The velocity distributions of electrons scattered by helium atoms, at angles ranging from 10\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{}, have been measured for electrons having energies of 800, 1000, and 1200 volts. The curves have a well-defined narrow maximum where the scattered electrons have the same velocity as the primary electrons, this being the well-known elastic scattering. In addition, for each angle of scattering, a single broad peak is superposed on the continuous distribution of velocities ranging from the maximum down to zero. This represents the inelastically scattered electrons. The position of each peak is such that the velocity corresponding to it, is given approximately by $v=ucos\ensuremath{\theta}$, where $u$ is the velocity of the electron before impact and $\ensuremath{\theta}$ the angle of scattering. This is the formula for the velocity of an electron when scattered through $\ensuremath{\theta}$, by a free electron initially at rest. The inference is that we may associate these inelastic peaks with collisions between the incident electrons and the atomic electrons when the binding energy is small in comparison with the energy transfers during the collision. Jauncey's theory of the breadth of the modified line in the Compton effect is discussed in relation to the breadth of the inelastic peak, on replacing the photon by the incident electron.