q the results are the same because the same track is retraced in 
the opposite direction. Equation (10.69) states formally that 
A(h',-q) equals A(h',q). Thus m+ 1 numbers are duplicates and 
can be discarded. Finally (2q+ 1)(m + 1) numbers result from the 
application of the procedures given by Tukey and Hamming [1949] to 
the recorded data. This is stated in (10.68). As a check, the 
total area under A(h) in em* should equal the total area under 
ACh',j*) for each j* to a high degree of accuracy. If not, the 
value of N is too small and the value of m is too large for re- 
liable results. 
It is now necessary to study how the #,9 plane mans into 
the Yo 5 plane and how area net elements in the first plane map 
into area net elements in the second plane. For this purpose, 
pick the values given by equation (10.70) for the mw axis and the 
values given by equation (10.71) for the 9 axis. The curves de- 
fined by the double lines are boundary curves of area elements. 
The unknown number, An(h,j), will designate the value of 
over the net area element defined by equations (10.73) and (10.74). 
It will be assumed that Ap (h, j) is constant over the area element. 
Figure 27 is an example of such a net of the pw ,& plane for 
the special case of m equal to 10 and q equal to 3. The values of 
4,(h,j) are shown in each of the area elements. The A,(h,j) are 
the unknowns which must be found to determine an approximation of 
[a5 (p ,@)]*. Near the origin of the coordinate system some of 
the values of A,(h,j) are not shown because the figure would be 
too crowded. There are (m + 1)(2q + 1) unknown values of A,(h,j). 
= ssa 
