101 



. . n-(10 — z) 

 4 ,^ 20 n-x 



U = — Z . cos -jrpr- 



TT , , IITT 20 



n = 1 n cosh — 



n-(10 — z) 

 4 ^^ = "- ^^^'^ 20 . n.x ,, 



'''-If -, TUT-- •'^"^-2^ + ^ 



n ziz 1 u cosli — 



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

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

 the series for x = 1, 2, ;^. 4, 5. (>, 7, 8. 9, 10 when z -- 1, and then Avhen 

 z = 2, 3, 4, 5, 0, 7, S, 9, 10, i. e., by making one hundred computations of 

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

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

 gave the flow at each of the 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 slight, but there is no 

 point in the entire area where there is no motion. This is imporrant if we 

 regard this as an innnense area in homogeneous ore-bearing rock. It 

 indicates that at every point of the area the water is continually moving 

 and coming into contact with new rock surfaces, thus increasing its 

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

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

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

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

 centrated at the bottom, and showing that underground waters must take 

 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 between the systems of curves varies from nearly a 

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

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

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

 tances along A B crowd near each other down near D, showing the 

 etfect of gravity upon them. If we cause the constant force g to cease to 

 ai?t in the case under consideration, the lines of floAV would be arcs of 

 circles cutting A B and A D at equal distances from A. The effect of 



