Chta-Shun Yth 
Of, 
Dap b Sy (15) 
Multiplying (12) by f > and (13) by £, , integrating over the do- 
main occupied by water, utilizing (8), (14), and (15) whenever neces- 
sary, and applying the well-known Green Theorem, we obtain 
2 
0 
| oh 2 
: 24 = I al “+ k aa - (16) 
ee JI = ll + k ‘ I 
g m mil 2 PaO! * TH) 
with 
I = fot tie CUAY os al = ( ) ; 
m0 iy m1 fee 2c ly Zy 
(18) 
a+b 
= d 
dis i fii, Sei 
a 
where a and a+b are the values of x atthe shore lines, so that 
b is the width of the free surface. The difference of (17) and (16) 
is 
, (19) 
so that in the limit (as k; approaches kp) 
1402 
