factor for type B particles. We define the $\alpha$ relaxation time $\tau$ as the time where $F_{\alpha}(k_{max},t)$ decays to $1/e$. At a temperature $T=0.2895858$ which is just below the mode coupling $T_C$, we find that $F_B(k,t)$ has fallen to $1/e$ at $\tau=(1.0\pm 0.1)\times 10^{6}$ md time steps for a system with 512 particles of which half are type B. This gives us a time scale by which to compare other times such as our run times. This value of $\tau$ shows no signs of aging [@Kob97b; @Kob00] and stays about the same even after 10$^8$ time steps. At higher temperatures this relaxation time is much shorter.

The runs used to determine the intermediate scattering function were done in a slightly different way from the other measurements. These runs were performed at a given temperature and density for $N_{\tau}$ md time steps with no change in temperature or density. The runs were started from a configuration that had been equilibrated at that temperature and density using parallel tempering. The parallel tempering technique is described in the appendix.

Specific Heat
=============

The specific heat is a thermodynamic quantity which undergoes a change signaling the glass transition. In experimental systems under constant pressure 