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7 - The Mechanical Description of Equipotential Lines

Published online by Cambridge University Press:  07 September 2010

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Summary

Fig. 1 represents two Peaucellier's cells, of which O1, O2 are the respective fulcra, which are fixed; A, P and B, P the poles. Let the moduli of the cells be respectively proportional to two charges of positive electricity at O1 and O2. Thus O1A = m1/O1P, O2B = m2/O2P, so that, if O1A + O2B is constant, P traces the equipotential line of m1 and m2 placed at O1 and O2 respectively. The constancy of O1A + O2B may be attained thus: Let the pivots at O1, O2, about which the cells turn, be two needles; fasten a piece of pack-thread to A, pass it round O1, round another needle E (driven into the drawing-board), round O2, and fasten the other end to B. The broken line in Fig. 1 represents this thread. Then, if P is moved so as to keep the thread taut, it describes one of the equipotential lines. If the needle E is shifted to F and G, we get other equipotential lines.

Fig. 2 represents the arrangement of the thread where one of the charges is negative. In this and the succeeding figures, fixed points are marked with crosses, and the needles are exaggerated so as to show the disposition of the strings, and the bars of the cells are omitted, leaving only the tracing point P and the other poles marked.

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The Scientific Papers of Sir George Darwin
Periodic Orbits and Miscellaneous Papers
, pp. 269 - 271
Publisher: Cambridge University Press
Print publication year: 2009
First published in: 1911

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