The paper describes a thermionic voltmeter which can be used to measure the peak and mean values of any alternating wave-form. The instrument is provided with two scales on one dial, corresponding to peak and mean values, and a change-over switch converts the voltmeter from one reading to the other. The peak value is measured by the mean grid current of a cumulative grid rectifier. It is shown by experiment that the mean grid potential is sensibly equal to the peak value of a sinusoidal voltage, and an approximate analysis is developed by which the mean grid current can be predicted very accurately. Approximate analysis shows that the mean grid current is sensibly proportional to the peak value of any wave-form, and results are tabulated of direct tests on five different wave-forms the oscillograms of which are reproduced; at least three of these wave-forms are extraordinarily irregular. Experiment shows that the accuracy of the peak measurement is about the same as can be obtained from an ordinary oscillogram. The mean-value measurement is made by omitting the grid condenser, and the accuracy of the method is discussed analytically and substantiated experimentally. An application of the voltmeter is illustrated by curves which show the distortion produced by a 4-stage thermionic amplifier.