A technique is presented by which the Fowler–Milne spectroscopic method can be applied to thermal plasmas containing two or more atomic elements. The technique requires the measurement of the emission coefficient for an atomic transition of each element. These values are normalized to the maximum emission coefficient for each transition in the respective single‐element plasmas. Neither calibration of the sensitivity of the apparatus nor knowledge of atomic transition probabilities is required. The technique allows the relative concentration of the elements to be derived significantly more precisely than other spectroscopic methods. The technique is applied to the measurement of the radial profiles of temperature and composition of free‐burning arcs in mixtures of argon and nitrogen. Significant demixing is observed, with the direction of the demixing depending on the relative concentrations of argon and nitrogen.