Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/458

is difficult, on account of the great resistance of these substances, to determine whether the feeble current which we can force through them is or is not associated with electrolysis.

On the Electric Resistance of Metals.

360.] There is no part of electrical research in which more numerous or more accurate experiments have been made than in the determination of the resistance of metals. It is of the utmost importance in the electric telegraph that the metal of which the wires are made should have the smallest attainable resistance. Measurements of resistance must therefore be made before selecting the materials. When any fault occurs in the line, its position is at once ascertained by measurements of resistance, and these measurements, in which so many persons are now employed, require the use of resistance coils, made of metal the electrical properties of which have been carefully tested.

The electrical properties of metals and their alloys have been studied with great care by MM. Matthiessen, Vogt, and Hockin, and by MM. Siemens, who have done so much to introduce exact electrical measurements into practical work.

It appears from the researches of Dr. Matthiessen, that the effect of temperature on the resistance is nearly the same for a considerable number of the pure metals, the resistance at 100°C being to that at 0°C in the ratio of 1.414 to 1, or of 1 to 70.7. For pure iron the ratio is 1.645, and for pure thallium 1.458.

The resistance of metals has been observed by Dr. C.W. Siemens^[1] through a much wider range of temperature, extending from the freezing point to 350°C, and in certain cases to 1000°C. He finds that the resistance increases as the temperature rises, but that the rate of increase diminishes as the temperature rises. The formula, which he finds to agree very closely both with the resistances observed at low temperatures by Dr. Matthiessen and with his own observations through a range of 1000°C, is

$r=\alpha T^{\frac {1}{2}}+\beta T\gamma$,

where $T$ is the absolute temperature reckoned from −273°C, and $\alpha ,\,\beta ,\,\gamma$ are constants. Thus, for

Platinum⁠	$r=0.039369T^{\frac {1}{2}}+0.00216407T-0.2413$,
Copper	$r=0.026577T^{\frac {1}{2}}+0.0031443T-0.22751$,
Iron	$r=0.072545T^{\frac {1}{2}}+0.0038133T-1.23971$.

1. Proc. R. S., April 27, 1871.