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| '''Barlow's law''' was an incorrect [[physical law]] proposed by [[Peter Barlow (mathematician)|Peter Barlow]] in 1825 to describe the ability of wires to conduct [[electricity]].<ref name=Barlow/><ref name=Mining/> It said that the strength of the effect of electricity passing through a [[wire]] varies inversely with the square root of its length and directly with the square root of its cross-sectional area, or, in modern terminology:
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| ::<math>I \propto \sqrt\frac{A}{L}</math>
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| where ''I'' is [[electric current]], ''A'' is the cross-sectional area of the wire, and ''L'' is the length of the wire. Barlow formulated his law in terms of the diameter ''d'' of a cylindrical wire. Since ''A'' is proportional to the square of ''d'' the law becomes <math>I \propto \frac{d}{\sqrt{L}}</math> for cylindrical wires.<ref name=Mining/>
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| Barlow undertook his experiments with the aim of determining whether long-distance [[electrical telegraph|telegraphy]] was feasible, and believed he proved that it was not.<ref name=Barlow/> Importantly, Barlow failed to recognize the dependence of the current strength on electric tension (that is, [[voltage]]) so neglected the possibility of solutions such as a high-intensity battery or step-up voltage converters to allow long-distance telegraphy. The publication of Barlow's law delayed research into telegraphy for several years, until 1831, when [[Joseph Henry]] and [[Philip Ten Eyck]] constructed a circuit 1,060 feet long, which used a large battery to activate an [[electromagnet]].<ref name=Schiffer/>
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| In 1827, [[Georg Ohm]] published a different law, stating that the current varies inversely with the wire's length, not its square root and varies directly with [[voltage]] (V); that is, <math>I \propto \frac{A}{L}\cdot V</math>. Experiments by a variety of scientists proved [[Ohm's law]] correct and Barlow's false.
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| == References ==
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| {{reflist|refs=
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| <ref name="Barlow">{{cite journal | title=On the Laws of Electro-Magnetic Action as depending on the Length and Dimensions of the conducting Wire and on the question Whether Electrical Phenomena are due to the transmission of a single or of a compound fluid? | last=Barlow | first=Peter | journal=Edinburgh Philosophical Journal | year=1825 | volume=12 | pages=[http://books.google.com/books?id=SYxKAAAAcAAJ&pg=PA105 105–113]}}</ref>
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| <ref name=Mining>{{cite book | last = Aligny | first = Henry Ferdinand Quarré | authorlink = | coauthors = Alfred Huet, F. Geyler, C. Lepainteur | title = Report on Mining and the Mechanical Preparation of Ores | publisher = United States of America Government Printing Office | date = 1870 | location = | pages = [http://books.google.com/books?id=Dg4LAAAAIAAJ&pg=PA9 9–10] | url = | doi = | id = | isbn = | quote = Barlow's law was, 'that the conductibility was inversely proportionate to the square root of the lengths and directly as the diameters of the wires or as the square roots of their sections.' }}</ref>
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| <ref name=Schiffer>{{cite book | last = Schiffer | first = Michael | authorlink = | coauthors = | title = Power Struggles: Scientific Authority and the Creation of Practical Electricity Before Edison | publisher = MIT Press | date = 2008 | location = | pages = [http://books.google.com/books?id=8yCle7H0Q_QC&pg=PA43 43–45] | url = | doi = | id = | isbn = 0-262-19582-8 | quote = Barlow's law had devastating implications for anyone who might have considered building an electromagnetic telegraph. Transmitted over a long distance, the current would be undetectable. Indeed, Barlow reported, 'I found such a sensible diminution with only 200 feet of wire, as at once to convince me of the impracticability of the scheme.'}}</ref>
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| {{DEFAULTSORT:Barlow's Law}}
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| [[Category:Circuit theorems]]
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| [[Category:History of science]]
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| [[Category:Obsolete scientific theories]]
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