  The extent to which information about fluctuations in hadron-nucleon total
cross sections in the frozen approximation can be extracted from very high
energy hadron-nucleus total cross section measurements for a range of heavy
nuclei is discussed. The corrections to the predictions of Glauber theory due
to these fluctuations are calculated for several models for the distribution
functions, and differences of the order of 50 mb are found for heavy nuclei.
The generating function for the moments of the hadron-nucleon cross section
distributions can be approximately determined from the derivatives of the
hadron-nucleus total cross sections with respect to the nuclear geometric cross
section. The argument of the generating function, however, it limited to the
maximum value of a dimensionless thickness function obtained at zero impact
parameter for the heaviest nuclear targets: about 1.8 for pions and 3.0 for
nucleons.
