LXXI. A Comparison of the Periods of the Electrical Vibrations associated with Simple Circuits. By J. A. POLLOCK, Professor of Physics in the University of Sydney. With an Appendix by J. C. CLOSE, Deas-Thomson Scholar in Physics*.

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Introductory.

THE object of the present research has been to compare the periods of the electrical vibrations connected with narrow rectangular closed circuits with those of the oscillations associated with straight wires and with open and closed rings.

The essential features of the experimental method adopted are as follows:-A condenser is discharged in the neighbourhood of a narrow rectangular closed circuit; oscillatory currents are thus set up in the rectangle, which in turn induce others in a third circuit of required shape. Observations of the amplitudes of the disturbances in the circuits are made with Rutherford's magnetic detectors, while the dimensions of the circuits are adjusted, step by step, until finally all three are in tune. The length of a circuit of any shape can thus be found which has the same period of electrical vibration as that of a given narrow rectangular closed circuit.

When the experiments were commenced, it was generally considered, on theoretical grounds, that the wave-length of the free oscillation connected with open resonators was equal to twice the length of the circuit; and certain experimental evidence had lately been published which apparently accorded with such a view. The well-known experiments of Sarasin and De la Rive and others, however, make the wavelength greater than twice the length of the resonator. It seemed essential therefore to strengthen, if possible, the experimental position, and with this object in view the present experiments were undertaken. Since their practical completion, theoretical support has been withdrawn from the results first mentioned, by the publication of Macdonald's Adams Prize Essay on Electric Waves (Cambridge, 1902), which has wholly changed the theoretical aspect.

Macdonald's calculations so closely agree with the bulk of

* Communicated by the Author. Read before the Royal Society of New South Wales.

Kirchhoff, Pogg. Ann. vol. exxi., 1864. Thomson, 'Recent Researches,' p. 340 (1893). Poincaré, 'Les Oscillations Electriques,' p. 273 (G. Carré, Paris, 1894).

Turpain, Journ. de Phys. vol. x. p. 425 (1901); Slaby, Electrotech. Zeit. No. 9, p. 165 (1902).

the experimental evidence, that there can no longer be any doubt that the wave-length of the free oscillation associated with open circuits is considerably greater than twice the length of the wire.

General Results.

Open Circuits.-A. Slaby (Electrotech. Zeit. No. 9, p. 165, 1902) has investigated with a spark-micrometer the potential at various points of a straight wire when electrical vibrations take place along it. He finds a stationary wave with potential loops at the ends, and a relative node at the middle. Such an experiment does not seem calculated to determine the actual wave-length of the vibration connected with the wire, but apparently Dr. Slaby is satisfied, from a consideration of the observations, that the wave-length of the oscillation is equal to twice the length of the wire. He has also theoretically discussed the problem, and "the calculation gives a full confirmation of the experimental results." The experiments were made with wires from one to ten metres long.

Drude, in Ann. der Phys. ix. 2, p. 293 (1902), publishes an account of an elaborate research on the vibration-period and self-induction of wire coils, in connexion with the construction of Tesla transformers. On page 328 he gives the results of the investigation with coils with few windings and with single circles. Drude does not measure the period of the vibration connected with straight wires, but states that for a thin straight wire the half wave-length is equal to the length of the wire. He refers to a calculation of Abraham (Wied. Ann. vol. lxvi. p. 471, 1898) which gives the half wavelength 0.85 per cent. greater than the wire-length, for a straight wire 0.25 cm. in diameter and 77 cms. long.

In the present experiments, the comparison of the periods has been made in all cases between circuits constructed of copper wire 0.33 cm. in diameter and rectangles of thin brass wire 0.04 cm. thick, the rectangles being 30 cms. wide.

It is found that the perimeters of the rectangles are greater than twice the length of straight wires which have the same period of electrical vibration, the ratio of the lengths varying from 2:45 for a rectangle 760 cms. in perimeter, to 2:31 for one whose perimeter is 1200 cms.

Approximately at least, the wave-length of the electrical vibration associated with narrow rectangular closed circuits may be taken as equal to the perimeters of the rectangles. It appears then from these experiments, that the wave-length

of the oscillation connected with a straight wire is much greater than twice the length of the wire, a result opposed to Slaby's conclusions and to Drude's statement.

For open circular resonators Sarasin and De la Rive* obtain results which are usually stated by saying that the wavelength of the free electrical oscillation connected with such circuits is equal to eight times the diameter of the circuit or to 2:55 times the wire-length. These results have been abundantly verified in a general sense, but it is doubtful if the statement is not too wide, as it takes no account of the diameter of the wire of which the resonator is made, nor of the shape or configuration of the ends of the circuit.

Turpain, from observations published quite recently, arrives at a different conclusion. He has investigated the problem of the vibration connected with circular resonators in an ingenious manner, by inclosing them in exhausted glass tubes, and judging of the electrical state of the wires by the luminosity produced in the rarefied gas. Turpain has published many accounts of his experiments, finally summarizing his work in the Journal de Physique, vol. x. p. 425 (1901). On p. 435 et seq. he describes experiments made with an open circular resonator and part of the inducing field inclosed in an exhausted vessel, and others where only the spark-gap was surrounded with rarefied gas. In both cases, it is stated that the resonator responds when one half the exciting wavelength is equal to the length of the resonator. Turpain considers it experimentally established that "the length of the wave of the electrical oscillation which excites a wireformed resonator is equal (allowance being made for the micrometer perturbation) to double the length of the resonator." That a perturbation set up at the spark-gap is not, however, responsible for any apparent discrepancy between theory and experiment, was shown by the work of Strindbergt, who confirmed Sarasin & De la Rive's results with a resonator in which no spark occurred. If Turpain has interpreted his experiments aright, his results must be considered at variance with the great body of experimental evidence and with present theory.

Drude (loc. cit. p. 330) gives the measures of the wave-length of the vibration connected with four open circles, three of them being supported by wooden cores and one being wholly surrounded by air. For the latter, the half wave-length is 259 cms. when the length of the wire is 243 cms., the ratio * Sarasin & De la Rive, C. R. vol. cx. 1890, vol. cxii. 1891, vol. cxv. 1892.

+ Strindberg, C. R. vol. cxxii. p. 1403 (1896).

being 1065. Drude concludes from this experiment that "the half natural wave-length of a nearly closed thin wire circle is 65 per cent. greater than its length." This value I believe to be far too small.

With the circuits used, the present experiments give for the ratio of the perimeters of rectangles 30 cms. in width to the lengths of open circular circuits, when both have the same period of vibration, values varying from 2:38 for a rectangle with a perimeter of 760 cms., to 2:28 for one whose perimeter is 1050 cms., the gaps in the circles being about 15 cms. long to avoid any appreciable capacity effect due to the proximity of the ends of the circuit.

Comparing this result with that given just above for straight wires, it is found that the electrical vibration connected with a wire bent into the form of a circle, with a considerable gap in its circumference, has a shorter period than that associated with a straight wire of the same length. The actual result obtained is that a copper wire 0:33 cm. in diameter, if bent into the form of a circular arc, with its ends separated by a distance of about 15 cms., requires to be 32 per cent. longer than a straight wire of the same gauge 310 cms. long to give a radiation of the same wave-length, and 34 per cent. longer than a straight wire 445 cms. in length. This result is to be expected when the ends of the circular arc are not brought too closely together, as the inductance of the wire is less in the circular form than when straight and the capacity is practically unaltered (see Thomson, Recent Researches,' § 385).

A further decrease of inductance without appreciable change of capacity can be made by bending the wire forming the open circle into the shape of a narrow rectangle with an open end. One would expect, therefore, the period of vibration in such a circuit to be somewhat less than that in an open circle of the same perimeter. That the periods of electrical vibration connected with such circuits are, at least. nearly equal when the perimeters are the same, is shown by a result obtained by Sarasin & De la Rive* in connexion with their experiments with waves along wires. In these experiments it was found that the distance from the free ends of the wires to the first node was nearly equal to half the circumference of the resonator, and in such a case of parallel wires with free ends, the end section may be considered to correspond with an open rectangle. Macdonald, ‘Electric Waves,' p. 121, in giving the distance to the first node from the end of the wire as 0.1922, makes the ratio of wave-length

* Sarasin & De la Rive, C. R. vol. cx. 1890.

to perimeter of open rectangle 260, or the period of vibration in such a circuit longer than in the case of an open circle of the same perimeter. Bumstead, in the Am. Journ. Sci. vol. xiv. p. 359 (1902), investigates theoretically the reflexion of electric waves at the free ends of a parallel wire system. If I understand the result aright, it means that the distance from the free end of the wire to the first node is always less than a quarter the wave-length along the wires by half the distance between them. This cannot be generally true.

Kiebitz (Ann. der Physik, v. 4, p. 872, 1901) has found the length of an open circle resonator when in tune with a straight-rod oscillator. The rod being 250 cms. long, 248 cms. was finally taken as the resonance-length for the open circle, a result slightly different from that given above, where the distance between the ends of the resonator was much greater than in Kiebitz's experiment.

Sarasin & De la Rive, as the result of their final measurements*, give the wave-length of the vibration connected with open resonators, made of stout wire 1 cm. in diameter, as 600 cms. for an open circle 234 cms. in circumference, and 400 cms. for one 156 cms. in circumference. This makes the wave-length 2:56 times the length of the circuit.

Macdonald, Electric Waves,' p. 111, in considering the question of stationary waves in open circuits, calculates the wave-length for any resonator, and finds for the fundamental mode of vibration, A=2531 where is the length of the circuit, a value in wonderful agreement with Sarasin & De la Rive's conclusions. Apparently, according to theory, the wave-length is independent, within wide limits, of the diameter of the wire of which the resonator is made, and the ratio of wave-length to length of circuit independent of the size of the circle.

By extrapolation (see fig. 2) the present experiments give, for a circle 200 ems in circumference, the ratio of perimeter of rectangle to length of circuit 2:45. This is less than the ratio of wave-length to circumference as given above by Sarasin & De la Rive for a similar-sized circle and as calculated by Macdonald. In considering the difference it is necessary to remember that extra capacity effects at the ends of the resonator may not have been altogether negligible in Sarasin & De la Rive's apparatus. On the other hand, the wavelength of the vibration connected with narrow rectangular closed circuits, made of wire of finite thickness, may be a little longer than their perimeters. Again, the wave-length

* Sarasin & De la Rive, C. R. vol. cxv. p. 1280 (1892).