The paper takes the space‐charge theory developed by Langmuir and applies it to the accelerating‐field range along with the image‐potential theory suggested by Schottky. The combined theory produces a current‐voltage curve which begins at the zero‐field current and voltage calculated from space‐charge theory, and then gradually approaches the curve generated by Schottky theory. The paper summarizes in a single equation the solution procedure outlined by Langmuir. Based on this equation, the paper discusses the behavior of the current‐voltage curve at the transition points from the exponential range into the space‐charge range and from the space‐charge range into the accelerating field range.