The paper deals with the experimental harmonic analysis of electromotive force and current wave-forms. A brief outline of existing methods is given and their limitations are discussed. A modification of the dynamometer method, which allows a much higher degree of accuracy to be attained, and in which the properties of an oscillatory circuit are used to obtain a sinusoidal current wave of suitable frequency, is described. This current is passed through one coil of a dynamometer, whilst the wave to be analysed is passed through the other. The values of the coefficients in the Fourier series representing the wave-form being analysed are obtained from the readings of the dynamometer and an ammeter.The final method advocated aims at analysing waveforms up to at least the 23rd harmonic and correct to within 0.1 per cent of the fundamental. The accuracy of the method must be established by comparison with a method more accurate than the commonly employed oscillograph method, the accuracy of which is considerably improved upon. Such a standard method, which, involves the use of a synchronously driven commutator, is dealt with in detail in the first part of the paper and its own accuracy is established. Most of the principles involved are common to the two succeeding methods. A full discussion of the errors involved in the three methods is given, and the design of the necessary instruments is considered. For convenience, most of the mathematics involved is given in appendixes and only the results are quoted in the paper itself.