In this paper we present results of the spectroscopic measurements of the electron density in a microwave surface wave sustained discharge in Ar at atmospheric pressure. The discharge in the form of a plasma column was generated inside a quartz tube cooled with a dielectric liquid. The microwave power delivered to the discharge was applied in the range of 200 ÷ 1 500 W. In all investigations presented in this paper the argon flow rate was relatively low (0.5 l/min), so the Ar plasma column was generated in the form of a single filament, and the lengths of the upstream and downstream plasma columns were almost the same. The electron density in the Ar plasma column was determined using the method based on the Stark broadening of H β spectral line spontaneously emitted by the plasma. Both theories, i.e. GKS (Griem, Kolb, Shen) and Gig-Card (Gigosos, Cardeñoso), were used to work out the experimental results.PACS : 52.75.Hn, 52.80.Tn