80
(Expressions (3-34) and (3-35) above are not exact, since they are
derived from the logistic equation (3-23), which is itself only an
approximation.) Since F^q = S|_ (Bg)g/2 and = SL ^BL^0 we
finally obtain, after elimination of F^g and (Fg)g and some
rearrangement and simplification,
KdC FC50 x 2KdL^SL"^BL^0^^BL^0 + 2SL
+ 2SLKdL-3SL(BL)0]. (3-36)
This is a much better approximation than the Cheng-Prusoff
equation (3-33), to which it reduces when (Bg)g is neglected and Fg5Q is
replaced by ED^g. Equation (3-36) remains approximately valid, and is
still superior to equation (3-33), when ED5q is substituted for F^:
KdC ^ ^ x 2KdL[V(BlV/t(Bl^)2 + 2SL2
+ 2SLKdL-3SL(BL)g]. (3-37)
Equation (3-36) will, however, always be superior to equation (3-37);
similarly, the Cheng-Prusoff expression itself will always be more
nearly exact if a good estimate of Fg5g is substituted for the estimate
of EDgg. Table 3-1 lists, for the example that we have been
considering, the K^g estimates derived from the two different
approximations; each method has been used in combination with both the
estimated and the exact values of Fg^g and ED^g listed above. It will
be seen that the retention of (Bg)g in the approximation is required for