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An earlier treatment, which proved useful when dealing with zero‐emittance beams, is suitably modified to describe the space‐charge spread of finite‐emittance charged‐particle beams. The actual beam shape is obtained as a function of the initial shape by integrating first‐order motion and field equations, which are listed explicitly. Formulas applying to elliptically shaped beams are worked out and numerical results are given for a circular‐cross‐section drifting beam.