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Absolute total emission cross sections have been measured for electron-impact excitation of He giving radiation from the 6 '$-2 'P, 5 '$-2 'P, 4 '$-2 'P, and 3 '$-2 'P transitions. Electron energies were 50, 100, 500, 1000, and 2000 eV. Particular care was taken to make the measurements accurate and to make knowledgeable assessments of uncertainties, so that the results serve as reliable benchmarks for calibration of other excitation apparatus as well as for comparison with theory. The most accurate results are for 505+V electron energy, where the mean uncertainty is only 3.5% high confidence level. The measured eaiission cross sections are modified to account for branching and cascade to give level-excitation cross sections, and results are compared with other experimental data and theoretical predictions. At 2000 eV, the measurements average 2.5% below Born-approximation calculations.