Abstract:A measurement of the inclusive cross section for the deep-inelastic scattering of positrons o protons at HERA is presented at momentum transfers 8:5 Q 2 35 GeV 2 and large inelasticity y = 0:7, i.e. for the Bjorken-x range 0:00013 x 0:00055. Using a next-to-leading order QCD t to the structure function F 2 at lower y values, the contribution of F 2 to the measured cross section at high y is calculated and, by subtraction, the longitudinal structure function F L is determined for the rst time with an average value of F L = 0:52 0:03 (stat) +0:25 0:22 (syst) at Q 2 = 1 5 : 4 GeV 2 and x = 0 : 000243.