  Thermodynamic critical field curves have been measured for
$La_{2-x}Sr_{x}CuO_{4+\delta}$ over the full range of carrier concentrations
where superconductivity occurs in order to determine changes in the normal
state density of states with carrier concentration. There is a substantial
window in the $H-T$ plane where the measurements are possible because the
samples are both thermodynamically reversible and the temperature is low enough
that vortex fluctuations are not important. In this window, the data fit
Hao-Clem rather well, so this model is used to determine $H_c$ and $\kappa_c$
for each temperature and carrier concentration. Using N(0) and the ratio of the
energy gap to transition temperature, $\Delta (0)/k_BT_c$, as fitting
parameters, the $H_c vs T$ curves give $\Delta (0)/k_BT_c \sim 2.0$ over the
whole range of $x$. Values of N(0) remain rather constant in the optimum-doped
and overdoped regime, but drops quickly toward zero in the underdoped regime. .
