The one-dimensional motion of an electron gas in a regular and infinite ion-grid is described by the development in time of the disturbance f(v,t)e<sup>ikz</sup> of the distribution function. The Fourier transform of f with respect to v is shown to develop in time like a wave propagating towards infinity with velocity k in the transform space. The wave form and its distortion are governed by a function D closely related to the Fourier transform of the undisturbed velocity distribution. For kv<sub>t</sub>&#139;&#139;&#969;<sub>p</sub> there is in addition a standing wave oscillating with the plasma frequency &#969;<sub>p</sub> (v<sub>t</sub>=thermal velocity).