Abridgment of flux linkages and electromagnetic induction in closed circuits

It is shown that the flux linkages of a circuit may be changed in two very different ways — either the flux may be varied causing a voltage to be induced according to Faraday's Law of Electromagnetic Induction, or the turns may be varied by a substitution of circuit without inducing a voltage. In the Appendix, it is mathematically shown that the flux may be changed either by transformer or cutting action, but that the presence of one or the other of these actions is dependent on the choice of reference axes. Thus, any argument to the effect that one of them in particular is a necessary part of all induction phenomena is futile. It is possible to identify in every d-c. machine the building up of flux linkages so as to generate a voltage, and the reduction of flux linkages by a substitution of circuit so as not to generate a voltage. The alternate working of these two methods for changing the flux linkages of a circuit is an essential and necessary feature of every d-c. dynamo-electric machine. General criteria are introduced for ascertaining in any given case the nature of the changes in inter-linkages which occur, and whether voltages are induced thereby. By way of application, a new restriction on the use of coefficients of inductance is pointed out, the sliding contact and homopolar machine are discussed, and finally a table has been prepared illustrating the various types of flux linkages found in familiar apparatus.