\chapter*{Summary}
\addcontentsline{toc}{chapter}{\numberline{}{Summary}}
\markboth{Summary}{Summary}

During a special data taking period of the HERA collider in the year
2000, called shifted vertex run, the interaction region of electrons
and protons has been shifted into the direction of the incoming
proton.
This allows to study the proton structure at virtualities of the
exchanged photon \mbox{$Q^{2} \approx 1\, \mathrm{GeV^{2}}$} where the
transition takes place from a region of the phase space where
perturbative calculations based on Quantum Chromodynamics, the theory
of the strong interaction, can be performed to a domain where only
phenomenological models are able to describe the data.

The topic of the present thesis is a measurement of the inclusive DIS
cross-section based on the data recorded with the H1 detector during
the shifted vertex run. This requires an accurate reconstruction of
the scattered electron. Its polar angle is determined with the help of
the Backward Drift Chamber (BDC) and the interaction vertex
reconstructed by the Central Tracker, its energy is measured in the
backward calorimeter SpaCal. Hence the alignment of BDC and SpaCal
w.r.t. the Central Tracker has been studied in detail. The
calibration of the SpaCal has been performed in~\cite{Vargas:2006}.

The cross-section determination relies on a comparison of the number
 of observed events between the data and a Monte Carlo simulation of
 the scattering process and the detector response. After imperfections
 in the implementation of the simulation have been identified and
 overcome a detailed comparison of the detector response between data
 and Monte Carlo has been carried out. The remaining differences are
 taken into account by correction factors to the Monte Carlo sample.

The dominant background contribution to this analysis are
photoproduction events (\mbox{$Q^{2} \approx 0\, \mathrm{GeV^{2}}$})
in which a particle of the hadronic final state mimics the scattered
electron. Their contribution is subtracted statistically from the
data, again based on a Monte Carlo model. All other background sources
are found to be negligible.

With $x$ being the fraction of the proton's momentum carried by the
struck quark the data allow to measure the cross-section in the
kinematic range \mbox{$0.2 < Q^{2} < 3.5\, \mathrm{GeV^{2}}$} and
\mbox{$3 \cdot 10^{-5} < x < 8 \cdot 10^{-4}$}. Based on this the
structure function $F_{2}$, parameterising the quark composition of
the proton, can be extracted. For all investigations carried out in
this analysis uncertainties have been derived and the resulting
systematic errors on $F_{2}$ have been determined. The total errors
vary between 4\% and 5\% for \mbox{$Q^{2} > 0.85\, \mathrm{GeV^{2}}$},
only at the smallest values of $x$ they are larger due to the
uncertainty on the contribution of the photoproduction events. At
lower virtualities, $Q^{2} < 0.85\, \mathrm{GeV^{2}}$, the total
errors reach 20\%, dominated either by the statistical error or the
uncertainty on the reconstruction efficiency for the interaction
vertex. The errors are typically \mbox{$30-50\%$} smaller than for the
analysis of a previous shifted vertex run performed in
1995. Furthermore the results are in agreement with a second analysis
using the same data but employing the Backward Silicon Tracker for the
reconstruction of the polar angle of the scattered
electron~\cite{Vargas:2006}. A combined publication of both analyses
is anticipated.

