  The spin filtering in storage rings is based on the multiple passage of a
stored beam through a polarized internal gas target. Apart from the
polarization by transmission, a unique geometrical feature of interaction with
the target in such a filtering process, pointed out by H.O. Meyer \cite{Meyer},
is a scattering of stored particles within the beam. A rotation of the spin in
the scattering process affects the polarization buildup. We derive here a
quantum-mechanical evolution equation for the spin-density matrix of the stored
beam which incorporates scattering within the beam. We show how the interplay
of transmission and scattering with the beam changes from polarized electrons
to polarized protons in the atomic target. After discussions of the FILTEX
results on the filtering of stored protons \cite{FILTEX}, we comment on the
strategy of spin filtering of antiprotons for the PAX experiment at GSI FAIR
\cite{PAX-TP}.
