310 Scientific Proceedings, Royal Dublin Society. 
in fig. 6, there is less room for the tubes to crop out in the side of 
the ditch. For a still lower surface than that of fig. 6, the flowing 
area in the side of the ditch will be so small in comparison with 
the ditch-bottom that any variation in it may be neglected. Also 
the length of each tube above the level of the ditch-bottom is in 
the longer ones a small fraction of its total length. That is to say, 
its resistance does not alter much. From this, and from the 
observed similarity of the surfaces in figs. 5 and 6, it is clear that 
a further diminution of ae will not cause the surface to alter its 
Kgp a 
form, and that its central ordinate will be proportional to ae 
P 
This greatly generalizes the graphic method. Any lower rainfall 
can be calculated from fig. 6. 
Further, we see that if Kio suddenly stops and remains zero, 
then the whole surface will begin to fall at the same rate. The 
portion half-way between the two ditches will subside according to 
the equation, height = Exp {—- /(time)}, where the constant / can 
be reckoned when the capacity of the soil for free water is known. 
The lower parts of the original surface must subside at a more 
rapidly diminishing rate, as all must reach the level of the ditch- 
bottom together. 
The following is an example of the application of the foregoing 
diagrams :—In a country where the rainfall is 40 inches per year, 
how far apart must surface-ditches on a deep bog be cut in order 
that the level of saturation of the peat may not rise higher than 
one foot above the bottom of the ditches P 
Well, 40 inches per year is 3:2 x 10-° centimetres per second. 
We will neglect evaporation, and take this as the value of JV. 
Then taking the porosity K as 107 C.G.8. units (see §7), we have 
W 3:2 x 10-5 
gok 981x107 ee 
Now. in fir. 6 2 = -068. and the watereuriacohe eae 
Ww, 10 g- Kgp = 3 e water-suriace Yrl1ses to 15 
of the distance between the centres of two adjacent ditches above 
the level of their floor. Further, we have shown above that Fes 
p 
is proportional to the height of rise for forms like fig. 6, with equal 
