103 



9 9 



where c varies from - . b or — . a down to zero, and d varies from a or b 



down to r-- . b or ^. a. Solving the ten equations for the ten different 



values of f and a, we get the following table: 



No.... 1 2 3 4 5 6 7 8 9 10 



a .958 .875 .800 .726 .664 .611 .566 .535 .512 .502 

 f .042 .126 .216 .315 .424 .556 .716 .935 1.24 2.07 



Table I. 

 It will be seen from the table l)y counting the divisions from A as 1, 2, 3, 

 etc.. that nearly half the water flows through the first three divisions 

 and that there is a gradual decrease toward B. The relative value of f 

 from the different divisions sbows a very slight tlowage from the Hrst 

 division with a rajjid increase from each of the succeeding divisions until 

 the two lower divisions at I) carry off one-half of the amount absorbed. 

 This shows in a very vivid way the iironounced effect of gravity or any 

 constant external force upon a liquid. The amount going in along A B is 

 of course equal to the amount flowing out along A D. since the equation 

 of continuity must hold true. 



It is interesting to note that the curve given by plotting the flowage 

 from A D is very nearly a tractrix or antifriction curve. See Fig. 3. It 

 would undoubtedly be an exact tractrix had the number of divisions of 

 A D been taken small enough, i. e., if twenty or thirty equal divisions had 

 been taken instead of ten. 



In Fig. 3 the line O X corresponds to the distance A D in Fig. 1. and 

 the y-coordinates of the curve are given by the values f taken from 

 'xable I. 



Fig. 4 shows the distribution of absorption into the area A B C D 

 along A B, the line A B of the figure corresponding to the line .^ B of the 

 area. The y-eoordinates of the curve being taken from Table I as the 

 different values of a. 



Figs. 3 and 4 then show the distril)ution of absorption ana flowage 

 along A B and A D. 



Extending this method ])y taking A B one hundred and keeping A D 

 ten, we get approximately an artesian well area. The values of f and a 

 for this case are given 1)elow: 



No.... 1 2 3 4 5 



a 5.51 1.44 .139 .044 .028 

 f .040 .162 .210 .348 .446 



