Both of these can be calculated from the model described above.

Figure \[prom\] panel (a) shows a quiescent prominence seen on the NW solar limb on 2007 October 03 observed by the SOT with the Ca [II]{} H filter at a cadence of 30 s. The time series of this observation was between 01:16UT and 04:59UT. This prominence presents many interesting dynamic features, for example the start of this observation (01:16UT) a large bubble has formed inside the prominence similar to those described in [@BERG2010]. There are also a number of bright threads and downwardly propagating knots that occur during the duration of the observations as well as the upwardly ejected plasma blobs presented in [@HILL2011]. In this paper we are interested in the rising plume and, in particular, the bright rim that forms at the top of the plume. This is shown in panel (b) of Figure \[prom\].

Calculation of the Plume Mach Number {#MACH}
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Before the plasma $\beta$ is calculated, it is necessary to calculate the Mach number of the rising plume. Following the method applied in Section \[SIMPlume\], we create a time-distance plot to show how the height of the plume changes with time. The dashed 