The properties of the planar diode with space charge and thermal emission velocities were first calculated by Langmuir. His results cannot be presented in analytic form, but only as a table of data. The comparison of these data with experiment is difficult on account of the well-known uncertainty of the total emission of oxide-coated cathodes.In the present paper the properties of the diode are expressed as thirty partial differential coefficients of five interdependent variables. Using Langmuir's assumptions, the expressions for the differentials turn out to be very simple functions of the five variables and three constants. A table of the relations between the differentials is given.Some of the differentials are experimentally measurable. It is possible therefore to use the table either to calculate properties not accessible to direct measurement, or to use it to verify the assumptions made in deriving them. For example, measurements of the characteristic at two different cathode temperatures enable the effect of changing the distance between the electrodes to be calculated. If, however, the electrode separation is in fact variable at will, a comparison of the calculated and observed results will give an indication of the validity of the assumptions made in the theory.The main interest in the differentials is in the motional transconductance, i.e. the change in anode current for unit change in anodecathode spacing. This differential enters into the theory of scale changes in valves and into the theory of their microphonic properties.