Barlow's law is an incorrect

physical law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...

proposed by Peter Barlow in 1825 to describe the ability of wires to conduct

electricity Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...

. It says that the strength of the effect of electricity passing through a

wire file:Sample cross-section of high tension power (pylon) line.jpg, Overhead power cabling. The conductor consists of seven strands of steel (centre, high tensile strength), surrounded by four outer layers of aluminium (high conductivity). Sample d ...

varies inversely with the square root of its length and directly with the square root of its cross-sectional area, or, in modern terminology: :

I \propto \sqrt\frac,

where ''I'' is

electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

, ''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

I \propto d/\sqrt

for cylindrical wires. Barlow undertook his experiments with the aim of determining whether long-distance

telegraphy Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas pi ...

was feasible and believed that he proved that it was not. The publication of Barlow's law delayed research into telegraphy for several years, until 1831 when

Joseph Henry Joseph Henry (December 17, 1797– May 13, 1878) was an American physicist and inventor who served as the first secretary of the Smithsonian Institution. He was the secretary for the National Institute for the Promotion of Science, a precursor ...

and Philip Ten Eyck constructed a circuit 1,060 feet long, which used a large battery to activate an

electromagnet An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire (likely copper) wound into a electromagnetic coil, coil. A current through the wire creates a magnetic ...

. Barlow did not investigate the dependence of the current strength on electric tension (that is,

voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...

). He endeavoured to keep this constant, but admitted there was some variation. Barlow was not entirely certain that he had found the correct law, writing "the discrepancies are rather too great to enable us to say, with confidence, that such is the law in question." In 1827,

Georg Ohm Georg Simon Ohm (; ; 16 March 1789 – 6 July 1854) was a German mathematician and physicist. As a school teacher, Ohm began his research with the new electrochemical cell, invented by Italian scientist Alessandro Volta. Using equipment of his o ...

published a different law, in which current varies inversely with the wire's length, not its square root; that is, :

I \propto \frac,

where

c

is a constant dependent on the circuit setup.

Ohm's law Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...

is now considered the correct law, and Barlow's false. The law Barlow proposed was not in error due to poor measurement; in fact, it fits Barlow's careful measurements quite well.

Heinrich Lenz Heinrich Friedrich Emil Lenz (; also Emil Khristianovich Lenz; ; 12 February 1804 – 10 February 1865), usually cited as Emil Lenz or Heinrich Lenz in some countries, was an Estonian physicist who is most noted for formulating Lenz's law in el ...

pointed out that Ohm took into account "all the conducting resistances … of the circuit", whereas Barlow did not. Ohm explicitly included a term for what we would now call the

internal resistance In electrical engineering, a practical electric power source which is a linear circuit may, according to Thévenin's theorem, be represented as an ideal voltage source in series with an impedance. This impedance is termed the internal resis ...

of the battery. Barlow did not have this term and approximated the results with a power law instead. Ohm's law in modern usage is rarely stated with this explicit term, but nevertheless an awareness of it is necessary for a full understanding of the current in a circuit.

References

{{DEFAULTSORT:Barlow's Law History of science Obsolete theories in physics