Abstract
LONDON. Physical Society, February 25.—Prof. H. L. Callendar, F.R.S., president, in the chair.—Prof. J. Perry: Telephone Circuits. The author published a paper in the Proceedings of the society in 1893 showing how voltage v and current c are attenuated along a telephone or submarine telegraph line, a line with resistance r, capacity k, inductance l, and leakance s per unit length; currents are of the form sin qt. When lq/r is considerable the mathematical expressions become simple. It was pointed out that the introduction of l is of great benefit. The author now points out that k may be made negative by the use of inductance leaks to earth, and l may be made negative by the use of condensers in series with the line. To introduce l, as Mr. Pupin has done, by inductance coils at equidistant places on the line, or to introduce the other properties mentioned by placing other contrivances at equal distances, is a mathematical problem of great complexity. Contrivances placed close together have the same effect as the continuous distribution of properties, but there is considerable expense; the problem is to find how far apart the contrivances may be placed so that the effect produced shall still be beneficial. Mr. Pupin has given a rule for the spacing of his coils, but practical men dispute its accuracy; nobody has given a rule for other contrivances; the object of the author is to give an easy method of calculation which is practically correct, and can be used when the contrivance is any network or other combination of resistances, inductances, and capacities—some being leaks to earth—and it may include transformers, motors, and generators. Suppose there are contrivances at the equidistant places A, B, &c., m miles apart in a cable which has the above-mentioned properties r, k, l, and s. There is a contrivance the terminals of which are A and A0, another the terminals of which are B and B0; between A0 and B there is m miles of cable. Let the currents in the line at A, A0, and B be c, c0, and C. Let the voltages at these points be v, v0, and V. The assumption on which the whole method is based is that V/C = v/c = p. This is practically true everywhere in a long line except near the ends. Now whatever be the nature of the contrivance, we can calculate v0 and c0 from v and c. It is also known that
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Societies and Academies . Nature 83, 118–120 (1910). https://doi.org/10.1038/083118a0
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DOI: https://doi.org/10.1038/083118a0