TransactionsPublished under the care of the General Secretary and the Treasurer . be solved, the formerand more practical problem is immediately capable of approximatesolution. The problem is, therefore, to determine the system of al-ternating currents on a cable subjected to an alternating of the rectangular wave type. 74 KENNELLY: SPEED OVER CABLES. If t=J be the cyclic magnitude ab of a rectangular a, b, c,^> «./> 9> Fig 2, then it is well known that this is equivalentto the following harmonic series of sinusoidal s. E F ^ = Esin cot -4-—sin 3ODt
TransactionsPublished under the care of the General Secretary and the Treasurer . be solved, the formerand more practical problem is immediately capable of approximatesolution. The problem is, therefore, to determine the system of al-ternating currents on a cable subjected to an alternating of the rectangular wave type. 74 KENNELLY: SPEED OVER CABLES. If t=J be the cyclic magnitude ab of a rectangular a, b, c,^> «./> 9> Fig 2, then it is well known that this is equivalentto the following harmonic series of sinusoidal s. E F ^ = Esin cot -4-—sin 3ODt 4-— sin 5 cot + .3 ^6 volts (8) where E :-lM maximum cj^clic volts (9) and the fundamental sinusoid E sin cot has the same period as therectangular That is, the fundamental sinusoidal hasthe frequency of the rectangular , but has a maximum cent greater, as shown at g. A, B, C, D, in Fig. 2. The effectiveor of this sinusoid is volts, or nearly 10 per centless than the rectangular. The successive harmonics increase di- i!II a. Fig. 2.— Diagram of eectangular and fundamental sinusoid of THE SAME. rectly in frequency, and inversely in amplitude, as the successive oddnumbers. If we superpose a rectangular of ± 10 volts upon a con-tinuous of + 10 volts, we obtain a rectangular a, hj,c, d, e, f, g entirely above the zero line HJ, Fig. 2. This corre-sponds to dot impulses from -|- 20 volts, successively followedby pauses e, f, of equal duration with the cable to ground. A suc-cession of 20-volt dots and pauses, say four to the second, is, there-fore, the equivalent of a steady application of -|- 10 volts com-bined with a rectangular alternating of ± 10 volts. Thisrectangular would be the equivalent of tlie following sinu-soidal : volts maximum with the frequency 4 cycles per volts maximum with the frequency 12 cycles per second. KEN NELLY: HfEEU OVEK CABLEIS. 75
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