The lack of precision of measurements with alternate currents, as compared with those using direct currents, is mainly due to the relative sensitiveness of the instruments available for such tests. The fact that the turning moment acting on the moving system depends in one case on the square of the current and in the other on the first power of the current, readily explains the high ratio between the currents needed to cause the minimum measurable deflection in the two cases, but this ratio is, nevertheless, most striking when a numerical comparison is actually made on some fair basis. The only likely way at present of improving alternate current instruments is to use iron cored electromagnets to increase the strength of the magnetic field. I have found that the difficulties due to varying permeability and hysteresis of the iron can be avoided by exciting the electromagnet in shunt. It proves possible, with careful design, to construct an electromagnet whose flux is connected with the exciting voltage by a strict mathematical law involving no variable physical properties like permeability, etc. Such an electromagnet is eminently suited for measuring purposes. The theoretical and experimental study of instruments constructed on this principle has brought out certain novel points which are set forth in the present paper. The first part discusses the mathematical relations of cyclic quantities having a common fundamental period, and constitutes a development of a method already published. This method is the only one known to me which is independent of assumptions in regard to the wave form of the quantities dealt with. The usual methods, which are based on the erroneous assumptions of sine law wave form, are not any simpler in working, and are most unsatisfactory when the accuracy of new results has to be critically examined. All alternate current measurements refer to mean squares or to mean products, and the natural method of obtaining the connections between such squares and products is to study the properties of quadratic functions of the variables. The earliest instance of this in alternate current theory was in connection with the “three voltmeter method.” Such processes lead to a very simple form of calculus appropriate to cyclic quantities.
Sleep: The Night-Life Tour