The role of impurities in a low‐pressure arc is theoretically investigated by use of a system of coupled rate equations. Some of the coefficients may be unknown; it is shown that by measuring a few parameters it is possible to obtain a set of equations at least equal in number to the number of unknown coefficients. The analysis is then particularized to the case when the introduction of the additive results in a perturbation sufficiently small that a linear treatment is applicable. This results in a system of seven linear equations, the left‐hand side of which is obtained by adding seven terms, each a product of aknowncoefficient times perturbation on a certain plasma parameter (population of an excited level, electron density, electric field, etc.) whereas the right‐hand side is linear in the pressure of the additive, the coefficient depending upon the characteristic properties of the additive.