Surface Brightness Fitting and Determination of $r_{\textrm{\scriptsize {c}}}$.

Measurements of the core radii, $r_{\textrm{\scriptsize {c}}}$, were made for each cluster to allow a more accurate conversion from the detected count rate to the total count rate. This was carried out by fitting a King profile to the surface brightness taking into account blurring by the PSPC psf. The free parameters were the right-ascension and declination of the cluster centre, the core radius, and the normalisation. The index, $\beta$ was frozen at $\frac{2}{3}$ and it was assumed that the cluster was symmetric. The measured value of the core radius was then used to recompute the total flux. Examples of the fitted surface brightness profiles are shown in figure 3.2.

Figure 3.2: Radial profiles of the clusters MS1358 and MS1512. Also show are the best fitting King profiles. Details of the fits to all the clusters can be found in table 3.1.