When a well is pumped or otherwise discharged, water‐levels in its neighborhood are lowered. Unless this lowering occurs instantaneously it represents a loss of storage, either by the un‐watering of a portion of the previously saturated sediments if the aquifer is nonartesian or by release of stored water by the compaction of the aquifer due to the lowered pressure if the aquifer is artesian. The mathematical theory of ground‐water hydraulics has been based, apparently entirely, on a postulate that equilibrium has been attained and therefore that water‐levels are no longer falling. In a great number of hydrologic problems, involving a well or pumping district near or in which water‐levels are falling, the current theory is therefore not strictly applicable. This paper investigates in part the nature and consequences of a mathematical theory that considers the motion of ground‐water before equilibrium is reached and, as a consequence, involves time as a variable.