where the first term in brackets is I/sin 16max. Algebraic manipulation then yields Eq. (16-115). From Fig. 16-7, we see that

Note that tp is the third Euler angle in a 3-1-3 sequence and that as if/ increases, the projection of L onto the x —y plane moves clockwise. By examining the spherical triangle .¿-Sun-;, we obtain

and tan

which gives /3m as a function of 0^, 0,1, and ¿. From this, AySm can be calculated so that Eq. (16-113) can be inverted to determine which is the unknown in real data. The maximum and minimum values of P„ and hence Rp are found numerically for a given 0^, 0, and I. Note that the dependence of Rp on I is only through the parameter Rj. Values of Rp for 0maxa* 2 deg and y3=90 deg are shown in Fig. 16-9. Numerical tests indicate that Rp is insensitive to 0^ and ft so that the curves in Fig. 16-9 are accurate to 5 to 10% when 20max < p and Rg >0.15. They were constructed for Ix<Iy<I, and the slit plane in the first quadrant; they may be extended to other quadrants by symmetry. These curves have the

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