for the unknown (i.e. $\beta$) in Equation \[Meqn\]. This value is slightly higher than the input value, but sufficiently close to show that the method can estimate the plasma $\beta$ using the compression of the plume. Figure \[chisqu\] shows the chi-squared for the density distribution for models using different plasma $\beta$ values and the simulated distribution. The minimum of the $\chi^2$ distribution at a $\beta$ value that is close the value of plasma $\beta$ in the simulation.

![$\chi^2$ distribution calculate for different values of plasma $\beta$ giving different density distributions and the simulated distribution.[]{data-label="chisqu"}](figure9.eps){height="8cm"}

Application to Observed Prominence Data {#PROM_SEIS}
=======================================

In this section we apply the method presented above to determine the plasma $\beta$ of the plume displayed in Figure \[prom\]. In contrast to Section \[SIM\], this is treated as an inverse problem, where using the intensity and rise velocity allows the plasma $\beta$ of the prominence to be deduced. Due to the timescales of these compressions ($\sim100$s) being shorter than the timescales for the cooling ($\sim 1000$s), we can assume to first-order approximation that the increased intensity comes through purely adiabatic effects. These adiabatic effects would be an increased column density and a temperature rise from the compression. 