rents, and the actual values of the currents for the position of the figure shown are OA, OB, OC, respectively, corresponding in relative magnitude with the lengths of the arrows which are attached to A, B, C. in Figs. 18 and 20, and in direction with the arrows attached to the latter figure, on the assumption that a current is regarded as

time, but differing by 120° in phase, and it is seen that the sum of the three ordinates-that is, the ordinate of the top curve-varies from H + 2H sin 30°, when the time equals t, to 2H sin 60°, when the time equals t', so that the ordinate of the summation curve varies from 2H to √3H, corresponding with a variation of 14 per cent. But this

m

positive when it circulates round the iron ring in such a direction as to tend to send a north pole counter-clockwise round the iron ring. Now the sum of the projections on POQ of any three lines Oa, OB, Oy (Fig. 22) is simply the projection of Og found by drawing ae and e parallel and equal to O8 and Cy respectively. But if such a con

is exactly the variation that we obtained in Fig. 19, hence if there be twice as many convolutions in each of the three coils of Fig. 20, as in each of the six coils of Fig. 18-that is, the same total number of coils in the whole ring-and if the three equal harmonic alternating currents differing by 120° in phase have each the same

Since the three coils both for the open and the closed methods of winding (Figs. 20 and 24) are connected together, and since the current in any one coil varies like the current in the preceding coil, with a lag of 120°, each value of the current may be regarded as travelling round the ring from each coil to the next. This idea has led Mr. Dobrowolski to call such a motor a rotatory current or "drehstrom" motor.

In joining up a three-phase drehstrom motor, we have to decide whether we shall adopt the arrangement shown in Fig. 20 or that illustrated in Fig. 24. The latter, or closed winding, would be employed when we desired that the maximum potential difference between the terminals of any one of the three coils should be equal to the maximum potential difference between any two of the mains; while with the open method of winding (Fig. 20) the maximum difference of potential between the terminals

of any one of the three coils would be only√3 or o'5744

3

3

is done by taking one-third of the diagonals of each of three parallelograms constructed respectively on Oa and 03 produced backwards, on 03 and Oy produced back wards, and on Oy and Oa produced backwards. In this way is obtained the three-legged figure, 01, 02, 03, with three equal sides making angles of 30 with Oa, 03, Oy, respectively; then OI, OII, and OIII, the projections of O1, O2, and 03 on PQ, give us the direction and magnitude of the three currents in the coils I, II, III 'Fig. 24. Hence we see that the current in coil I lags 30 behind the current in A, the current in coil II 30° behind the current in B, and similarly the current in coil III 30 behind the current in C.

Q

F15. 25-Projections of Oa, OB, Oy give direction and relative magnitude of currents in the mains A, B, C of Figs. 20, 24, 27, 29, and 31, and of currents in coils I, II, III of Fig. 20. Projections of O1, 02, 03 completely represent currents in coils I, II, III of Fig. 24: and projections of 01, 02, 03 completely represent currents in coils I, II, III of Fig. 27.4

times the maximum potential difference between any two of the mains. The open method has the further advantage that the middle point where the single current branches into two (Fig. 20) can be permanently connected with the earth; so that, while the maximum potential difference between each pair of mains may be, say, 20,000 volts, the potential of no point of the whole system can ever differ from that of the earth by more than 10,000 volts, a result which of course enables the insulation of separate aerial conductors to be more easily carried out.

The open method of winding has therefore been adopted for the transformers at Lauffen and at Frankfort, as well as for the motor at Frankfort; but, for the reasons which follow, the actual winding employed is more complex than that indicated in Fig. 20.

In addition to the defect possessed by the two-phase. alternate current motor arising from the variation in the strength of the rotating magnetic field, there is another defect caused by the rotation of the field not proceeding

but as one-half of the coil is wrapped one way round the iron ring, and the other half the other way, the currents, as far as sending a north pole round the ring is concerned, will have diametrically opposite effects-that is, will differ by 180° in phase. Hence, while the currents in the three coils I, II, III, in Fig. 24, differed by 120° in phase, the currents in the six coils I, II, III, I, II, III2 (Fig. 27) will differ by 60° in phase, so that, as far as the magnetization of the iron ring is concerned, we have arrived at exactly the arrangement of currents shown in Fig. 18. There is, however, this important difference-that, whereas in Fig. 18 six main wires were required, in Fig. 27 only three are needed.

The difference in phase between the currents in the six coils (Fig. 27) and the currents in the mains can be at once obtained from Fig. 25. For it is easy to show that the current

FIG. 26.-Transformation of a three-phase alternate current motor (closed winding), with currents differing by 120° in phase, into a six-phase motor, with currents differing by 60° in phase.

the motor in Fig. 24 to be wound in the opposite direction; then an arrangement, symbolically indicated in Fig. 26, would be obtained, where the six halves of the former three coils, I, II, III, are now called I, I, II, II, III, and III, as we go round the triangle, Fig. 26. If now, with

where A, B, and C represent simply the arithmetical values of the currents in the three main leads. Arithmetically, then, for the same currents in the mains A, B, C, the currents in the three coils I, II, III of Fig. 27 are the same as the currents in the three coils I, II, III of Fig. 24. But while, as far as sending north polarity counterclockwise round the iron ring is concerned, the current in coil II of Fig. 24 was negative, that in coil II of

out separating any of the connections, the coils I, and II be made to change places, as well as 11, and III, we obtain the arrangement of winding shown on the motor in Fig. 27.

Now it is to be observed that since the coils I and I (Fig 27) are in series, being in fact simply parts of the ame coil I of Fig. 26, the current in the one must be, of course, exactly the same as the current in the other;

Fig. 27 is positive. Hence, while it was the projection of O2 (Fig. 25) that gave the current in coil II of Fig. 24, it will be the projection of O2' that will completely represent the current in coil II of Fig. 27, &c.

Hence, in Fig. 27 the current in the coil I will be O I, the projection of O1; the current in the coil II will be O11', the projection of O2'; that in coil III will be OIII, the projection of O3; that in coil 1, will be O 12, the projection of