Long Island simulates in a general way an aquifer in the form of an infinite strip confined between parallel boundaries at constant head (sea‐level), over which recharge precipitation is assumedly uniform. The non‐steady flow of water in this idealized system is analyzed assuming provisionally that the effective thickness of saturated beds below sea‐level is great compared to the maximum height of the water‐table above sea‐level. The rate of accretion to the water‐table is assumed to vary discontinuously, supposedly being constant for each of the successive periods (yearly or monthly) and proportional to the average rate of precipitation during that period. The decay of the water‐table profile, beginning with any one of the succession of super‐posed non‐steady states, is shown to follow in general a relation composed of terms varying with time as exp(−t/t_o) in which t_o is a function of the effective porosity, the thickness and the transmission‐constant of the aquifer. This exponential curve may be approximated by a parabola which is used to determine values of “effective average rate of precipitation” from published records in annual or monthly precipitation. By the “effective average rate of precipitation” at any time is meant that rate of precipitation which, had it been maintained uninterruptedly throughout the past, would have produced the same water‐table profile as actually existed at that particular time. It is demonstrated that fee effective average rate of precipitation may be determined also simply by cumulating departures from progressive averages of precipitation, multiplying the values thus determined by a known rational coefficient, and adding the appropriate initial value of effective average precipitation.