Here a0 and are two more undetermined multipliers to be accounted for. We now have the relations These equations do not allow us to find absolute values of a0, at and XW1 but only certain ratios. Actually, this is all that is required. To obtain the appropriate equation for the X’s, we make use of the expression for yt given in equation (24). Substituting this value into equation (28), we end up with where X = i,j = 1,2, ... n and i j in the summation. This is a rather remarkable set of equations in that not only are they linear and homogeneous in the unknown X’s, but each coefficient is only a function of the nondimensional power collection ratio 0 and the nondimensional radius parameter X = (27t/Xz)Z?(>2?1. The only way these equations can have solutions other than Xj = X2 . . . Xn = 0 is for the determinant of the coefficients to be zero. Consequently, all we need do is pick a particular value of /?, compute the matrix of coefficients with X being the unknown and then by a computer program, determine the smallest X for which the determinant of the coefficient matrix is zero. This takes only a short while and we thus arrive at values of X as a function of /3. This computation is made once and for all; we exhibit a table of p vs X in the numerical section of this report. Radii of the antennas and the minimum cost Once we have A1 as a function of /3, we can immediately determine the radius of the
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