302 Scientific Proceedings, Royal Dublin Society. 
medium is multiplied by ee Kap . Call the product ¢,; then the space- 
: Lae 
rate is now —— times its original value at the same particle of 
Kg 
the medium. Consequently it still vanishes over the bottom ; 
and over the top surface »., which depends on the form, but not 
on the size, being unchanged, we have from (7) 
W nal Os Ops 2 8 
Be eet eS). (8) 
The value of ¢, over the top was by (5) equal to Xgpz. Therefore 
the value of ¢. over the same surface, now stretched, is :—that 
is to say, it is proportional to the height of the stretched medium 
as g, was to that of the unstretched. 
Now, because J does not appear in the formula (8), it is clear 
that W does not depend on the size of the mass of peat, but only 
on its shape, and on Kgp. 
To determine ¢, we have the following four relations : 
V’o2 = 0 everywhere. (9) 
2 is equal to the height on the water-air-surface. (10) 
The water-tight bottom is a surface of flow. (11) 
Uae Oz Ope 
| Kas Car AC Tay 2 le By + Ny Ae) over the upper water-surface. 
(8) = (12) 
§ 4. SoLurion oF THE DIFFERENTIAL EQUATIONS. 
As the drains in peat-moss are commonly long in comparison 
with their distance apart, we will, for simplicity, consider the flow in 
a section normal to the smallest drains, and neglect altogether the 
flow across the plane of the section, and, with it, the coordinate y. 
An attempt to solve the equations (9), (10), (11), (12) by a 
series of terms of the type ¢: = cos mw sinh mz, led to great com- 
plications on account of the awkward surface-conditions (10) and 
(12), and was given up as hopeless. 
Instead of algebra, a freehand graphic method has been em- 
ployed. One draws two sets of lines, namely, stream-iines, marking 
off tubes of equal flow, and contours drawn at equal intervals of the 
