Once again, in order to evaluate the mean value of the Quality in the region of the maximum, the curve
is approximated by a parabola, that is in terms of its z argument.
Employing similar algebra as for 
the second derivative of the Quality in the region of the maximum
becomes
which can be evaluated at the position of the maximum, 
, giving
Therefore the Quality in the region of its maximum has the Taylor expansion,
with I and R dependences in 
, 
and the curvature, retained explicitly.
This expansion may be integrated directly for an arbitrary t range. The lowest t value for which the
expansion provides a good fit is 
and so for an integral from this lower bound to
arbitrary t,
A useful range of integration is for t between the uncorrected maximums of 
and the Quality. This
is listed with some other possible ranges and given in the form of the mean,<Quality>.
The full expression for the Quality and its second order approximation are plotted in fig 5.
=6in
