Electric conduction
From LoveToKnow 1911
CONDUCTION, ELECTRIC. The electric conductivity of a substance is that property in virtue of which all its parts come spontaneously to the same electric potential if the substance is kept free from the operation of electric force. Accordingly, the reciprocal quality, electric resistivity, may be defined as a quality of a substance in virtue of which a difference of potential can exist between different portions of the body when these are in contact with some constant source of electromotive force, in such a manner as to form part of an electric circuit.
All material substances possess in some degree, large or small, electric conductivity, and may for the sake of convenience be broadly divided into five classes in this respect. Between these, however, there is no sharply-marked dividing line, and the classification must therefore be accepted as a more or less arbitrary one. These divisions are: (1) metallic conductors, (2) non-metallic conductors, (3) dielectric conductors, (4) electrolytic conductors, (5) gaseous conductors. The first class comprises all metallic substances, and those mixtures or combinations of metallic substances known as alloys. The second includes such non-metallic bodies as carbon, silicon, many of the oxides and peroxides of the metals, and probably also some oxides of the non-metals, sulphides and selenides. Many of these substances, for instance carbon and silicon, are well-known to have the property of existing in several allotropic forms, and in some of these conditions, so far from being fairly good conductors, they may be almost perfect non-conductors. An example of this is seen in the case of carbon in its three allotropic conditions - charcoal, graphite and diamond. As charcoal it possesses a fairly well-marked but not very high conductivity in comparison with metals; as graphite, a conductivity about one-four-hundredth of that of iron; but as diamond so little conductivity that the substance is included amongst insulators or nonconductors. The third class includes those substances which are generally called insulators or non-conductors, but which are better denominated dielectric conductors; it comprises such solid substances as mica, ebonite, shellac, india-rubber, guttapercha, paraffin, and a large number of liquids, chiefly hydrocarbons. These substances differ greatly in insulating power, and according as the conductivity is more or less marked, they are spoken of as bad or good insulators. Amongst the latter many of the liquid gases hold a high position. Thus, liquid oxygen and liquid air have been shown by Sir James Dewar to be almost perfect non-conductors of electricity.
The behaviour of substances which fall into these three classes is discussed below in section I., dealing with metallic conduction. The fourth class, namely the electrolytic conductors,`comprises all those substances which undergo chemical decomposition when they form part of an electric circuit traversed by an electric current. They are discussed in section II., dealing with electrolytic conduction.
The fifth and last class of conductors includes the gases. The conditions under which this class of substance becomes possessed of electric conductivity are considered in section III., on conduction in gases.
In connexion with metallic conductors, it is a fact of great interest and considerable practical importance, that, although the majority of metals when in a finely divided or powdered condition are practically non-conductors, a mass of metallic powder or filings may be made to pass suddenly into a conductive condition by being exposed to the influence of an electric wave. The same is true of the loose contact of two metallic conductors. Thus if a steel point, such as a needle, presses very lightly against a metallic plate, say of aluminium, it is found that this metallic contact, if carefully adjusted, is non-conductive, but that if an electric wave is created anywhere in the neighbourhood, this non-conducting contact passes into a conductive state. This fact, investigated and discovered independently by D. E. Hughes, C. Onesti, E. Branly, O. J. Lodge and others, is applied in the construction of the " coherer," or sensitive tube employed as a detector or receiver in that form of " wireless telegraphy " chiefly developed by Marconi. Further references to it are made in the articles Electric Waves and Telegraphy: Wireless.
International Ohm. - The practical unit of electrical resistance was legally defined in Great Britain by the authority of the queen in council in 1894, as the " resistance offered to an invariable electric current by a column of mercury at the temperature of melting ice, 14.4521 grammes in mass, of a constant cross-sectional area, and a length 106.3 centimetres." The same unit has been also legalized as a standard in France, Germany and the United States, and is denominated the " International or Standard Ohm." It is intended to represent as nearly as possible a resistance equal to 10° absolute C.G.S. units of electric resistance. Convenient multiples and subdivisions of the ohm are the microhm and the megohm, the former being a millionth part of an ohm, and the latter a million ohms. The resistivity of substances is then numerically expressed by stating the resistance of one cubic centimetre of the substance taken between opposed faces, and expressed in ohms, microhms or megohms, as may be most convenient. The reciprocal of the ohm is called the mho, which is the unit of conductivity, and is defined as the conductivity of a substance whose resistance is one ohm. The absolute unit of conductivity is the conductivity of a substance whose resistivity is one absolute C.G.S. unit, or one-thousandth-millionth part of an ohm. Resistivity is a quality in which material substances differ very widely. The metals and alloys, broadly speaking, are good conductors, and their resistivity is conveniently expressed in microhms per cubic centimetre, or in absolute C.G.S. units. Very small differences in density and in chemical purity make, however, immense differences in electric resistivity; hence the values given by different experimentalists for the resistivity of known metals differ to a considerable extent.
I. Conduction in Solids
It is found convenient to express the resistivity of metals in two different ways: (I) 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 crosssection 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 volumeresistivity and the density of the material in the following manner: - The mass-resistivity, expressed in microhms per metregramme, 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 1, uniform crosssection s, and density d, then taking p for the volume-resistivity we have i o 9 R = pl/s; but lsd = M, where M is the mass of the wire. Hence io, R= pol 2 /M. If l = Too and M =I, then R=p' =resistivity in ohms per metre-gramme, and io 9 p' = io,000dp, or p= 10 5 p'/d, and p' = io,000MR/l2.
The following rules, therefore, are useful in connexion with these measurements. To obtain the mass-resistivity per metregramme 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.
| Metal. | Resistance at 0° C. in International Ohms of a Wire I Metre long and Weighing 1 Gramme. | Approximate Tem- perature Co- efficient near 20° C. |
| Silver (annealed). . | 1523 | 0.00377 |
| Silver (hard-drawn) . | 16 57 | .. |
| Copper (annealed). . | 1421 | 0 o0388 |
| Copper (hard-drawn) . | (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). . | 1.0581 | |
| Tin (pressed).. . | .9618 | 0.00365 |
| Lead (pressed) . | 2.2268 | 0.00387 |
| Antimony (pressed) . | 2.3787 | 0.00389 |
| Bismuth (pressed. . | 12.85541 | 0.00354 |
| Mercury (liquid). . | 12.8852 | 0.00072 |
[[Table I]].- Electric Mass-Resistivity of Various Metals at o° C., or Resistance per Metre-gramme in International Ohms at o° C. (Matthiessen.) 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 Xo 9866X 105=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.
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. or Electrician, 1888, 21, p. 538; " Recent Determinations of the Absolute Resistance of Mercury," R. T. Glazebrook, Electrician, 1890, 2 5, 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 1 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 massresistivity 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 o° C.
| Metal. | Volume-Resistivity at o° C. in C.G.S. Units. |
| Silver (annealed) . | 1,502 |
| Silver (hard-drawn). ... . | 1,629 |
| Copper (annealed) . | 1,594 |
| Copper (hard-drawn) | 1,630 1 |
| 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 |
| Metal. | Resistance at o° C. per Centimetre- cube in C.G.S. Units. | Mean Temperature Coefficient between o C. and 100 C. |
| Silver (electrolytic and well annealed) 4 | 1,468 | 0.00400 |
| Copper (electrolytic and well annealed) 4.. | 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) 4 . | 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) 5 | 110,000 | 0.00433 |
[[Table Ii]].- Electric Volume-Resistivity of Various Metals at o° C., or Resistance per Centimetre-cube C.G.S. Units at o° C. various observers, the constant being expressed (a) in terms of the resistance in ohms of a column of mercury one millimetre in crosssection and 100 centimetres in length, taken at o° C.; and (b) in terms of the length in centimetres of a column of mercury one square millimetre in cross-section taken at o° C. The result of all the most careful determinations has been to show that the resistivity of pure mercury at o° 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 [[Table Ii]]I.- 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.) resistance at o° 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 1 The value (1630) here given for hard-drawn copper is about % 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.
2 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 I % greater than the value adopted at present as the mean of the best results, namely 94,070.
4 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.
| Observer. | Date. | Method. | Value of B.A.U. in Ohms. | Value of loo Centi- metres of Mercury in Ohms. | Value of Ohm in Centi- metres of Mercury. |
| Lord Rayleigh. . | 1882 | Rotating coil | 98651 | .94133 | 106.31 |
| Lord Rayleigh. . | 1883 | Lorenz method | 98677 | .. | 106.27 |
| G. Wiedemann. . | 1884 | Rotation through180° | .. | .. | 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 | 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 determin- | 94056 | 106.32 | |
| Hutchinson . | 1888 | ation of resistanc€ | 94074 | 106.30 | |
| E. Salvioni. . | 1890 | was not made. The | 94054 | 106.33 | |
| E. Salvioni. . | . , | value 98656 has been used | .94076 | 106.30 | |
| Mean value | 94076 | 106.31 | |||
| H. F. Weber. . | 1884 | Induced current | 105.37 | ||
| H. F. Webe | Rotating coil | Absolute measure- | 106.16 | ||
| A. Roiti. .. . | 1884 | Mean effect of in- | ments compared | 105.89 | |
| duced current | with German silver | ||||
| F. Himstedt.. . | 1885 | wire coils issued by | 105.98 | ||
| Siemens and Streker | |||||
| 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 | ||
| Alloys. | Resistivity at o° C. | Tempera- ture Co- efficient 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 io% |
| Gold-silver | 6,280 | 00124 | Au 90%, Ag io % |
| Manganese-steel. . | 67,148 | 00127 | Mn 12%, Fe 78 |
| Nickel-steel | 29,452 | 00201 | Ni 4.35%, remain . ing percentage chiefly iron, but uncertain |
| German silver.. . | 29,982 | 000273 | Cu5Zn3N12 |
| Platinoid 2 | 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 | .000645 | Cu 87%, Ni 6.5%, Al 6.5 |
| Titanium-aluminium. . | 3,887 | 00290 |
[[Table Iv]].- Determinations of the Absolute Value of the Volume-Resistivity of Mercury and the Mercury Equivalent of the Ohm. TABLE V. -Volume-Resistivity of Alloys of known Composition at o° C. in C.G.S. Units per Centimetre-cube. Mean Temperature Coe f ficients taken at 15° C. (Fleming and Dewar.) the resistance of a wire of pure hard-drawn copper one 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.
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, 2 5, p. 45 6, 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 electrotechnical 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 massresistivity 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 o° C. For many purposes it is more convenient to express temperature in Fahrenheit degrees, and the recommendation of the 1899 committee on copper conductors 1 is as follows :-" Matthiessen's standard for hard-drawn conductivity commercial copper shall be considered to be alloys, with their chemical composition. Generally speak ng, 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 1 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 manufactures of insulated copper wire and cables.
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 2 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.
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 harddrawn 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 14 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 o° C. is. 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 volumeresistivity of pure annealed copper at o° C. is 1.594 microhms per c.c., or 1594 C.G.S. units, and that of pure hard-drawn copper at o° 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 o° C. of a number of well-known 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 52 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. | |
| .. . | 8000 | |
| Jablochkoff candle carbon. . | .. . | 4.000 |
| 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 Soo |
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 o-376 ohm per centimetre-cube, or 376,000 microhms per centimetre-cube, whereas that of metallic alloys only in few cases exceeds zoo 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.
| 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 ap- | 25.0 at 18° C. | Value estimated |
| proximates probably to | by F. Kohl- rausch and A. | |
| Heydweiler. | ||
| All very dilute aqueous salt | Poo at 18° C. | From results by |
| solutions having a concen- | F. Kohlrausch | |
| tration of about o. 00001 of an equivalent gramme molecule' per litre ap- proximate to | and others. |
In Table VII. are given the names of a few of these badlyconducting liquids, with the values of their volume-resistivity in megohms per centimetre-cube: [[Table Vii]]. - Electric Volume-Resistivity of Various BadlyConducting Liquids in Megohms per Centimetre-cube. 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 centimetrecube, or in megohms per quadrant-cube, the quadrant being a cube the side of which is 10 9 cms. (see Table VIII.).
Ef f ects of Heat. - Temperature affects the resistivity of these different classes of conductors in different ways. In all cases, so 1 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. NaC1= 58.5.
| Substance. | Resistivity. | Tempera- ture Cent. | |
|---|---|---|---|
| Mega- megohms per c.c. | Megohms per Quad- rant-cube. | ||
| Bohemian glass. . | 61 | .061 | 60° |
| Mica | 84 | .084 | 20° |
| Gutta-percha. .. . | 450 | 45 | 24° |
| Flint glass | 1,020 | 1.02 | 60° |
| Glover's vulcanized india- rubber | 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° |
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 Table - 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 io° ems. 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 ioo° 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 o° 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 (P t ) at any temperature (t) is a simple linear function of the resistivity (p 0 ) at o° C., then we can write p t = p o (1 +at), or a = (p t - Po)/Pot.
| SOLIDS] |
The quantity a 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 dp/pdt the temperature coefficient corresponding to any temperature t at which the resistivity is p. 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. Meg. 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 o° C. is 0.0057; at 765° C. it rises to a maximum value 0.0204; but at m000° 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 Pt = p321' +0.0023708 (t - 32) +0.0000034548 (t - 32)21.
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 indiarubbercovered 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-inglass 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.)
II. Conduction in Liquids
Through liquid metals, such as mercury at ordinary temperatures and other metals at temperatures above their melting points, the electric current flows as in solid metals without changing the state of the conductor, except in so far as heat is developed by the electric resistance. But another class of liquid conductors exists, and in them the phenomena are quite different. The conductivity of fused salts, and of solutions of salts and acids, although less than that of metals, is very great compared with the traces of conductivity found in so-called nonconductors. In fused salts and conducting solutions the passage of the current is always accompanied by definite chemical changes; the substance of the conductor or electrolyte is decomposed, and the products of the decomposition appear at the electrodes, i.e. the metallic plates by means of which the current is led into and out of the solution. The chemical phenomena are considered in the article Electrolysis; we are here concerned solely with the mechanism of this electrolytic conduction of the current.
To explain the appearance of the products of decomposition at the electrodes only, while the intervening solution is unaltered, we suppose that, under the action of the electric forces, the opposite parts of the electrolyte move in opposite directions through the liquid. These opposite parts, named ions by Faraday, must therefore be associated with electric charges, and it is the convective movement of the opposite streams of ions carrying their charges with them that, on this view, constitutes the electric current.
In metallic conduction it is found that the current is proportional to the applied electromotive force - a relation known by the name of Ohm's law. If we place in a circuit with a small electromotive force an electrolytic cell consisting of two platinum electrodes and a solution, the initial current soon dies away, and we shall find that a certain minimum electromotive force must be applied to the circuit before any considerable permanent current passes. The chemical changes which are initiated on the surfaces of the electrodes set up a reverse electromotive force of polarization, and, until this is overcome, only a minute current, probably due to the slow but steady removal of the products of decomposition from the electrodes by a process of diffusion, will pass through the cell. Thus it is evident that, considering the electrolytic cell as a whole, the passage of the current through it cannot conform to Ohm's law. But the polarization is due to chemical changes, which are confined to the surfaces of the electrodes; and it is necessary to inquire whether, if the polarization at the electrodes be eliminated, the passage of the current through the bulk of the solution itself is proportional to the electromotive force actually applied to that solution. Rough experiment shows that the current is proportional to the excess of the electromotive force over a constant value, and thus verifies the law approximately, the constant electromotive force to be overcome being a measure of the polarization. A more satisfactory examination of the question was made by F. Kohlrausch in the year5;1873 to 1876. Ohm's law states that the current C is proportional to the electromotive force E, or C = kR, where k is a constant called the conductivity of the circuit. The equation may also be written as C = E/R, where R is a constant, the reciprocal of k, known as the resistance of the circuit. The essence of the law is the proportionality between C and E, which means that the ratio E/C is a constant. But E/C = R, and thus the law may be tested by examining the constancy of the measured resistance of a conductor when different currents are passing through it. In this way Ohm's law has been confirmed in the case of metallic conduction to a very high degree of accuracy. A similar principle was applied by Kohlrausch to the case of electrolytes, and he was the first to show that an electrolyte possesses a definite resistance which has a constant value when measured with different currents and by different experimental methods.
Measurement of the Resistance of Electrolytes
There are two effects of the passage of an electric current which prevent the possibility of measuring electrolytic resistance by the ordinary methods with the direct currents which are used in the case of metals. The products of the chemical decomposition of the electrolyte appear at the electrodes and set up the opposing electromotive force of polarization, and unequal dilution of the solution may occur in the neighbourhood of the two electrodes. The chemical and electrolytic aspects of these phenomena are treated in the article Electrolysis, but from our present point of view also it is evident that they are again of fundamental importance. The polarization at the surface of the electrodes will set up an opposing electromotive force, and the unequal dilution of the solution will turn the electrolyte into a concentration cell and produce a subsidiary electromotive force either in the same direction as that applied or in the reverse according as the anode or the cathode solution becomes the more dilute. Both effects thus involve internal electromotive forces, and prevent the application of Ohm's law to the electrolytic cell as a whole. But the existence of a definite measurable resistance as a characteristic property of the system depends on the conformity of the system to Ohm's law, and it is therefore necessary to eliminate both these effects before attempting to measure the resistance.
The usual and most satisfactory method of measuring the resistance of electrolytes consists in eliminating the effects of polarization by the use of alternating currents, that is, currents that are reversed in direction many times a second.' The chemical action produced by the first current is thus reversed by the second current in the opposite direction, and the polarization caused by the first current on the surface of the electrodes is destroyed before it rises to an appreciable value. The polarization is also diminished in another way. The electromotive force of polarization is due to the deposition of films of the products of chemical decomposition on the surface of the electrodes, and only reaches its full value when a continuous film is formed. If the current be stopped before such a film is completed, the reverse electromotive force is less than its full value. A given current flowing for a given time deposits a definite amount of substance on the electrodes, and therefore the amount per unit area is inversely proportional to the area of the electrodes - to the area of contact, that is, between the electrode and the liquid. Thus, by increasing the area of the electrodes, the polarization due to a given current is decreased. Now the area of free surface of a platinum plate can be increased enormously by coating the plate with platinum black, which is metallic platinum in a spongy state, and with such a plate as electrode the effects of polarization are diminished to a very marked extent. The coating is effected by passing an electric current first one way and then the other between two platinum plates immersed in a 3% solution of platinum chloride to which a trace of lead acetate is sometimes added. The platinized plates thus obtained are quite satisfactory for the investigation of strong solutions. They have the power, however, of absorbing a certain amount of salt from the solutions and of giving it up again when water or more dilute solution is placed in contact with them. The measurement of very dilute solutions is thus made difficult, but, if the plates be heated to 1 F. Kohlrausch and L. Holborn, Das Leitvermogen der Elektrolyte (Leipzig, 1898).
redness after being platinized, a grey surface is obtained which possesses sufficient area for use with dilute solutions and yet does not absorb an appreciable quantity of salt.
Any convenient source of alternating current may be used. The currents from the secondary circuit of a small induction coil are satisfactory, or the currents of an alternating electric light supply may be transformed down to an electromotive force of one or two volts. With such currents it is necessary to consider the effects of self-induction in the circuit and of electrostatic capacity. In balancing the resistance of the electrolyte, resistance coils may be used in which self-induction and the capacity are reduced to a minimum by winding the wire of the coil backwards and forwards in alternate layers.
With these arrangements the usual method of measuring resistance by means of Wheatstone's bridge may be adapted to the case of electrolytes. With alternating currents, however, it is impossible to use a galvanometer in the usual way. The galvanometer was therefore replaced by Kohlrausch by a telephone, which gives a sound when an alternating current passes through it. The most common plan of the apparatus is shown diagrammatically in fig. 1. The electrolytic cell and a resistance box form two arms of the bridge, and the sliding contact is moved along the metre wire which forms the other two arms till no sound is heard in the telephone. The resistance of the electrolyte is to that of the box as that of the right-hand end of the wire is to that of the left-hand end. A more accurate method of using alternating currents, and one more pleasant to use, gets rid of the telephone (Phil. Trans., 1900, 1 94, p. 321). The current from one or two voltaic cells is led to an ebonite drum turned by a motor or a hand-wheel and cord. On the drum are fixed brass strips with wire brushes touching them in such a manner that the current from the brushes is reversed several times in each revolution of the drum. The wires from the brushes are connected with the Wheatstone's bridge. A moving coil galvanometer is used as indicator, its connexions being reversed in time with those of the battery by a slightly narrower set of brass strips fixed on the other end of the ebonite commutator. Thus any residual current through the galvanometer is direct and not alternating. The high moment of inertia of the coil makes the period of swing slow compared with the period of alternation of the current, and the slight periodic disturbances are thus prevented from affecting the galvanometer. When the measured resistance is not altered by increasing the speed of the commutator or changing the ratio of the arms of the bridge, the disturbing effects may be considered to be eliminated.
The form of vessel chosen to contain the electrolyte depends on the order of resistance to be measured. For dilute solutions the shape of cell shown in fig. 2 will be found convenient, while for more concentrated solutions, that indicated in fig. 3 is suitable. The absolute resistances of certain solutions FIG. 2. FIG. 3. have been determined by Kohlrausch by comparison with mercury, and, by using one of these solutions in any cell, the constant of that cell may be found once for all. From the observed resistance of any given solution in the cell the resistance of a centimetre cube - the so-called specific resistance - may be calculated. The reciprocal of this, or the conductivity, is a more generally useful constant; it is conveniently expressed in terms of a unit equal to the reciprocal of an ohm. Thus Kohlrausch found that a solution of potassium chloride, containing one-tenth of a gram equivalent (7.46 grams) per litre, has at 18° C. a specific resistance of 89.37 ohms per centimetre cube, or a conductivity of I. 119 X I O 2 mhos or I -1'9 X I 011 C.G.S. units. As the temperature variation of conductivity is large, usually about 2% per degree, it is necessary to place the resistance cell in a paraffin or water bath, and to observe its temperature with some accuracy.
Another way of eliminating the effects of polarization and of dilution has been used by W. Stroud and J. B. Henderson (Phil. Mag., 18 97 [5], 43, p. 19). Two of the arms of a Wheatstone's bridge are composed of narrow tubes filled with the solution, the tubes being of equal diameter but of different length. The other two arms are made of coils of wire of equal resistance, and metallic resistance is added to the shorter tube till the bridge is balanced. Direct currents of somewhat high electromotive force are used to work the bridge. Equal currents then flow through the two tubes; the effects of polarization and dilution must be the same in each, and the resistance added to the shorter tube must be equal to the resistance of a column of liquid the length of which is equal to the difference in length of the two tubes.
A somewhat different principle was adopted by E. Bouty in 1884. If a current be passed through two resistances in series by means of an applied electromotive force, the electric potential falls from one end of the resistances to the other, and, if we apply Ohm's law to each resistance in succession, we see that, since for each of them E = CR, and C the current is the same through both, E the electromotive force or fall of potential between the ends of each resistance must be proportional to the resistance between them. Thus by measuring the potential difference between the ends of the two resistances successively, we may compare their resistances. If, on the other hand, we can measure the potential difference in some known units, and similarly measure the current flowing, we can determine the resistance of a single electrolyte. The details of the apparatus may vary, but its principle is illustrated in the following description. A narrow glass tube is fixed horizontally into side openings in two glass vessels, and an electric current passed through it by means of platinum electrodes and a battery of considerable electromotive force. In this way a steady fall of electric potential is set up along the length of the tube. To measure the potential difference between the ends of the tube, tapping electrodes are constructed, e.g. by placing zinc rods in vessels with zinc sulphate solution and connecting these vessels (by means of thin siphon tubes also filled with solution) with the vessels at the ends of the long tube which contains the electrolyte to be examined. Whatever be the contact potential difference between zinc and its solution, it is the same at both ends, and thus the potential difference between the zinc rods is equal to that between the liquid at the two ends of the tube. This potential difference may be measured without passing any appreciable current through the tapping electrodes, and thus the resistance of the liquid deduced.
Equivalent Conductivity of Solutions
As is the case in the other properties of solutions, the phenomena are much more simple when the concentration is small than when it is great, and a study of dilute solutions is therefore the best way of getting an insight into the essential principles of the subject. The foundation of our knowledge was laid by Kohlrausch when he had developed the method of measuring electrolyte resistance described above. He expressed his results in terms of " equivalent conductivity," that is, the conductivity (k) of the solution divided by the number (m) of gram-equivalents of electrolyte per litre. He finds that, as the concentration diminishes, the value of k/m approaches a limit, and eventually becomes constant, that is to say, at great dilution the conductivity is proportional to the concentration. Kohlrausch first prepared very pure water by repeated distillation and found that its resistance continually increased as the process of purification proceeded. The conductivity of the water, and of the slight impurities which must always remain, was subtracted from that of the solution made with it, and the result, divided by m, gave the equivalent conductivity of the substance dissolved. This procedure appears justifiable, for as long as conductivity is proportional to concentration it is evident that each part of the dissolved matter produces its own independent effect, so that the total conductivity is the sum of the conductivities of the parts; FIG. I.
when this ceases to hold, the concentration of the solution has in general become so great that the conductivity of the solvent may be neglected. The general result of these experiments can be represented graphically by plotting k/m as ordinates and -t m as abscissae, -Om being a number proportional to the reciprocal of the average distance between the molecules, to which it seems likely that the molecular conductivity may be related. The general types of curve for a simple neutral salt like potassium or sodium chloride and for a caustic alkali or acid are shown in fig. 4. The curve for the neutral salt comes to a limiting value; that for the acid attains a maximum at a certain very small concentration, and falls again when the dilution is carried farther. It has usually been considered that this destruction of conductivity is due to chemical action between the acid and the residual impurities in the water. At such great dilution these a/ impurities are present in quantities comparable with the amount of acid which they convert into a less m highly conducting neutral salt. In FIG. 4. the case of acids, then, the maxi mum must be taken as the limiting value. The decrease in equivalent conductivity at great dilution is, however, so constant that this explanation seems insufficient. The true cause of the phenomenon may perhaps be connected with the fact that the bodies in which it occurs, acids and alkalis, contain the ions, hydrogen in the one case, hydroxyl in the other, which are present in the solvent, water, and have, perhaps because of this relation, velocities higher than those of any other ions. The values of the molecular conductivities of all neutral salts are, at great dilution, of the same order of magnitude, while those of acids at their maxima are about three times as large. The influence of increasing concentration is greater in the case of salts containing divalent ions, and greatest of all in such cases as solutions of ammonia and acetic acid, which are substances of very low conductivity.
Theory of Moving Ions. - Kohlrausch found that, when the polarization at the electrodes was eliminated, the resistance of a solution was constant however determined, and thus established Ohm's Law for electrolytes. The law was confirmed in the case of strong currents by G. F. Fitzgerald and F. T. Trouton (B.A. Report, 1886, p. 312). Now, Ohm's Law implies that no work is done by the current in overcoming reversible electromotive forces such as those of polarization. Thus the molecular interchange of ions, which must occur in order that the products may be able to work their way through the liquid and appear at the electrodes, continues throughout the solution whether a current is flowing or not. The influence of the current on the ions is merely directive, and, when it flows, streams of electrified ions travel in opposite directions, and, if the applied electromotive force is enough to overcome the local polarization, give up their charges to the electrodes. We may therefore represent the facts by considering the process of electrolysis to be a kind of convection. Faraday's classical experiments proved that when a current flows through an electrolyte the quantity of substance liberated at each electrode is proportional to its chemical equivalent weight, and to the total amount of electricity passed. Accurate determinations have since shown that the mass of an ion deposited by one electromagnetic unit of electricity, i.e. its electrochemical equivalent, is I 036X 10 -4 X its chemical equivalent weight. Thus the amount of electricity associated with one gram-equivalent of any ion is Io 4 /1 036=9653 units. Each monovalent ion must therefore be associated with a certain definite charge, which we may take to be a natural unit of electricity; a divalent ion carries two such units, and so on. A cation, i.e. an ion giving up its charge at the cathode, as the electrode at which the current leaves the solution is called, carries a positive charge of electricity; an anion, travelling in the opposite direction, carries a negative charge. It will now be seen that the quantity of electricity flowing per second, i.e. the current through the solution, depends on the number of the ions concerned, (2) the charge on each ion, and (3) the velocity with which the ions travel past each other. Now, the number of ions is given by the concentration of the solution, for even if all the ions are not actively engaged in carrying the current at the same instant, they must, on any dynamical idea of chemical equilibrium, be all active in turn. The charge on each, as we have seen, can be expressed in absolute units, and therefore the velocity with which they move past each other can be calculated. This was first done by Kohlrausch (Göttingen Nachrichten, 1876, p. 213, and Das Leitvermogen der Elektrolyte, Leipzig, 1898) about 1879.
In order to develop Kohlrausch's theory, let us take, as an example, the case of an aqueous solution of potassium chloride, of concentration n gram-equivalents per cubic centimetre. There will then be n gram-equivalents of potassium ions and the same number of chlorine ions in this volume. Let us suppose that on each gramequivalent of potassium there reside +e units of electricity, and on each gram-equivalent of chlorine ions - e units. If u denotes the average velocity of the potassium ions, the positive charge carried per second across unit area normal to the flow is n e u. Similarly, if v be the average velocity of the chlorine ions, the negative charge carried in the opposite direction is n e v. But positive electricity moving in one direction is equivalent to negative electricity moving in the other, so that, before changes in concentration sensibly supervene, the total current, C, is ne(u+v). Now let us consider the amounts of potassium and chlorine liberated at the electrodes by this current. At the cathode, if the chlorine ions were at rest, the excess of potassium ions would be simply those arriving in one second, namely, nu. But since the chlorine ions move also, a further separation occurs, and nv potassium ions are left without partners. The total number of gram-equivalents liberated is therefore n(u+v). By Faraday's law, the number of grams liberated is equal to the product of the current and the electro-chemical equivalent of the ion; the number of gram-equivalents therefore must be equal to nC, where n denotes the electro-chemical equivalent of hydrogen in C.G.S. units. Thus we get n(u +v) =nC = nne(u+v), and it follows that the charge, e, on I gram-equivalent of each kind of ion is equal to I/n. We know that Ohm's Law holds good for electrolytes, so that the current C is also given by k.dP/dx, where k denotes the conductivity of the solution, and dP/dx the potential gradient, i.e. the change in potential per unit length along the lines of current flow. Thus - 77 (u +v) =kdP/dx; kd therefore u+v = n dx Now n is 1.036 X t04, and the concentration of a solution is usually expressed in terms of the number, m, of gram-equivalents per litre instead of per cubic centimetre. Therefore u+v = 1.036XIO-1md P .
When the potential gradient is one volt (10 8 C.G.S. units) per centimetre this becomes u+v =1 036X107 X k/m.
Thus by measuring the value of km, which is known as the equivalent conductivity of the solution, we can find u+v, the velocity of the ions relative to each other. For instance, the equivalent conductivity of a solution of potassium chloride containing onetenth of a gram-equivalent per litre is 1119 X 1013 C.G.S. units at 18° C. Therefore u+v = l 036X 107 X1119XIO-13 =1.159 X 103 = 0.001159 cm. per sec.
| k m` |
| LI Q UIDS] |
In order to obtain the absolute velocities u and v, we must find some other relation between them. Let us resolve u into 2 (u+v) in one direction, say to the right, and 2(u - v) to the left. Similarly v can be resolved into 2(v +u) to the left and 1(v - u)to the right. On pairing these velocities we have a combined movement of the ions to the right, with a speed of 1(u - v)and a drift right and left, past each other, each ion travelling with a speed of 1(u ±v), constituting the electrolytic separation. If u is greater than v, the combined movement involves a concentration of salt at the cathode, and a corresponding dilution at the anode, and vice versa. The rate at which salt is electrolysed, and thus removed from the solution at each electrode, is z (u+v). Thus the total loss of salt at the cathode is 2 (u+v) - z (u - v), or v, and at the anode, 2 (v+u) - 1(v - u), or u. Therefore, as is explained in the article Electrolysis, by measuring the dilution of the liquid round the electrodes when a current passed, W. Hittorf (Pogg. Ann., 18 5318 59, 8 9, p. 1 77; 98, p. I; 103, p. I; 106, pp. 337 and 513) was able to deduce the ratio of the two velocities for simple salts when no complex ions are present, and many further experiments have been made on the subject (see Das Leitvermogen der Elektrolyte). By combining the results thus obtained with the sum of the velocities, as determined from the conductivities, Kohlrausch calculated the absolute velocities of different ions under stated condi tions. Thus, in the case of the solution of potassium chloride considered above, Hittorf's experiments show us that the ratio of the velocity of the anion to that of the cation in this solution is .51: 49. The absolute velocity of the potassium ion under unit potential gradient is therefore 0.000567 cm. per sec., and that of the chlorine ion 0.000592 cm. per sec. Similar calculations can be made for solutions of other concentrations, and of different substances.
Table IX. shows Kohlrausch's values for the ionic velocities of three chlorides of alkali metals at 18° C., calculated for a potential gradient of i volt per cm.; the numbers are in terms of a unit equal to 106 cm. per sec.: TABLE IX.
| KC1 | NaC1 | LiC1 | |||||||
| m | u -{-v | u | v | u -{-v | u | v | u -{-v | u | v |
| o | 1350 | 660 | 690 | 1140 | 450 | 690 | 1050 | 360 | 690 |
| 0 0001 | 1 335 | 6 54 | 681 | 1129 | 44 8 | 681 | 1037 | 356 | 681 |
| 00 1 | 1313 | 6 43 | 670 | IIIO | 440 | 670 | 1013 | 343 | 670 |
| oI | 1263 | 619 | 6 44 | 1 0 59 | 4 1 5 | 644 | 962 | 318 | 644 |
| 03 | 1218 | 597 | 621 | 1013 | 39 0 | 623 | 917 | 298 | 619 |
| I | 1153 | 5 6 4 | 5 8 9 | 95 2 | 3 6 0 | 59 2 | 8 53 | 2 59 | 594 |
| 3 | 1088 | 53 1 | 557 | 8 7 6 | 3 2 4 | 55 2 | 774 | 21 7 | 557 |
| I o | IOII | 49 1 | 520 | 765 | 278 | 487 | 651 | 169 | 482 |
| 3.0 | 911 | 44 2 | 4 6 9 | 582 | 206 | 37 6 | 463 | 115 | 348 |
| 5 0 | 438 | 1 53 | 285 | 334 | 80 | 254 | |||
| 10 0 | 117 | 25 | 92 |
These numbers show clearly that there is an increase in ionic velocity as the dilution proceeds. Moreover, if we compare the values for the chlorine ion obtained from observations on these three different salts, we see that as the concentrations diminish the velocity of the chlorine ion becomes the same in all of them. A similar relation appears in other cases, and, in general, we may say that at great dilution the velocity of an ion is independent of the nature of the other ion present. This introduces the conception of specific ionic velocities, for which some values at r8° C. are given by Kohlrausch in Table X.: Table X.
| K . | 66 0- 5 cms. per sec. | 69 X Io - 5 per sec. | |
| Na | 45 „ | I . | 69 |
| Li . | 36 | NO 3 . | 64 |
| NH4 . | 66 „ | OH . | 162 |
| H . | 320 „ | C2H302 | 36 |
| 57 | C3H502 | 33 |
Having obtained these numbers we can deduce the conductivity of the dilute solution of any salt, and the comparison of the calculated with the observed values furnished the first confirmation of Kohlrausch's theory. Some exceptions, however, are known. Thus acetic acid and ammonia give solutions of much lower conductivity than is indicated by the sum of the specific ionic velocities of their ions as determined from other compounds. An attempt to find in Kohlrausch's theory some explanation of this discrepancy shows that it could be due to one of two causes. Either the velocities of the ions must be much less in these solutions than in others, or else only a fractional part of the number of molecules present can be actively concerned in conveying the current. We shall return to this point later.
Friction on the Ions
It is interesting to calculate the magnitude of the forces required to drive the ions with a certain velocity. If we have a potential gradient of I volt per centimetre the electric force is Io 8 in C.G.S. units. The charge of electricity on 1 gramequivalent of any ion is 1/. 0001036=9653 units, hence the mechanical force acting on this mass is 9653 X10 8 dynes. This, let us say, produces a velocity u; then the force required to produce unit velocity is p A = 9'653u Ioll dynes= 9 84u 105 kilograms-weight.
If the ion have an equivalent weight A, the force producing unit velo city when acting on I gram is P 1 =9.84XA kilograms-weight. Thus the aggregate force required to drive 1 gram of potassium ions with a velocity of I centimetre per second through a very dilute solution must be equal to the weight of 38 million kilograms.
| Kilograms-weight. | Kilograms-weight. | |||||
|---|---|---|---|---|---|---|
| P A | P1 | PA | P1 | |||
| K . | .. 15 X10 8 | 38 8 | 14 X10 8 | |||
| N a . | .. 22 | „ | 95 „ | I.. | . 14 „ | II „ |
| Li | .. 27 | „ | 39 0 „ | NO 3 . | . 15 „ | 25 |
| NH4 | .. 15 | „ | 83 „ | OH . | . 5.4 „ | 32 |
| H . | .. 3 I | ,, | 3 10 , | C2 H 302 . | . 27 „ | 46 |
| 17 | „ | i 6 „ | C 3 H S O 2 | . 3 0 „ | 4 1 „ | |
Since the ions move with uniform velocity, the frictional resistances brought into play must be equal and opposite to the driving forces, and therefore these numbers also represent the ionic friction coefficients in very dilute solutions at 18° C.
Direct Measurement of Ionic Velocities
Sir Oliver Lodge was the first to directly measure the velocity of an ion (B.A. Report, 1886, p. 389). In a horizontal glass tube connecting two vessels filled with dilute sulphuric acid he placed a solution of sodium chloride in solid agar-agar jelly. This solid solution was made alkaline with a trace of caustic soda in order to bring out the red colour of a little phenol-phthalein added as indicator. An electric current was then passed from one vessel to the other. The hydrogen ions from the anode vessel of acid were thus carried along the tube, and, as they travelled, decolourized the phenolphthalein. By this method the velocity of the hydrogen ion through a jelly solution under a known potential gradient was observed to about 0.0026 cm. per sec., a number of the same order as that required by Kohlrausch's theory. Direct determinations of the velocities of a few other ions have been made by W. C. D. Whetham (Phil. Trans. vol. 184, A, p. 337; vol. 186, A, p. 507; Phil. Mag., October 1894). Two solutions having one ion in common, of equivalent concentrations, different densities, different colours, and nearly equal specific resistances, were placed one over the other in a vertical glass tube. In one case, for example, decinormal solutions of potassium carbonate and potassium bichromate were used. The colour of the latter is due to the presence of the bichromate group, Cr 2 O 7. When a current was passed across the junction, the anions CO 3 and Cr207 travelled in the direction opposite to that of the current, and their velocity could be determined by measuring the rate at which the colour boundary moved. Similar experiments were made with alcoholic solutions of cobalt salts, in which the velocities of the ions were found to be much less than in water. The behaviour of agar jelly was then investigated, and the velocity of an ion through a solid jelly was shown to be very little less than in an ordinary liquid solution. The velocities could therefore be measured by tracing the change in colour of an indicator or the formation of a precipitate. Thus decinormal jelly solutions of barium chloride and sodium chloride, the latter containing a trace of sodium sulphate, were placed in contact. Under the influence of an electromotive force the barium ions moved up the tube, disclosing their presence by the trace of insoluble barium sulphate formed. Again, a measurement of the velocity of the hydrogen ion, when travelling through the solution of an acetate, showed that its velocity was then only about the one-fortieth part of that found during its passage through chlorides. From this, as from the measurements on alcohol solutions, it is clear that where the equivalent conductivities are very low the effective velocities of the ions are reduced in the same proportion.
Another series of direct measurements has been made by Orme Masson (Phil. Trans. vol. 192, A, p. 331). He placed the gelatine solution of a salt, potassium chloride, for example, in a horizontal glass tube, and found the rate of migration of the potassium and chlorine ions by observing the speed at which they were replaced when a coloured anion, say, the Cr 2 O 7 from a solution of potassium bichromate, entered the tube at one end, and a coloured cation, say, the Cu from copper sulphate, at the other. The coloured ions are specifically slower than the colourless ions which they follow, and in this case it follows that the coloured solution has a higher resistance than the colourless. For the same current, therefore, the potential gradient is higher in the coloured solution and lower in the colourless one. Thus a coloured ion which gets in front of the advancing boundary finds itself acted on by a smaller force and falls back into line, while a straggling colourless ion is pushed forward again. Hence a sharp boundary is preserved. B. D. Steele has shown that with these sharp boundaries the use of coloured ions is unnecessary, the junction line being visible owing to the difference in the optical refractive indices of two colourless solutions. Once the boundary is formed, too, no gelatine is necessary, and the motion can be watched through liquid aqueous solutions (see R. B. Denison and B. D. Steele, Phil. Trans., 1906).
All the direct measurements which have been made on simple binary electrolytes agree with Kohlrausch's results within the limits of experimental error. His theory, therefore, probably holds good in such cases, whatever be the solvent, if the proper values are given to the ionic velocities, i.e. the values expressing the velocities with which the ions actually move in the solution of the strength taken, and under the conditions of the experiment. If we know the specific velocity of any one ion, we can deduce, from the conductivity of very dilute solutions, the velocity of any other ion with which it may be associated, a proceeding which does not involve the difficult task of determining the migration constant of the compound. Thus, taking the specific ionic velocity of hydrogen as o 00032 cm. per second, we can find, by determining the conductivity of dilute solutions of any acid, the specific velocity of the acid radicle involved. Or again, since we know the specific velocity of silver, we can find the velocities of a series of acid radicles at great dilution by measuring the conductivity of their silver salts.
By such methods W. Ostwald, G. Bredig and other observers have found the specific velocities of many ions both of inorganic and organic compounds, and examined the relation between constitution and ionic velocity. The velocity of elementary ions is found to be a periodic function of the atomic weight, similar elements lying on corresponding portions of a curve drawn to express the relation between these two properties. Such a curve much resembles that giving the relation between atomic weight and viscosity in solution. For complex ions the velocity is largely an additive property; to a continuous additive change in the composition of the ion corresponds a continuous but decreasing change in the velocity. The following table gives Ostwald's results for the formic acid series: Table Xii.
| Velocity. | Difference for CH2. | |
| Formic acid.. HCO 2 | 51 2 | . . |
| Acetic „. .. H 3 C 2 O 2 | 38.3 | - 12.9 |
| Propionic „. .. H 5 C 3 0 2 | 34'3 | - 4.0 |
| Butyric „. .. H 7 C 4 0 2 | 30 8 | - 3'5 |
| Valerie „. .. H9C502 | 28.8 | - 2.0 |
| Caprionic „. .. H,10 6 02 | 27.4 | - 1.4 |
Nature of Electrolytes
We have as yet said nothing about the fundamental cause of electrolytic activity, nor considered why, for example, a solution of potassium chloride is a good conductor, while a solution of sugar allows practically no current to pass.
All the preceding account of the subject is, then, independent of any view we may take of the nature of electrolytes, and stands on the basis of direct experiment. Nevertheless, the facts considered point to a very definite conclusion. The specific velocity of an ion is independent of the nature of the opposite ion present, and this suggests that the ions themselves, while travelling through the liquid, are dissociated from each other. Further evidence, pointing in the same direction, is furnished by the fact that since the conductivity is proportional to the concentration at great dilution, the equivalent-conductivity, and therefore the ionic velocity, is independent of it. The importance of this relation will be seen by considering the alternative to the dissociation hypothesis. If the ions are not permanently free from each other their mobility as parts of the dissolved molecules must be secured by continual interchanges. The velocity with which they work their way through the liquid must then increase as such molecular rearrangements become more frequent, and will therefore depend on the number of solute molecules, i.e. on the concentration. On this supposition the observed constancy of velocity would be impossible. We shall therefore adopt as a working hypothesis the theory, confirmed by other phenomena (see Electrolysis), that an electrolyte consists of dissociated ions.
It will be noticed that neither the evidence in favour of the dissociation theory which is here considered, nor that described in the article Electrolysis, requires more than the effective dissociation of the ions from each other. They may well be connected in some way with solvent molecules, and there are several indications that an ion consists of an electrified part of the molecule of the dissolved salt with an attendant atmosphere of solvent round it. The conductivity of a salt solution depends on two factors - (I) the fraction of the salt ionized; (2) the velocity with which the ions, when free from each other, move under the electric forces.' When a solution is heated, both these factors may change. The coefficient of ionization usually, though not always, decreases; the specific ionic velocities increase. Now the rate of increase with temperature of these ionic velocities is very nearly identical with the rate of decrease of the viscosity of the liquid. If the curves obtained by observations at ordinary temperatures be carried on they indicate a zero of fluidity and a zero of ionic velocity about the same point, 38.5° C. below the freezing point of water (Kohlrausch, Sitz. preuss. Akad. Wiss., 1901, 42, p. 1026). Such relations suggest that the frictional resistance to the motion of an ion is due to the ordinary viscosity of the liquid, and that the ion is analogous to a body of some size urged through a viscous medium rather than to a particle of molecular dimensions finding its way through a crowd of molecules of similar magnitude. From this point of view W. K. Bousfield has calculated the sizes of ions on the assumption that Stokes's theory of the motion of a small sphere through a viscous medium might be applied (Zeits. phys. Chem., 1905, 53, p. 2 57; Phil. Trans. A, 1906, 206, p. 101). The radius of the potassium or chlorine ion with its envelope of water appears to be about I 2 X to - 8 centimetres.
For the bibliography of electrolytic conduction see Electrolysis. The books which deal more especially with the particular subject of the present article are Das Leitvermogen der Elektrolyte, by F. Kohlrausch and L. Holborn (Leipzig, 1898), and The Theory of Solution and Electrolysis, by W. C. D. Whetham (Cambridge, 1902). (W. C. D. W.)
III. Electric Conduction through Gases
A gas such as air when it is under normal conditions conducts electricity to a small but only to a very small extent, however small the electric force acting on the gas may be. The electrical conductivity of gases not exposed to special conditions is so small that it was only definitely established in the early years of the 10th century, although it had engaged the attention of physicists for more than a hundred years. It had been known for a long time that a body charged with electricity slowly lost its charge even when insulated with the greatest care, and though long ago some physicists believed that part of the leak of electricity took place through the air, the general view seems to have been that it was due to almost unavoidable defects in the insulation or to dust in the air, which after striking the charged body was repelled from it and went off with some of the charge.
C. A. Coulomb, who made some very careful experiments which were published in 1785 (Mem. de l'Acad. des Sciences, 1785, p. 612), came to the conclusion that after allowing for the leakage along the threads which supported the charged body there was a balance over, which he attributed to leakage through the air. His view was that when the molecules of air come into contact with a charged body some of the electricity goes on to the molecules, which are then repelled from the body carrying their charge with them. We shall see later that this explanation is not tenable. C. Matteucci (Ann. chim. phys., 1850, 28, p. 390) in 1850 also came to the conclusion that the electricity from a charged body passes through the air; he was the first to prove ' It should be noticed that the velocities calculated in Kohlrausch's theory and observed experimentally are the average velocities, and involve both the factors mentioned above; they include the time wasted by the ions in combination with each other, and, except at great dilution, are less than the velocity with which the ions move when free from each other.
| GASES] |
that the rate at which electricity escapes is less when the pressure of the gas is low than when it is high. He found that the rate was the same whether the charged body was surrounded by air, carbonic acid or hydrogen. Subsequent investigations have shown that the rate in hydrogen is in general much less than in air. Thus in 1872 E. G. Warburg (Pogg. Ann., 1872, 1 45, p. 578) found that the leak through hydrogen was only about one-half of that through air: he confirmed Matteucci's observations on the effect of pressure on the rate of leak, and also found that it was the same whether the gas was dry or damp. He was inclined to attribute the leak to dust in the air, a view which was strengthened by an experiment of J. W. Hittorf's (Wied. Ann., 1 8 79, 7, p. 595), in which a small carefully insulated electroscope, placed in a small vessel filled with carefully filtered gas, retained its charge for several days; we know now that this was due to the smallness of the vessel and not to the absence of dust, as it has been proved that the rate of leak in small vessels is less than in large ones.
| Gas. | Relative Rate of Leak. | Rate of Leak. Sp. Gr. |
| Air. . | I 00 | I |
| H 2.. . | 184 | 2.7 |
| CO,. . | 1.69 | I I 0 |
| SO, . | 2.64 | I.21 |
| CH 3 C1 . | 4.7 | 1.09 |
| Ni(CO). . | 5.1 | 867 |
Great light was thrown on this subject by some experiments on the rates of leak from charged bodies in closed vessels made almost simultaneously by H. Geitel (Phys. Zeit., 1900, 2, p. 116) and C. T. R. Wilson (Proc. Camb. Phil. Soc., 1900, 11, p. 32). These observers established that (I) the rate of escape of electricity in a closed vessel is much smaller than in the open, and the larger the vessel the greater is the rate of leak; and (2) the rate of leak does not increase in proportion to the differences of potential between the charged body and the walls of the vessel: the rate soon reaches a limit beyond which it does not increase, however much the potential difference may be increased, provided, of course, that this is not great enough to cause sparks to pass from the charged body. On the assumption that the maximum leak is proportional to the volume, Wilson's experiments, which were made in vessels less than 1 litre in volume, showed that in dust-free air at atmospheric pressure the maximum quantity of electricity which can escape in one second from a charged body in a closed volume of V cubic centimetres is about io-8V electrostatic units. E. Rutherford and S. T. Allan (Phys. Zeit., 1902, 3, p. 225), working in Montreal, obtained results in close agreement with this. Working between pressures of from 43 to 743 millimetres of mercury, Wilson showed that the maximum rate of leak is very approximately proportional to the pressure; it is thus exceedingly small when the pressure is low - a result illustrated in a striking way by an experiment of Sir W. Crookes (Proc. Roy. Soc., 1879, 28, p. 347) in which a pair of gold leaves retained an electric charge for several months in a very high vacuum. Subsequent experiments have shown that it is only in very small vessels that the rate of leak is proportional to the volume and to the pressure; in large vessels the rate of leak per unit volume is considerably smaller than in small ones. In small vessels the maximum rate of leak in different gases, is, with the exception of hydrogen, approximately proportional to the density of the gas. Wilson's results on this point are shown in the following table (Proc. Roy. Soc., 1901, 60, p. 277): The rate of leak of electricity through gas contained in a closed vessel depends to some extent on the material of which the walls of the vessel are made; thus it is greater, other circumstances being the same, when the vessel is made of lead than when it is made of aluminium. It also varies, as Campbell and Wood (Phil. Mag. [6], 13, p. 265) have shown, with the time of the day, having a well-marked minimum at about 3 o'clock in the morning: it also varies from month to month. Rutherford (Phys. Rev., 1903, 16, p. 183), Cooke (Phil. Mag., 1903 [6], 6, p. 4 0 3) and M'Clennan and Burton (Phys. Rev., 1903, 16, p. 184) have shown that the leak in a closed vessel can be reduced by about 30% by surrounding the vessel with sheets of thick lead, but that the reduction is not increased beyond this amount, however thick the lead sheets may be. This result indicates that part of the leak is due to a very penetrating kind of radiation, which can get through the thin walls of the vessel but is stopped by the thick lead. A large part of the leak we are describing is due to the presence of radioactive substances such as radium and thorium in the earth's crust and in the walls of the vessel, and to the gaseous radioactive emanations which diffuse from them into the atmosphere. This explains the very interesting effect discovered by J. Elster and H. Geitel (Phys. Zeit., 1901, 2, p. 560), that the rate of leak in caves and cellars when the air is stagnant and only renewed slowly is much greater than in the open air. In some cases the difference is very marked; thus they found that in the cave called the Baumannshohle in the Harz mountains the electricity escaped at seven times the rate it did in the air outside. In caves and cellars the radioactive emanations from the walls can accumulate and are not blown away as in the open air.
The electrical conductivity of gases in the normal state is, as we have seen, exceedingly small, so small that the investigation of its properties is a matter of considerable difficulty; there are, however, many ways by which the electrical conductivity of a gas can be increased so greatly that the investigation becomes comparatively easy. Among such methods are raising the temperature of the gas above a certain point. Gases drawn from the neighbourhood of flames, electric arcs and sparks, or glowing pieces of metal or carbon are conductors, as are also gases through which Röntgen or cathode rays or rays of positive electricity are passing; the rays from the radioactive metals, radium, thorium, polonium and actinium, produce the same effect, as does also ultra-violet light of exceedingly short wavelength. The gas, after being made a conductor of electricity by any of these means, is found to possess certain properties; thus it retains its conductivity for some little time after the agent which made it a conductor has ceased to act, though the conductivity diminishes very rapidly and finally gets too small to be appreciable.
This and several other properties of conducting gas may readily be proved by the aid of the apparatus represented in fig. 5.
A C Pump - FIG. 5.
V is a testing vessel in which an electroscope is placed. Two tubes A and C are fitted into the vessel, A being connected with a water pump, while the far end of C is in the region where the gas is exposed to the agent which makes it a conductor of electricity. Let us suppose that the gas is made conducting by Röntgen rays produced by a vacuum tube which is placed in a box, covered except for a window at B with lead so as to protect the electroscope from the direct action of the rays. If a slow current of air is drawn by the water pump through the testing vessel, the charge on the electroscope will gradually leak away. The leak, however, ceases when the current of air is stopped. This result shows that the gas retains its conductivity during the time taken by it to pass from one end to the other of the tube C.
The gas loses its conductivity when filtered through a plug of glass-wool, or when it is made to bubble through water. This can readily be proved by inserting in the tube C a plug of glasswool or a water trap; then if by working the pump a little harder the same current of air is produced as before, it will be found that the electroscope will now retain its charge, showing that the conductivity can, as it were, be filtered out of the gas.
The conductivity can also be removed from the gas by making the gas traverse a strong electric field. We can show this, by replacing the tube C by a metal tube with an insulated wire passing down the axis of the tube. If there is no potential difference between the wire and the tube then the electroscope will leak when a current of air is drawn through the vessel, but the leak will stop if a considerable difference of potential is maintained between the wire and the tube: this shows that a strong electric field removes the conductivity from the gas.
The fact that the conductivity of the gas is removed by filtering shows that it is due to something mixed with the gas which is removed from it by filtration, and since the conductivity is also removed by an electric field, the cause of the conductivity must be charged with electricity so as to be driven to the sides of the tube by the electric force. Since the gas as a whole is not electrified either positively or negatively, there must be both negative and positive charges in the gas, the amount of electricity of one sign being equal to that of the other. We are thus led to the conclusion that the conductivity of the gas is due to electrified particles being mixed up with the gas, some of these particles having charges of positive electricity, others of negative. These electrified particles are called ions, and the process by which the gas is made a conductor is called the ionization of the gas. We shall show later that the charges and masses of the ions can be determined, and that the gaseous ions are not identical with those met with in the electrolysis of solutions.
One very characteristic property of conduction of electricity through a gas is the relation between the current through the gas and the electric force which gave rise to it. This relation is not in general that expressed by Ohm's law, which always, as far as our present knowledge extends, expresses the relation for conduction through metals and electrolytes. With gases, on the other hand, it is only when the current is very small that Ohm's law is true. If we represent graphically by means of a curve the relation between the current passing between two parallel metal plates separated by ionized gas and the difference of potential between the plates, the curve is of the character shown in fig. 6 when the ordinates represent the current and the abscissae the difference of potential between the plates. We see that when the potential difference is very small, i.e. close to the origin, the curve is approximately straight, but that soon the current increases much less rapidly than the potential difference, and that a stage is reached when no appreciable increase of current is produced when the potential difference is oi increased; when this stage is reached the current is constant, and this value of the current is called the " saturation " value. When the potential difference approaches the value at which sparks would pass through the gas, the current again increases with the potential difference; thus the curve representing the relation between the current and potential difference over very wide ranges of potential difference has the shape shown in fig. 7; curves of this kind have been obtained by von Schweidler (Wien. Ber., 1899, 108, p. 273), and J. E. S. Townsend Phil. Mag., Igor [6], 1, p. 198). We shall discuss later the causes of the rise in the current with large potential differences, when we consider ionization by collision.
The general features of the earlier part of the curve are readily explained on the ionization hypothesis. On this