Methods to measure absolute differential elastic and vibrational excitation cross sections using an electron spectrometer with a magnetic angle changer are discussed. Emphasized are the need to by‐pass drifts and to properly correct for the instrumental response function when angle of detection or electron energy are varied. The results are illustrated with cross sections in nitrogen, methane and neopentane. The good agreement of the results with the experimental data from other leading groups (taken mostly without the angle changer) and with some theories indicate that the measurements are reliable. The angle‐integrated data agrees well with the results of electron‐transport experiments. Good agreement with theory is obtained for nitrogen, even in the difficult low‐energy region. Electronic excitation in rare gases is also briefly mentioned.