In the calculations as applied to Deuce, allowance is made for the complete circuit, consisting of a.c. supply system, rectifier transformer, interphase transformers, anode chokes, rectifier tank, series reactor, if any, and also for the feed-in from any parallel-connected rectifiers or rotating plant, as well as the feed-back from the load system, whether this be rotating plant or electrolytic cells.In the second example illustrated in the same paper, the methods were applied to a bi-phase rectifier equipment. In the past, most rectifiers of any appreciable power have operated from a 3-phase system, usually having a d.c. output corresponding to 6-phase operation, and resulting in a d.c. ripple current which is sufficiently small to warrant using the general assumption of infinite d.c.-side inductance. In the case of bi-phase operation, this no longer holds, as ripple currents are often as high as 50% or 60%. The presence of high ripple currents modifies things in such a way that the intersection of the two open-circuit anode voltages cannot be considered as the start of commutation, i.e. an inherent delay angle is introduced. As this angle is not known, and depends on various circuit parameters, the Deuce provides an excellent method of accurately determining the circuit performance without going through much laborious mathematical calculation.Prof. D. R. Hartree {communicated): The Runge-Kutta method used by Mr. Birtwistle and Miss Dent for the integration of the set of eqns. (1) is a general method, and as such does not take advantage of some special features of these equations, namely that they are second-order with first derivative absent, which is the simplest form for numerical integration, and that they are not only linear but linear with constant coefficients. An alternative method, which does take advantage of these simplifying features, may be found to be quicker to run on the machine, as well as being simpler to programme. This method is an extension of that of Numerov* for a single linear second-order equation (not necessarily with constant coefficients.) First, to avoid the need for differentiating twice the input function e(t) [which raises difficulties when e(t) is a step function], write yj for
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