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Recently developed means for measuring tube admittances on short waves are described in a general way in the introduction. Admittances, which are chiefly dealt with, are the input admittance between the input grid and the cathode and the complex transconductance between the input grid and the anode. In section II a pentode, consisting of a cathode, grid 1, grid 2, grid 3, and an anode is considered. Grid 1 is negative, grid 2 positive, grid 3 either negative or positive, and the anode positive. The probability of an electron, arriving before grid 3, to pass through grid 3 is called α and the probability that an electron, which is returned before grid 3, arrives a second time before grid 3 is called β. Input grid admittance is calculated in terms of α and β, two expressions being obtained, one being the additional input damping due to electrons returning before grid 3 and the other being the additional input capacitance due to the same cause. Measurements of these quantities for pentodes, hexodes, heptodes, and octodes are described in section III, whereas α and β are calculated from these measurements in section IV, several checks being obtained. In section V formulas for the influence of returning electrons on complex transconductance are derived and applied to measurements in section VI.