Mechanical computation of root mean square values

Varying values of electric current with time are practically the ever-present condition in applications of electricity. There are two main divisions: First, varying loads, producing such data as are given, for example, by the current record of a curve-drawing ammeter; the time is recorded in hours, minutes or seconds. Second, the condition of varying currents in the alternating-current waves themselves or in electrical transient phenomena, as given by a photographic record of an oscillograph (a galvanometer capable of recording instantaneous values of current). The time is here recorded in thousandths of a second. In both cases the energy is proportional neither to the instantaneous nor average value of the current, but to the square of the instantaneous current, as expressed in the familiar equation (i
²
R). The process of squaring successive instantaneous values, averaging the square, and extracting the square root, is quite tedious and laborious. After reviewing some prominent labor-saving methods the writer points out that the root-mean-square (R M S) value can be quickly calculated mechanically by a device, invented some sixty-five years ago and widely used for other purposes. Fig. 3 shows the picture of this device, called Amsler's Mechanical Integrator.