\chapter*{Summary}
%\markboth{Zusammenfassung}{Zusammenfassung}
\addcontentsline{toc}{chapter}{Summary}

The measurement of the inclusive DIS cross section and the extraction
of the proton structure function $F_2$ in the 
kinematical region of $0.2<Q^2<3.5\,$GeV$^2$ for low values of
$9.5 \times 10^{-6} < x < 8.0 \times 10^{-3}$ have been performed. The data sample analysed correspond to a special data taking period where the 
interaction point of the $ep$ scattering was moved from its
nominal position in order to access low values of $Q^2$. 
%The luminosity used in the analysis is $450^{-1}\,$nb.

In order to minimize the total error of the measurement over the
accessed phase space, usually two kinematical reconstruction methods are 
employed, the electron and the $\Sigma$ method. The electron method is
used in this analysis up to values of $x<10^{-4}$, while the $\Sigma$
method is used for the interval $10^{-4} \leq x \leq 8.0 \times 10^{-3}$. Both
methods are influenced by several systematic errors which
were studied in detail to determine the total error
of the $F_2$ measurement. The present analysis concentrated on the
understanding of the uncertainty of the energy measurement of the
scattered electron and of the energy flow of the hadronical final state. 

Since for $ep$ collision at low values of $Q^2$, the electron
is scattered into the backward region of the H1 detector, a precise 
calibration of the electromagnetic part of the SpaCal was performed. 
The uncertainty of the energy measurement is found to be $0.02\%$ for
energies of the scattered electron close to the 
incoming electron energy $E_{inc}^{0} \approx 27.5\,$GeV, while $1\%$ is
obtained for small energies around $E\approx 2\,$GeV. Using a
linear interpolation of the uncertainty of the energy measurement, the
resulting systematic error of the $F_2$ measurement varies 
between $0.5\%$ and $4\%$.
%In order to extend the measurement to higher values of $x\approx
%10^{-3}$, the $\Sigma$ method was used. 

Using the energy measurement of the scattered electron as the
reference scale, the energy flow of 
the hadronic final state was studied in terms of its transverse and
longitudinal momentum. Since 
the $\Sigma$ method uses the reconstruction of all particles building
the final state, detailed studies of the calorimeter noise and its
influence on the reconstruction of the kinematical variables were
performed. The noise originating from the beams and the electronics
circuits of the
LAr calorimeter was found to have a negligible influence on the
kinematical reconstruction. The noise substraction algorithm was found
to have an influence of $10\%$ over the accessed phase space.
The uncertainty of the energy flow identified as coming from the real
$ep$ collision was assigned to $10\%$ at $y=10^{-3}$ and to $2\%$ at
$y=10^{-1}$. The correlated systematic error of the $F_2$ measurement
due to the uncertainty of the hadronic energy measurement accounts to
values between $0.5\%$ and $4\%$.

The cross section measurement in the same kinematical region and using
the same data sample was performed in \cite{olaf}, but the CTD and
the BDC were used instead of the BST in order to reconstruct the angle of the
scattered electron coming from the $ep$ collision. The cross section
measurement and the proton structure function performed in \cite{olaf}
and the one derived in this thesis are in good agreement.

The measurement of the proton structure function
here presented agrees with the previous measurement of H1
using shifted vertex data taken in the year $1995$. The total
error of the measurement presented here have a higher precision
than the previous shifted vertex data for values of $Q^2>1.5\,$GeV$^2$.
The total error of the $F_2$ measurement achieves the same precision 
as the low $Q^2$ analysis of H1 using data of $1996$ and
$1997$, having a total error which 
varies between $3\%-4\%$ for values of $Q^2>2\,$GeV$^2$ and $8\%-15\%$ for
$Q^2<2\,$GeV$^2$. 

