The relation between ground water and surface water was studied in Brandywine Creek basin, an area of 287 square miles in the Piedmont physiographic province in southeastern Pennsylvania. Most of the basin is underlain by crystalline rocks that yield only small to moderate supplies of water to wells, but the creek has an unusually well-sustained base flow. Streamflow records for the Chadds Ford, Pa., gaging station were analyzed; base flow recession curves and hydrographs of base flow were defined for the calendar years 1928-31 and 1952-53. Water budgets calculated for these two periods indicate that about two-thirds of the runoff of Brandywine Creek is base flow--a significantly higher proportion of base flow than in streams draining most other types of consolidated rocks in the region and almost as high as in streams in sandy parts of the Coastal Plain province in New Jersey and Delaware. Ground-water levels in 16 observation wells were compared with the base flow of the creek for 1952-53. The wells are assumed to provide a reasonably good sample of average fluctuations of the water table and its depth below the land surface. Three of the wells having the most suitable records were selected as index wells to use in a more detailed analysis. A direct, linear relation between the monthly average ground-water stage in the index wells and the base flow of the creek in winter months was found. The average ground-water discharge in the basin for 1952-53 was 489 cfs (316 mgd), of which slightly less than one-fourth was estimated to be loss by evapotranspiration. However, the estimated evapotranspiration from ground water, and consequently the estimated total ground-water discharge, may be somewhat high. The average gravity yield (short-term coefficient of storage) of the zone of water-table fluctuation was calculated by two methods. The first method, based on the ratio of change in ground-water storage as calculated from a witner base-flow recession curve is seasonal change in ground-water stage in the observation wells, gave values of about 7 percent using 16 wells) and 7 1/2 percent (using 3 index wells). The second method, in which the change in ground water storage is based on a hypothetical base-flow recession curve (derived from the observed linear relation between ground-water stage in the index wells and base flow), gave a value of about 10 1/2 percent. The most probable value of gravity yield is between 7 1/2 and 10 percent, but this estimate may require modification when more information on the average magnitude of water-table fluctuation and the sources of base flow of the creek become available. Rough estimates were made of the average coefficient of transmissibility of the rocks in the basin by use of the estimated total ground-water discharge for the period 1952-53, approximate values of length of discharge areas, and average water-table gradients adjacent to the discharge areas. The estimated average coefficient of transmissibility for 1952-53 is roughly 1,000 gpd per foot. The transmissibility is variable, decreasing with decreasing ground-water stage. The seeming inconsistency between the small to moderate ground-water yield to wells and the high yield to streams is explained in terms of the deep permeable soils, the relatively high gravity yield of the zone of water-table fluctuation, the steep water-table gradients toward the streams, the relatively low transmissibility of the rocks, and the rapid decreases in gravity yield below the lower limit of water-table fluctuation. It is concluded that no simple relation exists between the amount of natural ground-water discharge in an area and all the proportion of this discharge that can be diverted to wells.