It is shown that in the cathode drop region of a metal vapor arc, there are four equations and two limiting conditions relating five dependent variables. The five dependent variables treated are temperature of the cathode spot, electric field at the cathode, total current density, current density carried by electrons, and the radius of the spot. When these equations are combined, a current level is found below which no solution exists. It is proposed that this current corresponds to the point at which a vacuum arc extinguishes in an alternating‐current circit. Experimental measurements of the current level at which this event occurs have been made, and the results are compared with the theoretical calculations.