300 Scientific Proceedings, Royal Dublin Society. 
that is, in the usual symbols of hydrodynamics, 
Dove, 
ath Ox 
v Op 
ral oy (1) 
ea ae 
sa Oz 
Take the z-axis vertically downwards; then X = O= Y, and 
Z = gp, where p is the density of water, namely, 1:00 grams per c.c. 
The equations may now be written 
0 
u = a K (gps — p) 
“ K(gpz - p) }, or in vectors V= VK (gps -p). (2) 
w= A K (gps - p) 
Therefore (gps - p) is the velocity-potential, and the ~ 
motion is irrotational. | 
Put ¢ = K(gpz - p). (3) 
We have also div v=0, which becomes 
0p Of Oo _ 
eee a 0. (4) 
On account of the small porosity, the effects of acceleration 
are negligible; and the above is true for varying motion as well as 
steady. 
All over the outside and upper water-surface p is atmospheric ; 
and therefore 
» = Kyps — K x (atmospheric pressure). 
Since adding a constant to @ has no effect on the motion, we 
may take the atmospheric pressure as zero, so that over the surface 
exposed to the air 
~ = Kype. (5) 
