It is found that the resistance of a linear conductor of uniform cross-section is proportional (1) directly to the length of the conductor, (2) inversely to the area of its cross-section and (3) directly- to a certain nu• merical factor 'Characteristic of each material, and which is called the. resistances of the material. The sspecific resistance' (or of a substance is the resistance, at the freezing point'Of water, of a conductor composed of the kiveni substance, and having a length of one centimeter and a _cross-section of one SQnfire centimeter, The specific resist ance of metal- varies to a certain extent with physical condition-of the metal, but the values given in accompanying table will be found useful for many purposes: In practice; mercury columns are not used as standards 'of resistance, because they are not convenient to manipulate. The mercury column is selected in defining the (ohms for general purposes, because it is easy to obtain mercury in a satisfactory state of purity, and also because all uncertainties relating to in ternal stress and physical State are eliminated by the use of a fluid standard. An isolated ob server, for example, who wishes to construct a resistance of one ohm for experimental pur-.
poses, can do so- readily- enough by preparing a column of pure mercury of known length and cross-section. Ile can' then compute the re sistance•of this column, at the freezing. point of water, and in this way he can obtain a standard of considerable accuracy. In practi cal work, however, it is customary to employ, as standards of resistance, coils of wire that are wound upon spools or bobbins. These are standardized either by comparison with other coils whose resistance are known, or by di rect comparison with a mercury column of known dimensions and assured purity. A bob bin that is wound with wire as an ordinary spool is wound with thread ,possesses a con siderable coefficient of self-induction if the length of wire is at all great; this tends to impair its efficiency as a standard, because in the practical measurement of resistance it is desirable to have the self-induction of the standard as small as possible. Standard resist ance coils are, therefore, wound in a special way, with the idea of reducing the self-induc tion as much as possible. One-half of the wire is wound about the central core (or spool) in one direction, and the other half is wound in the opposite direction so that if an iron core were placed in the axis of the spool, and a current were sent through coil, the magnetic effect upon the central iron core would be zero. By winding the wire in this way, the self-in duction of the coil may be rendered negligible.
The resistance of a conductor varies with temperature and, although the magnitude of the variation differs with different metals, and even with the physical state of any one metal, it may be taken, roughly, as increasing by about 0.21 of 1 per cent, for each Fahren
heit degree of rise of temperature, for copper and silver and several of the other pure metals. The resistance of liquid mercury increases much more slowly with temperature, the coefficient of mercury being only about one-fifth of that stated above. The resistance of carbon dimin ishes as the temperature rises. In accurate electrical work it is evidently essential, in view of the variation of resistance with temperature, either to keep the temperature of the standard coils constant, or to ascertain the coefficient of Variation of resistance with temperature with considerable care, so that a suitable correction may be applied for any departure of the tem perature of the standard coils from the one temperature at which their resistances are ac curately known. In practice it is usual to de termine the temperature coefficient with as much accuracy as possible, and then to keep the temperature of the coil as near as prac ticable to the temperature at which it has been standardized. Any error in the determination of the temperature coefficient will then have but small effect upon the calculated resistance of the standard. Many attempts have been made to prepare alloys which shall have neg ligible temperature coefficient; and while no alloy has been found whose electrical resist ance is absolutely independent of the tempera ture, several have been prepared whose tern petature coefficients are quite small. German silver is one of the commonest of these alloys, the composition of that which is used in the preparation of resistance wire being (by weight) four parts of copper, two of nickel and one of zinc. The specific resistance of this alloy is about 13 times that of copper, and its tem perature coefficient is only about 0.022 of 1 per cent, per degree Fahrenheit. (Platinum silver,)) as used for electrical resistance stand ards, is composed of two parts (by weight) of platinum to one part of silver. It has a specific resistance about 15 times as great as that of copper, and its temperature co efficient per Fahrenheit degree, is only about 0.017. of 1 per cent. (Manganin* has largely come into favor for electrical resistance stand ards in recent years, the composition recom mended by the Reichsanstalt being (by weight) 84 per cent of copper, 12 per cent of man ganese and 4 per cent of nickel. Its specific resistance is about 20 times that of copper, and its temperature coefficient is only about 0.0013 of 1 per cent per Fahrenheit degree, at ordinary temperatures; the coefficient di minishing as the temperature rises, until,. at about F., the coefficient becomes rigorously zero. At still higher temperatures, the coefficient of manganin becomes negative; but at all tem peratures it is so small that it can be neglected for all purposes save those in which the highest attainable degree of accuracy is required.