# 1911 Encyclopædia Britannica/Conduction, Electric/Solids

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I. Conduction in Solids
It is found convenient to express the resistivity of metals in two different ways: (1) We may state the resistivity of one cubic centimetre of the material in microhms or absolute units taken between opposed faces. This is called the volume-resistivity; (2) we may express the resistivity by stating the resistance in ohms offered by a wire of the material in question of uniform cross-section one metre in length, and one gramme in weight. This numerical measure of the resistivity is called the mass-resistivity. The mass-resistivity of a body is connected with its volume-resistivity and the density of the material in the following manner:—The mass-resistivity, expressed in microhms per metre-gramme, divided by 10 times the density is numerically equal to the volume-resistivity per centimetre-cube in absolute C.G.S. units. The mass-resistivity per metre-gramme can always be obtained by measuring the resistance and the mass of any wire of ​uniform cross-section of which the length is known, and if the density of the substance is then measured, the volume-resistivity can be immediately calculated.
If R is the resistance in ohms of a wire of length l, uniform cross-section s, and density d, then taking ρ for the volume-resistivity we have 10$^9$R = ρl/s; but lsd = M, where M is the mass of the wire. Hence 10$^9$R = ρdl$^2$/M. If l = 100 and M = 1, then R = ρ′;= resistivity in ohms per metre-gramme, and 10$^9$ρ′; = 10,000dρ, or ρ = 10$^5$ρ′;/d, and ρ′; = 10,000MR/l$^2$.
The following rules, therefore, are useful in connexion with these measurements. To obtain the mass-resistivity per metre-gramme of a substance in the form of a uniform metallic wire:—Multiply together 10,000 times the mass in grammes and the total resistance in ohms, and then divide by the square of the length in centimetres. Again, to obtain the volume-resistivity in C.G.S. units per centimetre-cube, the rule is to multiply the mass-resistivity in ohms by 100,000 and divide by the density. These rules, of course, apply only to wires of uniform cross-section. In the following Tables I., II. and III. are given the mass and volume resistivity of ordinary metals and certain alloys expressed in terms of the international ohm or the absolute C.G.S. unit of resistance, the values being calculated from the experiments of A. Matthiessen (1831–1870) between 1860 and 1865, and from later results obtained by J. A. Fleming and Sir James Dewar in 1893.
Table I.—Electric Mass-Resistivity of Various Metals at 0° C., or Resistance per Metre-gramme in International Ohms at 0° C. (Matthiessen.)
| Metal. | Resistance at 0° C. in International Ohms of a Wire 1 Metre long and Weighing 1 Gramme. | Approximate Temperature Coefficient near 20° C. |
| Silver (annealed) | .1523 | 0.00377 |
| Silver (hard-drawn) | .1657 | .. |
| Copper (annealed) | .1421 | 0.00388 |
| Copper (hard-drawn) | .1449 (Matthiessen’s | Standard) |
| Gold (annealed) | .4025 | 0.00365 |
| Gold (hard-drawn) | .4094 | .. |
| Aluminium (annealed) | .0757 | .. |
| Zinc (pressed) | .4013 | .. |
| Platinum (annealed) | 1.9337 | .. |
| Iron (annealed) | .765 | .. |
| Nickel (annealed) | 1.058 | .. |
| Tin (pressed) | .9618 | 0.00365 |
| Lead (pressed) | 2.2268 | 0.00387 |
| Antimony (pressed) | 2.3787 | 0.00389 |
| Bismuth (pressed) | 12.8554 | 0.00354 |
| Mercury (liquid) | 12.885 | 0.00072 |
The data commonly used for calculating metallic resistivities were obtained by A. Matthiessen, and his results are set out in the Table II. which is taken from Cantor lectures given by Fleeming Jenkin in 1866 at or about the date when the researches were made. The figures given by Jenkin have, however, been reduced to international ohms and C.G.S. units by multiplying by (π/4)×0.9866 × 10$^5$ = 77,485.
Subsequently numerous determinations of the resistivity of various pure metals were made by Fleming and Dewar, whose results are set out in Table III.
Table II.—Electric Volume-Resistivity of Various Metals at 0° C., or Resistance per Centimetre-cube in C.G.S. Units at 0° C.
| Metal. | Volume-Resistivity. at 0° C. in C.G.S. Units |
| Silver (annealed) | 1,502 |
| Silver (hard-drawn) | 1,629 |
| Copper (annealed) | 1,594 |
| Copper (hard-drawn) | 1,630 |
| Gold (annealed) | 2,052 |
| Gold (hard-drawn) | 2,090 |
| Aluminium (annealed) | 3,006 |
| Zinc (pressed) | 5,621 |
| Platinum (annealed) | 9,035 |
| Iron (annealed) | 10,568 |
| Nickel (annealed) | 12,429 |
| Tin (pressed) | 13,178 |
| Lead (pressed) | 19,580 |
| Antimony (pressed) | 35,418 |
| Bismuth (pressed) | 130,872 |
| Mercury (liquid) | 94,896 |
Resistivity of Mercury.—The volume-resistivity of pure mercury is a very important electric constant, and since 1880 many of the most competent experimentalists have directed their attention to the determination of its value. The experimental process has usually been to fill a glass tube of known dimensions, having large cup-like extensions at the ends, with pure mercury, and determine the absolute resistance of this column of metal. For the practical details of this method the following references may be consulted:—“The Specific Resistance of Mercury,” Lord Rayleigh and Mrs Sidgwick, Phil. Trans., 1883, part i. p. 173, and R. T. Glazebrook, Phil. Mag., 1885, p. 20; “On the Specific Resistance of Mercury,” R. T. Glazebrook and T. C. Fitzpatrick, Phil. Trans., 1888, p. 179, or Proc. Roy. Soc., 1888, p. 44, or Electrician, 1888, 21, p. 538; “Recent Determinations of the Absolute Resistance of Mercury,” R. T. Glazebrook, Electrician, 1890, 25, pp. 543 and 588. Also see J. V. Jones, “On the Determination of the Specific Resistance of Mercury in Absolute Measure,” Phil. Trans., 1891, A, p. 2. Table IV. gives the values of the volume-resistivity of mercury as determined by various observers, the constant being expressed (a) in terms of the resistance in ohms of a column of mercury one millimetre in cross-section and 100 centimetres in length, taken at 0° C.; and (b) in terms of the length in centimetres of a column of mercury one square millimetre in cross-section taken at 0° C. The result of all the most careful determinations has been to show that the resistivity of pure mercury at 0° C. is about 94,070 C.G.S. electromagnetic units of resistance, and that a column of mercury 106.3 centimetres in length having a cross-sectional area of one square millimetre would have a resistance at 0° C. of one international ohm. These values have accordingly been accepted as the official and recognized values for the specific resistance of mercury, and the definition of the ohm. The table also states the methods which have been adopted by the different observers for obtaining the absolute value of the resistance of a known column of mercury, or of a resistance coil afterwards compared with a known column of mercury. A column of figures is added showing the value in fractions of an international ohm of the British Association Unit (B.A.U.), formerly supposed to represent the true ohm. The real value of the B.A.U. is now taken as .9866 of an international ohm.
Table III.—Electric Volume-Resistivity of Various Metals at 0° C., or Resistance per Centimetre-cube at 0° C. in C.G.S. Units. (Fleming and Dewar, Phil. Mag., September 1893.)
| Metal. | Resistance at 0° C. per Centimetre-cube in C.G.S. Units. | Mean Temperature Coefficient between 0° C. and 100° C. |
| Silver (electrolytic and well annealed) | 1,468 | 0.00400 |
| Copper (electrolytic and well annealed) | 1,561 | 0.00428 |
| Gold (annealed) | 2,197 | 0.00377 |
| Aluminium (annealed) | 2,665 | 0.00435 |
| Magnesium (pressed) | 4,355 | 0.00381 |
| Zinc | 5,751 | 0.00406 |
| Nickel (electrolytic) | 6,935 | 0.00618 |
| Iron (annealed) | 9,065 | 0.00625 |
| Cadmium | 10,023 | 0.00419 |
| Palladium | 10,219 | 0.00354 |
| Platinum (annealed) | 10,917 | 0.003669 |
| Tin (pressed) | 13,048 | 0.00440 |
| Thallium (pressed) | 17,633 | 0.00398 |
| Lead (pressed) | 20,380 | 0.00411 |
| Bismuth (electrolytic) | 110,000 | 0.00433 |
Table IV.—Determinations of the Absolute Value of the Volume-Resistivity of Mercury and the Mercury Equivalent of the Ohm.
| Observer. | Date. | Method. | Value of B.A.U. in Ohms. | Value of 100  Centimetres of  Mercury in Ohms. | Value of Ohm  in Centimetres  of Mercury. |
| Lord Rayleigh | 1882 | Rotating coil | .98651 | .94133 | 106.31 |
| Lord Rayleigh | 1883 | Lorenz method | .98677 | .. | 106.27 |
| G. Wiedemann | 1884 | Rotation through 180° | .. | .. | 106.19 |
| E. E. N. Mascart | 1884 | Induced current | .98611 | .94096 | 106.33 |
| H. A. Rowland | 1887 | Mean of several methods | .98644 | .94071 | 106.32 |
| F. Kohlrausch | 1887 | Damping of magnets | .98660 | .94061 | 106.32 |
| R. T. Glazebrook | $\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$1882 1888 | Induced currents | .98665 | .94074 | 106.29 |
| Wuilleumeier | 1890 | | .98686 | .94077 | 106.31 |
| Duncan and Wilkes | 1890 | Lorenz | .98634 | .94067 | 106.34 |
| J. V. Jones | 1891 | Lorenz | .. | .94067 | 106.31 |
| | | Mean value | .98653 | | |
| Streker | 1885 | An absolute determination | | .94056 | 106.32 |
| Hutchinson | 1888 | of resistance was not | | .94074 | 106.30 |
| E. Salvioni | 1890 | made. The value .98656 | | .94054 | 106.33 |
| E. Salvioni | .. | value .98656 has been used | | .94076 | 106.30 |
| | | Mean value | Mean value | .94076 | 106.31 |
| H. F. Weber | 1884 | Induced current | Absolute measurements | Absolute measurements | 105.37 |
| H. F. Weber | .. | Rotating coil | compared with German | compared with German | 106.16 |
| A. Roiti | 1884 | Mean effect of induced current | silver wire coils issued by | silver wire coils issued by | 105.89 |
| F. Himstedt | 1885 | | Siemens and Streker | Siemens and Streker | 105.98 |
| F. E. Dorn | 1889 | Damping of a magnet | | | 106.24 |
| Wild | 1883 | Damping of a magnet | | | 106.03 |
| L. V. Lorenz | 1885 | Lorenz method | | | 105.93 |
For a critical discussion of the methods which have been adopted in the absolute determination of the resistivity of mercury, and the value of the British Association unit of resistance, the reader may be referred to the British Association Reports for 1890 and 1892 (Report of Electrical Standards Committee), and to the Electrician, 25, p. 456, and 29, p. 462. A discussion of the relative value of the results obtained between 1882 and 1890 was given by R. T. Glazebrook in a paper presented to the British Association at Leeds, 1890.
Resistivity of Copper.—In connexion with electro-technical work the determination of the conductivity or resistivity values of annealed and hard-drawn copper wire at standard temperatures is a very important matter. Matthiessen devoted considerable attention to this subject between the years 1860 and 1864 (see Phil. Trans., 1860, p. 150), and since that time much additional work has been carried out. Matthiessen’s value, known as Matthiessen’s Standard, for the mass-resistivity of pure hard-drawn copper wire, is the resistance of a wire of pure hard-drawn copper one metre long and weighing one gramme, and this is equal to 0.14493 international ohms at 0° C. For many purposes it is more convenient to express temperature in Fahrenheit degrees, and the recommendation of the 1899 committee on copper conductors is as follows:—“Matthiessen’s standard for hard-drawn conductivity commercial copper shall be considered to be the resistance of a wire of pure hard-drawn copper one metre long, weighing one gramme which at 60° F. is 0.153858 international ohms.” Matthiessen also measured the mass-resistivity of annealed copper, and found that its conductivity is greater than that of hard-drawn copper by about 2.25% to 2.5% As annealed copper may vary considerably in its state of annealing, and is always somewhat hardened by bending and winding, it is found in practice that the resistivity of commercial annealed copper is about 11/4% less than that of hard-drawn copper. The standard now accepted for such copper, on the recommendation of the 1899 Committee, is a wire of pure annealed copper one metre long, weighing one gramme, whose resistance at 0° C. is 0.1421 international ohms, or at 60° F., 0.150822 international ohms. The specific gravity of copper varies from about 8.89 to 8.95, and the standard value accepted for high conductivity commercial copper is 8.912, corresponding to a weight of 555 lb per cubic foot at 60° F. Hence the volume-resistivity of pure annealed copper at 0° C. is 1.594 microhms per c.c., or 1594 C.G.S. units, and that of pure hard-drawn copper at 0° C. is 1.626 microhms per c.c., or 1626 C.G.S. units. Since Matthiessen’s researches, the most careful scientific investigation on the conductivity of copper is that of T. C. Fitzpatrick, carried out in 1890. (Brit. Assoc. Report, 1890, Appendix 3, p. 120.) Fitzpatrick confirmed Matthiessen’s chief result, and obtained values for the resistivity of hard-drawn copper which, when corrected for temperature variation, are in entire agreement with those of Matthiessen at the same temperature.
The volume resistivity of alloys is, generally speaking, much higher than that of pure metals. Table V. shows the volume resistivity at 0° C. of a number of well-known alloys, with their chemical composition.
Table V.—Volume-Resistivity of Alloys of known Composition at 0° C. in C.G.S. Units per Centimetre-cube. Mean Temperature Coefficients taken at 15° C. (Fleming and Dewar.)
| Alloys. | Resistivity at 0° C. | Temperature Coefficient at 15° C. | Composition in per cents. |
| Platinum-silver | 31,582 | .000243 | Pt 33%, Ag 66% |
| Platinum-iridium | 30,896 | .000822 | Pt 80%, Ir 20% |
| Platinum-rhodium | 21,142 | .00143 | Pt 90%, Rd 10% |
| Gold-silver | 6,280 | .00124 | Au 90%, Ag 10% |
| Manganese-steel | 67,148 | .00127 | Mn 12%, Fe 78% |
| Nickel-steel | 29,452 | .00201 | Ni 4.35%, remaining percentage |
| | | | chiefly iron, but uncertain |
| German silver | 29,982 | .000273 | Cu$_5$Zn$_3$Ni$_2$ |
| Platinoid | 41,731 | .00031 | |
| Manganin | 46,678 | .0000 | Cu 84%, Mn 12%, Ni 4% |
| Aluminium-silver | 4,641 | .00238 | Al 94%, Ag 6% |
| Aluminium-copper | 2,904 | .00381 | Al 94%, Cu 6% |
| Copper-aluminium | 8,847 | .000897 | Cu 97%, Al 3% |
| Copper-nickel-aluminium | 14,912 | .000643 | Cu 87%, Ni 6.5%, Al 6.5% |
| Titanium-aluminium | 3,887 | .00290 | |
Generally speaking, an alloy having high resistivity has poor mechanical qualities, that is to say, its tensile strength and ductility are small. It is possible to form alloys having a resistivity as high as 100 microhms per cubic centimetre; but, on the other hand, the value of an alloy for electro-technical purposes is judged not merely by its resistivity, but also by the degree to which its resistivity varies with temperature, and by its capability of being easily drawn into fine wire of not very small tensile strength. Some pure metals when alloyed with a small proportion of another metal do not suffer much ​change in resistivity, but in other cases the resultant alloy has a much higher resistivity. Thus an alloy of pure copper with 3% of aluminium has a resistivity about 51/2 times that of copper; but if pure aluminium is alloyed with 6% of copper, the resistivity of the product is not more than 20% greater than that of pure aluminium. The presence of a very small proportion of a non-metallic element in a metallic mass, such as oxygen, sulphur or phosphorus, has a very great effect in increasing the resistivity. Certain metallic elements also have the same power; thus platinoid has a resistivity 30% greater than German silver, though it differs from it merely in containing a trace of tungsten.
The resistivity of non-metallic conductors is in all cases higher than that of any pure metal. The resistivity of carbon, for instance, in the forms of charcoal or carbonized organic material and graphite, varies from 600 to 6000 microhms per cubic centimetre, as shown in Table VI.:—
Table VI.—Electric Volume-Resistivity in Microhms per Centimetre-cube of Various Forms of Carbon at 15° C. :
| Substance. | Resistivity. |
| Arc lamp carbon rod | 8000 |
| Jablochkoff candle carbon | 4000 |
| Carré carbon | 3400 |
| Carbonized bamboo | 6000 |
| Carbonized parchmentized thread | 4000 to 5000 |
| Ordinary carbon filament from glow-lamp | |
| “treated” or flashed | 2400 to 2500 |
| Deposited or secondary carbon | 600 to  900 |
| Graphite | 400 to  500 |
The resistivity of liquids is, generally speaking, much higher than that of any metals, metallic alloys or non-metallic conductors. Thus fused lead chloride, one of the best conducting liquids, has a resistivity in its fused condition of 0.376 ohm per centimetre-cube, or 376,000 microhms per centimetre-cube, whereas that of metallic alloys only in few cases exceeds 100 microhms per centimetre-cube. The resistivity of solutions of metallic salts also varies very largely with the proportion of the diluent or solvent, and in some instances, as in the aqueous solutions of mineral acids; there is a maximum conductivity corresponding to a certain dilution. The resistivity of many liquids, such as alcohol, ether, benzene and pure water, is so high, in other words, their conductivity is so small, that they are practically insulators, and the resistivity can only be appropriately expressed in megohms per centimetre-cube.
In Table VII. are given the names of a few of these badly-conducting liquids, with the values of their volume-resistivity in megohms per centimetre-cube:—
Table VII.—Electric Volume-Resistivity of Various Badly-Conducting Liquids in Megohms per Centimetre-cube. :
| Substance. | Resistivity in Megohms per c.c. | Observer. |
| Ethyl alcohol | 0.5 | Pfeiffer. |
| Ethyl ether | 1.175 to 3.760 | W. Kohlrausch. |
| Benzene | 4.700 | |
| Absolutely pure water approximates probably to | 25.0 at 18° C. | Value estimated by F. Kohlrausch |
| | | and A. Heydweiler. |
| All very dilute aqueous salt solutions having a | 1.00 at 18° C. | From results by F. Kohlrausch |
| concentration of about 0.00001 of an equivalent | | and others. |
| gramme molecule per litre approximate to | | |
The resistivity of all those substances which are generally called dielectrics or insulators is also so high that it can only be appropriately expressed in millions of megohms per centimetre-cube, or in megohms per quadrant-cube, the quadrant being a cube the side of which is 10$^9$ cms. (see Table VIII.).
Table VIII.—Electric Volume-Resistivity of Dielectrics reckoned in Millions of Megohms (Mega-megohms) per Centimetre-cube, and in  Megohms per Quadrant-cube, i.e. a Cube whose Side is 10$^9$ cms. :
| Substance. | Resistivity. | Resistivity. | Temperature Cent. |
| Substance. | Mega-megohms per c.c. | Megohms per Quadrant-cube. | Temperature Cent. |
| Bohemian glass | 61 | .061 | 60° |
| Mica | 84 | .084 | 20° |
| Gutta-percha | 450 | .45 | 24° |
| Flint glass | 1,020 | 1.02 | 60° |
| Glover’s vulcanized indiarubber | 1,630 | 1.63 | 15° |
| Siemens’ ordinary pure vulcanized indiarubber | 2,280 | 2.28 | 15° |
| Shellac | 9,000 | 9.0 | 28° |
| Indiarubber | 10,900 | 10.9 | 24° |
| Siemens’ high-insulating fibrous material | 11,900 | 11.9 | 15° |
| Siemens’ special high-insulating indiarubber | 16,170 | 16.17 | 15° |
| Flint glass | 20,000 | 20.0 | 20° |
| Ebonite | 28,000 | 28. | 46° |
| Paraffin | 34,000 | 34. | 46° |
Effects of Heat.—Temperature affects the resistivity of these different classes of conductors in different ways. In all cases, so far as is yet known, the resistivity of a pure metal is increased if its temperature is raised, and decreased if the temperature is lowered, so that if it could be brought to the absolute zero of temperature (−273° C.) its resistivity would be reduced to a very small fraction of its resistance at ordinary temperatures. With metallic alloys, however, rise of temperature does not always increase resistivity: it sometimes diminishes it, so that many alloys are known which have a maximum resistivity corresponding to a certain temperature, and at or near this point they vary very little in resistance with temperature. Such alloys have, therefore, a negative temperature-variation of resistance at and above fixed temperatures. Prominent amongst these metallic compounds are alloys of iron, manganese, nickel and copper, some of which were discovered by Edward Weston, in the United States. One well-known alloy of copper, manganese and nickel, now called manganin, which was brought to the notice of electricians by the careful investigations made at the Berlin Physikalisch-Technische Reichsanstalt, is characterized by having a zero temperature coefficient at or about a certain temperature in the neighbourhood of 15° C. Hence within a certain range of temperature on either side of this critical value the resistivity of manganin is hardly affected at all by temperature. Similar alloys can be produced from copper and ferro-manganese. An alloy formed of 80% copper and 20% manganese in an annealed condition has a nearly zero temperature-variation of resistance between 20° C. and 100° C. In the case of non-metals the action of temperature is generally to diminish the resistivity as temperature rises, though this is not universally so. The interesting observation has been recorded by J. W. Howell, that “treated” carbon filaments and graphite are substances which have a minimum resistance corresponding to a certain temperature approaching red heat (Electrician, vol. xxxviii. p. 835). At and beyond this temperature increased heating appears to increase their resistivity; this phenomenon may, however, be accompanied by a molecular change and not be a true temperature variation. In the case of dielectric conductors and of electrolytes, the action of rising temperature is to reduce resistivity. Many of the so-called insulators, such as mica, ebonite, indiarubber, and the insulating oils, paraffin, &c., decrease in resistivity with great rapidity as the temperature rises. With guttapercha a rise in temperature from 0° C. to 24° C. is sufficient to reduce the resistivity of one-twentieth part of its value at 0° C., and the resistivity of flint glass at 140° C. is only one-hundredth of what it is at 60° C.
A definition may here be given of the meaning of the term Temperature Coefficient. If, in the first place, we suppose that the resistivity (ρ$_t$) at any temperature (t) is a simple linear function of the resistivity (ρ$_0$) at 0° C., then we can write ρ$_t$ = ρ$_0$(1 + αt), or α = (ρ$_t$ − ρ$_0$)/ρ$_0$t.
The quantity α is then called the temperature-coefficient, and its reciprocal is the temperature at which the resistivity would become ​ zero. By an extension of this notion we can call the quantity dρ/ρdt the temperature coefficient corresponding to any temperature t at which the resistivity is ρ. In all cases the relation between the resistivity of a substance and the temperature is best set out in the form of a curve called a temperature-resistance curve. If a series of such curves are drawn for various pure metals, temperature being taken as abscissa and resistance as ordinate, and if the temperature range extends from the absolute zero of temperature upwards, then it is found that these temperature-resistance lines are curved lines having their convexity either upwards or downwards. In other words, the second differential coefficient of resistance with respect to temperature is either a positive or negative quantity. An extensive series of observations concerning the form of the resistivity curves for various pure metals over a range of temperature extending from −200° C. to +200° C. was carried out in 1892 and 1893 by Fleming and Dewar (Phil. Mag. Oct. 1892 and Sept. 1893). The resistance observations were taken with resistance coils constructed with wires of various metals obtained in a state of great chemical purity. The lengths and mean diameters of the wires were carefully measured, and their resistance was then taken at certain known temperatures obtained by immersing the coils in boiling aniline, boiling water, melting ice, melting carbonic acid in ether, and boiling liquid oxygen, the temperatures thus given being +184°.5 C., +100° C., 0° C., −78°.2 C. and −182°.5 C. The resistivities of the various metals were then calculated and set out in terms of the temperature. From these data a chart was prepared showing the temperature-resistance curves of these metals throughout a range of 400 degrees. The exact form of these curves through the region of temperature lying between −200° C. and −273° C. is not yet known. As shown on the chart, the curves evidently do not converge to precisely the same point. It is, however, much less probable that the resistance of any metal should vanish at a temperature above the absolute zero than at the absolute zero itself, and the precise path of these curves at their lower ends cannot be delineated until means are found for fixing independently the temperature of some regions in which the resistance of metallic wires can be measured. Sir J. Dewar subsequently showed that for certain pure metals it is clear that the resistance would not vanish at the absolute zero but would be reduced to a finite but small value (see “Electric Resistance Thermometry at the Temperature of Boiling Hydrogen,” Proc. Roy. Soc. 1904, 73, p. 244).
The resistivity curves of the magnetic metals are also remarkable for the change of curvature they exhibit at the magnetic critical temperature. Thus J. Hopkinson and D. K. Morris (Phil. Mag. September 1897, p. 213) observed the remarkable alteration that takes place in the iron resistance temperature curve in the neighbourhood of 780° C. At that temperature the direction of the curvature of the curve changes so that it becomes convex upwards instead of convex downwards, and in addition the value of the temperature coefficient undergoes a great reduction. The mean temperature coefficient of iron in the neighbourhood of 0° C. is 0.0057; at 765° C. it rises to a maximum value 0.0204; but at 1000° C. it falls again to a lower value, 0.00244. A similar rise to a maximum value and subsequent fall are also noted in the case of the specific heat of iron. The changes in the curvature of the resistivity curves are undoubtedly connected with the molecular changes that occur in the magnetic metals at their critical temperatures.
A fact of considerable interest in connexion with resistivity is the influence exerted by a strong magnetic field in the case of some metals, notably bismuth. It was discovered by A. Righi and confirmed by S. A. Leduc (Journ. de Phys. 1886, 5, p. 116, and 1887, 6, p. 189) that if a pure bismuth wire is placed in a magnetic field transversely to the direction of the magnetic field, its resistance is considerably increased. This increase is greatly affected by the temperature of the metal (Dewar and Fleming, Proc. Roy. Soc. 1897, 60, p. 427). The temperature coefficient of pure copper is an important constant, and its value as determined by Messrs Clark, Forde and Taylor in terms of Fahrenheit temperature is
Time Effects.—In the case of dielectric conductors, commonly called insulators, such as indiarubber, guttapercha, glass and mica, the electric resistivity is not only a function of the temperature but also of the time during which the electromotive force employed to measure it is imposed. Thus if an indiarubber-covered cable is immersed in water and the resistance of the dielectric between the copper conductor and the water measured by ascertaining the current which can be caused to flow through it by an electromotive force, this current is found to vary very rapidly with the time during which the electromotive force is applied. Apart from the small initial effect due to the electrostatic capacity of the cable, the application of an electromotive force to the dielectric produces a current through it which rapidly falls in value, as if the electric resistance of the dielectric were increasing. The current, however, does not fall continuously but tends to a limiting value, and it appears that if the electromotive force is kept applied to the cable for a prolonged time, a small and nearly constant current will ultimately be found flowing through it. It is customary in electro-technical work to consider the resistivity of the dielectric as the value it has after the electromotive force has been applied for one minute, the standard temperature being 75° F. This, however, is a purely conventional proceeding, and the number so obtained does not necessarily represent the true or ohmic resistance of the dielectric. If the electromotive force is increased, in the case of a large number of ordinary dielectrics the apparent resistance at the end of one minute’s electrification decreases as the electromotive force increases.
Practical Standards.—The practical measurement of resistivity involves many processes and instruments (see Wheatstone’s Bridge and Ohmmeter). Broadly speaking, the processes are divided into Comparison Methods and Absolute Methods. In the former a comparison is effected between the resistance of a material in a known form and some standard resistance. In the Absolute Methods the resistivity is determined without reference to any other substance, but with reference only to the fundamental standards of length, mass and time. Immense labour has been expended in investigations concerned with the production of a standard of resistance and its evaluation in absolute measure. In some cases the absolute standard is constructed by filling a carefully-calibrated tube of glass with mercury, in order to realize in a material form the official definition of the ohm; in this manner most of the principal national physical laboratories have been provided with standard mercury ohms. (For a full description of the standard mercury ohm of the Berlin Physikalisch-Technische Reichsanstalt, see the Electrician, xxxvii. 569.) For practical purposes it is more convenient to employ a standard of resistance made of wire.
Opinion is not yet perfectly settled on the question whether a wire made of any alloy can be considered to be a perfectly unalterable standard of resistance, but experience has shown that a platinum silver alloy (66% silver, 33% platinum), and also the alloy called manganin, seem to possess the qualities of permanence essential for a wire-resistance standard. A comparison made in 1892 and 1894 of all the manganin wire copies of the ohm made at the Reichsanstalt in Berlin, showed that these standards had remained constant for two years to within one or two parts in 100,000. It appears, however, that in order that manganin may remain constant in resistivity when used in the manufacture of a resistance coil, it is necessary that the alloy should be aged by heating it to a temperature of 140° C. for ten hours; and to prevent subsequent changes in resistivity, solders containing zinc must be avoided, and a silver solder containing 75% of silver employed in soldering the manganin wire to its connexions.
The authorities of the Berlin Reichsanstalt have devoted considerable attention to the question of the best form for a wire standard of electric resistance. In that now adopted the resistance wire is carefully insulated and wound on a brass cylinder, being doubled on itself to annul inductance as much as possible. In the coil two wires are wound on in parallel, one being much finer than the other, and the final adjustment of the coil to an exact value is made by shortening the finer of the two. A standard of resistance for use in a laboratory now generally consists of a wire of manganin or platinum-silver carefully insulated and enclosed in a brass case. Thick copper rods are connected to the terminals of the wire in the interior of the case, and brought to the outside, being carefully insulated at the same time from one another and from the case. The coil so constructed can be placed under water or paraffin oil, the temperature of which can be exactly observed during the process of taking a resistance measurement. Equalization of the temperature of the surrounding medium is effected by the employment of a stirrer, worked by hand or by a small electric motor. The construction of a standard of electrical resistance consisting of mercury in a glass tube is an operation requiring considerable precautions, and only to be undertaken by those experienced in the matter. Opinions are divided on the question whether greater permanence in resistance can be secured by mercury-in-glass standards of resistance or by wire standards, but the latter are at least more portable and less fragile.
A full description of the construction of a standard wire-resistance coil on the plan adopted by the Berlin Physikalisch-Technische ​Reichsanstalt is given in the Report of the British Association Committee on Electrical Standards, presented at the Edinburgh Meeting in 1892. For the design and construction of standards of electric resistances adapted for employment in the comparison and measurement of very low or very high resistances, the reader may be referred to standard treatises on electric measurements.
Bibliography.—See also J. A. Fleming, A Handbook for the Electrical Laboratory and Testing Room, vol. i. (London, 1901); Reports of the British Association Committee on Electrical Standards, edited by Fleeming Jenkin (London, 1873); A. Matthiessen and C. Vogt, “On the Influence of Temperature on the Conducting Power of Alloys,” Phil. Trans., 1864, 154, p. 167, and Phil. Mag., 1865, 29, p. 363; A. Matthiessen and M. Holtzmann, “On the Effect of the Presence of Metals and Metalloids upon the Electric Conducting Power of Pure Copper,” Phil. Trans., 1860, 150, p. 85; T. C. Fitzpatrick, “On the Specific Resistance of Copper,” Brit. Assoc. Report, 1890, p. 120, or Electrician, 1890, 25, p. 608; R. Appleyard, The Conductometer and Electrical Conductivity; Clark, Forde and Taylor, Temperature Coefficients of Copper (London, 1901).  (J. A. F.)
* ↑ The values for nickel and bismuth given in the table are much higher than later values obtained with pure electrolytic nickel and bismuth.
* ↑ The value here given, namely 12.885, for the electric mass-resistivity of liquid mercury as determined by Matthiessen is now known to be too high by nearly 1%. The value at present accepted is 12.789 ohms per metre-gramme at 0° C.
* ↑ The value (1630) here given for hard-drawn copper is about ¼% higher than the value now adopted, namely, 1626. The difference is due to the fact that either Jenkin or Matthiessen did not employ precisely the value at present employed for the density of hard-drawn and annealed copper in calculating the volume-resistivities from the mass-resistivities.
* ↑ Matthiessen’s value for nickel is much greater than that obtained in more recent researches. (See Matthiessen and Vogt, Phil. Trans., 1863, and J. A. Fleming, Proc. Roy. Soc., December 1899.)
* ↑ Matthiessen’s value for mercury is nearly 1% greater than the value adopted at present as the mean of the best results, namely 94,070.
* ↑ The samples of silver, copper and nickel employed for these tests were prepared electrolytically by Sir J. W. Swan, and were exceedingly pure and soft. The value for volume-resistivity of nickel as given in the above table (from experiments by J. A. Fleming, Proc. Roy. Soc., December 1899) is much less (nearly 40%) than the value given by Matthiessen’s researches.
* ↑ The electrolytic bismuth here used was prepared by Hartmann and Braun, and the resistivity taken by J. A. Fleming. The value is nearly 20% less than that given by Matthiessen.
* ↑ In 1899 a committee was formed of representatives from eight of the leading manufacturers of insulated copper cables with delegates from the Post Office and Institution of Electrical Engineers, to consider the question of the values to be assigned to the resistivity of hard-drawn and annealed copper. The sittings of the committee were held in London, the secretary being A. H. Howard. The values given in the above paragraphs are in accordance with the decision of this committee, and its recommendations have been accepted by the General Post Office and the leading manufacturers of insulated copper wire and cables.
* ↑ Platinoid is an alloy introduced by Martino, said to be similar in composition to German silver, but with a little tungsten added. It varies a good deal in composition according to manufacture, and the resistivity of different specimens is not identical. Its electric properties were first made known by J. T. Bottomley, in a paper read at the Royal Society, May 5, 1885.
* ↑ An equivalent gramme molecule is a weight in grammes equal numerically to the chemical equivalent of the salt. For instance, one equivalent gramme molecule of sodium chloride is a mass of 58.5 grammes. NaCl = 58.5.