If there are two currents differing by 90 degrees, this variation of the magnetism will be about 40 per cent.; with three currents differing 60 degrees, about 14 per cent; with six currents differing 30 degrees it will be only about 4 per cent., and so on. It will be seen, therefore, that by doubling the three-phase system the pulsations are already very greatly reduced. But this would require six wires, while the three-phase system requires only three wires (as each of the three leads can readily be shown to serve as a return lead for the other two in parallel). It is to combine the advantages of both that he designed the following very ingenious system. By this system he can obtain as small a difference of phase as desired, without increasing the number of wires above three, a statement which might at first seem paradoxical. Before explaining this ingenious system, it might be well to call attention to a parallel case to the above in continuous current machines and motors. The first dynamos were constructed with two commutator bars. They were soon found to work much better with four, and finally still better as the number of commutator bars (or coils) was increased, up to a practical limit. Just as the pulsations in the continuous current dynamos were detrimental to proper working, so are these pulsations in few-phased alternating current motors, though the objections manifest themselves in different ways--in the continuous current motors as sparking and in the alternating current motors as detrimental inductive effects. The underlying principle of this new system may be seen best in Figs. 4, 5, 6, 7 and 8. In Fig. 4 are shown two currents, I_{1} and I_{2}, which differ from each other by an angle, D. Suppose these two currents to be any neighboring currents in a simple rotary current system. Now, if these two currents be united into one, as shown in the lower part of the figure, the resulting current, I, will be about as shown by the dotted line; that is, it will lie between the other two and at its maximum point, and for a difference of phases equal to 90 degrees it will be about 1.4 times as great as the maximum of either of the others; the important feature is that the phase of this current is midway between that of the other two. Fig. 5 shows the winding of a cylinder armature and Fig. 7 that, of a Gramme armature for a simple three-phase current with three leads, with which system we assume that the reader is familiar. [Illustration: FIG. 4.] [Illustration: FIG. 5.] [Illustration: FIG. 6.] [Illustration: FIG. 7.] [Illustration: FIG. 8.]