from an observation well located at an arbitrary distance from the pumped well without the use of antecedent drawdown data. The fundamental result is in the form of a series based on the Theis recovery equation and up to the number of terms given is exact. The assumptions of radial flow in a confined aquifer that is homogeneous, isotropic, and semi‐infinite, which are implicit in the Theis development, are, of course, made in the current work as well. Two numerical examples using actual field data are given.

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