spectrum of the disturbance. The first integral in equation 
(8.28) involves the evaluation of equation (8.35). All of the 
terms in the integrand are odd, the integration is even, and 
the result is that equation (8.35) is zero. The second integral 
in equation (8.28) involves the evaluation of equation (8.36). 
The integration is straight-forward and the result is given in 
equation (8.36). 
The results of equation (8.36) can be substituted into 
equation (8.28). An integral would then result over the sum of 
two terms from zero to infinity. The integral is approximated 
in equation (8.37), for ease of evaluation, by an integration 
from minus infinity to plus infinity of the term which gives 
the important contribution for p * positive. 
For all equations subsequent to equation (8.37), all of 
RS es re en SS ES 
stars for simplicity of notation. By the transformations indi- 
cated in equations (8.38), (8.39), (8.40), and (8.41), equation 
(8.37) can be put in the form of equation (8.42). 
The pair of equations given by equations (8.43) and (8.44) 
define a transformation of the spate over which the integration 
is to be carried out. The inverse of the transformation is given 
by equations (8.45) and (8.46). The Jacobian of the transforma- 
tion is given by equation (8.47). The application of this trans- 
formation to equation (8.42) yields equation (8.48) in which the 
original strip over which the integral was to have been evaluated 
in the # ,p plane now maps into the whole a,8 plane. | 
Were it not for the very complicated coefficient of x in 
- 192 - 
