A geometrical analysis of open carbon arc phenomena

The behaviour of a carbon arc with a resistance in parallel is first developed geometrically and proved experimentally. From this the conditions governing the musical arc are deduced and the growth of arc oscillations is traced. Geometrical methods are employed because no direct integration of the differential equations is possible. The analysis shows that a musical arc, in which the current oscillates about a point on the volt-ampere characteristic, is possible but that it is unstable. An experimental example is given in Table 1. Stability is improved by the presence of the "hysteresis loop". The tendency for the arc oscillations to grow until extinction ensues is next traced, and this leads to a discussion of discontinuous oscillations. The necessity for the introduction of a thermal term in the equations, and its effect in permittingthese discontinuous oscillations to persist, are explained, and an experimental example is given. Observation of the discontinuous oscillations leads to the conclusion that no high-frequency inductance is essential, and experiments proving the correctness of this prediction are given, together with oscillograms of the current and voltage under these conditions. It is suggested that this phenomenon has important consequences for power station engineers, and that it forms the best starting-point for the examination of arc oscillations. The dynamic characteristics for the examples quoted are deduced from the oscillograms, and their main features are analysed.