$\beta_N$ measured in the C- and N-arms. A two-dimensional $\beta_C{-}\beta_N$ plot on Fig. \[2-dim-bb\] illustrates this procedure.

The calibration done provided a linear scale of velocities in the range $\beta  = 0.6{-}1$ with errors of about 3% ($1\sigma$). We have checked the linearity of the scale by using cosmic rays and setting different distances between detectors.

Results and comparison with simulations {#results-and-comparison-with-simulations .unnumbered}
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Measurement runs have mostly been done in 2009 at two maximal beam energies: $E_{\gamma\;\rm max} =  650$ MeV and 850 MeV. The on-line trigger was a coincidence of particles in the C- and N-arms within a time gate of 50 ns.

For further off-line analysis events were selected with an additional condition of sufficiently long ranges of the charged particles, E\_i &gt; E\_i\^[thr]{} \[eq:selection\] with experimentally adjusted thresholds $E_i^{\rm thr}$. In this way low-energy particles in the C-arm were rejected.

A two-dimensional histogram in the variables $\Delta E{-}\beta_C$, where $\Delta E$ is the minimal energy loss in the $\Delta E_i$ detectors, E=\_i(E\_i), is shown in Fig. \[2-dim-bE\] for the beam energy $E_{\gamma\;\rm
max} = 850$ MeV. Results of simulations using the Intra Nuclear Cascade (INC) model [@pschenichnov97] in the GEANT-3 framework are shown in Fig. \[2-dim-bE-INC\] 