An investigation of the polar angle distribution of charged hadrons is presented using data taken by the JADE experiment at the PETRA e^+e^- collider at centre-of-mass energies of 35 and 44 GeV. From fits to the polar angle distribution the longitudinal, sigma_L, and transverse, sigma_T, cross-section relative to the total hadronic are determined at an average energy scale of 36.6 GeV. The results are sigma_L/sigma_tot = 0.067 +/- 0.013, sigma_T/sigma_tot = 0.933 -/+ 0.013 where total errors

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... given and the results are exactly anti-correlated. Using the next-to-leading order QCD prediction for the longitudinal cross-section, the value alpha_S(36.6 GeV) = 0.150 +/- 0.025 of the strong coupling constant is obtained in agreement with the world average value of alpha_S evolved to an energy scale of 36.6 GeV.