
\section{Further investigation and Additional Checks}
To evaluate the quality of the produced chambers several studies were performed. All checks indicate that the chambers are produced according to their
specifications. some of the checks are discussed below.


\input{multi.tex}

\subsection{Temperature Gradients}
The chambers are constructed from aluminium that expands typically
 24~\um/m/K. Ovrall temperature changes are not seen by the RASNIK systems,
 but are monitored by the temperature sensors and can relatively easy be corrected for. In contrast, temperature gradients are more difficult to monitor
 and to correct for. In addition, the expected temperature gradients in ATLAS
are not well predicted. Estimations vary, but over a chamber, between
two multilayers, we should be  prepared for gradients of 1 K. This implies
that the chamber should not sag more that 100~\um/K to keep the
wire sufficiently centrered and the cross-plate should not sag more than
 20~\um/K. Of course, the gradient over the cross plate is monitored by the
temperature sensorers and the effect is also seen to some level 
by the in-plane alignment, but we wish to avoid large corrections.

We conducted an small experiment by covering the BOL0 chamber (in its horizontal position) by electrical heat blankets.
 These blankets produce 50W/m$^2$, leading to
gradients of several degrees. Figure~\ref{boltemp} shows a side view of the
chamber and the location of the temperature sensors.
Figure~\ref{inheat}a~and~b show the $Y$ readings of the in-plane and cross-plate RASNIK system respectively during heating.

From the measurements we extract the  values listed in table~\ref{bt}. 
for the chamber and cross-plate sag we obtain 50~\um/K and 6~\um/K which is
well below our requirements.



\begin{table}[thb]
\begin{center}
\begin{tabular}{||l|c|c||} \hline
Quantity   &  Effect & Effect Normalised  \\
           &         & to 1K over ML \\ \hline
$T$ gradient over multilayers  & 4K & 1K \\
$T$ gradient over cross-plate  & $\approx$0.3K & 0.1K \\
$T$ gradient over tube-layers in ML  & $\approx$0K & 0K \\
Chamber Sag                          & 200~\um & 50~\um \\
Cross-Plate Sag                          & 25~\um & 6~\um \\ \hline
\end{tabular}
\caption{\sl The effects of heating the BOL0 chamber using electrical bleankets.}
\label{bt}
\end{center}
\end{table}


\begin{figure}[tpbh]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(0,0){\mbox{\epsfysize=7cm\epsffile{boltemp.eps}}}
\end{picture}
\end{center}
\label{boltemp}
\caption{\sl  Schematic view of the BOL0 chamber. The readings of the temperature sensors are indicated.}
\end{figure}



\begin{figure}[tpbh]
\begin{center}
\setlength{\unitlength}{1cm}
\begin{picture}(14,14)
\put(-5,0){\mbox{\epsfysize=10cm\epsffile{inheat.eps}}}
\put(6,0){\mbox{\epsfysize=10cm\epsffile{cpheat.eps}}}
\end{picture}
\end{center}
\label{inheat}
\caption{\sl a) Average $Y$ of the in-plane system during heating, which is a measure of the chamber sag $\times$ 2. 
b) Measurement ($Y$) of a cross-plate RASNIK system , which is a measure of the cross-plate sag $\times$ 2.  }
\end{figure}







