Apparent local wave length 
An apparent local wave length can be obtained by an analysis 
similar to the one carried out for the apparent local period. In 
the derivation of the apparent local period, no approximations 
were made until equation (4.23) was obtained. The derivation 
showed that higher order effects could be neglected, and so it 
is possible to simplify the derivation of the apparent local wave 
length on this basis. 
Equation (4.24) defines the argument of the sinusoidal part 
of the solution as a function of x and t. If equation (4.24) is 
partially differentiated with respect to time, and then if finite 
increments are taken as in equation (4.25), T* can be found im- 
mediately in the form of equation (4.26). Equation (4.13) would 
then give equation (4.23) from equation (4.26). 
Now the derivation of the apparent local wave length can be 
carried out easily. Equation (4.27) leads to the apparent local 
wave length as given in equation (4.28). Note that L* is not 
equal to g(T*)°/2r. 
Equation (4.29) shows that t can be considered a fixed value 
and redefined in terms of a fixed x by means of the group velo- 
city relationship. Also x can be treated as the sum of two terms. 
The Xy is the large term which determines the location of the 
maximum amplitude of the wave group, and the x' determines the 
distance from this maximum. With these equations, an alternate 
relationship for L* can be given by equation (4.31). 
Equation (4.31) shows that L* is almost equal to the wave 
length of a sinusoidal wave of period T in infinitely deep water 
Big = 
