296 Scientific Proceedings, Royal Dublin Society. 
which contains air as well as water is not here dealt with. For 
the purposes of mathematical analysis, the peat is treated as if it 
were a continuous medium. Thus, in what follows, the ‘ velocity 
of the water” in any direction at a point does not refer to the 
actual mean velocity in the interstices, but rather to the quantity 
of water crossing a plane several square centimetres in area, 
normal to the said direction, divided by the said area. 
In the present imperfect stage of the theory of drainage, 
there is no need to apologize for taking a simplified case. 
Thus, actual peat is always somewhat stratified ; and its 
porosity will be different in different directions at the same 
point. But it is here assumed to be isotropic, so that the 
“‘velocity of the water” at any point is a simple vector, 
its magnitude in any direction being the projection of a 
certain line on to that direction. 
Again, after heavy rainfall peat-mosses are known to 
swell, even to bursting. The peat has a velocity as well 
as the water. But it is here assumed that the peat 
remains unmoved. ‘This will be true either if the excess 
of rainfall over evaporation is steady, or if the peat has an 
inextensible porous structure. 
§ 2. THe Law: FLow ProporrionaL To ForRcE. 
The equations for the percolation of water in a non- 
expanding porous soil are given by Boussinesq (1904e). 
They are founded on the supposition that the general 
velocity of the water is proportional to the pressure- 
gradient, which, on the theory of viscous liquids, would 
imply that the motion of the water through the inter- 
stices is steady, not turbulent. In order to test whether 
this assumption held good for peat, I made the following 
experiment :— 
A glass tube 150 em. long and 28 cm. uniform 
internal diameter had one end expanded, as in the figure 
(fig. 1). Into this end there was squeezed a plug of 
litter-peat taken from the Bog of Allen, Ireland, below 
the water-line, and preserved in the wet state. The plug 
was secured by a piece of muslin tied over the expanded end. 
