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<br />with tile rates of flow of ground water into the zone is expressed in mathematical " <br />form it leads to differential equations of the type treated by Fourier. This imme- <br />diately makes it pos sible to adapt the brilliant developments of Fourier, and <br />his successors, to the calculation of ground water movements. Because of the <br />interest aroused by Fourier's original paper the mathematical resources in this <br />field are exceptionally good. It will be clear that these methods are not new <br />since they represent some 300 years of development by able mathematicians. <br /> <br />The condition of continuity <br /> <br />The types of differential equation described above are obtained if the flow <br />of ground water is computed by the Dupuit-Forschheimer idealization, which <br />applies the surface gradient of the water table, at any point, to the entire satu- <br />rated thickness below that point and by computing the flow on ti1e basis that the <br />original saturated thickness of the aquifer remains unchanged. <br /> <br />On this basis the requirement that the difference of flow across two planes <br />a distance dx apart in the direction of flow should be compatible with the rate <br />of rise of the water table between the two planes is <br /> <br />a'h <br />ct ax' = <br /> <br />ah <br />at <br /> <br />. . . (1) <br /> <br />\Vhpre <br /> <br />h represents the height of the water table measured upward from <br />an assumed original stable water table level. <br /> <br />t time <br /> <br />x a distance measured along the path of flow, <br /> <br />and <br /> <br />ct <br /> <br />KD <br />= <br />V <br /> <br />where <br /> <br />K represents the permeability of tile aquifer <br /> <br />D the original saturated depth <br /> <br />V the ratio of drainable or fillable voids to the total volume. <br /> <br />.' <br /> <br />- ?- <br />w <br />