constant period and amplitude in deep water. 
The form of E,(#,0) for example two is given by equation 
(9.36a) and the appearance of the function is given on the little 
figure to the left. wW(,0) is defined in small strips which 
cover the jumps in Eo(H 50), and it can be anything otherwise as 
shown by equation (9.37a). A partial sum, if the net points are 
close together, for the element which encloses the point (#7729), 
then yields for the square root term the value 
2 2 2 W/y 
The final result, in the limit is given by equation (9.38a). From 
the above two examples, it is evident that all of the examples 
given in Chapter 7 are special cases of the integral given by 
equation (9.1) in which the sea surface does not vary in the y 
direction. 
In example three, Eo( # ,e) is given by equation (9.36b), and 
W(#H,°8) is zero. For the area element which encloses the point 
(17/6), the radical in the partial sum for that term is given 
2 aO)l/] =iae The dnteprel We consequentayeieen 
ip Ge Seen 
by equation (9.38b). Equation (9.38b) is just a specific example 
of equation (8.4) as far as the direction of the two waves is 
concerned. 
In example four, the form of E,(#,0) is given by equation 
(9.39), and W(#,@0) equals 37/2. The integral is then a special 
case of equation (8.5). Infact, the integral is equal to the 
equation given in figure £3 when t is zero. E> (# 50) is an inter- 
esting function in this particular case, and a three dimensional 
sketch of the surface involved is given in figure 20. Note the 
= BG < 
