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Barlow's law was an incorrect physical law proposed by Peter Barlow in 1825 to describe the ability of wires to conduct electricity. 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:

$I\propto \sqrt{\frac{A}{L}}$

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 $I\propto \frac{d}{\sqrt{L}}$ for cylindrical wires.

Barlow undertook his experiments with the aim of determining whether long-distance telegraphy was feasible, and believed he proved that it was not. 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.

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, $I\propto \frac{A}{L}\cdot V$. Experiments by a variety of scientists proved Ohm's law correct and Barlow's false.

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