102 



gravity then is to pull these ares of circles out into cycloidal-like curves 

 crowding near 1) C. As a matter of fact the curve drav^-n from x = 5, 

 z = 10 is nearly a cycloid. Those in the upper left-hand corner being too 

 low and long and those in the lower right-hand corner too short and high 

 for cycloids. 



The lines of pressure are hyperbola-like curves drawn for pressures, 

 1, 2, 3, 4, etc., all the curves beginning and ending in the boundary. 



It is easy to see that we maj^ take a similar area a b to the right of 

 A B C D and leaving an open face similar to A D and an impervious bot- 

 tom and water at zero pressure along the top. We should then have these 

 two areas one on each side of B C with the liquid flowing in op])osite 

 directions. The liquid in each area flows directly down B C and so the 

 motion will not be interrupted if B C be removed. That is, the method 

 of images is applicable horizontally. If. however, a similar area to A B 

 C D be taken just below C D we can not say that the method of images 

 as usually applied holds true. We may regard A D in the upper area as 

 an absorbing slit and A D in the lower area as a similar slit and the 

 position C D between them as a mirror the corresponding parts of A D 

 in the upper and lower slits are not found at equal distances above and 

 beh)w C D. Tliey are found drawn down by gravity so that the 

 method of images must be modihed for vertical distributions. Bj' 



9 9 



integrating u with respect to z between the limits b and tt; • b; r,. b and 



g 



ZTTT. b, etc., tlie amount of flowage from eacli of the ten equal divisions of 



A D may be calculated. And in a similar way the amount of liquid going 

 in at each of the ten equal divisions of A B is obtained by integrating 



9 9 8 



w with respect to x between the limits a and T7;-a.; tt. • a and tt; • a, 



etc. The equations for the flowage and the amount absorbed are then: 



, n TT (b — z) 



n= Gc cosh ^ -,A 



f_ fd „^, _ Sag^k ^ 2a__ .os^L^L^r 



2a J c 



/ 



2a 



n 77 xl d Id 



cos--— gpkxl 

 2a J c Jc 



