particular » and for a fixed value of x, if the time of the 
observation, top» lies between t,, and t, then the component 
sinusoidal wave for that particular # is present as shown by 
equation (7.42). Substitution of equations (7.41) and (7.42) 
into (7.43) yields equation (7.44). Rearrangement of equation 
(7.44) then yields equation (7.45). 
For a fixed time and place of observation, and for a fixed 
duration of the waves, those spectral values of # are present 
which lie between the values g(t.) - D)/2x and gt op / ax. The 
other values in this simplified case are not present. The upper 
value of # which is present is given by equation (7.46), and 
the lower value, by equation (7.47). The band width present, 
Ap , depends directly on D, and inversely on x as shown by 
equation (7.48). 
Figure 15 shows how these considerations can be used to con- 
struct a forecasting diagram. The top part of the figure is a 
graph of the straight lines given by equation (7.46) and (7.47) 
as functions of t and » for various fixed values of x and for 
Do equal to 10 hours. Pick a time, t = top? say, twenty hours 
and a fixed x, say, 200 kilometers. The line for t = 20 hours 
intersects the two parallel lines which apply to x = 200 km, and 
a segment of the # axis is cut off between the two parallel lines. 
The orojection of this segment onto the # axis then gives the 
band of frequencies present at x = 200 km, 20 hours after the 
start of the storm. 
Practically nothing is known about the power spectrum of 
waves at the edge of an area of generation in a storm at sea. 
=e 
