This paper discusses the various factors that influence the design dimensions for an ellipsoid voltmeter to be used for the precision measurement of a specified range of high alternating voltages. Having selected the overall dimensions of the ellipsoid itself, methods for evaluating the constants of the instrument are discussed, and a method is given for determining the necessary constants for a given ellipsoid from a series of weighted measurements.The theory leading to the simple equation giving the field strength as a function of the period of the ellipsoid makes certain simplifying assumptions, and the magnitudes of the errors arising from these are considered. Where they are of the order of 0.01% or more, correction curves are given by means of which the necessary allowances can be made in any given case.The theoretical treatment is illustrated throughout by reference to a particular instrument, and it is concluded that, after its performance had been analysed on the above lines, it would give results having an estimated error of less than ±0.03%.