The problem of water table fluctuations in response to repeated recharges is considered. The effect on the water table of intermittent constant recharge (recharge applied intermittently at a constant rate) and of intermittent instantaneous recharge (recharge applied instantaneoulsy at regular intervals) is analyzed in detail. The final results are shown to consist of a combination of periodic and transient components; the transients are monotonic decreasing functions.The theory may be applied to problems of ground-water flow through aquifers and to land drainage problems.

Three fundamental theorems on the movement of air through anisotropic soil are stated. New and simple proofs for two of the theorems are given; proof for one is referred to in the literature. On the basis of these theorems, formulas are derived for converting, to horizontal and vertical permeabilities, air flow measurements, previously reported in the literature, on soil clods. It is shown that the reported values of anisotropic permeabilities are apparent values, and that these apparent values depart considerably, in certain cases, from the correct values. As an extreme example, the reported ratio of the apparent horizontal to apparent vertical permeability for clod samples of Clarion soil, is 2.09, whereas the corrected ratio is 13.0. One particularly interesting general result of the theory is that an apparent value of the vertical permeability is, in fact, the geometric mean of the vertical and horizontal permeabilities of the sample. It is finally shown that the arithmetric mean of the apparent vertical and apparent horizontal permeability does not deviate greatly from the arithmetic mean of the true horizontal and true vertical permeability, the deviation being, for the Clarion sample, only 24%.

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