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<br />The integral which appears in this expression has been extensively tabulated. <br />(4) (5) (6) It is called the "Probability Integral". Charts of a general nature <br />can be constructed from such expressions. A sample is given in figure 1. <br /> <br />~ <br /> <br />By integrating this expression with respect to time the total depletion of the <br />river can be obtained in the form: <br /> <br />\ \ I dt <br /> <br />,0 <br />Qt <br /> <br />: l- <br /> <br />2 <br />.r; <br /> <br />Xl <br /> <br /> <br />~ j4at" <br />-u~ <br />e du <br /> <br />o <br /> <br />; (,:': )"r:~' <br /> <br /> <br />, Xl <br /> <br />~ <br /> <br />du . . . (5) <br /> <br />A plot of this expresSlOn is s;,own in figure 2. The integral <br /> <br />"r, <br /> <br /> <br />J4at <br /> <br />-uZ <br />e <br />u' <br /> <br />du <br /> <br />I,;,,, hppn t~hill"t"'rl hy Mr. M. W. Blttinger. This table may be found in <br />reference 3. It m"-'y be nolod tl>"" llJ"",,, ('harts are of a very general nature <br />and can be applied to a wide range of condition" if only thp aquifer properties <br />::>'l-e known. <br /> <br /> A solution of equation 1 subject to the conditions <br />h : H for 0 < x < L when t : 0 <br />h : 0 when x : 0 for t > 0 <br />h : 0 when x : L for t > 0 <br />is: (2) (3) <br /> <br />-4- <br />