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\noindent                                                                 
%========================title page=============================   
\begin{titlepage}                                                    
\noindent
% {\bf H-UM \& JS: version of \today} \\[.3em] 
Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000

\vspace*{3cm}

\begin{center}                                                                 

\begin{LARGE}                                               
{\bf
 Deep-Inelastic Inclusive {\boldmath $ep$}
 Scattering \\
  at Low  {\boldmath $x$}
 and a Measurement of  {\boldmath $\alpha_s$} \\}
\vspace*{2.cm}                                                                 
H1 Collaboration
\\                                                          
\end{LARGE}  
\end{center}
%=======================abstract==============================        
\vspace*{2.cm}                                                                 
\begin{abstract}
  \noindent A precise measurement at HERA of the inclusive 
  deep-inelastic $e^+p$ scattering cross section is reported for
  four-momentum transfers squared $1.5 \leq Q^2 \leq 150{~ \rm GeV^2}$
  and Bjorken-$x$ values $3 \cdot 10^{-5} \leq x \leq 0.2$ using new
  instrumentation in the backward region of the H1 detector. In
  most of  this kinematic range the cross section $\sigma$ is
  determined to good approximation by the proton structure function
  \F.  At intermediate $Q^2$ and large $x$, the data confirms the
  measurements of previous fixed target muon-proton scattering
  experiments. At smallest $x$, the longitudinal structure function
  \FL is determined.  The behaviour of the measured cross section and
  of the derivatives, $\partial \sigma / \partial \ln y$ and $\partial
  F_2 / \partial \ln Q^2$, is in accord with perturbative Quantum
  Chromodynamics. In a DGLAP QCD fit to H1 $ep$ and BCDMS $\mu p$
  inclusive cross section data, the gluon momentum distribution \xgc
  and the strong interaction coupling constant \as are determined
  simultaneously.  A value of \amz =
  $0.1150~~\pm~~0.0017~(exp)~~^{+~~0.0011}_{-~~0.0012}~(model)$ is
  obtained in next-to-leading order
  QCD with an extra theoretical error of about $\pm 0.005$
  due to renormalisation scale uncertainties.
%\end{quotation} 
\end{abstract}
%\end{titlepage}
%\end{document}
\vfill
\vspace{1cm}
\begin{flushleft}
  {\bf Abstract: 944,945 } \\
  {\bf Parallel session: 2,3} \\
  {\bf Plenary talk: 12,11}
\end{flushleft}

\end{titlepage}
%\end{center}
\cleardoublepage                     
%\end{titlepage}
%
%\end{document}
\newpage
%
% -- authors
%
%\include{h1auts}
%
\newpage
%
%--------------------------------------------------------------------
%%
%\section{Introduction}    
%%
%Since the discovery of Bjorken scaling~\cite{bj} of the proton
%structure function \F at $x~\sim~0.2$ \cite{slac} and the advent of
%Quantum Chromodynamics~\cite{qcd}, deep-inelastic lepton-nucleon
%scattering (DIS)~\cite{feyn} 
%has become a classic field for investigating strong
%interactions~\cite{tamps}.  Previous fixed target DIS experiments have
%observed logarithmic scaling violations, for $x \geq 0.01$, which are
%well described by perturbative QCD.  The DGLAP equations~\cite{dglap}
%relate the $Q^2$ evolution of \Fc to the gluon momentum density in the
%proton, \xgc, and to the strong interaction coupling constant,
%\as. These can be determined with precision cross section data
%measured in a wide range of Bjorken-$x$ and momentum transfer squared
%$Q^2$.

%The first measurements of \Fc at low $x \sim 10^{-3}$ and $Q^2 \sim
%20$~\gv at HERA revealed a steep rise of \F towards low $x$ at fixed
%$Q^2$~\cite{h1f292, zeus92}.  The strong scaling violations observed
%at low $x$ are attributed to a high gluon density in the proton.  At
%extremely low $x$ non-linear gluon interaction effects have been
%considered in order to damp the rise of the cross section in
%accordance with unitarity requirements~\cite{glr}. Modified evolution
%equations have been developed~\cite{bfkl, ccfm} to account for the
%large logarithms of $1/x$ in the new kinematic region.

%This paper presents new cross section data in the kinematic region of
%four-momentum transfers squared $1.5 \leq Q^2 \leq 150{~ \rm GeV^2}$
%and Bjorken-$x$ values $0.00003~\leq~x~\leq~0.2$ taken 
%with positrons of $E_e=27.6~$GeV and protons of 
%$E_p=820~$GeV, corresponding to an energy of $\sqrt{s} = 300.9$~GeV in
%the centre of mass system, where $s = 4 E_e E_p$.

%The measurement uses the upgraded backward detector of H1 and much
%increased HERA luminosity, of about 20~\ipb, which enables an accuracy
%of typically 3\% to be reached for the DIS cross section.  It thus
%considerably improves the former H1 structure function
%measurements~\cite{sf94,sfsvx} at $Q^2 \leq 150$~GeV$^2$.  The
%kinematic range is extended to larger $x$ which yields an overlap of
%H1 data with fixed target $\mu p$ data for the first time.  The paper
%presents also a measurement of the derivatives \pdff which serve as a
%sensitive test of strong interaction dynamics.  Measurements of the
%proton structure function \Fc in the DIS region at low $x$ at HERA 
%were reported  previously also by the ZEUS 
%Collaboration~\cite{zeusf2}. 

%The longitudinal structure function \FL is obtained here with improved
%precision and much extended range as compared to its first
%determination at low $x$ by the H1 Collaboration based on the 1994
%data~\cite{sfl}. This has been made possible with precision tracking
%in front of the backward calorimeter.  A new method is introduced in
%order to extract \FL at low $Q^2 < 10$~\gv using the cross section
%derivative \pdsi, where $y=Q^2/sx$ is the inelasticity variable.


%A NLO DGLAP QCD analysis is made using inclusive lepton-proton
%scattering data only.  It is thus independent of corrections for
%nuclear binding effects in the deuteron or heavier nuclei.  This
%analysis utilises a novel flavour decomposition of the structure
%function \Fc. For the first time, a QCD analysis is performed using only
%H1 inclusive cross section measurements. In a fit to these low $x$
%data, and the recently published high $Q^2$~\cite{hiq} H1 data, the gluon
%density at low $x$ is determined, and the fixed target lepton-proton
%scattering data are found to be rather well described.  The
%combination of precision low $x$ and high $x$ data enables both \xg
%and \amz to be simultaneously determined. The analysis uses all
%available information regarding the experimental uncertainties of the
%data sets considered.  A new, accurate value of the strong coupling
%constant \amz~is derived using H1 $ep$ data and previous BCDMS $\mu p$
%data~\cite{BCDMS}.

%The paper is organised as follows: Section~2 defines the inclusive cross
%section and the methods of kinematics reconstruction used.  The
%detector, and the event selection and simulation, are described in
%section~3.  Section~4 presents the alignment and calibration methods and
%summarises the cross section measurement.  Section~5 presents the
%measurement of the cross section derivative with respect to $\ln y$
%and the determination of the longitudinal structure function \FL.  The
%results for the proton structure function \Fc and its derivative
%$\partial F_2 / \partial \ln Q^2$ at low $Q^2$ are given in
%section~6.  The QCD interpretation of the data is discussed in section~7 which
%refers to an appendix presenting details of the analysis. The
%paper is summarised in section~8.
%%
%% ------------------------------------------------------------
%%
%\section{Cross Section and Kinematic Reconstruction \label{kin}}
%%
% The inclusive DIS
%cross section depends on two independent
%kinematic variables, chosen to be $x$ and $Q^2$, and on the energy 
%squared $s$ since $y=Q^2/sx$.
%In the one-photon exchange approximation the 
%double differential cross section, $d^2\sigma /dxdQ^2$,
%is defined as 
%\begin{equation}
%   \frac{Q^4 x}{2\pi \alpha^2 Y_+}  \cdot \frac{d^2\sigma}{dxdQ^2}  =
% \sigma_r =        F_2(x,Q^2) - \frac{y^2}{Y_+} \cdot F_L(x,Q^2),
%       \label{sig}
%\end{equation}  
%with $Y_+ = 1+ (1-y)^2$.  Here the reduced cross section, $ \sigma_r$,
%is introduced.  Due to the positivity of the cross sections for
%longitudinally and transversely polarised photons scattering off
%protons, the two proton structure functions \Fc and \FLc obey the
%relation $0 \leq F_{L} \leq F_{2}$. Thus the contribution of the
%longitudinal structure function \FLc to the cross section can be
%sizeable only at large values of the inelasticity $y$, and in most of
%the kinematic range the relation $\sigma_r = F_2$ holds to very good
%approximation.

%The HERA collider experiments allow the DIS kinematics to be
%reconstructed using either the scattered positrons, the hadronic final
%state, or a combination of the two.  This is important for
%the coverage of the kinematic range.


%In the ``electron method''
%the event kinematics can be determined using the
%measured energy of the scattered positron $E_e'$ and its polar angle
%$\theta_e$ according to the relations
%%
%\begin{equation}
%Q^2_e= \frac{E^{'2}_e \sin^2{\theta_e}}{ 1-y_{e}},
% \hspace*{2cm}
%y_e=1-\frac{E_e'}{E_e}~\sin^2(\theta_e/2).
%\label{qy}
%\end{equation}
%%
%Here the polar angle is defined with respect to the proton beam 
%direction which defines the $z$ axis. While this method is 
%accurate at large $y$, corresponding to low $E_e'$, the
%resolution rapidly degrades $ \propto 1/y$ as $E_e'$
%approaches the positron beam energy, $E_e$. 

%The measurement of the hadronic final state
%determines $y$ as \cite{jb}
%\begin{equation}
%       y_h=\frac{\Sigma_{i}(E_i-p_{z,i})}{2E_e} = \frac{\Sigma_h}{2E_e},
%       \label{yh}
%\end{equation}
%where $E_i$ and $p_{z,i}$ are the energy and longitudinal 
%momentum component of a final state particle $i$,
%the masses being neglected. 
%In this analysis the kinematics are reconstructed also using the 
%``$\Sigma$ method'' based on the variables~\cite{babe}
%\begin{equation}
%   Q^2_{\Sigma} = \frac{E^{'2}_e \sin^2{\theta_e}}{ 1-y_{\Sigma}},
%   \hspace*{2cm}
%   y_{\Sigma} = \frac{y_h}{ 1+y_h-y_e} =
%   \frac{\Sigma_h}{\Sigma_h+E_e'(1-cos \theta_e)}.
%   \label{ys}
%\end{equation}
%The $y_h$ and $y_{\Sigma}$ variables can be well measured down to low
%$y \simeq 0.003$.
%  The $\Sigma$ variable $y_{\Sigma}$ is less sensitive to initial
%state radiation since in equation~\ref{ys} the initial energy $E_e$ is
%calculated using the total energy reconstructed in the detector.



%The mass of the virtual photon-proton system is given by 
%\begin{equation}
%  W^2=\frac{Q^2}{x} \cdot (1-x) +M_p^2,
%\end{equation}
%where $M_p$ is the proton mass.
%%
%The hadronic scattering angle is defined as
%\begin{equation}
%    \tan \frac{\theta_{h}}{2} = \frac{\Sigma_h}{P_{t,h}}
%%   \cos \theta_{h}= \frac{P^{2}_{t,h} - \Sigma^{2}}
%%                       {P^{2}_{t,h} + \Sigma^{2}},
%                       \label{thetah}
%\end{equation}
%where $P_{t,h}$ is the total transverse momentum of the hadronic 
%final state particles. In the quark parton model, $\theta_{h}$ defines the 
%direction of the struck quark.
%For $y > 0.5$ the positron scattering angle $\theta_{e}$ is 
%smaller than $\theta_{h}$, and the hadronic final state is scattered
%backwards. This can be deduced from
%                               \begin{equation}
%           \tan \frac{\theta_{h}}{2} =
%                \frac{y}{1-y} \cdot
%           \tan \frac{\theta_{e}}{2}.
%                        \label{teh}
%                                 \end{equation}       
%This relation, together with the definition of $y_e$
% (equation~\ref{qy}) determines
%the scattered positron energy from  $\theta_{e}$ 
%and  $\theta_{h}$ in the ``double angle method''~\cite{dang}.              
%%
%% ------------------------------------------------------------
%%
%\section{Experimental Procedure}
%%
%\subsection{H1 Detector}
%%
%The H1 detector~\cite{h1detec} is a nearly hermetic apparatus with a
%solenoidal magnetic field of 1.15~T built to investigate high-energy
%$ep$ interactions at HERA.  The low $Q^2$ cross section measurement
%relies mainly on the central and backward tracking systems, on the backward
%calorimeter and on the Liquid Argon (LAr) calorimeter. These
%components are briefly described below.
 
%The energy of the positron, when scattered into the backward
%region of the H1 detector ($153^o < \theta_e < 177^o$), is measured in
%the lead-fibre calorimeter (SPACAL \cite{Spacal}).  The SPACAL has an
%electromagnetic energy resolution of $7.1\%/\sqrt{E} \oplus 1.0\%$, a
%hadronic section and an integrated timing
%function to veto proton beam induced background interactions.  Due to
%its fine granularity the SPACAL provides a determination of the $x$
%and $y$ cluster coordinates with a few mm accuracy.  Identification
%of the scattered positron and the polar angle measurement make use of
%a backward drift chamber (BDC), situated in front of the SPACAL, and a
%new backward silicon strip detector (BST). The BST~\cite{BST} is
%arranged concentrically around the beam axis. It consists of four
%detector planes equipped with  wedge shaped, double metal
%strip detectors of active radii between
%5.9~cm and 12.0~cm.

%The hadronic final state is reconstructed with the Liquid Argon (LAr)
%calorimeter~\cite{LAr}, the tracking detectors and the SPACAL.  The
%LAr is built of eight wheels of modules with an octant structure.  The
%interaction vertex is determined with the central tracking detector
%(CT) consisting of two jet drift chambers (CJC) and two concentric $z$
%drift chambers (CIZ and COZ).  The vertex determination is complemented
%at lower angles ($167^o < \theta_e < 171^o$) by the inner proportional
%chamber CIP and at larger angles ($171^o < \theta_e < 176.5^{o}$) by
%the silicon tracker BST.

%The luminosity is determined from the cross section of the elastic
%bremsstrahlung process, measured with a precision of 1.5\% using the
%method outlined in~\cite{lumi}.  The final state photon and the
%positron scattered at very low $Q^2$ can be detected in calorimeters
%(``electron and photon taggers'') which are situated close to the beam
%pipe at distances of 33~m and 103~m from the interaction point in the
%positron beam direction. The luminosity measurement is corrected by
%about 7\% for the occurrence of late and early proton beam satellites
%which do not enter the selected data sample.
%%
%\subsection{Data Samples and Interaction Triggers \label{datrig}}
%%
%The analysis comprises two different DIS event samples:
%\begin{itemize}
%\item{$A$ - data taken in the years 1996 and 1997 with luminosities of
%    4.5~pb$^{-1}$ and 13.4~pb$^{-1}$ respectively. These two data sets
%    are combined to provide the cross section measurement for $Q^2$
%    between 15~\gv  and 150~GeV$^2$ and for $Q^2=12$~GeV$^2$ at $y > 0.17$.}
%%
%\item{$B$ - data taken in the fall of 1997 during a two weeks period
%    dedicated to the lower $Q^2$ region. The data of this special run
%    with a luminosity of 1.8~pb$^{-1}$ are used in the $Q^2$ range from
%    1.5~GeV$^2$ to 8.5~GeV$^2$ and for $Q^2=$12~GeV$^2$ at low $y <
%    0.17$.}
%\end{itemize}
%The event trigger for the data of sample $A$ requires the local
%energy sums in the SPACAL calorimeter to be above an energy threshold
%of 6~GeV. This threshold is lowered to 5~GeV in the low $Q^2$ run
%$B$.

%A large contribution to the data samples is due to photoproduction
%processes, $Q^2 \simeq 0$, in which the scattered positron escapes
%detection in the backward apparatus. Part of those is detected
%in the electron tagging calorimeter. In such events there is a small
%probability that a particle in the hadronic final state mimics the
%signature of a scattered positron of low energy.  Because of the very
%large photoproduction cross section, the high $y$ region can be
%accessed only with dedicated triggers which suppress this background.

%A special high $y$ trigger was developed which requires more than
%2~GeV of energy to be deposited in a SPACAL cluster above certain
%radius, and a vertex signature in the proportional chamber system.
%The data accumulated with this trigger correspond to a luminosity of
%2.8~pb$^{-1}$ in 1996 and 3.4~pb$^{-1}$ in 1997.  The SPACAL energy
%triggers are monitored with independent track triggers and found to be
%fully efficient for energies of about 1~GeV above threshold. The high
%$y$ trigger efficiency is found to be 97\% as monitored with
%independent calorimeter triggers. This small trigger inefficiency is
%corrected for in the cross section analysis.

%In the on-line data reconstruction, loose
%rejection criteria are applied prior to writing the events to tape.
%These criteria primarily remove those interactions which cannot be
%validated from reconstructed detector information. From monitor data,
%a maximum loss of  0.5\% of the DIS events is established.
%A global correction for this loss is applied and taken into account 
%in the normalisation uncertainty.
%%
%\subsection{Event Selection \label{evsel}}
%%
%DIS events at low $Q^2$ are characterised by a positron scattered into
%the backward part of the H1 apparatus.  The scattered positron is
%identified with the cluster of maximum transverse momentum $p_{t}$ in
%the SPACAL calorimeter.  Electromagnetic energy deposition leads to
%clusters of smaller radial extension~\cite{awe, Spacal} than hadronic
%energy deposition.  An unbiased estimate for the maximum possible
%positron cluster radius at low energies is obtained using photon
%tagged radiative DIS events and also QED Compton events.  The positron
%cluster radius is thus measured down to 3~GeV energy, and a radius cut
%of $\leq 4$~cm is established. This cut removes a sizeable fraction of
%the photoproduction background while retaining more than
%99\% of the DIS signal.

%A positron candidate cluster has to be associated with a signal in the
%BDC. A signal is required in the CIP for the larger $Q^{2}$ events, or
%in the BST for the lower $Q^{2}$ events. A BST track segment can be
%built out of two or more hits associated with a SPACAL cluster.  The
%efficiency of the BDC is measured to be 98\% on average with small
%radius dependent variations. The efficiency of the CIP is about 98\%.
%The track efficiency of the BST is found to be about 93\% consisting
%of an internal efficiency of 98\% and of 5\% readout losses which
%occurred in the 1997 special run period. Efficiencies for electron
%detection at low energies are determined using Compton scattering
%events and radiative DIS events in which a photon is radiated from the
%incoming positron and detected in the photon tagger.

%For the determination of the event kinematics and background
%suppression, the interaction vertex position has to be reconstructed.
%In the intermediate $y$ region this is provided by hadrons measured in
%the central tracking chambers with an efficiency exceeding 98\%.
%However, at low $y < 0.03$, and occasionally at high $y > 0.5$, the
%hadronic final state escapes detection in forward or backward
%direction, respectively.  For such events the track of the scattered
%positron defines the vertex if it falls within the acceptance of the
%CIP or the BST.
%%
%\begin{table}[tb] \centering 
%\begin{tabular}{|l|c|}
%\hline 
%                SPACAL energy  &  $ >$ 6.9~GeV              \\
%cluster radius          &  $< 4$cm                 \\
%fraction of hadronic energy         &  $<$ 15\% of $E_{e}'$    \\
%cluster-BDC track matching     &  $\delta r < 1.5$cm      \\
%cluster-BST track matching     &  $\delta r < 1.0$cm       \\
%$z$ vertex position            &  $|z| < 30$cm            \\
%total $E-p_{z}$                &  $> 35$ GeV              \\
%\hline
%\end{tabular}
%\caption{\label{tabcut} \sl Basic  criteria to
%select DIS events. The fraction of hadronic energy denotes the
%relative energy measured in the hadronic section of SPACAL
%behind the electromagnetic cluster. The cluster radius~\cite{awe, sasha}
%defines the extension of energy deposition in the transverse
%plane.  Additional cuts are made in the
%high $y$ region as discussed in Section 
%\ref{sechihy}.}
%\end{table}  
%%
%Radiative events are suppressed
%by imposing energy-momentum balance requiring $E-p_{z} > 35$~GeV.
%The criteria to select DIS events are summarised in Tab.~\ref{tabcut}.
%%
%\subsection{Simulation \label{simp}}
%%
%For the calculation of the detector acceptance and the efficiency
%control about $ 10^7$ inelastic events are simulated. Deep-inelastic
%events are generated using the DJANGO~\cite{django} event generator.
%This program is based on HERACLES~\cite{heracles} for the electroweak
%interaction and on the Lund Monte Carlo generator program
%ARIADNE~\cite{ari}, which includes the generation of diffractive
%events.  This generator, when tuned to HERA data~\cite{herafi2},
%presently gives the most reliable description of the final state
%properties~\cite{herafin}. To describe higher order QCD radiation
%processes the ARIADNE program uses the Colour Dipole Model
%(CDM)~\cite{CDM}.  For hadron fragmentation the JETSET program is
%used~\cite{jetset}.  Compton events are generated using the program
%COMPTON~\cite{comp}. For comparison some studies are done using the
%generator LEPTO~\cite{lepto}.  At low masses $W$ of the hadronic
%system, events are also generated with the HERWIG event
%generator~\cite{herwig}.  HERWIG is the only program used which
%includes the resonance region. This is important for describing
%distributions of rejected events at very low $y$~\cite{vova}.
%Photoproduction background is generated with the PHOJET \cite{phoj}
%program using the parameterisation of CKMT~\cite{ckmt} to determine
%the virtual photon-proton interaction cross section. The normalisation
%of the PHOJET event sample is adjusted to the data measured with the
%electron tagging calorimeter. It is found to agree within 20\% with
%the calculation of the cross section using the Weizs\"acker-Williams
%approximation including small corrections for photon radiation which
%are calculated in leading logarithmic approximation~\cite{job}.  

%The detector response is simulated in detail with the program
%H1SIM~\cite{h1sim} which is based on GEANT \cite{geant}.  The Monte
%Carlo events are subjected to the same reconstruction and analysis
%chain as the real data. In the comparisons subsequently shown, the
%simulated distributions are normalised to
%the measured luminosity.
%%
%% ------------------------------------------------------------
%%
%\section{Measurement of the Cross Section}
%%
%\subsection{Detector Alignment}
%%
%The coordinate system of the H1 detector is defined by the central
%tracking chambers. The $z$ chambers and the CJC are aligned using
%cosmic tracks. The central tracker CT determines the spatial
%coordinates of the interaction vertex.  The inclination of the beam
%axis with respect to the $z$ axis of the CT is determined from the
%variation of the vertex position in the $x, y$ plane along the beam
%direction. For the mean $z$ vertex position, the $x$ ($y$) vertex 
%coordinates are offset by about 4(3) mm. 

% The $\phi$ angle of tracks and their momenta are measured
%with the CJC. The polar angle measurement of the CT is determined by
%the inner $z$ chamber CIZ, and by both $z$ chambers CIZ and COZ for
%smaller polar angles ($\theta_e < 162^o$).

%The alignment of the BDC and of the SPACAL with respect to the central
%tracker is done by studying the difference of the polar angles
%measured by these detectors as a function of the azimuthal angle. This
%results in 1-2~mm adjustments of the nominal detector positions in the
%plane perpendicular to the central axis. QED
%Compton events are used as a cross check for the
%alignment of the SPACAL requiring a common origin of the positron
%and photon clusters in the transverse plane.


%The BST has 16 $\phi$ sectors, each with four planes of wafers. These
%planes are adjusted
%using the high resolution of the silicon detectors
%leading to corrections of the measured radial positions of typically
%60~$\mu$m. Using the event vertex $z$
%coordinate measured with the CT the spatial position
%of the BST is determined.
 
%The alignment procedure is checked by comparing the polar angle
%measured with the BDC and the BST. An average difference $\Delta
%\theta$ of less than 0.1~mrad is found~\cite{vova}.  From the residual
%dependence of $\Delta \theta$ on the azimuthal angle and the
%uncertainties of the alignment procedure a measurement error of
%0.3~mrad is estimated for the angle of the scattered positron.
%%
%\subsection{Calibration of the Energy Measurements}
%%
%The energy of the scattered positron is measured in the highly
%granular lead-fibre calorimeter SPACAL. The response of the SPACAL
%cells is equalised using cosmic particles, and its time dependence is
%monitored with an LED system. Showering in the central
%tracker end-flange leads to energy losses which are corrected for
%using the charge collected in the backward drift
%chamber~\cite{rainer}. With this correction the resolution of the
%positron energy measurement is improved.  A
%cell-by-cell calibration of the SPACAL energy response
%is performed using the double angle
%method~\cite{dang}. This method is applied to the data of the various
%run periods, and for consistency also to the simulated events.
%Agreement of the energy scales is found at the level of 0.2\%.
%A further uncertainty of 0.2\% of the electromagnetic energy
%scale is estimated to account for details of the hadronic final state
%simulation and for local effects due to dead material in front of the
%SPACAL.  Thus a systematic error of the $E_e'$ scale of
%0.3\% is obtained for most of the SPACAL area.
%An analysis of Compton
%events leads to an estimated maximum energy
%scale uncertainty of 2.7\% at 3~GeV. This uncertainty is taken to
%approach linearly the 0.3\% level at maximum energies $E_e' \simeq E_e$.
%The SPACAL response at lowest energies considered 
%is cross checked by reconstructing the $\pi^0$ mass from the two
%decay photons~\cite{sasha} which cover the momentum range 
%of 0.8-4~GeV.  

%Figures~\ref{contm}a,b and \ref{contsp}a,b show the energy and polar
%angle distributions for both data samples which are well described by
%the simulation of DIS and photoproduction events. The DIS event
%simulation is reweighted to a QCD fit to the data with an initial
%scale $Q^2_0=1$~\gv, see section~\ref{qcdana}.


%The particle response of the LAr calorimeter was originally tuned with
%test beam data. Weighting techniques are applied to account for the
%non-compensating type of energy measurement~\cite{LAr1}. In the
%present analysis the hadronic $y$ variable has to be reconstructed
%well in order to measure the inclusive cross section at larger
%Bjorken-$x$.  
%An additional LAr calorimeter noise suppression is performed in order to
%improve the cross section measurement at low $y$. Isolated cells with
%energies less than 400~MeV (800~MeV) in the central (forward) region
%of the LAr calorimeter are excluded from the analysis of both data and
%simulated events. This leads to a small signal loss but improves the
%$y$ resolution at low $y$. Uncertainties in this subtraction procedure
%are included into the systematic errors.

%The electromagnetic and hadronic energy scales of wheels and octants
%of the LAr calorimeter are determined using a global minimisation
%technique~\cite{vova} which utilises the event $p_t$ balance between
%the scattered positron and the hadronic final state.  At low $y$ the
%final state is scattered in the forward direction, and the BST defines
%the track of the scattered positron. This enables the very forward
%calorimeter parts to be calibrated more accurately than hitherto.
 
%The hadronic energy calibration is performed also by imposing
%local transverse momentum balance in an iterative, wheel dependent
%procedure. Both calibrations are compared in all $Q^2, x$ bins, and a
%systematic uncertainty of 2\% of the hadronic energy scale in the LAr
%calorimeter is determined. The results of the energy calibration
%procedure, when applied to the high $Q^2$ data, are found to be
%consistent with those recently presented~\cite{hiq}.

%Figures~\ref{contm}c and \ref{contsp}c show the experimental $y_h$
%distributions over three orders of magnitude in $y$ which are well
%described by the simulation. In the simulation, the $y_h$
%reconstruction is found to be stable within an accuracy of a few~\%
%over a wide range of $y_h$. The hadronic measurement has thus been
%extended to $y=0.003$.
 
%The response of the SPACAL to hadrons is calibrated using the $E-p_z$
%conservation in the DIS events.  Since the calorimeter has a thickness
%of only two interaction lengths, energy losses occur resulting in a
%correction factor of about 1.5 with an uncertainty of about 5\%. This
%scale uncertainty affects the final cross section data at large $y$
%through the $E-p_z$ momentum balance requirement.
%%
%\subsection{Measurement at Large {\boldmath $y$}} \label{sechihy}

%Reaching the maximum possible values of $y$ is essential for the
%measurement of the longitudinal structure function.  At lower $Q^2 <
%10$~\gv, the high $y$ range is accessed by requiring a track signal in
%the BST using a minimum bias SPACAL trigger of 5~GeV threshold.  This
%requirement removes a sizeable fraction of the background which is due
%to $\pi_0 \rightarrow \gamma \gamma$ decays.  The remaining
%background, due to showering in the passive material, possible overlap
%of $\pi_0$ decays with charged tracks, and also misidentified charged
%pions, is subtracted bin by bin using the PHOJET event
%simulation. Figures~\ref{contbst}a and b illustrate the range of polar
%angle and energy for high $y$ events with a track in the BST.

%The size of subtracted background is cross checked with a data sample
%of photoproduction events which have a positron tagged downstream the
%positron beam. For these events figure~\ref{contbst}c shows the energy
%spectrum for SPACAL clusters obeying the DIS selection criteria, apart
%from the $E-p_z$ requirement. This distribution is well described by
%the simulation.

%At larger $Q^2 > 10$~\gv, the photoproduction background is subtracted
%by employing the charge assignment of tracks associated to the
%positron candidate clusters. This subtraction relies only on the data
%which avoids relying on the simulation of the photoproduction
%background. Thus the $E'$ range is extended down to 3~GeV,
%corresponding to $y <0.89$.  For $12 \leq Q^2 \leq 35$~GeV$^2$ tracks
%reconstructed in the CJC can be associated to low energy SPACAL
%clusters with an efficiency of 95\% (93)\% in 1996 (1997). For these
%linked tracks the charge is determined with an efficiency of 99.5\%
%for tracks with $ 3 < E' < 15$~GeV.


%This statistical subtraction procedure requires the study of possible
%charge asymmetry in the background processes.  This can be measured
%using tagged photoproduction events which fulfil the DIS event
%selection criteria.  A small charge asymmetry $(N_+ - N_-)/(N_+ +
%N_-)$ is found with an average of -4.8\% with a statistical accuracy
%of 1.9\%, for $0.65 < y < 0.89$. Here $N_+(N_-)$ is the number of
%events with positive (negative) charge of the track associated to the
%SPACAL cluster.  A similar excess of tracks with negative charge is
%also observed in the hadronic final state of DIS events.  Comparing
%the energy distribution for a sample of negative tracks in $e^+p$
%scattering, taken in 1996/1997, with that for a sample of positive
%tracks in $e^-p$ scattering, taken in 1999, a consistent asymmetry of
%$(-3.5 \pm 2.5)$\% is measured.  Based on background simulation
%studies and measurements of the ionisation loss in the CJC, the small
%asymmetry observed is traced back to the antiproton interaction
%cross-section exceeding the one of proton interactions at low
%energies~\cite{pdg}.

   
%The measured charge asymmetry is corrected for when the negative
%track sample is statistically subtracted to obtain the positron DIS
%cross section at high $y$.  Some control distributions of this large
%$y$ measurement, see also~\cite{sasha, doris}, are shown in
%figure~\ref{conthyq}. These illustrate the understanding of this
%kinematic region down to scattered positron energies of
%$E_e' = 3~$GeV.
%%
%\subsection{Results \label{sigmeas}}
%%
%An iterative bin-wise unfolding procedure is adopted for the
%extraction of the double differential cross section $\sigma_{r}$.
%This procedure requires the bin sizes to be adapted to the finite
%resolution in the measurement of the kinematic variables. As is
%illustrated in figure~\ref{bins}, the data and the simulated events are
%binned in a grid in $x$ with five bins per decade and in $Q^{2}$ with
%eight bins per decade.  At low $y$ the resolution of the measurement
%degrades and the bin size is widened.  For $y > 0.6$ the data are
%divided in bins of $y$, with the same $Q^2$ division.  In this region
%the cross section may receive a large negative contribution from \FLc
%proportional to $y^2$ and so a fine binning in $y$ is desirable.  Bins
%are accepted if the purity and stability are bigger than 30\% with
%typical numbers of 60\%. Here the purity (stability) is defined as the
%number of simulated events which originate in a bin and which are
%reconstructed in it, divided by the number of reconstructed
%(generated) events in that bin.

%The program HERACLES \cite{heracles}, which is used in the DIS event
%simulation, accounts for first order radiative contributions.  Using a
%high statistics calculation within the HERACLES Monte Carlo program,
%the radiative corrections are extracted and compared with the results
%of the numerical program HECTOR~\cite{hechec} which includes higher
%order and hadronic corrections.  Agreement of the corrections is found
%to better than 0.5\%. This is connected with the momentum
%conservation constraint, $E-p_z > 35$~GeV, which limits the amount of
%radiative corrections to at most 5\% at high $y$.


%At $y > 0.15$ the kinematics are reconstructed with the variables
%$Q^2_e$ and $y_e$. At $y < 0.15$, where the resolution of $y_e$
%degrades, the $\Sigma$ variables $Q^2_{\Sigma}$ and $y_{\Sigma}$ are
%used, see section~\ref{kin}. The results of the measurement are
%summarised in
% tables~\ref{tabsiga},\ref{tabsigb},\ref{tabsigc},\ref{tabsigd}. Details
%regarding the analysis can be found in~\cite{sasha, rainer, doris,
%vova}.  The error calculation for the H1 data is presented below.

% The cross section measurement is shown in figure~\ref{sigqcd} as a
% function of $x$ for different $Q^2$.  Due to the extension of the
% measurement towards low $y$, the H1 data reach the kinematic region
% of the NMC experiment for $x \sim 0.02$.  The cross section rises at
% low $x$. For many of the $Q^2$ bins, this rise is observed to be
% damped at the smallest values of $x$ which is attributed to the
% longitudinal structure function, see section~\ref{flsec}.  The cross
% section is well described by the QCD fit to the H1 data which is
% discussed in section~\ref{qcdana}.

%\subsection{Systematic Errors}
%The statistics of the data presented here exceed 10$^4$ events in most
%of the $Q^2,x$ bins.  An improved precision for the measurement is
%reached with typical systematic errors of 3\%. To reach this
%precision, it is mandatory to distinguish between different sources of
%systematic errors.  These are classified into global normalisation
%uncertainties, kinematically correlated errors and uncorrelated local
%systematic errors.

%Table~\ref{tabsy1} lists those errors which result in a possible global
%shift of all data points.  The resulting normalisation uncertainty of
%the data is 1.7\% which is dominated by the 1.5\% error of the
%luminosity.
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|l|c|}
%\hline
%  source  &  cross section error [\%]  \\
%\hline
% filter farm losses        &  0.5       \\
% BDC efficiency            &  0.5       \\
% trigger                   &  0.5       \\
% luminosity measurement    &  1.5       \\
%\hline
%\end{tabular}
%\caption{\label{tabsy1}
%  \sl Sources and amount of normalisation errors.}
%\end{table}
%%

%Energy calibration and alignment uncertainties cause systematic errors
%which depend on the kinematics and  introduce correlations
%between the measured data points. The correlated error sources are
%listed in table~\ref{tabsy2}.  These errors are calculated with the
%DIS simulation program and with an analytic calculation for cross
%checks. They are found to be symmetric to good approximation.

%The scattered positron is identified with the cluster of maximum
%transverse momentum $p_{t}$.  At low $Q^{2}$ the fluctuations of the
%transverse momentum of the hadronic system become more pronounced,
%leading to the possibility that a particle from this system may be
%misidentified as the scattered positron.  Thus, as a cross check, the
%scattered positron is considered to be the cluster of maximum energy.
%When these electron identification criteria are interchanged the cross
%sections are found to agree within 1\%
%which is taken into account in the systematic error.
%Detailed studies using different event generators with differing
%simulations of the hadronic final state verify the reliability of the
%positron identification procedure within the quoted systematic
%uncertainty~\cite{sasha}.

%\begin{table}[h] \centering 
%\begin{tabular}{|l|c|c|}
%\hline
%source &  size of uncertainty & effect on cross section in \%    \\
%\hline
%scattered positron energy & 0.003 $E_e'$ at $E_e' \simeq E_e $  & 1  \\
%                          & 0.027
% $E_e'$   at $E_e'=3$~GeV & 2    \\
%scattered positron angle   & 0.3 mrad                & 0.5        \\
%hadronic energy scale in LAr & 0.02 $E_h$                   & 2   \\
%LAr noise         & 0.25 of $y_{noise}$ &  max of 5 at lowest $y$ \\
%photoproduction background   & 0.20 of background  & 3 at large $y$ \\
%\hline
%\end{tabular}
%\caption{\label{tabsy2}
%  \sl Sources of correlated systematic errors and their typical effect
%  on the cross section measurement accuracy.
%}
%\end{table}
%%

%Uncertainties due to radiative corrections, electron identification
%and final state simulation details are treated as uncorrelated
%systematic errors. The errors introduced by the track based
%background subtraction procedure in the high $y$ data analysis
%(section~\ref{sechihy}) are summarised in table~\ref{tabhiy}.
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|l|c|}
%\hline
%  source  &   error of cross section [\%]   \\
%\hline
% positron identification                    &  1    \\
% track charge determination                 &  0.5  \\
% charge asymmetry                           &  1    \\
% CJC-SPACAL track link efficiency           &  2    \\
% hadronic track requirement in CJC          &  1    \\
% high $y$ trigger efficiency                &  1    \\
% radiative corrections                      &  1    \\   
%\hline
%\end{tabular}
%\caption{\label{tabhiy}
%\sl 
%Additional sources of systematic errors of the high $y$ data analysis
%with tracks in the central jet chamber
%and their contribution to the cross section error.}
%\end{table}

%The complete analysis was performed independently by two groups the
%results of which agree to better than 2\% with a few local exceptions.
%A special cross check analysis is performed for the low $Q^2$ region
%based only on the BST and SPACAL detectors~\cite{vova} which is found
%to be consistent with the standard analysis.
%%
%% ------------------------------------------------------------
%%
%\section{Longitudinal Structure Function 
% \boldmath{$F_L(x,Q^2)$} \label{flsec}}
%%
%At low $Q^2$, the inclusive DIS cross section is determined by the
%dominating proton structure function \Fc and by the longitudinal
%structure function \FLc. At high $y$ the contribution of \FLc can be
%sizeable, the reduced cross section $\sigma_r$ tending to \Fc - \FLc
%for $y
%\rightarrow 1$, see equation~\ref{sig}. In the quark-parton model the
%longitudinal structure function is zero for spin half
%quarks~\cite{calgro}.  In QCD \FLc acquires a non-zero value because
%of gluon radiation~\cite{altmar}.  Thus \FL contains independent
%information about the gluon distribution and about strong interaction
%dynamics. For example, \FL is expected to be particularly sensitive to
%twist~4 corrections in QCD~\cite{zijner}.  A direct measurement of \FL
%requires a variation of the centre of mass energy~\cite{lat}.

%An important advantage of HERA, compared to the fixed target DIS
%lepton-nucleon experiments, is the wide range of $y$ values covered.
%This range in $y$ is used to fix the behaviour of \F at low $y$ and
%extrapolate it into the region of highest $y$, corresponding at fixed
%$Q^2$ to the smallest $x$, where the cross section is sensitive to
%\FLc.  Two methods are used here to perform such an extraction of \FL:
%at low $Q^2 < 10$~\gv the smooth behaviour of \F as function of $y$ is
%used in a novel extraction method based on the cross section
%derivative \pdsi.  For larger $Q^2$, a NLO DGLAP QCD fit is used to
%extrapolate \Fc into the high $y$ region as previously
%described~\cite{sfl}. This fit uses only H1 data in the restricted
%kinematic range $y<0.35$ and $Q^2 \geq 3.5$~\gv.
% Details of this and other QCD fits to H1 and
%other data are presented in section \ref{qcdana}.

%\subsection{Cross Section Derivative
%{\boldmath $\partial \sigma_r / \partial \ln y$ }}
%%
%The longitudinal structure function can be extracted from the
%inclusive cross section only in the region of large
%$y$. A quantity with particular sensitivity to \FLc is
%the cross section derivative   
%%
%\begin{equation}
%  \frac {\partial \sigma_r }{ \partial \ln y} =
%    \frac {\partial F_2 }{ \partial \ln y} 
%   - F_L \cdot 2y^2 \cdot \frac{2-y}{Y_+^2}
%   -\frac {\partial F_L }{ \partial \ln y} \cdot \frac{y^2}{Y_+}
%       \label{dsig}
%\end{equation}
%%
%taken at fixed $Q^2$ for $y=Q^2/sx$.

%To obtain a measurement of $\partial \sigma_r / \partial \ln y$,
%differences $\Delta \sigma_r$ are calculated between cross section
%points adjacent in $y$ at fixed $Q^2$. A bin-centre correction is
%applied to obtain the derivative at each $y$ point, which is chosen to
%be the average of the two $y$ values involved. A full error analysis is
%performed in order to account for the correlations of errors, which
%partially cancel.  Contrary to a standard representation of the data
%where systematic errors introduce positive correlations between
%neighbouring points, the two adjacent measurements of $ \partial
%\sigma_r / \partial \ln y$ are anti-correlated since they contain the
%same cross section measurement with different sign.  The measurements
%of the cross section derivative are shown in figure~\ref{dsigy}, and
%the values are quoted in table~\ref{tabder1},\ref{tabder2}.

%For low $Q^2 \leq 40$~GeV$^2$ and $y < 0.2$ the derivative is observed
%to be a linear function of $\ln y$~\footnote{This is in agreement with
%  expectation. At low $y$ the
%cross section derivative is determined by $\partial
%  F_2 / \partial \ln y$ and \Fc behaves $\propto y^{\lambda} =
%  \exp{(\lambda \cdot \ln y)}$. For small $\lambda$ one can expand
%  this function to obtain $\lambda \cdot (1 + \lambda
%  \cdot \ln y + \frac{\lambda^2}{2} \cdot \ln^2 y)$ for the partial
%  derivative. Thus for $\lambda \simeq 0.1$ the derivative is linear
%  to very good approximation while for larger $\lambda \simeq 0.3$
%  curvatures are expected. These are visible in the solid QCD curves
%  at large $Q^2$, figure~\ref{dsigy}, which describe the measurement
%  well.}. At large $y$ the derivative becomes very sensitive to the
%longitudinal structure function. For $y \rightarrow 1$ the cross
%section derivative tends to the limit $ -\partial F_2 / \partial \ln
%x~ - ~2 \cdot F_L$ with a negligible contribution from the derivative
%of $F_L$. At largest $y$ the \FL contribution dominates the
%derivative.  This is in contrast to the $F_L$ influence on the
%non-differentiated cross section $\sigma_r$ where the contribution of
%$F_2$ dominates for all $y$ and thus has to be controlled with high
%precision. A further important advantage of the derivative method is
%that it can be applied down to very low $Q^2$ where precise
%assumptions on the QCD description of \F are prohibited.

%\subsection{Determination of \boldmath{$F_L$}}
%%
%The determination of \FLc at low $Q^2 < 10$~GeV$^2$ with the
%derivative method relies on the approximately linear dependence of
%$\partial \sigma_r / \partial \ln y$ on $\ln y$ in the lower $y$ region.
%In each $Q^2$ interval, straight line fits are made to the derivatives
%for $y <0.2$, which describe the data well.  The
%extrapolation of these straight lines is taken to represent the
%contribution of \Fc at high $y$.  The uncertainty on this estimate of
%\Fc at high $y$ is included into the systematic errors of the \FLc
%determination, taking into account the correlations of the low $y$
%with the high $y$ region. The extrapolations are compared with the
%values obtained from the QCD analysis, and very good agreement is found
%with the fit including all low $Q^2$ data.
%The contribution of $\partial F_L / \partial \ln y$ to the
%derivative, equation~\ref{dsig}, is neglected. Its size is estimated
%using the NLO QCD fit,  and its estimated amount
%is added to the error of the measured $F_L$.

%At larger $Q^2 > 10$~GeV$^2$ the NLO QCD fit of only the low $y<0.35$
%H1 data is used to estimate \Fc in the high $y$ region.  This is more
%accurate than the derivative method which is statistically limited in
%this $Q^2$ range. In the region of overlap, for $Q^2$ between 4~\gv
%and 15~\gv, the derivative method and
%the extrapolation method give consistent results.
%Figure~\ref{smstamp} compares the fit with the measured cross section
%for those five $Q^2$ bins above 10~\gv which access the high $y$
%region. The solid curve shows the cross section from the QCD fit and
%the dashed curve the structure function \F.
%% A full correlated error
%%analysis is performed, as described in~\cite{sfl}, in order to account
%%for the partial cancellation of those errors which affect the
%%cross section at low $y$ and at high $y$ in a correlated manner.
%The difference between the measured $\sigma_r$ and the extrapolated \Fc is
%used to determine \FL as described in~\cite{sfl}.  Systematic errors,
%which are common to the lower $y$ and the large $y$ region, are
%considered in a fit with error propagation as described
%in~\cite{zopa}.

%The \FLc values obtained are presented in table~\ref{tabfl}, see
%\cite{doris}.  The errors on the longitudinal structure function
%include several sources: the statistical errors, uncorrelated
%systematic errors and correlated systematic errors, resulting e.g.
%from the $y$ dependent amount of subtracted photoproduction
%background.  In addition, errors are introduced by the assumptions
%inherent to the extraction methods.  As can be seen in
%table~\ref{tabfl}, these errors are smaller than the experimental
%systematic errors.  In the derivative method they are mainly due to
%the assumed error for $\partial F_L / \partial \ln y $. In the
%extrapolation method they are dominated by the variation of
%$Q^2_{min}$ in the QCD fit.

%The values for \FLc are consistent with the former determination of
%\FL~\cite{sfl} at $y~=~0.68$, but are more accurate.  The H1 data extend
%the knowledge of the longitudinal structure function obtained from
%fixed target lepton-proton scattering experiments into the region of
%much lower $x$, see figure~\ref{figflu}. The increase of \FL towards
%low $x$ is consistently described by the NLO DGLAP QCD fit. The
%behaviour of \FLc reflects the rise of the gluon momentum distribution
%towards low $x$.
%%
%% ------------------------------------------------------------
%%
%\section{Structure Function \boldmath{$F_2(x,Q^2)$} and 
%Derivative
%  \boldmath{$\partial F_2 / \partial \ln Q^2$}}
%%
%In the previous section, determinations of \FLc from the high $y$
%region are described which rely on appropriate assumptions about the
%behaviour of \Fc at high $y$. This section describes the determination
%of \Fc from the low $y$ region, which necessitates assumptions for the
%behaviour of \FLc in this region. In order to limit the dependence on
%these assumptions, \Fc is extracted in the restricted range $y \leq
%0.6$.  The results are given in Table~\ref{tabfl}.

%Compared to the $F_2$ publication of the 1994 H1 data~\cite{sf94}, this
%measurement uses a completely new backward apparatus. It is thus
%important to notice that the \F values obtained here are consistent
%with the former result.  The statistics of the present measurement are
%about a factor of 5-10 larger, and the new instrumentation leads to
%improved systematic precision.
%The data agree well with the results of the muon-proton experiments in
%the region of overlap, see section~\ref{h1fit}.

%In figure~\ref{f2logq2} the structure function \F is shown as a function 
%of $Q^2$ for $x < 0.01$. The data are well described by the NLO QCD fit 
%(solid line), as is discussed in detail in section~\ref{h1fit}.
% The $\ln~Q^2$ dependence of \Fc is observed to be  non-linear. It 
%can be approximated by a quadratic expression
% $P_2 = a + b \ln Q^2 + c (\ln Q^2)^2$ (dashed line) which nearly
%coincides with the QCD fit in the kinematic range of this measurement.

%A quantity of direct importance for QCD studies is the derivative
%\pdff, taken at fixed $x$,
%which was advocated long ago as a substitute for the gluon
%distribution in an extraction of \as~\cite{wuki}.  
%In the absence of significant sea-quark contributions,
% for $Q^2 > 3$~\gv, it is
%closely related to the behaviour of the gluon density at low
%$x$~\cite{prytz}.  This quantity has been
%studied in~\cite{bartels} in view of anticipated
%effects~\cite{glr} from non-linear gluon interactions.  A study of the
%one-dimensional derivative $dF_2/d \ln Q^2$ at low $x$ was presented
%previously by the ZEUS Collaboration~\cite{zeuspheno} assuming \F
%to depend linearly on $\ln Q^2$.

%The accuracy of the present data at low $x$ permits the local
%derivatives \pdff  to be measured. These
%are shown in figure \ref{df21} for different $x$ as function of $Q^2$,
%and the values are quoted in 
% tables~\ref{tabderq1},\ref{tabderq2},\ref{tabderq3}.
%  These derivatives
%are not constant in $Q^2$ depending also on $x$. They are described
%for each bin of $x$ by the function $b + 2 \cdot c \ln Q^2$
%(solid lines) which is derived from the fit to \Fc.
% Small deviations from this linearity occur in NLO QCD
%(dashed lines), but cannot be established conclusively in the data.
%Using this linear expression the derivatives are calculated at fixed
%$Q^2$ and displayed as functions of $x$ in figure~\ref{df22}.  There
%is no departure observed from a rising behaviour of the $\ln Q^2$
%derivatives down to $Q^2$ of 3~GeV$^2$.  Figure~\ref{df22w} shows
%these derivatives as functions of $x$ for fixed $W \simeq \sqrt{sy} =
%\sqrt{Q^2/x}$.  Both the linear rise at fixed $Q^2$ and the turning
%behaviour at fixed $W$ are well described by NLO DGLAP QCD. The shape
%of \pdff is directly related to the $x,Q^2$ behaviour of the gluon
%distribution in the covered kinematic range. A variation of $x$ at
%fixed $W$ towards low $x$ is accompanied by a decrease of $Q^2$.
%Along this contour of fixed $W$, the gluon distribution varies rapidly
%and exhibits the same turn-over as the derivative.
%%
%%Below the range of the present derivative data, at somewhat
%%lower $Q^2 < 3$~\gv, the gluon distribution vanishes in NLO DGLAP
%%and acquires a valence like shape in $x$. The sea distribution
%%is increasingly responsible for the behaviour of \Fc
%%in fits extended to the region of $Q^2 \simeq 1$~\gv.
%%
%% -----------------------------------------------------------
%%
%\section{QCD Interpretation \label{qcdana}}
%%
%In perturbative 
%Quantum Chromodynamics the deep-inelastic lepton-proton scattering
%cross section appears as a convolution of parton distributions with
%calculable coefficient functions. The $Q^2$ evolution of the structure
%function \F is governed by the strong interaction coupling constant
%$\alpha_s(Q^2)$ and the gluon momentum distribution \xg.  At low $x$,
%quark-antiquark pair production from gluons is dominant, and the gluon
%density thus strongly correlated with \as.  At high $x$, the gluon
%density is small, and the scaling violations are connected with quark
%bremsstrahlung.  With these low $x$ precision data, and the H1
%measurements of $F_2$ at large $x$ and high $Q^2$,
% the correlation of \xgc and \as  may be resolved.
%  However, the most accurate
%determination of \amz requires the introduction of precise high $x$
%data at medium $Q^2 ={\cal O}(10)$~\gv.


%In this section a  comparison of the cross section
%measurements and a NLO DGLAP QCD calculation is made. In this
%comparison the strong coupling constant and the gluon density, in
%addition to two combinations of quark distributions, are determined.
%The $\chi^2$ minimisation procedure uses the DIS inclusive cross
%section, and not the structure function \Fc, to avoid the introduction
%of assumptions for the longitudinal structure function.  The analysis
%takes into account all experimental uncertainties and their
%correlations. Uncertainties due to the implementation of the model are
%estimated in a systematic exploration of the parameter space. These
%uncertainties include the dependence on the functional forms of the
%parton distributions, the initial scale $Q^2_0$ of these
%distributions, and the kinematic range of the data considered.

%%
%\subsection{Analysis Procedure\label{secanapro}}
%%
%In the quark-parton model the proton structure function \F
%is given by a sum of quark and anti-quark momentum distribution
%functions
%%
%\begin{eqnarray}\label{f2q}
% F_2 = x \sum_q{Q_q^2 \cdot [q(x,Q^2)+\bq(x,Q^2)}]
%\end{eqnarray}
%% 
%with the electric charges $Q_q = 2/3~(-1/3)$ for up (down) type
%quarks.  In the present analysis, the sum extends over up, down and
%strange ($u,~d,~s$) quarks.   The heavy flavours charm and beauty are
%introduced using photon-gluon fusion, and
%contribute about 20-30\% of the inclusive cross section at low $x$.


%Traditionally, QCD scaling violation analyses of charged lepton DIS
%experiments have been using proton and deuteron data~\cite{NMCg, mv, botje,
%alek, andreas, yndu}.  The evolution is then determined by three
%independent parton distribution combinations, often chosen to be the
%valence quark distributions $u_v$ and $d_v$ together with a sea
%distribution imposing some assumptions on the flavour composition of
%the sea. In these analyses the valence-quark counting rules
%$\int{u_v}dx=2$ and $\int{d_v}dx=1$ are employed.  However, the use of
%DIS data obtained with deuteron or heavier nuclear targets 
%requires corrections for nuclear binding effects
%to be applied which
%introduce an additional uncertainty to precision QCD analyses.

%The present study, described in detail in \cite{rainer},
%uses a novel flavour decomposition of \F
%into two independent, effective parton distribution functions
%\V and \A, according to
%\begin{equation}
%  \label{f2va}
%  F_2 =  \frac{1}{3}x V + \frac{11}{9}x A. 
%\end{equation}
%The $x$ dependences of \xgc, \Vc and \Ac are parameterised at an
%initial scale $Q_0^2$, and a $\chi^2$ minimisation determines these
%distributions and \as. The function \Vc is chosen such that it is
%defined by the valence-quark distributions, i.e.
%\begin{equation}
%  \label{vsimp}
%  V = \frac{9}{4} u_v - \frac{3}{2} d_v,
%\end{equation}
%for the conventional assumptions on the flavour symmetry
%of the sea $u_{sea}=\bu=d_{sea}=\bd$ and a strange 
%contribution $s+\bs = (\bu + \bd)/2$.
%The function \Ac~contains the sea-quark distribution and a
%small valence-quark correction. It is given as
%\begin{equation}
%  \label{asimp}
%  A = \bu - \frac{1}{4} u_v + \frac{1}{2} d_v,
%\end{equation}
%and determines the low $x$ behaviour of \F.
%A salient feature of this ansatz is the possibility to employ 
%the valence-quark counting rules, 
%\begin{equation}
%  \label{intV} 
% \int_0^1{V}dx=3,
%\end{equation}
%although the QCD analysis deals with proton data only.
%%The singlet distribution is  $\Sigma = V + 5A$.
%Further details of this flavour decomposition are explained in 
%Appendix~\ref{aflavour}.
% In particular, it is demonstrated that this procedure
%can be generalised to account for a different amount of strange
%sea, as measured in neutrino induced dimuon 
%production~\cite{ccfr}, and also for a broken flavour sea
%symmetry, i.e. $\bu \neq \bd$, as observed in a recent
%Drell-Yan experiment~\cite{handt}.

%The analysis is performed in 
%the $\overline{MS}$ renormalisation scheme using the
%DGLAP evolution equations~\cite{dglap} for three
%light flavours. The charm and beauty 
%contributions are added according to the NLO calculation
%of the photon-gluon fusion process \cite{lae2}
%in the on-mass shell renormalisation scheme. 
%The analysis uses an $x$ space program developed inside
%the H1 collaboration~\cite{zopa}. This program
%has been carefully checked against different evolution
%codes, and very good agreement was
% found~\cite{bluvo, botje}.

%In the fit procedure, a $\chi^2$ function is minimised which is
%defined in Appendix~\ref{achi2}. This takes into account correlations
%of data points caused by systematic uncertainties, e.g. of the energy
%scales. Depending on the accuracy and range of the large $x$ data sets
%considered, specific functional forms of the $x$ dependence for the
%distributions \V, \A and \xg at the initial scale $Q^2=Q^2_0$ are
%chosen~\footnote{ For each parameterisation a grid of about $10^3$
%  points is considered for ten initial scales $Q_0^2$, ranging between
%  1.5 and 20~GeV$^2$, eight values of $Q^2_{min}$,
%  ranging between the smallest $Q^2$ of the low
%  $x$ data 1.5~\gv and 12~GeV$^2$, and also for twelve different
%  values of \amz.  Including various cuts and combinations of data
%  sets this provides a set of about $2 \cdot 10^5$ fits. The quality
%  of fits has been checked with a statistical analysis of the various
%  fit parameters which are stored in Ntuples.}.  These are discussed
%in Appendix~\ref{apara}.  For the choice of $Q_0^2$, stability is
%required of $\chi^2$ in a range of $Q^2_0$ above the region $Q^2
%\simeq 1$~\gv where the gluon distribution is known to change rapidly
%its shape.

%%Data for $Q^2 > 3000$~\gv are excluded from this
%%analysis, and the cross section is corrected for the then
%%small effects due the structure function $xF_3$.
%% This
%%function is another non-singlet structure function
%%which would require to modify  the flavour decomposition
%%ansatz. Present HERA data, however, do not yield constraints
%%on $xF_3$ which had a significant influence on the
%%QCD analysis presented subsequently.
%% 
%\subsection{Fit to the H1 Cross Section Data Only \label{h1fit}}
%%
%The analysis procedure, developed for
%proton data alone, enables DGLAP QCD fits to be performed using only
%H1 inclusive DIS cross section data, combining the 
%present low $x$ data with the large $x$, high $Q^2$ data~\cite{hiq}
%requiring $Q^2 < 3000$~\gv.


%The behaviour of $\chi^2$ as a function of $Q_0^2$ is used to choose
%$Q_0^2=4$~\gv and to select the parameterisation CP3 for the fit to
%the H1 data, as described in Appendix~\ref{apara}.  A fit for $Q^2
%\geq 3.5$~\gv reproduces the data very well with a $\chi^2$ of 181 for
%224 degrees of freedom. The momentum fraction of the gluon rises with
%$Q^2$ and is insensitive to the inclusion of BCDMS proton or deuteron
%data, see figure~\ref{glumo}.  At $Q^2 = 7$~\gv the momentum fraction
%of the gluon is $0.449 \pm 0.015$, in good agreement with previous
%results~\cite{NMCg,cteqg}.  If the momentum sum rule is released the
%fit determines the integral $\int_0^1{x(\Sigma +g)}dx$ to be $1.016
%\pm 0.017 (exp)$.  This value is observed to be nearly independent of
%the minimum $Q^2$ value of data included in the analysis.


%A further fit to the H1 data is made for $y < 0.35$ which removes any
%significant influence of $F_L$ on the fit result. This fit is used
%for the extraction of \FLc for $Q^2 > 10$~\gv. The data are
%well described with a $\chi^2$ of 161 for 180 degrees of freedom.

%In figure~\ref{f2qa} the \Fc structure function data are shown as
%functions of $Q^2$ for $x < 0.01$.  The scaling violations at low $x$
%are very large and can be well described by the NLO DGLAP fit to the
%H1 data (solid curves).  The fit with the BCDMS $\mu p$
%data added (dashed curves) is at low $x$ nearly indistinguishable from
%the pure H1 fit.  The description and influence of the region of
%lowest $Q^2 < 3.5$~\gv and $x \leq 10^{-4}$ is discussed in detail
%below.

%Figure~\ref{f2qb} shows the H1 $F_2$ data for $0.013 \leq x \leq 0.65$
%together with low $Q^2$ data from the $\mu p$ experiments NMC and
%BCDMS.  In the region of overlap, between $x \simeq 0.01$ and $x
%\simeq 0.1$, the data of the NMC and the BCDMS collaborations are
%confirmed by this measurement within an accuracy of about 7\%, thus
%contradicting the extraction of \Fc in $\nu Fe$ DIS by the CCFR
%Collaboration~\cite{ccfrbod}.  At largest $x=0.65$ the BCDMS result,
%albeit measured at lower $Q^2$, exceeds the H1 data points
%by about half of the total error of the H1 measurement.  The two
%fits with (dashed curves) and without the BCDMS proton data (solid
%curves) thus differ at extremely large $x$.
%%

%Some dependence is observed of the DGLAP fit parameters on the minimum
%$Q^2$ of the low $x$ H1 data used. This is illustrated in
%figure~\ref{gsqmin}a which shows the result of the fit for the
%structure function \Fc in the region $x \leq 8 \cdot 10^{-4}$ for
%different values of $Q^2_{min}$.  The fit with $Q^2_{min} = 1.5$~\gv
%describes all low $x$ data very well (solid curve). With rising
%$Q^2_{min}$ the $Q^2$ dependence of \F becomes steeper at lowest
%$Q^2$. This implies that the gluon for larger $Q^2_{min}$ exhibits a
%steeper rise at low $x$ than for small $Q^2_{min}$, see
%figure~\ref{gsqmin}b.  This feature is observed also with large $x$
%BCDMS data included in the analysis.  These observations are accounted
%for in the uncertainty on \as and the error bands for \xg and \FLc.

%Theoretically one expects higher order logarithmic
%and  power corrections to be large for $Q^2 \simeq 1$~\gv
%such that a NLO DGLAP treatment is expected to be inadequate.
% For the determination of \amz and the gluon distribution
%a value of  $Q^2_{min}=3.5$~\gv is chosen.
%Further exploration of this interesting effect requires low $x$,
%high precision data at low $Q^2 \simeq 1$~\gv.
%%
%\subsection{Strong Coupling Constant \label{secas}}
%%
%% ----------------------------------------------------------------
%%
%The accuracy of the large $x$, high $Q^2$ H1 data~\cite{hiq} prevents
%a competitive determination of \amz using H1 data alone.  The most
%precise measurement of the DIS inclusive cross section at large $Q^2$
%and $x$ was obtained by the BCDMS muon-proton scattering experiment.
%In the region of large $x \geq 0.4$ and low $Q^2$, i.e. small $y$, the
%BCDMS data are in conflict with measurements of the $ep$ scattering
%cross section at SLAC~\cite{slacd, mrs}.  The BCDMS measurement
%accuracy in this region is dominated by systematic errors in contrast
%to the SLAC measurement.  A joint fit to the H1 and BCDMS cross
%section data, taking into account systematic error calculations,
%forces the low $y$ BCDMS data to move outside the quoted systematic
%error uncertainty.  Thus a cut of $y \geq 0.3$ is applied in all
%analyses involving BCDMS data. The \as result is then independent of
%whether the systematic errors of the BCDMS data are considered in the
%$\chi^2$ minimisation or not.
 
%As for the analysis of the H1 data alone (Section~\ref{h1fit}), the
%choice of a suitable parameterisation of the input distributions is
%guided by the dependence of $\chi^2$ on the initial scale $Q^2_0$.
%Compared to the parameterisation CP3 used for the pure H1 fit, the
%BCDMS large $x$ data require an additional term $\propto \sqrt{x}$ to
%be included in the parametrisation of the input gluon distribution.
%Addition of still further parameters does not improve the $\chi^2$ by
%more than one unit. Thus for the fit to the H1 and BCDMS data the
%parameterisation CP4 is chosen (see table~\ref{fs}).
%%
%\begin{table}[h]
%  \begin{center}
%    \begin{tabular}{|l|r|r|r|r|r|}
%\hline
%           &     a &     b &    c &    d  &    e   \\
%\hline
%%    gluon  & 0.449  & -0.337 & 15.6 &  --   & 85.7  \\
%    gluon  & 1.13  & -0.239 & 17.7 & -5.19 & 71.0  \\
%\hline
%%    V      & 185 & 1.63  & 5.70 & -2.87 & 2.83  \\
%    V      &  86.6 & 1.48  & 4.46 & -2.11 & 1.59  \\
%\hline
%%    A      & 0.198  & -0.146 & 18.6 & -2.99 & 26.8  \\
%    A       & 0.234  & -0.128 & 19.8 & -4.04 & 30.2  \\
%\hline
%    \end{tabular}
%    \caption { \sl Parameters of the input distributions 
%      $xq(x) = a_qx^{b_q}(1-x)^{c_q}[1+d_{q}\sqrt{x} +e_{q}x]$ for
%      \xg, \V and \A at the initial scale $Q^2_0=4$~\gv using H1
%      and BCDMS data for $Q^2 \geq 3.5$~\gv, see section~\ref{secas}.
%      A fit with $d_g = e_g = 0$ 
%      yields $c_g=6.5$, not far from  dimensional counting rule
%      expectation~\cite{cglue}, yet with a worsened
%      $\chi^2$.}
%    \label{h1fitpar}
%  \end{center}
%\end{table}
%%
%%As is demonstrated in figure~\ref{alfcont}b
%The value obtained for \amz is nearly independent of the chosen
%parameterisation of the input distributions, and the residual effect
%is considered in the error estimation of \as. The dependence of \as
%on the choice of $Q^2_{min}$ is shown in figure~\ref{alfcont}, and no
%systematic trend is observed.  Note that the BCDMS data are limited to
%$Q^2 \geq 7.5$~\gv such that a $Q^2_{min}$ below this value affects
%the H1 data only.

%As can be seen in figure~\ref{alfcont}, a fit of the H1 data combined
%with the NMC data, which extend to $Q^2 \simeq 1$~\gv, results in a
%significant dependence of \as on $Q^2_{min}$.  A consistent result
%between all three experiments is obtained for $Q^2 \geq 6.5$~\gv. In
%this kinematic range the NMC data provide no additional, significant
%constraint on \as, compared to the accurate BCDMS measurements.
%Previous studies, which included the NMC data at low $Q^2$, found it
%necessary to introduce phenomenological power correction terms $
%\propto 1/Q^2$ in the QCD analysis~\cite{NMCg, alek, botje}.


%For the \as analysis, the low $x$ and high $Q^2$ H1
%data are combined with the original $\mu p$ BCDMS data~\cite{BCDMS}.
%As the default condition a value of $Q^2_{min}$ of 3.5~\gv and 
%$Q_0^2=4$~\gv are chosen.
%This fit describes the measurements well with a $\chi^2$ of 394 for 451
%degrees of freedom.  The parameters of the input distributions are
%given in table~\ref{h1fitpar}.  The relative normalisations of the H1
%and BCDMS data sets are left free.  The change imposed by the fit to
%the BCDMS data is about -1.5\% within a total normalisation
%uncertainty of 3\%. The H1 data are moved by less than 1\% within a
%1.7\% error.  It can thus be concluded that the H1 and BCDMS data are
%well compatible with each other and with NLO DGLAP QCD. The fit is
%repeated with all normalisations fixed which worsens the $\chi^2$ by
%26 units. The effect of fixing the normalisations on \amz is small.


%In the fit to the H1 and BCDMS data, a remarkable correlation is
%observed (figure~\ref{bcalf}) between \amz and the gluon distribution
%parameter $b_g$ which governs the low $x$ behaviour of $xg$. A fit of
%the BCDMS data alone forces $b_g$ to be positive with a value of about
%0.2.  An \as analysis of \Fc data, performed prior to the observation
%of the low $x$ rise, used $xg =a_g \cdot (1-x)^{c_g}$~\cite{mv}, i.e.
%$b_g=0$.  Both of these results imply a behaviour of \xgc at low $x$
%which is incompatible with the H1 measurements.

%The \as value obtained from the H1 and BCDMS proton data is 
%%
%\begin{equation}
%\alpha_s(M_Z^2) = 0.1150~~\pm~~0.0017~(exp)~~^{+~~0.0011}_{-~~0.0012}~(model)
% \label{eqalf}
%\end{equation}  
%%
%in NLO DGLAP QCD. Here the strong coupling constant is defined 
%in the double logarithmic approximation. 
%%Solving the
%%renormalization group equation to order \as$^3$~\cite{zopa}
%%results in an increase of \amz by +0.0003.
%In equation~\ref{eqalf},
% the first error represents the uncertainties
%on the data sets. 
%The partial contributions of the two data sets to
%the total $\chi^2$ are of similar accuracy, and the minima are both
%compatible with the fit result for \amz, as shown in
%figure~\ref{allalf}. Fits to the H1 and BCDMS data separately yield
%\amz values of $0.115 \pm 0.005 (exp)$ and $0.110 \pm 0.003 (exp)$,
%respectively. Thus the \amz value from the combined fit is
%considerably more accurate than a simple combination of H1 and BCDMS
%measurements would imply which is due to the extension of the
%data range.


%The second error on \amz includes all uncertainties associated with
%the construction of the QCD model for the measured cross section, see
%table~\ref{dalf}.  In addition, a rather large theoretical uncertainty
%results from the renormalisation and factorisation scale choices. As
%is discussed in~\cite{andreas, renofac} this uncertainty amounts to
%about $\pm 0.005$ depending on how these scales are treated. This
%error is expected to be significantly diminished when next-to-NLO
%formulae are available~\cite{nnlo}.
%%
%\begin{table}[h]
%  \begin{center}
%    \begin{tabular}{|l|l|l|}
%\hline
%   analysis uncertainty & +$\delta$~\as &  -$\delta$~\as \\
%\hline
%    $ Q^2_{min} = 2$~\gv&    &  0.00002   \\
%    $ Q^2_{min} = 5$~\gv      &  0.00016 &   \\ 
%    parameterisations           &  0.00011 &  \\ 
%    $ Q^2_{0} = 2.5$~\gv      & 0.00023  & \\
%    $ Q^2_{0} =   6$~\gv      &  & 0.00018   \\
%    normalisations fixed      & 0.00051 &  \\
%    y(H1) $<$ 0.35               &  0.00012 & \\
%    x     $<$ 0.6                &  0.00033 & \\
%    y(BCDMS) $>$ 0.25            &   &  0.00108  \\
%    x     $> 5 \cdot 10^{-4}$     &  0.00053 & \\
%    systematics fixed       & 0.00054  & \\
%    sea flavour symmetry       &  & 0.00033   \\
%    strange quark contribution $\epsilon=0$  & 0.00010 & \\ 
%    $ m_c + 0.1$~GeV            & 0.00044 &  \\
%    $ m_c - 0.1$~GeV         &  & 0.00042   \\
%    $ m_b + 0.2$~GeV            & 0.00010 &  \\
%    $ m_b - 0.2$~GeV         &  & 0.00010   \\
%\hline
%sum & 0.0011   &  0.0012 \\
%%\hline
%%theory & & \\
%%\hline
%%  charm mass factorisation scale & in progress &  \\
%%  renormalisation scale          &  in progress &  \\
%\hline
%    \end{tabular}
%    \caption{ \sl Contributions to the error of \amz
%     in the analysis of H1 $ep$ and BCDMS $\mu p$
%     data which are due to the selection of data and the 
%     fit assumptions.}
%    \label{dalf}
%  \end{center}
%\end{table}
%%

%Inclusion of the BCDMS deuteron target data
%yields \amz = 0.1157 $\pm 0.0017 (exp)$, i.e. \amz
%increases by 0.0007. In this analysis 
%nuclear corrections~\cite{melni} and
%target-mass corrections~\cite{tarmas} are applied,
%and the conventional flavour decomposition
%into valence and sea quarks is used. The result of the joint
%fit to the H1 and NMC data, for $Q^2 > 6.5 $~\gv,
%taking into account the systematic error correlations,
%yields \amz$ = 0.115 \pm 0.003$.
%%
%\subsection{Determination of the Gluon Momentum Distribution \label{secxg}}
%%
%The NLO DGLAP QCD fit to the H1 $ep$ and BCDMS $\mu p$ cross section
%data, described above, yields a gluon distribution which is shown in
%figure~\ref{h1gluon} for $Q^2=5,~20$ and 200~GeV$^2$.  A rise of \xg
%is observed towards low $x$ which reflects the strong rise of \F with
%$\ln~Q^2$ at low $x$. The inner error band in figure~\ref{h1gluon}
%represents the experimental uncertainty of the determination of $xg$
%for \as fixed which is about 3\% at low $x \simeq 10^{-3}$ for $Q^2 =
%20$~\gv.  In the calculation of the experimental uncertainty of \xgc,
%the systematic errors are propagated to the covariance matrix of the
%fitted parameters as described in \cite{zopa}.  The middle error band
%illustrates the effect of the uncertainty on \as in the joint fit.
%The full error band includes both the experimental and the model
%uncertainties which are listed, for the \as determination, in
%table~\ref{dalf}.

%The solid line inside the error bands in figure~\ref{h1gluon}
%represents the first determination of the gluon distribution using 
%inclusive H1 cross section 
%data alone. It agrees remarkably well with the fit to
%the H1 and BCDMS data. This result is consistent with
%determinations of the gluon distribution by the H1 experiment in
%charm~\cite{gcharm} and deep-inelastic dijet production~\cite{gjet}.
% Consistent gluon
%distributions are obtained from a fit including H1 and NMC data, as
%well as from a fit including BCDMS deuteron target data in addition to
%the H1 and BCDMS proton data.


%In figure~\ref{gmellin} a comparison is shown, for $Q^2=20$~\gv,
%between the central value of \xgc in the fit to H1 data and the result
%of an otherwise identical fit using the massless treatment of heavy
%quarks~\cite{jack}. At low $x$ the gluon in the massless scheme is
%about 15\% lower than the standard result.  A consistent cross check
%of this massless fit result is obtained with a Mellin $n$ space
%program~\cite{mellin}.
%%
%\section{Summary}
%%
%%
%A new measurement of the deep inelastic positron-proton scattering
%cross section is presented based on data taken by the H1 Collaboration
%at HERA running with positrons of 27.6~GeV and protons of 820~GeV
%energy.  The statistical accuracy of the measured inclusive cross
%section  is better than 1\%, for a large part of the data. The
%systematic precision has reached 3\%, apart from the edges of the
%covered range.  Improvements are due to the enlarged statistics,
%compared to previous measurements, and to the new apparatus in the
%backward region of the H1 detector.


%Refined calorimeter calibration methods permit an extension of the $y$
%range to values as small as 0.004 such that the H1 data overlap with
%fixed target data. In the region of overlap this measurement confirms
%previous measurements of the proton structure function
% \Fc in muon-proton scattering to an accuracy of about 7\%.

%Drift chamber and silicon tracking enable the kinematic range to be
%extended to very high $y$, corresponding to minimum energies of the
%scattered positron of a few GeV. This provides new and more accurate
%values of the longitudinal structure function \FLc in an extended
%kinematic range.


%The precision of this measurement permits the cross section
%derivatives with respect to $\ln x$ (or $\ln y$) and $\ln Q^2$ to be
%determined.  The partial derivative $\partial \sigma_r / \partial \ln y$ is
%used to extract \FLc at low $Q^2$. The partial derivative $\partial F_2 /
%\partial \ln Q^2$ is studied as a function of $x$ at fixed $Q^2$ and
%also at fixed $W$. In the covered $Q^2$ and $x$ range no departure is
%observed from NLO DGLAP QCD.


%A detailed analysis is presented of the measured cross section within
%perturbative DGLAP QCD in next-to-leading order.  Using a novel
%flavour decomposition of \Fc, fits are made to $ep$ and $\mu p$ data
%alone without using lepton-deuteron scattering data.  Combination of
%the new precision low $x$ data with large $x$ data from the BCDMS
%muon-proton experiment resolves the correlation of \xgc and \as in
%deep-inelastic lepton-nucleon scattering and determines the strong
%coupling constant to be \amz = $0.1150 \pm 0.0017 (exp)
%^{+~~0.0011}_{-~~0.0012}(model)$.  In NLO QCD the renormalisation
%scale uncertainties contribute an extra theoretical error of about
%0.005 to the \as uncertainty.  A consistent result is obtained in a
%fit to the H1 $ep$ and NMC $\mu p$ data if the $Q^2$ range of the NMC
%data is restricted to $Q^2 \geq 6.5$~\gv.

%The QCD analysis leads to a new determination of the gluon density \xg
%with an experimental uncertainty of a few per cent using H1 and BCDMS
%data. In addition, the gluon distribution is determined with inclusive
%H1 data alone for the first time. These analyses do not rely 
%upon external information about the strong coupling constant.

%\vspace{1cm}
%\newpage
%%
%{\bf Acknowledgements}                                                         
%%=====================                                                         
%\normalsize   
%\noindent We are very grateful to the HERA machine group whose
%outstanding efforts made this experiment possible. We acknowledge the
%support of the DESY technical staff. We appreciate the substantial
%effort of the engineers and technicians who constructed and maintain
%the detector. We thank the funding agencies for financial support of
%this experiment.  We wish to thank the DESY directorate for the
%support and hospitality extended to the non-DESY members of the
%collaboration.  Finally we thank R.~Engel for help in the background
%simulation, and J.~Bl\"umlein, M.~Botje, W.~van~Neerven, R.~Roberts,
%W.-K.~Tung and A.~Vogt for interesting discussions on the QCD
%interpretation of this data.


%%
%%\newpage
%%
%\begin{appendix}
%\section{Details of the QCD Analysis}
%\subsection{Flavour Decomposition of {\boldmath $F_2$} \label{aflavour}}
%%
%The structure function \Fc can be written as
%%
%\begin{eqnarray}\label{f2ud}
% F_2 =  \frac{4}{9} \cdot xU + \frac{1}{9} \cdot xD
%\end{eqnarray}
%% 
%with $U=u+\bu$ and $D=d+\bd+s+\bs$, see equation~\ref{f2q}.
% A modified projection yields
%%
%\begin{eqnarray}\label{f2sns}
% F_2 =  \frac{2}{9} \cdot x \Sigma +
%          \frac{1}{3} \cdot x \Delta .
%\end{eqnarray}
%% 
%The sum $\Sigma=U+D$ defines a singlet combination of quark distributions
%which has a $Q^2$ evolution coupled to the gluon
%momentum distribution \xgc. The difference $\Delta=(2U-D)/3$ defines a
%non-singlet distribution which evolves independently of \xgc. Thus 
%\Fc is defined by two independent functions. 

%In this analysis two specific functions $V$ and $A$  are chosen which
%have simple relations to $U$ and $D$ according to
%%
%\begin{eqnarray}\label{UVA}
% U = \frac{2}{3} V +2 A 
%\end{eqnarray}
%% 
%and
%%
%\begin{eqnarray}\label{DVA}
% D = \frac{1}{3} V + 3 A.
%\end{eqnarray}
%%  
%The inverse relations  defining $V$ and $A$ are
%\begin{eqnarray}\label{V}
% V(x,Q^2) = \frac{3}{4} (3U-2D) = \frac{9}{4} u_v -  \frac{3}{2} d_v
% +  \frac{9}{2} \bu - 3 (\bd + \bs)  
%\end{eqnarray}
%% 
%and
%%
%\begin{eqnarray}\label{A}
% A(x,Q^2) = \frac{1}{4} (2D-U) = \bd + \bs -\frac{1}{2} \bu
% -  \frac{1}{4} u_v +  \frac{1}{2} d_v,
%\end{eqnarray}
%% 
%which for the conventional assumption $\bu = \bd = 2\bs$ leads to the
%relations presented in the introduction of the QCD analysis, see
%Section~\ref{secanapro}.  In this approximation the $V$ distribution
%vanishes for small $x < 0.01$. The behaviour for large $x$ is defined
%by $u_v$.  For small $x$ the function $A$ is given by the sea
%distribution $A \simeq \bu$. 
%% Because of the limitation of the
%%$d_v/u_v$ ratio at large $x$, $A$ approaches its $x \rightarrow 1$
%%limit from below, i.e. it may become negative in the high $x$
%%valence-quark region having changed sign.
%%The singlet function $\Sigma$ is simply given as
%%
%%\begin{eqnarray}\label{sing}
%% \Sigma = V + 5 A \simeq u_V + d_V + 5 \bu. 
%%\end{eqnarray} 
%%
%\subsection{Modifications}
%%
%Recent measurements of Drell-Yan muon pair production
%at the Tevatron~\cite{handt}
%have established a difference of the
%$\bu$ and $\bd$ distributions.
%Charged current neutrino-nucleon experiments determined the
%relative amount of strange quarks in the nucleon sea to be
%%
%\begin{eqnarray}\label{ssbar}
% s +\bs = (\frac{1}{2} + \epsilon) \cdot (\bu + \bd)
%\end{eqnarray} 
%%
%with a recent value of $\epsilon = -0.08$~\cite{nutev}.
%These results lead to 
% modifications of the simple assumptions on the sea~\footnote{
% The evolution  of $s+\bs$ in DGLAP
%QCD is found to yield a logarithmic $Q^2$ dependence of
% $\epsilon = a + b \ln Q^2$ which is used to transform the NuTeV result
%to $Q^2 = Q^2_0$.}. They
%have been accounted for by rewriting equation~\ref{DVA} as
%%
%\begin{eqnarray}\label{dmodi}
%  D  = \frac{1}{2} V + k A 
%\end{eqnarray} 
%%
%which gives
%%
%\begin{eqnarray}\label{Vmod}
% V(x,Q^2) = \frac{3}{2} \cdot \frac{1}{k-1} (kU-2D) 
%\end{eqnarray}
%%
%and $\Sigma = V + A \cdot (2+k)$.
%Choosing $k=3+2\epsilon$ can be shown to remove the strange
%contribution to the function $V$ yielding 
%%
%\begin{eqnarray}\label{Vmodq}
% V(x,Q^2) = \frac{3}{4} \cdot \frac{1}{1+\epsilon} [(3+2\epsilon) u_V
%            -2d_V + (5+2 \epsilon)(\bu-\bd)], 
%\end{eqnarray}
%%
%which coincides with equation~\ref{vsimp} for $\epsilon=0$ and $\bu=\bd$.
%Because the integral $\delta = \int (\bu-\bd) dx$ is
%finite~\footnote{The most accurate measurement
%of $\int_0^1 (\bu-\bd) dx$ has been performed by the E866/NuSea
%Collaboration~\cite{handt} which obtained a value of $-0.118 \pm 0.011$
%at $<Q^2> = 54$~GeV$^2$.},
% this choice of $k$ allows the counting rule constraint (equation~\ref{intV})
%to be maintained as
%%
%\begin{eqnarray}\label{Vintmod}
% \int_0^1{V}dx = 3 + \delta \cdot \frac{3}{4} \cdot
%                \frac{5+2\epsilon}{1+\epsilon} = v(\epsilon,\delta).
%\end{eqnarray}
%%
%The modified expression for the $A$ function
%in terms of quark distributions becomes
%%
%\begin{eqnarray}\label{Aqmod}
% A(x,Q^2) = \bu -\frac{1}{4} (u_V - 2 d_V)
%     -5 (\bu-\bd) + 2 \epsilon (\bu+\bd). 
%\end{eqnarray} 
%%
%%\subsection{Deuteron Case}
%%
%\subsection{Definition of Minimisation \label{achi2}}
%%
%The $\chi^2$ is computed as
%\begin{eqnarray}\label{lechi2}
%\chi^2
%&=&\sum_{exp} \sum_{dat}
% \frac{[{\sigma_r}^{dat}_{exp}-
%{\sigma_r}^{ fit}\times(1-\nu_{exp}\sigma_{exp}
%-\sum_k\delta^{dat}_k(s^{exp}_k))
%]^2}
%{\sigma_{dat,stat}^2+\sigma_{dat,uncor}^2}\nonumber\\
%&+&\sum_{exp}\nu_{exp}^2
%+\sum_{exp}\sum_k (s^{exp}_k)^2. \nonumber 
%\end{eqnarray}
%The first two sums run over the data ($dat$) of the
%various experiments ($exp$).
% $\sigma_{exp}$ is the relative overall normalisation uncertainty.
% $\sigma_{dat,stat}$ and $\sigma_{dat,uncor}$ are the statistical error
% and the uncorrelated systematic error,
%respectively,  corresponding to the datum $dat$.
% $\nu_{exp}$ is the number of standard deviations corresponding to
% the overall normalisation of the experimental sample $exp$.
% $\delta^{dat}_k(s^{exp}_k)$ is the relative shift of the datum $dat$
% induced by a change by $s^{exp}_k$ standard deviations of
% the $k^{th}$ correlated systematic uncertainty source
%  of the experiment $exp$.
%%
%\subsection{Parameterisations \label{apara}}
%%
%As explained above, three parton distributions ($xg$, $V$ and $A$) are
%necessary to describe the proton structure function \F and its $Q^2$
%evolution.  The following general type of parameterisations
%is used
%\begin{equation}
%xq(x) = a_qx^{b_q}(1-x)^{c_q}
%      [1+d_{q}\sqrt{x} +e_{q}x+f_{q}{x}^2]
%\label{eqpara}
%\end{equation}
%for $q = g,~V$~and $A$.  An attempt has been made to describe these
%functions with the least number of parameters in the brackets of
%equation~\ref{eqpara}.  Thus all distributions are calculated using recent
%parameterisations of parton distributions by GRV98, MRS99 and CTEQ5.
%The $V$ distribution is mainly a combination of valence quark
%distributions, see equation~\ref{Vmodq}.  The comparison with the global
%analysis distributions requires the presence of $d_V$ and $e_V$ but
%allows $f_V$ to be set to zero which is considered to be the standard
%parameterisation of $V$. For $xg$ and $A$ different parameter
%combinations are tested in a systematic way.



%The choice of a set of parameterisations is guided by the desire for
%a weak
%dependence of the $\chi^2$ function on the initial scale $Q_0^2$, and
%by the observed saturation of the $\chi^2$ when the number of parameters
%becomes too large.  This is demonstrated in figure~\ref{fh1para} for
%the fit to H1 data alone. The functions CP1, CP2 and CP5, CP6 show a
%steady decrease of $\chi^2$ with $Q_0^2$. As can be seen in
%table~\ref{fs} these functions have no term $\propto \sqrt{x}$ in the
%$A$ distribution. Stability is observed for $Q_0^2 \geq 4$~\gv for the
%other parameterisations.  Three of them have a similar $\chi^2$.  For
%the H1 fit the parameterisation CP3 is chosen which has the least
%number of parameters. The functions CP4 and CP8 have one more
%parameter but only one unit of $\chi^2$ is gained which points to
%saturation of the parameter list. Although for CP7 the best $\chi^2$
%is found, this parameterisation is not considered since it yields a
%too large gluon momentum as compared to all seven other
%parameterisations and previous analyses~\cite{NMCg}.
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|l|c|c|}
%\hline
%  type  &  gluon & A  \\
%\hline
% CP1     &  $1+ex$  &  $1+ex$ \\ 
% CP2    & $1+ d\sqrt{x} +ex $ & $1 +ex $ \\ 
%\hline
% CP3     & $1+ex $  & $1+ d\sqrt{x} +ex $ \\
% CP4     & $1+ d\sqrt{x} +ex $ & $1+ d\sqrt{x} +ex$ \\ 
%\hline
% CP5     & $1 +ex $ & $1 +ex+f{x}^2$ \\ 
% CP6     & $1+ d\sqrt{x} +ex $ & $1 +ex+f{x}^2$ \\
%\hline
% CP7     & $1 +ex $ & $1+ d\sqrt{x} +ex+f{x}^2$ \\
% CP8     & $1+ d\sqrt{x} +ex $ & $1+ d\sqrt{x} +ex+f{x}^2$ \\
%\hline
%\end{tabular}
%\caption{\label{fs}
%  \sl Types of parameterisations of the $xg$ and $A$ distributions
%  at the initial scale $Q_0^2$.}
%\end{table}

%The choice of parameterisation depends on the data set considered.  In
%a similar study for the fit to H1 and BCDMS data, instead of CP3, the
%parameterisation CP4 is found to be most adequate.

%  Use of
%parameterisations with a high $x$ term $(1+dx^e)$ as introduced by the
%CTEQ Collaboration~\cite{cteq} worsens the $\chi^2$ by eleven units
%and has thus not been considered further.
%\end{appendix}
%%
%\input{figpaper}
%%
%% ---------------------- all figures --------------------
%% 
%\newpage
%% ----------------  fig  1+2 --------------------------------------
%% ----------------------------------------------------------------
%%  control plots from shekel 5.7.00 
%% ----------------------------------------------------------------
 
%%fig 1: E', theta, yh of main sample
%\begin{figure}[tbp]
% \begin{picture}(200,80)
% \put(-10,-100){
% \epsfig{file=vs57nom.ps,
%%  \epsfig{file=etynom.ps,
%   width=17cm, height=20cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \end{picture}
%  \caption{ \sl  Distributions 
%    of the energy, the polar angle of the scattered positron, and of
%    $y_h$ for the main data sample ($A$) taken in 1996/97.  The
%    histograms are a sum of the DIS event simulation and the small
%    contribution from the simulated background due to photoproduction
%    (hatched). The simulated spectra are normalized to the luminosity
%    of the data.} \protect\label{contm}
%\end{figure}
%%
%%
%\begin{figure}[tbp]
% \begin{picture}(200,80)
%%fig 2: E', theta, yh of min bias sample
% \put(-10,-100){
% \epsfig{file=vs57zsp.ps,
%%  \epsfig{file=etysp.ps, 
%   width=17cm, height=20cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
%  \end{picture}
%  \caption{ \sl Distributions
%    of the energy, the polar angle of the scattered positron, and of
%    $y_h$ for the special low $Q^2$ data sample ($B$) taken in 1997.
%    The histograms are a sum of the DIS event simulation and the small
%    contribution from the simulated background due to photoproduction
%    (hatched). The simulated spectra are normalized to the luminosity
%    of the data.} \protect\label{contsp}
%\end{figure}
%%
%%
%\newpage
%% ----------------  fig  3,4 -------------------------------------
%% ----------------------------------------------------------------
%%  control plots high y large q2 and low q2  ok 3.8. 13:15 uhr
%% ----------------------------------------------------------------
%\begin{figure}[tbp]
%  \begin{picture}(200,70)
% \put(-10,-80){
%  \epsfig{file=hiybst56.ps,
%  width=17cm,height=21cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \end{picture}
%  \caption{ \sl
%    Distributions illustrating the cross-section measurement at high
%    $y$ and low $Q^2$, $2 < Q^2 < 5$~GeV$^2$, where the backward
%    silicon tracker BST is used to measure tracks linked to a low energy
%    cluster reconstructed in the backward calorimeter
%    SPACAL.  Distributions of the polar angle
%    (a) and of the energy (b) of the scattered positron candidate as
%    measured in SPACAL. Open histogram: Simulation of DIS and
%    photoproduction events (shaded).  c) SPACAL energy spectrum for
%    events in the BST acceptance with a positron tagged downstream.
%    Closed points: H1 data, histogram: simulation of photoproduction
%    events.} \protect\label{contbst}
%\begin{picture}(200,70)
% \put(-10,-80){
%  \epsfig{file=hiycjc56.ps,
%  width=17cm,height=21cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \end{picture}
%  \caption{ \sl
%    Distributions illustrating the cross-section measurement
%    at high $y$ and large $Q^2$, $10 < Q^2 < 35$~GeV$^2$, where the
%    central drift chamber is used to measure tracks linked to a low
%    energy cluster reconstructed in SPACAL: a) polar angle and b)
%    SPACAL energy distributions before subtraction of the
%    photoproduction background using the charge measurement by the
%    CJC. Solid points: data with positive charge assignment.  Shaded
%    histogram: data with negative charge assignment.  Open histogram:
%    superposition of data with negative charge assignment and DIS
%    event simulation, normalized to the data luminosity. c) Spectrum
%    of energy measured in the electron tagger for DIS candidate events
%    with a linked track of either positive charge (solid points)
%    or of negative
%    charge (histogram).} \protect\label{conthyq}
%\end{figure}
%%
%%
%\newpage
%% ----------------  fig  5 --------------------------------------
%%% ----------------------------------------------------------------
%%  binning
%% ----------------------------------------------------------------
%\begin{figure}[tbp]
%  \begin{picture}(200,100)
%  \put(-10,-40){
%   \epsfig{file=figbins.ps,
%   width=15cm,height=22cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
%  \end{picture}
%  \caption{\sl
% Division of $x, Q^2$ plane for the measurement of the
% inclusive DIS cross-section. At large $x$ the bin size
% in $x$ is widened due to resolution. At large $y$
% the data are binned in intervals of $Q^2$ and $y$ 
% in order to account for the 
% $y$ dependent effect of \FLc on the cross-section
% and the variation of the systematics with $y$.
%   } \protect\label{bins}
%\end{figure}
%
%
%\newpage
% ----------------  fig  6 --------------------------------------
% ----------------------------------------------------------------
%  cross-section
% ----------------------------------------------------------------
%
\newpage
% ----------------  fig  7 --------------------------------------
%% ----------------------------------------------------------------
%  cross-section
% ----------------------------------------------------------------
\begin{figure}[tbp]
  \begin{picture}(200,190)
  \put(-19,-10){
%  \epsfig{file=sigxbw.ps,
 \epsfig{file=f2dis00prel.ps, 
% \epsfig{file=f2dis00pap1907.ps,sigxbw.ps
   width=18cm,height=21cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
  \end{picture}
  \caption{\sl Measurement of the reduced DIS scattering cross-section, closed points. Triangles (squares) represent data by
    the NMC (BCDMS) muon proton experiments.  The solid curves
    illustrate the cross-section obtained in  a NLO DGLAP QCD fit
    to only the H1 data at low $x$ and high $Q^2$,
    with $Q^2_{min}= 3.5$~\gv. The dashed curves
    show the extrapolation of this fit towards lower $Q^2$.
   } \protect\label{sigqcd}


\end{figure}
%
%
\newpage
% ----------------  fig  8 --------------------------------------
% -------------------------------------------------
%  cross-section difference vs y      
% -------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,130)
 \put(-30,-80){
%  \epsfig{file=derivbandy207.ps,
  \epsfig{file=yderiva_prel.ps,
  width=20cm,height=30cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl Measurement of the derivative 
    $\partial \sigma_r / \partial \log y$.   The
    inner error bar is the statistical error and the total error bar
    denotes the statistical and systematic errors added in
    quadrature. The curves represent the
    QCD fit (solid curve) replacing the $F_L$ fit result
    by $F_L=0$ (dashed-dotted curve) or
   by $F_L = F_2$ (dotted curve).
   The inner error band is the experimental uncertainty of the
    fit result, and the outer band represents the additional
    uncertainty due to the fit assumptions. The fit results for
    $Q^2 < 3.5$~\gv are due to backward extrapolation.
} \protect\label{dsigy}
\end{figure}

\begin{figure}[bp]
 \begin{picture}(200,130)
 \put(-30,-80){
%  \epsfig{file=derivbandy207.ps,
  \epsfig{file=deriva_4.2.ps,
  width=20cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ zoom into Fig.\ref{dsigy}
} \protect\label{dsigy.a}
\end{figure}




%
\newpage
% ----------------  fig  9 --------------------------------------
% ----------------------------------------------------------------
%  stamp                            5.7. 
% ----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,170)
 \put(-20,-40){
%  \epsfig{file=stampsmall2007a.ps,
\epsfig{file=stampsmall2007ycut.ps,
  width=17cm,height=25cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl
  Measurement of the reduced DIS scattering cross-section, closed points. Triangles represent data by
    the BCDMS muon-proton experiment. The curves represent a NLO QCD fit
    to the H1 data alone, requiring $y < 0.35$
     and $Q^2 \geq 3.5$~\gv. The dashed curves 
    are the $F_2$ structure function values
     determined with this fit.
   The error bands represent the small experimental and model
   uncertainty of the QCD fit.
 At lowest $x$,
    corresponding to large $y \geq 0.5$, departures of the
    cross section from the rise of $F_2$ towards low $x$ occur which
    are attributed to \FLc. 
} \protect\label{smstamp}
\end{figure}

\begin{figure}[tbp]
 \begin{picture}(200,170)
 \put(-20,-40){
%  \epsfig{file=stampsmall2007a.ps,
\epsfig{file=stampnania_ycut_prel.ps,
  width=17cm,height=25cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl Zoom into Fig.~\ref{smstamp}
} \protect\label{smstamp.a}
\end{figure}





%%
\newpage
% ----------------  fig  10 --------------------------------------
%
% ----------------------------------------------------------------
%  FL world                               11.7.  4.15
% ----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(180,170)
 \put(-10,-40){
%  \epsfig{file=fl_207_fin9.ps,
  \epsfig{file=fl_prel.ps,
  width=17cm,height=25cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl Data on the longitudinal structure function \FL as obtained
    by this experiment, at low $x$, and by charged lepton-nucleon fixed
    target experiments at larger $x$.
    The data at $Q^2 < 10$~\gv are
    obtained with the derivative method while the points for larger
    $Q^2$ are due to the extrapolation method. The error on the
    data points is the total uncertainty of the determination
    of \FLc representing the statistical, the systematic and the
    model errors added in quadrature. The inner error
    bars denote the statistical measurement accuracy. 
    The error bands are due to the
    experimental (inner) and model (outer) uncertainty of the
    calculation of $F_L$ using the NLO QCD fit to the H1 
    data for $y < 0.35$ and $Q^2 \geq  3.5$.
     }
  \protect\label{figflu}
\end{figure}
\newpage
%\vspace{10cm}
\begin{figure}[tbp]
 \begin{picture}(18,30)
 \put(20,-40){
%  \epsfig{file=fl_207_fin9.ps,
  \epsfig{file=fl_4.2.ps,
  height=15cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl Zoom into Figure~\ref{figflu}
}
  \protect\label{figflu.a}
\end{figure}
%
\begin{figure}[tbp]
 \begin{picture}(18,30)
 \put(20,-40){
%  \epsfig{file=fl_207_fin9.ps,
  \epsfig{file=fl_20.ps,
  height=15cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl Zoom into Figure~\ref{figflu}
}
  \protect\label{figflu.aa}
\end{figure}









%
%
\newpage
% ----------------  fig  11 + 12 ---------------------------------
%-----------------------------------------------------------------
%  f2  vs logq2 for fixed x
%-----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,150)
 \put(-8,-80){
  \epsfig{file=deriv.scalviol.ps,
  width=17cm,height=28cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl Measured \Fc 
  structure function data as function of $Q^2$. The solid lines
  represent fits to \F in the $x$ bins according to
  $F_2 = a + b \ln Q^2 + c (\ln Q^2)^2$. The dashed lines result in
  the NLO QCD fit to the H1 data.
   The error bands are due to the 
  model uncertainty in the QCD fit which includes data
  for $Q^2 \geq 3.5$~\gv.
    } \protect\label{f2logq2}
\end{figure}
%
\newpage
%
%-----------------------------------------------------------------
%  df2/dlogq2 vs q2 for fixed x
%-----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,150)
 \put(-8,-80){
%  \epsfig{file=deriv217p4.ps,
  \epsfig{file=localderiv.ps,
  width=17cm,height=28cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \put(-8,-80){
%  \epsfig{file=dfdlnq1567.ps,
%  width=17cm,height=28cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{\sl
  Derivative $\partial F_2 / \partial \log Q^2$ taken at fixed $x$
 as functions of $Q^2$. The error bars represent the
  quadratic sum of statistical and systematic 
  errors. The straight solid lines are given by the function
  $ b + 2c \ln Q^2$ determined in fits to \F at fixed $x$.
  The dashed lines represent the
  derivatives of the structure function $F_2$
  in the QCD fit to the H1 data. The error bands are due to the 
  model uncertainty in the QCD fit which includes data
  for $Q^2 \geq 3.5$~\gv.
    } \protect\label{df21}
\end{figure}
%
%
\newpage
%
% ----------------  fig  13 + 14  --------------------------------
%-----------------------------------------------------------------
%  df2/dloq2 vs x (2-dimens.)
%-----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,80)
 \put(10,-30){
%  \epsfig{file=deriv217p1.ps,
  \epsfig{file=cald2dimprel.ps,
  width=11cm,height=13cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \put(10,-30){
%  \epsfig{file=vsder15p1.ps,
%  width=11cm,height=13cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl
Derivative $\partial F_2 / \partial \ln Q^2$, plotted
 as function of $x$ for
fixed $Q^2$,
for the H1 data 
(points) and the QCD fit (curves) to
the H1 data, for $Q^2 \geq 3.5$~\gv. 
 The dashed curves are extrapolations
to outside the data region considered in the fit.
The error bands represent the model uncertainty of the
QCD analysis. 
    } \protect\label{df22}
\end{figure}
%
%\newpage
%-----------------------------------------------------------------
%  df2/dloq2 vs x (2-dimens.) fixed W
%-----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,80)
 \put(10,-30){
%  \epsfig{file=deriv217p2.ps,
  \epsfig{file=cald2fixedw.ps,
  width=11cm,height=13cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \put(10,-30){
%  \epsfig{file=vsder15p2.ps,
%  width=11cm,height=13cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl
Derivative $\partial F_2 / \partial \ln Q^2$, plotted
 as function of $x$ for
fixed $W \simeq \sqrt{Q^2/x}$,
for the H1 data 
(points) and the QCD fit (curves) to
the H1 data, for $Q^2 \geq 3.5$~\gv. 
The dashed curves are extrapolations
to outside the data region considered in the fit.
The error bands represent the model uncertainty of the
QCD analysis.
  } \protect\label{df22w}
\end{figure}
%
%
\newpage
% ----------------  fig  15 --------------------------------------
% ----------------------------------------------------------------
%  gluon momentum fraction
% ----------------------------------------------------------------
\begin{figure}[t]
 \begin{picture}(150,150)
 \put(10,0){
  \epsfig{file=prelglumom.ps,
  width=12cm,height=15cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
%\put(10,0){
%   \epsfig{file=prelcover.ps,
%  width=12cm,height=15cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
  \end{picture}

  \caption{ \sl Momentum fraction of the gluon as function of 
   $\ln Q^2$ as obtained in different NLO DGLAP fits.
   Solid curve:  fit to H1 data alone;  
  dashed curve: fit to H1 and BCDMS proton data;
  dotted curve: fit to H1 $ep$ and BCDMS $\mu p$ and $\mu d$ data.
  The shaded error band represents the experimental uncertainty
  in the analysis of the H1 data alone. The solid point marks the result
  of a QCD analysis to NMC data~\cite{NMCg}.}
  \protect\label{glumo}

\end{figure}
%
%
\newpage
% ----------------  fig  16 --------------------------------------
% ----------------------------------------------------------------
%  cross-section vs Q2 low x    25.6. 
% ----------------------------------------------------------------
\begin{figure}[t]
 \begin{picture}(200,200)
 \put(-20,-65){
% \epsfig{file=f2lowq207.ps,
 \epsfig{file=scaling_lowx_prel.ps,
%scaling_extloq2-slac0707b.ps,
%  \epsfig{file=scalinglowx.ps,
  width=18cm,height=31cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl
    Structure function measurements by H1  and the NMC
    experiment. Solid curves: NLO DGLAP QCD fit to the H1
    cross-section data. Overlayed as dashed curves is the 
    QCD fit to the H1 $ep$ and
    BCDMS $\mu p$ data, for  $y_{BCDMS} < 0.3$,
    which is nearly indistinguishable from
    the pure H1 fit.
   Dotted curves represent the fit extrapolations
    at fixed $x$ into the region below $Q^2 = 3.5$~\gv.
    } \protect\label{f2qa}
\end{figure}
%
%
\newpage
% ----------------  fig  17 --------------------------------------
%
\begin{figure}[tbp]
 \begin{picture}(200,200)
 \put(-20,-55){
% \epsfig{file=f2hiq207.ps,
 \epsfig{file=scaling_hix_prel.ps,
%scaling_exthiq2-slac-fullbcdms0707b.ps,
%  \epsfig{file=scalinghix.ps,
  width=18cm,height=31cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl
     Structure function measurements by H1 and fixed 
     target muon-proton scattering experiments.
     Solid curves: fit to the H1
     cross-section data.  
    Dashed curves: fit to the H1 $ep$ and BCDMS $\mu p$ data,
    for $y_{BCDMS} < 0.3$.
  Dotted curves represent the extrapolations
    at fixed $x$ into the region below $Q^2 = 3.5$~\gv
    and beyond  the maximum $Q^2 = 3000$~\gv included in
  the fit. 
 } \protect\label{f2qb}
\end{figure}
%
\newpage
% ----------------  fig  18 + 19------------------------------------
%
% ----------------------------------------------------------------
%  dependence of xg and sigr on q2min
% ----------------------------------------------------------------
\begin{figure}
 \begin{picture}(200,180)
 \put(5,65){
%  \epsfig{file=figf2loxzoom.ps,
  \epsfig{file=zoombw_prel.ps,
  width=12cm,height=14cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}} 
 \put(5,65){
%  \epsfig{file=figf2loxzoom.ps,
  \epsfig{file=prelalow.ps,
  width=12cm,height=14cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}} 
 \put(5,-30){
%  \epsfig{file=papgluqcut_h10807b.ps,
  \epsfig{file=prelgluqcut.ps,
  width=12cm,height=14cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \put(5,-30){
%  \epsfig{file=papgluqcut_h10807b.ps,
  \epsfig{file=prelblow.ps,
  width=12cm,height=14cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl
  Effect of the $Q^2_{min}$ cut applied in
  the DGLAP QCD fit to the H1 data 
  on a) the structure function \Fc and b)
  the gluon distribution at $Q^2=5$~\gv.
  The experimental error bands for \xg extend to twice the
  minimum $x$ values of the data~\cite{prytz}, depending on $Q^2_{min}$, which
  allow a $Q^2$ slope to be measured from at least three data points
  at fixed $x$.}
  \protect\label{gsqmin}
\end{figure}
%
\clearpage
\newpage
% ----------------  fig  20 --------------------------------------
% ----------------------------------------------------------------
%%  alphas control 
%% ----------------------------------------------------------------
%\begin{figure}
% \begin{picture}(150,150)
%% \put(20,120){
%%  \epsfig{file=papycut2706a.ps,
%%  width=9cm,height=9cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
%% \put(20,50){
%%  \epsfig{file=pappara2706a.ps,
%%  width=9cm,height=9cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \put(10,-10){
%  \epsfig{file=papqcutdep_t0.ps,
%  width=12cm,height=14cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \end{picture}
%  \caption{ \sl
%%   Calculations of \amz  based on H1 and BCDMS data
%%   for a) different minimum values
%%   of inelasticity $y=\nu/E_{\mu}$ for the BCDMS data and b)
%%   for different parametrization sets.
%   Dependence of \amz obtained in fits to the H1 and BCDMS data 
%  (closed points) and to the H1 and NMC data (open points)
%   on the minimum $Q^2$ value used. Note that the NMC data extend to
%   low $Q^2$ while the BCDMS data have an intrinsic $Q^2_{min}$
%   of 7.5~\gv.
%  }
%  \protect\label{alfcont}
%\end{figure}
%
%
\newpage
% ----------------  fig  21 --------------------------------------
%
% ----------------------------------------------------------------
%  alphas-gluon correlations
% ----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(150,150)
 \put(0,-30){
  \epsfig{file=papbgas_t0.ps,
  width=12cm,height=17cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \put(75,-30){
%  \epsfig{file=papcgas2906a.ps,
%  width=8cm,height=17cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl Correlation of the gluon distribution parameter
  $b_g$  
  with \amz in the fit to
  H1 and BCDMS data. This parameter
  governs the low $x$ behaviour of \xgc $~\propto x^{b_g}$. }
  \protect\label{bcalf}
\end{figure}
%
%
\newpage
% ----------------  fig  22+23  ----------------------------------

% ----------------------------------------------------------------
%  all alfas h1 bcdms nmc 256
% ----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(150,150)
 \put(-5,-30){
%  \epsfig{file=papcentral_t0.ps,
  \epsfig{file=as_prelcentral.ps,
  width=8cm,height=18cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \put(-5,-30){
  \epsfig{file=prela.ps,
  width=8cm,height=18cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \put(70,-30){
%  \epsfig{file=pappartial_t0.ps,
  \epsfig{file=as_prelpartial.ps,
  width=8cm,height=18cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \put(70,-30){
%  \epsfig{file=pappartial_t0.ps,
  \epsfig{file=prelb.ps,
  width=8cm,height=18cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption {\sl
   Determination of the strong coupling constant \amz in NLO
   DGLAP QCD.
   a) Total $\chi^2$ for fits to the H1 $ep$ and BCDMS $\mu p$ data 
   and a fit using
   data of the two experiments. b) $\chi^2$ contributions
   H1 and BCDMS data in the fit using both experiments.
}
  \protect\label{allalf}
\end{figure}
%
%
\newpage
% ----------------  fig  24--------------------------------------
%
% ----------------------------------------------------------------
%  xg with H1+bcdms 77 
% ----------------------------------------------------------------
\begin{figure}[tbp]
 \begin{picture}(200,150)
 \put(-10,-45){
%  \epsfig{file=papgluon2007a.ps,
  \epsfig{file=prelgluon.ps,
  width=16cm,height=25cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
 \end{picture}
  \caption{ \sl
  Gluon distribution for \amz=0.1150
  resulting from the NLO DGLAP QCD fit 
   in the massive heavy flavour scheme to H1 
   $e^+p$ and  BCDMS $\mu p$ cross-section data using
   $Q^2_{min}=3.5$~\gv, $Q^2_{0}=4$~\gv.  
   The distribution is shown
   for different $Q^2 = 5, 20$~and $200$~GeV$^2$.
   The innermost error bands represent the experimental
   error for fixed \as. The middle error bands include in addition
   the contribution of fitting \as.
   The outer error bands are due to the  
   uncertainties related to the QCD model and data range.
   The solid lines inside the error band
   represent the gluon distribution obtained in the fit
   to the H1 data alone.}
  \protect\label{h1gluon}
\end{figure}
%
\newpage
%% ----------------  fig  25 --------------------------------------
%%
%% ----------------------------------------------------------------
%%  gluon cross checks
%% ----------------------------------------------------------------
%\begin{figure}[tbp]
% \begin{picture}(200,100)
% \put(10,-30){
%  \epsfig{file=papglumellin0707b.ps,
%  width=12cm,height=17cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \end{picture}
%  \caption{ \sl
%Comparison of  gluon distributions 
% obtained in NLO DGLAP QCD fits to the H1 data,
% for  $Q_0^2=4$~\gv,
% $Q_{min}^2=3.5$~\gv, using different prescriptions: solid curve:
%  massive heavy flavour scheme; dashed curve: massless
%  scheme; dashed-dotted curve: $n$ space program.}
%  \protect\label{gmellin}
%\end{figure}
%%
%\newpage
%% ----------------  fig  26 --------------------------------------
%% ----------------------------------------------------------------
%%  parametrizations vs q02 104 
%% ----------------------------------------------------------------
%\begin{figure}[tbp]
% \begin{picture}(200,150)
% \put(-10,-35){
% \epsfig{file=papq0stabil0707a.ps,
%%  \epsfig{file=~wallny/paper/q0stabil/papq0stabil_2706a.ps,
%  width=17cm,height=20cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
% \end{picture}
%  \caption{ \sl Dependence of
%   $\chi^2$ on the  initial scale parameter 
%   $Q^2_0$ for different parametrizations of the parton distributions
%   $xg$ and $A$ in the NLO QCD
%   fit to the H1 data.}
%  \protect\label{fh1para}
%\end{figure}
% 





\clearpage
\newpage
\begin{thebibliography}{99}
%\input{bibpaper}

%
\bibitem{NMCg}
M. Arneodo et al., NMC Collaboration, Phys. Lett. {\bf B309} (1993) 222.
\bibitem{prytz}
 K. Prytz, Phys. Lett. {\bf B311} (1993) 286.
\end{thebibliography}
%
%%
%% --- figures
%%

%
%\clearpage
%%
%\newpage
%%\end{document}
%%-----------------------------------------------------------------
%% all the tables at the end
%%-----------------------------------------------------------------
%%-- reduced xsection|
%%-------------------
%%
%% ---- mbias 1
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $\sigma_r$ & $F_L$ & $F_2$ & $\delta_{tot}$ & $\delta_{sta}$ & $\delta_{unc}$ & $\delta_{cor}$   \\
%\hline
%\input{rsec1mbi207}
%\hline
%\end{tabular}
%\caption{\label{tabsiga}
%\sl 
%Measurement of the reduced deep-inelastic cross section
% with the data taken in a dedicated
%low $Q^2$ trigger run in 1997. Errors are given in \%.
% For $y < 0.6$ the structure function
%\Fc is  extracted
% using \FLc values from a QCD fit to the H1 cross section data. 
%}
%\end{table}
%\newpage
%%
%% --- mbias 2
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $\sigma_r$ & $F_L$ & $F_2$ & $\delta_{tot}$ & $\delta_{sta}$ & $\delta_{unc}$ & $\delta_{cor}$   \\
%\hline
%%\input{rsec2mbi207}
%\hline
%\end{tabular}
%\caption{\label{tabsigb}
%\sl 
%Measurement of the reduced deep-inelastic cross section
% with the data taken in a dedicated
%low $Q^2$ trigger run in 1997. Errors are given in \%.
% For $y < 0.6$ the structure function
%\Fc is  extracted
% using \FLc values
%from a QCD fit to the H1 cross section data.
%}
%\end{table}
%%
%% --- nominal 1
%%
%\newpage
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $\sigma_r$ & $F_2$ & $F_L$ & $\delta_{tot}$ & $\delta_{sta}$ & $\delta_{unc}$ & $\delta_{cor}$   \\
%\hline
%%\input{rsec1nom207}
%\hline
%\end{tabular}
%\caption{\label{tabsigc}
%\sl 
%Measurement of the reduced deep-inelastic cross section
% with the data taken in 1996/97. Errors are given in \%.
% For $y < 0.6$ the structure function
%\Fc is  extracted
% using \FLc values
%from a QCD fit to the H1 cross section data.
%}
%\end{table}
%%
%% --- nominal 2
%%
%\newpage
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $\sigma_r$ & $F_2$ & $F_L$ & $\delta_{tot}$ & $\delta_{sta}$ & $\delta_{unc}$ & $\delta_{cor}$   \\
%\hline
%%\input{rsec2nom207}
%\hline
%\end{tabular}
%\caption{\label{tabsigd}
%\sl 
%Measurement of the reduced deep-inelastic cross section
% with the data taken in 1996/97. Errors are given in \%.
% For $y < 0.6$ the structure function
%\Fc is  extracted
% using \FLc values
%from a QCD fit to the H1 cross section data.
%}
%\end{table}
%%
%\newpage
%%
%%-------------------
%%-- d sigma/d lny  |
%%-------------------
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $ \partial \sigma_r / \partial \ln y$ & $\delta_{sta}$ & $\delta_{sys}$ & $\delta_{tot}$    \\
%\hline
%%\input{yder1tab207}
%\hline
%\end{tabular}
%%
%\caption{\label{tabder1}
%  \sl Measurement of the cross section derivative $\partial \sigma_r /
%  \partial \ln y = -\partial \sigma_r / \partial \ln x$ at fixed $Q^2$.
%  The errors are given in absolute values.  }
%\end{table}
%\newpage
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|}
%\hline
%$Q^2$ & x & y & $ \partial \sigma_r / \partial \ln y$ & $\delta_{sta}$ & $\delta_{sys}$ & $\delta_{tot}$    \\
%\hline
%%\input{deriva207_fin9}
%%\input{yder2tab207}
%\hline
%\end{tabular}
%\caption{\label{tabder2}
%  \sl 
% Measurement of the cross section derivative $\partial \sigma_r /
%  \partial \ln y = -\partial \sigma_r / \partial \ln x$ at fixed $Q^2$.
%  The errors are given in absolute.}
%\end{table}
%\newpage
%%
%%--      Fl         |
%%-------------------
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|c|c|c|c|c|}
%\hline
%$Q^2$ & $x$ & $y$ &  \FL & $\delta_{sta}$ & $\delta_{sys}$ & $\delta_{met}$ & $\delta_{tot}$    \\
%\hline
%%
%%\input{fltext_207.fin9}
%%
%%  q2       x       y        fl     sta     sys     meth   toterr
%\hline
%\end{tabular}
%\caption{\label{tabfl}
%  \sl Values of the longitudinal structure function \FL.
% The errors are given in absolute. The statistical errors
%represent the experimental statistics. The systematic errors
%consider all contributions from
%correlated and uncorrelated systematic error sources. $\delta_{met}$
%is due to the uncertainties connected with the representation
%of \Fc in the derivative method, for $Q^2 < 10$~\gv, and in the
%QCD extrapolation method, for $Q^2 > 10$~\gv.
%}
%\end{table}
%%\end{document}
%%
%%-------------------
%%-- d f2/d lnq  | part 1
%%-------------------
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $ \partial F_2 / \partial \ln Q^2$ & $\delta_{sta}$ & $\delta_{sys}$ & $\delta_{tot}$    \\
%\hline
%%\input{der1.tex}
%\hline
%\end{tabular}
%%
%\caption{\label{tabderq1}
%  \sl Measurement of the derivative $\partial F_2 /
%  \partial \ln Q^2$. The errors are given in absolute. }
%\end{table}
%%-------------------
%%-- d f2/d lnq  | part 2
%%-------------------
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $ \partial F_2 / \partial \ln Q^2$ & $\delta_{sta}$ & $\delta_{sys}$ & $\delta_{tot}$    \\
%\hline
%%\input{der2z.tex}
%\hline
%\end{tabular}
%%
%\caption{\label{tabderq2}
%  \sl Measurement of the derivative $\partial F_2 /
%  \partial \ln Q^2$.  The errors are given in absolute. }
%\end{table}
%%-------------------
%%-- d f2/d lnq  | part 3
%%-------------------
%%
%\begin{table}[h] \centering 
%\begin{tabular}{|r|c|c|r|r|r|r|}
%\hline
%$Q^2$ & $x$ & $y$ & $ \partial F_2 / \partial \ln Q^2$ & $\delta_{sta}$ & $\delta_{sys}$ & $\delta_{tot}$    \\
%\hline
%%\input{der2.tex}
%\hline
%\end{tabular}
%%
%\caption{\label{tabderq3}
%  \sl Measurement of the derivative $\partial F_2 /
%  \partial \ln Q^2$.  The errors are given in absolute. }
%\end{table}
%%
\end{document}
%%
%%
%\bibitem{slac}
%E.~D.~Bloom et al., Phys.~Rev.~Lett. {\bf 23} (1969) 930; \\ 
%M.~Breidenbach et al., Phys.~Rev.~Lett. {\bf 23} (1969) 935.
%\bibitem{feyn}
%R.~P.~Feynman, Phys.~Rev.~Lett. {\bf 23} (1969) 1415.
%%\bibitem{zeus93}
%%ZEUS Collaboration, M.~Derrick et al., Phys.~Lett. {\bf B316} (1993) 412.
%%
%\bibitem{deru}
%A.~De R\'ujula et al., Phys.~Rev. {\bf D10} (1974) 1649.
%%
%\bibitem{grv92}
%M. Gl\"uck, E.Reya and A.Vogt, Z. Phys. {\bf C53} (1992) 127
% and Phys. Lett. {\bf B306} (1993) 394.
%% ----------------------------------------------------------------
%%  control plot F2 e, mixed, sigma
%% ----------------------------------------------------------------
%%\begin{figure}[tbp]
%%  \begin{picture}(200,80)
%% \put(-10,-80){
%%  \epsfig{file=hiybst1011.ps,
%%  width=17cm,height=22cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}}
%% \end{picture}
%%  \caption{Measurement of the structure function \F with the electron
%%    method (closed points), the $\Sigma$ method (open circles)
%%    and the mixed method (open squares).}
%%  \protect\label{elsimi}
%%\end{figure}
%%%
%% ----------------------------------------------------------------
%%  gluon cross checks
%% ----------------------------------------------------------------
%%\begin{figure}[tbp]
%% \begin{picture}(200,100)
%% \put(10,-30){
%%  \epsfig{file=figfourgluons.ps,
%%  width=12cm,height=17cm,bbllx=0pt,bblly=0pt,bburx=557pt,bbury=792pt}} 
%% \end{picture}
%%  \caption{ \sl
%%Comparison of gluon distributions \xg at  $Q^2=5$~\gv
%%obtained in NLO DGLAP QCD fits
%%  in the massive heavy flavour scheme for $Q_0^2=4$~\gv,
%%$Q_{min}^2=3.5$~\gv and \amz=0.1150. Solid curve: standard fit to H1
%% data; dashed curve: fit to H1 and BCDMS proton data; dotted curve:
%% fit to H1 and BCDMS proton and deuteron data; dashed-dotted curve:
%% fit to H1 and NMC proton data.}
%%  \protect\label{gchecks}
%%\end{figure}