have passed. 
Under these conditions the upper value of # in the fre- 
quency band present at the point x at the time of observation, 
top? as given by #u , can be found by setting top = te and 
HK =/-Fu , and using equation (7.52). The result is equation 
(7.55). For those “ greater than py , the wave trains will 
not yet have arrived. 
The lower value of # in the frequency band present at the 
point x at the time of observation, top? as given by p, , can 
be found by setting top = ty and = pM, » and using equation 
(7.53). The result is equation (7.56). For those # less than 
Hi » the wave trains have already passed. 
Those wave trains present at the point, x, at the time of 
observation, top? are consequently associated with values of p 
which satisfy the inequality given by equation (7.57). A slight 
extension of the forecasting graphs given by figure 15 will make 
it possible to devise a forecasting graph for this model with 
the use of equations (7.55), (7.56) and (7.57). 
The band width, of the square cornered filter which applies 
to this case is given by equation (7.58). An alternate formula- 
tion is given by equation (7.59). The first term in equation 
(7.59) is the same as in the previous case and the second term 
is a correction for the finite length of the fetch. At a fixed 
x, the band width increases as t,, increases. Stated another 
way, the band width is wider for higher values of » at a fixed 
x as the filter tunes through the original spectrum at the source. 
The square filter for a wave system at the source represented 
= 16184 
