1904 - 5 .] Prof. Chrystal on Mathematical Theory of Seiches. 639 
A and A', corresponding to x = ±a, the conditions under which 
our equations give a good approximation are violated more and 
more. In fact, the points x = ± a are essential singularities for 
the solution (12). We cannot, therefore, utilise the complete 
curve, but must suppose our lake closed by two vertical walls at 
the cross-sections P and Q, corresponding to x —p , x = q , situated 
at finite distances from A and A' respectively. P and Q may, 
of course, be on the same side of 0; but in most cases they 
would be on opposite sides, and then q would be negative and 
p positive in sign. 
The boundary conditions at P and Q would be £=0. Hence, if 
a = log {(a + p)j(a-p)} , P = log {(a + q)/(a-q)}, (131 
