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The trapped-electron method is applied to the measurement of the slopes of the vibrational cross sections near their respective thresholds. Absolute values are obtained by normalization to positive-ion cross sections. The values obtained in H2 are 43 for v=1, 0.72, for v=2, 0.04, for v=3, and 0.003, for v=4, in units of 10-18 cm2/eV. The values for N2 are 2.5 for v=1 and about 0.02 for v=2, whereas, the values for CO are much larger, i.e., 120 for v=1 and 2.4 for v=2. Various corrections that are necessary for determining absolute cross sections from trapped-electron data are discussed. The validity of the corrections is studied for the case of the 23S excitation function in He.