An oscillographic method is described for measuring the electric gradient $E$ (volts ${\mathrm{cm}}^{\ensuremath{-}1}$), current density $I$ (amp. ${\mathrm{cm}}^{\ensuremath{-}2}$), total voltage $e$ (volts) as a function of current $i$ in the discharge. The method is applied to arcs in the 0-10-ampere range under conditions of free convection in ${\mathrm{N}}_{2}$, A, and He in the 1-50-atmosphere pressure range, and to air, C${\mathrm{O}}_{2}$, and steam at atmospheric pressure. The exponent $n$ and $B$ in $E={\mathrm{Bi}}^{\ensuremath{-}n}$ are determined for these cases. The range of $n$ is $0.54<n<0.73$, and some dependence on pressure is observed. The exponent $m$ in $E={B}_{0}{p}^{m}$ is measured for ${\mathrm{N}}_{2}$, ${\mathrm{H}}_{2}$, He, and A, and is found to be 0.31, 0.32, 0.20, and 0.16, respectively, with some dependence on current. The method is applied to arcs between electrodes of a number of common metals in air.