E,(# ,®) is the cumulative power distribution in the p ,6 
plane. It represents the amount of power present in the system 
below the wave frequency # and between the directions -1/2 and 
®. E,(p,@) is defined for values of © between -1/2 and 17/2 and 
for all positive values of #. As required by equations (9.2), 
(9.3), and (9.4), E,(#,0) is zero at the origin, zero along the 
line © = -7r/2, and bounded from above for all p and @. 
Equations (9.5) through (9.10) require that E,(f,®) be mono- 
tonically non-decreasing in both # and @. 
Some properties of Eo (pe 58) at a set of four points at the 
corners of an elemental area element are also needed. The required 
property is stated in equation (9.11). Equation (9.11) yields 
equation (9.12) and equation (9.13) through the usual operations 
with inequalities. Equation (9.13) is very important. This par- 
ticular combination of the values of E,(p,®) at the four corners 
of the area element must always be greater than or equal to zero, 
if equations (9.5) through (9.11) hold. 
In order to define the. integral given by equation (9.1), it 
is first necessary to define a net over the / ,@ plane described 
above. The # axis is first broken up into a finite number of 
intervals as given in equation (9.14). Equations (9.15), (9.16), 
and (9.17) state that the smallest interval is A, pw and, that the 
largest interval is AiHe Next, the angular coordinate, ©, is 
broken up into 2S angular segments in the interval between -7/2 
and 7/2, Equations (9.19), (9.20) and (9.21) state that the small- 
est angular segment is A 5° and that the largest is 4,9: 
Equation (9.1) is then the limit of the partial sum given by 
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