I. CONDUCTION IN SOLIDS_Encyclopaedia Britannica, 11th Edition, "Conduction, Electric" Volume 6, Slice 8

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 [rho] for the

volume-resistivity we have 10^9R = [rho]l/s; but lsd = M, where M is

the mass of the wire. Hence 10^9R = [rho]dl^2/M. If l = 100 and M = 1,

then R = [rho]'= resistivity in ohms per metre-gramme, and 10^9[rho]'

= 10,000d[rho], or [rho] = 10^5[rho]'/d, and [rho]' = 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 deg. C.,

or Resistance per Metre-gramme in International Ohms at 0 deg. C._

(Matthiessen.)

+---------------------+---------------------+-------------+

| | Resistance at 0 deg.| |

| | C. in International | Approximate |

| Metal. | Ohms of a Wire | Temperature |

| | 1 Metre long and | Coefficient |

| | Weighing | near 20 |

| | 1 Gramme. | deg. 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[1] | .. |

|Tin (pressed) | .9618 | 0.00365 |

|Lead (pressed) | 2.2268 | 0.00387 |

|Antimony (pressed) | 2.3787 | 0.00389 |

|Bismuth (pressed) | 12.8554[1] | 0.00354 |

|Mercury (liquid) | 12.885[2] | 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 ([pi]/4) X 0.9866 X 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 deg.

C., or Resistance per Centimetre-cube in C.G.S. Units at 0 deg. C._

+---------------------+---------------------+

| | Volume-Resistivity. |

| Metal. | at 0 deg. C. in |

| | C.G.S. Units |

+---------------------+---------------------+

|Silver (annealed) | 1,502 |

|Silver (hard-drawn) | 1,629 |

|Copper (annealed) | 1,594 |

|Copper (hard-drawn) | 1,630[3] |

|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[4] |

|Tin (pressed) | 13,178 |

|Lead (pressed) | 19,580 |

|Antimony (pressed) | 35,418 |

|Bismuth (pressed) | 130,872 |

|Mercury (liquid) | 94,896[5] |

+---------------------+---------------------+

TABLE III.--_Electric Volume-Resistivity of Various Metals at 0 deg.

C., or Resistance per Centimetre-cube at 0 deg. C. in C.G.S. Units._

(Fleming and Dewar, _Phil. Mag._, September 1893.)

+--------------------------+------------------+------------------+

| | Resistance | Mean Temperature |

| Metal. | at 0 deg. C. per | Coefficient |

| | Centimetre-cube | between 0 deg. C.|

| | in C.G.S. Units. | and 100 deg. C. |

+--------------------------+------------------+------------------+

|Silver (electrolytic and | | |

| well annealed)[6] | 1,468 | 0.00400 |

|Copper (electrolytic and | | |

| well annealed)[6] | 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] | 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)[7] | 110,000 | 0.00433 |

+--------------------------+------------------+------------------+

_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 deg. C.; and (b) in terms of the

length in centimetres of a column of mercury one square millimetre in

cross-section taken at 0 deg. C. The result of all the most careful

determinations has been to show that the resistivity of pure mercury

at 0 deg. 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 deg. 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 IV.--_Determinations of the Absolute Value of the

Volume-Resistivity of Mercury and the Mercury Equivalent of the

Ohm._

+-----------------+------+----------------------+--------+----------+---------+

+-----------------+------+----------------------+--------+----------+---------+

|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 |

| | | deg. | | | |

|E. E. N. Mascart | 1884 | Induced current | .98611 | .94096 | 106.33 |

|H. A. Rowland | 1887 | Mean of several | .98644 | .94071 | 106.32 |

|F. Kohlrausch | 1887 | Damping of magnets | .98660 | .94061 | 106.32 |

|R. T. Glazebrook | 1882 | Induced currents | .98665 | .94074 | 106.29 |

| | 1888 | | | | |

|Wuilleumeier | 1890 | | .98686 | .94077 | 106.31 |

|Duncan and Wilkes| 1890 | Lorenz | .98634 | .94067 | 106.34 |

|J. V. Jones | 1891 | Lorenz | .. | .94067 | 106.31 |

| | | +--------+----------+---------+

| | | | | |

|Streker | 1885 | An absolute determin-| | .94056 | 106.32 |

|Hutchinson | 1888 | ation of resistance| | .94074 | 106.30 |

|E. Salvioni | 1890 | was not made. The | | .94054 | 106.33 |

|E. Salvioni | .. | value .98656 has | | .94076 | 106.30 |

| | | | +----------+---------+

| | | Mean value .94076 | 106.31 |

| | | | |

|F. Himstedt | 1885 | | by Siemens and | 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 deg. C.

For many purposes it is more convenient to express temperature in

Fahrenheit degrees, and the recommendation of the 1899 committee on

copper conductors[8] 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 deg. 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 1-1/4% 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 deg. C. is 0.1421 international ohms, or at 60 deg. 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 deg. F. Hence the volume-resistivity of pure annealed

copper at 0 deg. C. is 1.594 microhms per c.c., or 1594 C.G.S. units,

and that of pure hard-drawn copper at 0 deg. 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

deg. C. of a number of well-known alloys, with their chemical

composition.

TABLE V.--_Volume-Resistivity of Alloys of known Composition at 0 deg.

C. in C.G.S. Units per Centimetre-cube. Mean Temperature Coefficients

taken at 15 deg. C._ (Fleming and Dewar.)

+-----------------------+-----------+-------------+-------------------+

+-----------------------+-----------+-------------+-------------------+

|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|

|German silver | 29,982 | .000273 |Cu5Zn3Ni2 |

|Platinoid[9] | 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 5-1/2 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 deg. C._

+-----------------------------------------+---------------+

| Substance. | Resistivity. |

+-----------------------------------------+---------------+

| Arc lamp carbon rod | 8000 |

| Jablochkoff candle carbon | 4000 |

| Carre 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._

+---------------------------+----------------+---------------------+

| | Resistivity | |

| Substance. | in Megohms | Observer. |

| | per c.c. | |

+---------------------------+----------------+---------------------+

| Ethyl alcohol | 0.5 | Pfeiffer. |

| Ethyl ether | 1.175 to 3.760 | W. Kohlrausch. |

| Benzene | 4.700 | |

| Absolutely pure water | 25.0 at 18 deg.| Value estimated |

| approximates probably to | C. | by F. Kohlrausch |

| | | and A. Heydweiler. |

| All very dilute aqueous | 1.00 at 18 deg.| From results by |

| salt solutions having a | C. | F. Kohlrausch |

| concentration of about | | and others. |

| 0.00001 of an equivalent | | |

| gramme molecule[10] 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.).

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 deg. 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 deg. 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 deg. C. and 100 deg. 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 deg. C. to 24 deg.

C. is sufficient to reduce the resistivity of one-twentieth part of its

value at 0 deg. C., and the resistivity of flint glass at 140 deg. C. is

only one-hundredth of what it is at 60 deg. C.

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._

+------------------------+---------------------------+----------+

| | Resistivity. | |

| +------------+--------------+ Tempera- |

+------------------------+------------+--------------+----------+

|Bohemian glass | 61 | .061 | 60 deg. |

|Mica | 84 | .084 | 20 deg. |

|Gutta-percha | 450 | .45 | 24 deg. |

|Flint glass | 1,020 | 1.02 | 60 deg. |

| indiarubber | 1,630 | 1.63 | 15 deg. |

| vulcanized indiarubber | 2,280 | 2.28 | 15 deg. |

|Shellac | 9,000 | 9.0 | 28 deg. |

|Indiarubber | 10,900 | 10.9 | 24 deg. |

| fibrous material | 11,900 | 11.9 | 15 deg. |

| indiarubber. | 16,170 | 16.17 | 15 deg. |

|Flint glass | 20,000 | 20.0 | 20 deg. |

|Ebonite | 28,000 | 28. | 46 deg. |

|Paraffin | 34,000 | 34. | 46 deg. |

+------------------------+------------+--------------+----------+

A definition may here be given of the meaning of the term _Temperature

Coefficient_. If, in the first place, we suppose that the resistivity

([rho]t) at any temperature (t) is a simple linear function of the

resistivity ([rho]0) at 0 deg. C., then we can write [rho]t = [rho]0(1

+ [alpha]t), or [alpha] = ([rho]t - [rho]0)/[rho]0t.

The quantity [alpha] 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

d[rho]/[rho]dt the temperature coefficient corresponding to any

temperature t at which the resistivity is [rho]. 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 deg. C. to +200 deg. 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 deg..5

C., +100 deg. C., 0 deg. C., -78 deg..2 C. and -182 deg..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 deg. C. and -273 deg. 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 deg. 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 deg. C. is 0.0057; at 765 deg. C. it rises

to a maximum value 0.0204; but at 1000 deg. 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

[rho]t = [rho]32 {1 + 0.0023708(t - 32) + 0.0000034548(t - 32)^2}.

_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 deg. 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 deg. 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.)

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