is given by: $$\beta=\frac{2(\gamma-1)}{\gamma}\frac{M_*^2}{M_{\infty}^2-M_*^2}$$ The results for the plasma $\beta$ for different values of $\gamma$ are given in Table \[gam\_table\]. The range of values covers two orders of magnitude from $\beta=0.044 \pm 0.078$ for $\gamma=1.05$ to $\beta=2.666 \pm 0.080$ for $\gamma=2.0$. However, the value for $\gamma$ in a prominence is likely to be in the range $\gamma=1.4$-$1.7$, giving a range of plasma $\beta$ of $\beta=0.47 \pm 0.079$ to $1.13\pm 0.080$. This is a range of only a factor of $\sim2.5$.

   $\gamma$   $\chi^2$ of fit   $M_*^2$   $\sigma(M_*^2)$   $\beta$   $\sigma(\beta)$
  ---------- ----------------- --------- ----------------- --------- -----------------
    $1.05$        $1.410$       $0.61$        $0.027$       $0.04$        $0.078$
    $1.1$         $1.407$       $0.62$        $0.027$       $0.09$        $0.079$
    $1.15$        $1.404$       $0.63$        $0.027$       $0.14$        $0.079$
    $1.2$         $1.401$       $0.63$        $0.028$       $0.20$        $0.079$
    $1.25$        $1.400$       $0.64$        $0.028$       $0.26$        $0.079$
    $1.3$         $1.394$       $0.65$        $0.029$       $0.32$        $0.079$
    $1.35$        $1.390$       $0.65$        $0.029$       $0.39$        $0.079$
    $1.4$         $1.386$       $0.66$        $0.030$       $0.47$        $0.079$
    $1.45$        $1.382$       $0.67$        $0.030$       $0.56$        $0.080$
    $1.5$         $1.377$       $0.67$        $0.030$       $0.64$        $0.080$
    $1.55$        $1.372$       $0.68$        $0.036$       $0.74$        $0.080$
    $1.6$         $1.367$       $0.68$        $0.031$       $0.86$        $0.090$
    $1.65$        $1.362$       $0.69$        $0.031$       $0.99$        $0.080$
    $1.7$         $1.357$       $0.70$        $0.031$       $1.13$        $0.080$
    $1.75$        $1.351$       $0.71$        $0.032$       $1.30$        $0.080$
    $1.8$         $1.345$       $0.71$        $0.032$       $1.49$        $0.080$
    $1.85$        $1.339$       $0.72$        $0.032$       $1.72$        $0.080$
    $1.9$         $1.333$       $0.73$        $0.033$       