put.in the form of equation (9.57). The points x and y are treated 
as constants. © is treated as a variable, and when 9 equals 0,,, 
as © is increased, the term in the filter passes through the value 
one half. For © greater than ey the term rapidly becomes zero. 
The result is that tan ©, is given by [y + we/2) 1/x. Similarly 
equation (8.67) yields equation (9.59). For ® less than ®,, the 
term in the filter is nearly zero, when © equals 6, it is one half, 
and for 9 greater than oy. but less than Pee) the term is essentially 
two. 
The properties of the filter which cause it to cut off all 
‘ but a certain angular band width of the power spectrum at the 
source can be explained by reference to figure 18 and to figure 
23. Figure 18 shows that for a fixed value of 6, the disturbance 
in the x,y plane remains between the two lines, ve = cos 6,W/2 
and Y, = - cos O,W/2- Consider then in the x,y plane, the area 
which can be occupied by a disturbance which travels along the 
line da = 0, for a fixed point x = x, and y = y,. The lowermost 
part of that disturbance as shown by the dashed line a = - cos @,W/2 
will just miss the point XiYy> and any disturbance which leaves the 
source at directions greater than 8. will never be observed at the 
point X1Yz°- Similarly the disturbance which travels along the line 
X = 0, will pass just below the point x,,y,, as shown by the 
dashed line, Y, 
source with a direction less than 8, will never be observed at the 
= cos 0, W,/2- Any disturbance which leaves the 
point X,,y,- Equations (9.58) and (9.60) have a simple interpre- 
tation in terms of these considerations when interpreted with the 
= 2 = 
