308 | Scientific Proceedings, Royal Dublin Society. 
In these an alteration in the height of the surface at any part, 
equal to =, of its greatest elevation above the bottom of the ditch, 
was found to throw the chequer-work decidedly out of shape. On 
the other hand, in fig. 4, where the tubes are nearly vertical 
at the surface, the form of the latter cannot be determined by this 
graphic method. It is, however, an unpractical case, and so it need 
not concern us. 
The excess of rainfall over evaporation, which we called W, is 
determined from the diagrams in the following manner. All 
through we must remember that in the transformed equation (8) 
the peat has been replaced by a hypothetical medium. The flow 
in the unsaturated medium above the “ water-line”’ is. i, per 
p 
unit horizontalarea. We will here suppose a diagram to represent 
a slab of unit thickness, so that horizontal length is equivalent to 
horizontal area. Now, in the diagrams, vertical tubes in the 
unsaturated medium are carried on into curved tubes in the satu- 
rated part; and the total flow in a tube must, of course, be the 
same all along it. Whence, equating the flows in unsaturated 
and saturated portions, we have 
ie x (horizontal width of tube in unsaturated portion) is equal to 
ft) ’ 
(width of chequer across flow) 
(diff. of potential between contours) x (length of chequer along flow) 
No specific resistance appears in this, because the flow referred 
to is not a flow of real water, but only of the auxiliary flux 
Vo:. Now by equation (10) the difference of potential between 
successive contours is simply the difference of level between the 
ends of the equipotentials, where they crop out on the upper 
surface. ‘Therefore 
(diff. of level of outcropping equipotentials) 
(horizontal width of tube in unsat. portion) 
,, (width of chequer across flow) W 
* (length of chequer along flow  Kyp' 
The ieft-hand side can be obtained at once from the drawings. 
Its value is independent of the unit of measurement. The greatest 
error is that due to the chequers not having all the same ratio of 
