101 



. , 1177(10 — 2) 

 „ _ X Slllll — '- 



i sr 20 n-x 



COS 



V 



~ , ,1171- 20 



u ^ 1 11 cosh — 



, ii-(10 — z) 

 X cosh 



V 



20 . IITTX . 



i\=^\ u cosh -— 



From these equations the vahies of P, u and w were found at each of 

 the one hundred points given in the area. This was done by computing 

 the series for x — 1, 2. 3. 4, 5. G, 7, 8. 0, 10 when z =--^ 1, and then when 

 z=^2, o, 4. 5, G. 7, 8. !>, 10, i. e., by making one liundred computations of 

 eacli series. The value of u and av being found for each point it was not 

 ditficult to determine the resultant in both magnitude and direction. This 

 gave the flow at eacli of tlie points of tlie area. We find from Fig. 1 

 that there is actual motion throughout the whole area. 



The motion, indeed, at some points is very sliglit, but there is no 

 point in the entire area wliere there is no motion. Tliis is imporraut if we 

 regard this as an immense area in lioinogeneous ore-bearing rocli. It 

 indicates tliat at every point of tlie area the water is continually moving 

 and coming into contact witli new roclv surfaces, thus increasing its 

 capacity for dissolving the mineral salts from the area. From the length 

 and direction of the arroAvs it is seen that at the corner D the lines are 

 crowded doAvn closer together than at A. This shows that the constant 

 force gravity has distorted the field, causing the lines of flow to be con- 

 centrated at the bottom, and shoAving that underground waters must talce 

 very long journeys before reaching their destination and so come in con- 

 tact with a very great area of rock surface. 



As before stated, the relations of the equipressure lines to the lines 

 of flow differ from that found in horizontal planes. From Fig. 1 it is 

 seen that the angle lietween the systems of cuiwes varies from nearly a 

 right ancle to two right angles, that is, to tangency. In fact, there is in 

 the area Avhat may be called a line of tangency meeting the sides A D 

 1 and D C. These lines of floAv as before indicated taken at equal dis- 

 tances along A B croAvd near each other doAvii near D, shoAving the 

 effect of graA'ity upon them. If we cause the constant force g to cease to 

 act in the case under consideration, the lines of flow Avould be arcs of 

 circles cutting A B and A D at e(jnal distances from A. The effect of 



