equal to 1 they are zero, and for h' less than 4 or greater than 7 
they are zero. Therefore only four values have to be found out of 
the 77. From figures 29 and 30, B(6,1,7',1°,0*) and B(8,0,7°,aa—a0 
have the same numerical value. Thus only a few of the values act- 
ually have to be determined. 
The evaluation of B(8,1,5',1',0O*) will be discussed as a par- 
ticular example. It is the number which results from the double 
integration of (1/2)(g/cos OyY ye d vdeo, over the shaded area 
indicated in figure 29. Three sections of the boundary curves are 
given by constant values of y and 85° Two of the boundary curves 
fo) 
are functions of v é and 85° By breaking up the area shown into 
three sub-areas shown by the heavy lines, and then, by integration 
over vy, first, the center area works out immediately with respect 
to the next integration over 86° The other two areas become 
elliptic integrals over 85 which can be evaluated from tables such 
as those in Janke-Emde [1945]. 
For a complicated function, [A5( v ,9)1°, and for m equal to 
10 and q equal to 3 as in the figures, seven analyses of the form 
described by Tukey and Hamming [1949] would have to be carried out. 
Each might require four or five hours on a computing machine. The 
evaluation of the B(h,j,j',j',j might require several days. The 
result would be 77 linear inhomogeneous simultaneous equations with 
77 unknownse The matrix of the equations has certain symmetry 
properties and if its inverse could be found easily, then the numer- 
ical work would involve another day of work. With time for checks 
of the computation, it would take about ten days to determine the 
= 3080- 
