A mathematical theory is given for the discharge of a well of constant drawdown, discharging as by natural flow from an effectively infinite aquifer of uniform transmissibility and uniform compressibility. This theory is based on the solution by L. P. Smith of the analogous problem in heat conduction. The mathematical function involved in the solution, which cannot be integrated directly, is evaluated by numerical integration. A table of its values is given for a wide range of its argument. This function is compared with other,asymptotic solutions, and simple, useful approximations are given.

Two graphical methods are outlined for determining the coefficients of storage and transmissibility from variations in the rate of discharge of wells flowing at constant drawdown. Data from the Grand Junction, Colo., artesian basin are treated by these methods. In the Grand Junction artesian basin there are about 25 flowing wells ranging in depth from 600 to 1600 ft, most of which obtain water from the Entrada sandstone. A few of the wells obtain water from a sandstone in the overlying Morrison formation and a few tap the underlying Wingate sandstone.

The procedure of the tests is outlined, and the “ink-well” mercury gage used to measure the artesian pressures is described. Recovery tests were run on the same wells after the discharge tests. Values of transmissibility obtained from the recovery tests check those obtained by means of the discharge tests.