This report covers the theoretical advantages and practical ramifications of a proposed new technique for compensating for the daily loss of lift (gamma) experienced by long-duration high-altitude scientific balloon flights. This technique, 'Gas Replenishment', would transfer stored helium from an onboard dewar to the balloon, to replace gas lost due to temperature excursions. It would be a direct substitute for systems presently in use which drop ballast, that is, reduce system gross weight, to compensate for loss of lift. (With gas replenishment, lift is restored directly, with only a small change in system gross weight. A short summary of zero-pressure balloon flight theory is given at the start, to lead into the explanation of conventional ballast practices and computations. The ballast equations are then modified to apply to the gas replenishment technique. Calculations for typical constant-gamma flights are summarized for each method of loss compensation and the clear superiority of gas replenishment is demonstrated in the areas of gross system weight of launch, usable payload weight and anticipated flight duration. Basic equations are then developed for a more complicated model of the gas replenishment system in which the value of gamma varies from day to day. Computations using these formulas are summarized in tabular form. The final section of the report is given over to the design problems associated with the type of dewar and heat exchange equipment needed to implement the gas replenishment concept. (Author).