  Transport and thermodynamic properties of a sintered pellet of the newly
discovered $MgB_2$ superconductor have been measured to determine the
characteristic critical magnetic fields and critical current densities. Both
resistive transition and magnetization data give similar values of the upper
critical field, $H_{c2}$, with magnetization data giving $dH_{c2}/dT=0.44~T/K$
at the transition temperature of $T_c=40.2 K$. Close to the transition
temperature, magnetization curves are thermodynamically reversible, but at low
temperatures the trapped flux can be on the order of one Tesla. The value of
$dH_c/dT$ at $T_c$ is estimated to be about $12~mT/K$, a value similar to
classical superconductors like Sn. Hence, the Ginsburg-Landau parameter $\kappa
\sim 26$. Estimates of the critical supercurrent density, $J_c$, using
hysteresis loops and the Bean model give critical current densities on the
order of $10^5~A/cm^2$. Hence the supercurrent coupling through the grain
boundaries is comparable to intermetallics like $Nb_3Sn$.
