Measurement of the beta asymmetry in $^{19}$Ne and a new determination of $V_{ud}$.

A new analysis of the 1996 Princeton $^{19}$Ne beta asymmetry experiment was undertaken with particular emphasis on correcting for the effect of positron scatters off of the detector faces. The experiment was simulated using the Monte Carlo package PENELOPE. Applying the correction generated by the simulation to the data yields a zero energy intercept of the asymmetry (A$_0$) with a 2.0% uncertainty. The value of the element V$_{ud}$ in the CKM matrix which describes quark mixing is calculated. Using the value of the asymmetry from the Princeton experiment and the average from the results of all published $^{19}$Ne lifetime measurements, V$_{ud}$ is extracted with an uncertainty of 0.12%; the most precise value from a mirror decay (including the neutron).