An intermediate relation obtained byJellinek in his derivation of theLangmuir adsorption isotherm equation is found to be equivalent tode Witte's extension ofJ. J. Thomson's adsorption theorem. To transform this relation into theLangmuir equationJellinek assumes the quantity\(b' = \frac{{RT}}{b}e^{\frac{{ - \Delta W_\alpha }}{{RT}}} \), to be a function of temperature only and independent of pressure (or concentration). Making use of known surface tension-concentration data we can test this assumption by numerical integration of theThomson-de Witte differential adsorption equation.