(b). The cross marks show the position of the top of the plume. The rise velocity of the plume is found to be $\sim 12$kms$^{-1}$. Panel (b) shows the dimensions of the ellipse used to model the rising plume.[]{data-label="timedist"}](figure10_b.eps "fig:"){height="8cm"}

To calculate the Mach number of a flow it is necessary to know the sound speed of the ambient material. The sound speed of the dense prominence material is $C_s=[\gamma (R/\mu)T_{prom}]^{1/2}=11$kms$^{-1}$ for $\gamma=5/3$, $R=8.3\times 10^7$ergK$^{-1}$mol$^{-1}$, $\mu=0.9$ and $T_{prom}=8000$K. Using the velocity calculated above we find the Mach number of the flow to be $M_{\infty}=1.12 \pm 0.05$ in the case where $\gamma=5/3$.

Panel (b) of Figure \[timedist\] shows the dimensions of the ellipse used. In this case $a=1.3$arcsec and $b=2.35$arcsec. These lengthscales can now be used to determine the normalising length scales for the system, so that the plume head becomes circular. Now the prominence plasma $\beta$ can be determined.

Determining Plasma $\beta$ of Observed Prominences
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Figure \[intfit\] shows the normalised intensity. Using the emissions for heights greater than $4$ in Figure \[intfit\] a linear fit was used to de-trend the data (as was applied to the simulations). This intensity is used as a proxy for the column density assuming 