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3. On the Flow of Electricity in Conducting Surfaces

Published online by Cambridge University Press:  15 September 2014

W. R. Smith
W. R. Smith
Affiliation:
Assistant to the Professor of Natural Philosophy in theUniversity of Edinburgh.
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Extract

The conditions of a steady flow of electricity in a conducting surface are completely determined, if we know either the nature of the electrical distribution throughout the surface, or the direction and intensity of the flow at every point. On the first of these ways of considering the question, the problem is solved if we can express the potential v at any point as a function of the co-ordinates, and the nature of the distribution will be indicated to the eye by forming the equipotential curves

Type
Proceedings 1869-70
Information
Proceedings of the Royal Society of Edinburgh , Volume 7 , 1872 , pp. 79 - 99
Copyright
Copyright © Royal Society of Edinburgh 1872

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References

page 80 note * See Thomson and Tait's Natural Philosophy, i. 542.

page 80 note † Poggendorff's Annalen, Bd. lxiv.

page 81 note * Camb. and Dub. Math. Journ. vol. i. p. 124.

page 81 note † Cambridge Phil. Trans. vol x.

page 86 note * I have since found that this result has been already proved for plane curves by Professor Rankine and Professor Stokes (Proc. R.S., 1867), and for spherical harmonics by Sir W. Thomson and Professor Tait, in their treatise on Natural Philosophy.

page 96 note * That a greater variety of curves might be given, without overcrowding the figure, the two sides of one of the diagrams have been made unsymmetrical, some of the curves being given (in half) on the one side, others on the other.