A rigorous mathematical theory of the static machine is given and applied in detail to a simple four element machine of a type exemplified by the Kelvin replenisher. It is shown that the potentials of each of the inductors after cycles satisfies an equation of the form , where and are constants which depend only on the coefficients of capacity and the coefficients of induction of the elements in two configurations, and and are constants which depend both on the initial values of the potentials of the inductors and the coefficients of capacity and of induction of the elements in the two determining configurations. The values of the various constants for a non-symmetrical machine, and also for a symmetrical machine are given in tables. It is shown that theoretically the potential produced by an ordinary static machine will increase without limit, approach a constant value, or decrease to zero, depending on the phase at which the brushes are grounded.
- Received 1 August 1924
- Published in the issue dated December 1924
© 1924 The American Physical Society