A Treatise on Electricity and Magnetism, Vol. 1 (1881) — part 28 of 28

• [In the Philosophical Magazine for 1857, vol. i. pp. 515-525, Mr. Oliver Lodge has pointed out as a defect in Mance's method that as the electromotive force of the battery depends upon the current passing through the battery, the deflexion of the galvanometer needJe cannot be the same in the two cases when the key is down or up, if the equation a a = cy is true. Mr. Lodge describes a modification of Mance's method which he has employed with success.]

452

MEASUREMENT OF RESISTANCE.

[358-

The method of Art. 356 for finding the resistance of the galva- nometer differs from this only in making and breaking contact between 0 and A instead of between 0 and B, and by exchanging a and 3 we obtain for this case

y

On the Comparison of Electromotive Forces.

358.] The following method of comparing the electromotive forces of voltaic and thermoelectric arrangements, when no current passes through them, requires only a set of resistance coils and a constant battery.

Let the electromotive force E of the battery be greater than that of either of the electromotors to be compared, then, if a sufficient

resistance, R19 be interposed between the points Alt B1 of the primary circuit EB1A1E, the electromotive force from B: to Al may be made equal to that of the electromotor E±. If the elec- trodes of this electromotor are now connected with the points Al9 Bl no current will flow through the electromotor. By placing a galvanometer G± in the circuit of the electromotor El9 and adjusting the resistance between A1 and Blt till the galvanometer G± indicates no current, we obtain the equation

where Rl is the resistance between A1 and B19 and C is the strength of the current in the primary circuit.

In the same way, by taking a second electromotor E% and placing its electrodes at A2 and B2, so that no current is indicated by the galvanometer 6r2,

COMPARISON OF ELECTROMOTIVE FORCES. 453

where 7?2 is the resistance between A2 and JS2. If the observations of the galvanometers Gt and G2 are simultaneous, the value of C, the current in the primary circuit, is the same in both equations, and we find

EI : E2 i '• RI '• H2»

In this way the electromotive force of two electromotors may be compared. The absolute electromotive force of an electromotor may be measured either electrostatically by means of the electrometer, or electromagnetically by means of an absolute galvanometer.

This method, in which, at the time of the comparison, there is no current through either of the electromotors, is a modification of Poggendorff's method, and is due to Mr. Latimer Clark, who has deduced the following values of electromotive forces :

Concentrated v u

solution of

Daniell I. Amalgamated Zinc HSO4 + 4 aq. Cu SO4 Copper = 1.079

II. „ HS04 + 12aq. CuS04 Copper =0.978

III. „ HS04+12aq. CuNOa Copper =1.00 JSunsenl. „ „ „ HNOfl Carbon » 1.964

II. „ „ „ sp. g. 1.38 Carbon =1.888

Grove „ HS04+ 4 aq. HNO, Platinum = 1.956

A Volt is an electromotive force equal to 100,000,000 units of the centimetre-gramme- second system.

CHAPTER XII.

ON THE ELECTRIC RESISTANCE OF SUBSTANCES.

359.] THERE are three classes in which we may place different substances in relation to the passage of electricity through them.

The first class contains all the metals and their alloys, some sulphurets, and other compounds containing metals, to which we must add carbon in the form of gas-coke, and selenium in the crystalline form.

In all these substances conduction takes place without any decomposition, or alteration of the chemical nature of the substance, either in its interior or where the current enters and leaves the body. In all of them the resistance increases as the temperature rises.

The second class consists of substances which are called electro- lytes, because the current is associated with a decomposition of the substance into two components which appear at the electrodes. As a rule a substance is an electrolyte only when in the liquid form, though certain colloid substances, such as glass at 100°C, which are apparently solid, are electrolytes. It would appear from the experiments of Sir B. C. Brodie that certain gases are capable of electrolysis by a powerful electromotive force.

In all substances which conduct by electrolysis the resistance diminishes as the temperature rises,

The third class consists of substances the resistance of which is so great that it is only by the most refined methods that the passage of electricity through them can be detected. These are called Dielectrics. To this class belong a considerable number of solid bodies, many of which are electrolytes when melted, some liquids, such as turpentine, naphtha, melted paraffin, &c., and all gases and vapours. Carbon in the form of diamond, and selenium in the amorphous form, belong to this class.

The resistance of this class of bodies is enormous compared with that of the metals. It diminishes as the temperature rises. It

360.] RESISTANCE. 455

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

On the Electric Resistance of Metals.

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

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

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

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

r = aT* + /37+y,

where T is the absolute temperature reckoned from — 273CC, and a, )3, y are constants. Thus, for

Platinum r= 0.039369 T* + 0.00216407 7-0.2413,

Copper r= 0.026577 7* + 0.0031443 7-0.22751,

Iron.! r = 0.072545 2*4 0.0038133 T- 1.23971.

• Proe. R. S., April 27, 1871.

456 RESISTANCE. [361.

From data of this kind the temperature of a furnace may be determined by means of an observation of the resistance of a platinum wire placed in the furnace.

Dr. Matthiessen found that when two metals are combined to form an alloy, the resistance of the alloy is in most cases greater than that calculated from the resistance of the component metals and their proportions. In the case of alloys of gold and silver, the resistance of the alloy is greater than that of either pure gold or pure silver, and, within certain limiting proportions of the con- stituents, it varies very little with a slight alteration of the pro- portions. For this reason Dr. Matthiessen recommended an alloy of two parts by weight of gold and one of silver as a material for reproducing the unit of resistance.

The effect of change of temperature on electric resistance is generally less in alloys than in pure metals.

Hence ordinary resistance coils are made of German silver, on account of its great resistance and its small variation with tem- perature.

An alloy of silver and platinum is also used for standard coils.

361.] The electric resistance of some metals changes when the metal is annealed; and until a wire has been tested by being repeatedly raised to a high temperature without permanently altering its resistance, it cannot be relied on as a measure of resistance. Some wires alter in resistance in course of time without having been exposed to changes of temperature. Hence it is important to ascertain the specific resistance of mercury, a metal which being fluid has always the same molecular structure, and which can be easily purified by distillation and treatment with nitric acid. Great care has been bestowed in determining the resistance of this metal by W. and C. F. Siemens, who introduced it as a standard. Their researches have been supplemented by those of Matthiessen and Hockin.

The specific resistance of mercury was deduced from the observed resistance of a tube of length I containing a weight w of mercury, in the following manner.

No glass tube is of exactly equal bore throughout, but if a small quantity of mercury is introduced into the tube and occupies a length A of the tube, the middle point of which is distant x from one end of the tube, then the area s of the section near this point

Q

will be s = — , where C is some constant.

A

362.] OF METALS. 457

The weight of mercury which fills the whole tube is

w — p I sdx — pCl, (-} -> J vAy n

where n is the number of points, at equal distances along the tube, where A has been measured, and p is the mass of unit of

volume.

The resistance of the whole tube is

where r is the specific resistance per unit of volume. Hence wR = rp 2 (A) 2 (i) ^ ,

wR n2

and

-J2

pl

gives the specific resistance of unit of volume.

To find the resistance of unit of length and unit of mass we must multiply this by the density.

It appears from the experiments of Matthiessen and Hockin that the resistance of a uniform column of mercury of one metre in length, and weighing one gramme at 0°C, is 13.071 Ohms, whence it follows that if the specific gravity of mercury is 13.595, the resistance of a column of one metre in length and one square millimetre in section is 0.96146 Ohms.

362.] In the following table R is the resistance in Ohms of a column one metre long and one gramme weight at 0°C, and r is the resistance in centimetres per second of a cube of one centi- metre, according to the experiments of Matthiessen *.

Percentage increment of

Specific resistance for

gravity R r 1°C at 20°C.

Silver ....... 10.50 hard drawn 0.1689 1609 0.377

Copper ...... 8.95 hard drawn 0.1469 1642 0.388

Gold ....... 19.27 hard drawn 0.4150 2154 0.365

Lead ....... H.391 pressed 2.257 19847 0.387

Mercury ..... 13.595 liquid 13.071 96146 0.072

Gold 2, Silver 1 . . 15.218 hard or annealed 1.668 10988 0.065

Selenium at 1 00°C Crystalline form 6 x 1 013 1.00

• Phil. Mag., May, 1865.

458 EESTSTANCE. [363.

On the Electric Resistance of Electrolytes.

363.] The measurement of the electric resistance of electrolytes is rendered difficult on account of the polarization of the electrodes, which causes the observed difference of potentials of the metallic electrodes to be greater than the electromotive force which actually produces the current.

This difficulty can be overcome in various ways. In certain cases we can get rid of polarization by using electrodes of proper material, as, for instance, zinc electrodes in a solution of sulphate of zinc. By making the surface of the electrodes very large com- pared with the section of the part of the electrolyte whose resist- ance is to be measured, and by using only currents of short duration in opposite directions alternately, we can make the measurements before any considerable intensity of polarization has been excited by the passage of the current.

Finally, by making two different experiments, in one of which the path of the current through the electrolyte is much longer than in the other, and so adjusting the electromotive force that the actual current, and the time during which it flows, are nearly the same in each case, we can eliminate the effect of polarization altogether.

364.] In the experiments of Dr. Paalzow * the electrodes were in the form of large disks placed in separate flat vessels filled with the electrolyte, and the connexion was made by means of a long siphon filled with the electrolyte and dipping into both vessels. Two such siphons of different lengths were used.

The observed resistances of the electrolyte in these siphons being R^ and R2, the siphons were next filled with mercury, and their resistances when filled with mercury were found to be R± and 222'.

The ratio of the resistance of the electrolyte to that of a mass of mercury at 0°C of the same form was then found from the

formula 7> r>

HI— H.->

= F/^-

To deduce from the values of p the resistance of a centimetre in length having a section of a square centimetre, we must multiply them by the value of r for mercury at 0°C. See Art. 361.

• Berlin Monatsbericht, July, 1868.

365-] OF ELECTROLYTES. 459

The results given by Paalzow are as follow : —

Mixtures of Sulphuric Acid and Wafer.

Temp Resistance compared

with mercury.

H2SO4 15CC 96950

H2SO4+ 14 IPO 19CC 14157

H2SO4 + 13H20 22°C 13310

H2S04+499H20 22CC 184773

Sulphate of Zinc and Water.

ZnSO4-f- 23 IPO 23CC 194400

ZnSO4+ 24H20 23°C 191000

ZnSO4+105H2O 23°C 354000

Sulphate of Copper and Water.

CuSO4 + 45 IPO 22°C 202410

CuSO4+105H2O 22CC 339341

Sulphate of Magnesium and Water.

MgSO4-f 34H20 22°C 199180

MgSO4+107H2O 22°C 324600

Hydrochloric Acid and Water.

HC1 + 15 IPO 23CC 13626

HC1 + 500IPO 23°C 86679

365.] MM. F. Kohlrausch and W. A. Nippoldt* have de- termined the resistance of mixtures of sulphuric acid and water. They used alternating magneto-electric currents, the electromotive force of which varied from \ to 7*T of that of a Grove's cell, and by means of a thermoelectric copper-iron pair they reduced the electromotive force to T^^TTO of ^na^ °f a Grove's cell. They found that Ohm's law was applicable to this electrolyte throughout the range of these electromotive forces.

The resistance is a minimum in a mixture containing about one- third of sulphuric acid.

The resistance of electrolytes diminishes as the temperature increases. The percentage increment of conductivity for a rise of 1°C is given in the following table.

• Pogg., Ann. cxxxviii. p. 286, Oct. 1869.

460

RESISTANCE.

[366.

Resistance of Mixtures of Sulphuric Acid and Water at 22°C in terms of Mercury at 0°C. MM. Kohlrausch and Nippoldt.

Specific gravity at 18°5

Percentage ofH2SO,

Resistance at 22°C (Hg-1)

Percentage increment of conductivity . for 1°C

0.9985

0.0

746300

0.47

1.00

0.2

465100

0.47

1.0504

8.3

34530

0.653

1.0989

14.2

18946

0.646

1.1431

20.2

14990

0.799

1.2045

28.0

13133

1.317

1.2631

35.2

13132

1.259

1.3163

41.5

14286

1.410

1.3547

46.0

15762

1.674

1.3994

50.4

17726

1.582

1.4482

55.2

20796

1.417

1.5026

60.3

25574

1.794

On the Electrical 'Resistance of Dielectrics.

366.] A great number of determinations of the resistance of gutta-percha, and other materials used as insulating media, in the manufacture of telegraphic cables, have been made in order to ascertain the value of these materials as insulators.

The tests are generally applied to the material after it has been used to cover the conducting wire, the wire being used as one electrode, and the water of a tank, in which the cable is plunged, as the other. Thus the current is made to pass through a cylin- drical coating of the insulator of great area and small thickness.

It is found that when the electromotive force begins to act, the current, as indicated by the galvanometer, is by no means constant. The first effect is of course a transient current of considerable intensity, the total quantity of electricity being that required to charge the surfaces of the insulator with the superficial distribution of electricity corresponding to the electromotive force. This first current therefore is a measure not of the conductivity, but of the capacity of the insulating layer.

But even after this current has been allowed to subside the residual current is not constant, and does not indicate the true conductivity of the substance. It is found that the current con- tinues to decrease for at least half an hour, so that a determination

366.] OF ELECTROLYTES. 461

of the resistance deduced from the current will give a greater value if a certain time is allowed to elapse than if taken immediately after applying the battery.

Thus, with Hooper's insulating material the apparent resistance at the end of ten minutes was four times, and at the end of nineteen hours twenty-three times that observed at the end of one minute. When the direction of the electromotive force is reversed, the resistance falls as low or lower than at first and then gradually rises.

These phenomena seem to be due to a condition of the gutta- percha, which, for want of a better name, we may call polarization, and which we may compare on the one hand with that of a series of Leyden jars charged by cascade, and, on the other, with Hitter's secondary pile, Art. 271.

If a number of Leyden jars of great capacity are connected in series by means of conductors of great resistance (such as wet cotton threads in the experiments of M. Gaugain), then an electro- motive force acting on the series will produce a current, as indicated by a galvanometer, which will gradually diminish till the jars are fully charged.

The apparent resistance of such a series will increase, and if the dielectric of the jars is a perfect insulator it will increase without limit. If the electromotive force be removed and connexion made between the ends of the series, a reverse current will be observed, the total quantity of which, in the case of perfect insulation, will be the same as that of the direct current. Similar effects are observed in the case of the secondary pile, with the difference that the final insulation is not so good, and that the capacity per unit of surface is immensely greater.

In the case of the cable covered with gutta-percha, &c , it is found that after applying the battery for half an hour, and then con- necting the wire with the external electrode, a reverse current takes place, which goes on for some time, and gradually reduces the system to its original state.

These phenomena are of the same kind with those indicated by the 'residual discharge' of the Leyden jar, except that the amount of the polarization is much greater in gutta-percha, &c. than in glass.

This state of polarization seems to be a directed property of the material, which requires for its production not only electromotive force, but the passage, by displacement or otherwise, of a con-

462 RESISTANCE. [367.

siderable quantity of electricity, and this passage requires a con- siderable time. When the polarized state has been set up, there is an internal electromotive force acting1 in the substance in the reverse direction, which will continue till it has either produced a reversed current equal in total quantity to the first, or till the state of polarization has quietly subsided by means of true con- duction through the substance.

The whole theory of what has been called residual discharge, absorption of electricity, electrification, or polarization, deserves a careful investigation, and will probably lead to important dis- coveries relating to the internal structure of bodies.

367.] The resistance of the greater number of dielectrics di- minishes as the temperature rises.

Thus the resistance of gutta-percha is about twenty times as great at 0°C as at 24CC. Messrs. Bright and Clark have found that the following formula gives results agreeing with their experiments. If r is the resistance of gutta-percha at temperature T centigrade, then the resistance at temperature T-- 1 will be

E = rx 0.8878*, the number varies between 0.8878 and 0.9.

Mr. Hockin has verified the curious fact that it is not until some hours after the gutta-percha has taken its temperature that the resistance reaches its corresponding value.

The effect of temperature on the resistance of india-rubber is not so great as on that of gutta-percha.

The resistance of gutta-percha increases considerably on the application of pressure.

The resistance, in Ohms, of a cubic metre of various specimens of gutta-percha used in different cables is as follows *.

Name of Cable.

Red Sea , 267 x 1012 to .362 x 1012

Malta-Alexandria 1.23 x 1012

Persian Gulf... 1.80 x 1012

Second Atlantic 3.42 X 1012

Hooper's Persian Gulf Core... 74.7 x 1012 Gutta-percha at 24°C 3.53 x 1012

368.] The following table, calculated from the experiments of

• Jenkin's Cantor Lectures.

37°-] OF DIELECTRICS. 403

M. Buff, described in Art. 271, shews the resistance of a cubic metre of glass in Ohms at different temperatures.

Temperature. Resistance.

200CC 227000

250° 13900

300° 1480

350° 1035

400° 735

369.] Mr. C. F. Varley * has recently investigated the conditions of the current through rarefied gases, and finds that the electro- motive force E is equal to a constant EQ together with a part depending on the current according to Ohm's Law, thus

For instance, the electromotive force required to cause the current to begin in a certain tube was that of 323 Daniell's cells, but an electromotive force of 304 cells was just sufficient to maintain the current. The intensity of the current, as measured by the galvanometer, was proportional to the number of cells above 304. Thus for 305 cells the deflexion was 2, for 306 it was 4, for 307 it was 6, and so on up to 380, or 304-1-76 for which the deflexion was 150, or 76 x 1.97.

From these experiments it appears that there is a kind of polarization of the electrodes, the electromotive force of which is equal to that of 304 DanielFs cells, and that up to this electro- motive force the battery is occupied in establishing this state of polarization. When the maximum polarization is established, the excess of electromotive force above that of 304 cells is devoted to maintaining the current according to Ohm's Law.

The law of the current in a rarefied gas is therefore very similar to the law of the current through an electrolyte in which we have to take account of the polarization of the electrodes.

In connexion with this subject we should study Thomson's results, described in Art. 57, in which the electromotive force required to produce a spark in air was found to be proportional not to the distance, but to the distance together with a constant quantity. The electromotive force corresponding to this constant quantity may be regarded as the intensity of polarization of the electrodes.

370.] MM. Wiedemann and Riihlmann have recently f investi-

• Proc. R. £., Jan. 12, 1871.

t Berichte der Konigl. Sachs. Gesellschaft, Oct. 20, 1871.

464 RESISTANCE OF DIELECTRICS.

gated the passage of electricity through gases. The electric current was produced by Holtz's machine, and the discharge took place between spherical electrodes within a metallic vessel containing rarefied gas. The discharge was in general discontinuous, and the interval of time between successive discharges was measured by means of a mirror revolving along with the axis of Holtz's machine. The images of the series of discharges were observed by means of a heliometer with a divided object-glass, which was adjusted till one image of each discharge coincided with the other image of the next discharge. By this method very consistent results were obtained. It was found that the quantity of electricity in each discharge is independent of the strength of the current and of the material of the electrodes, and that it depends on the nature and density of the gas, and on the distance and form of the electrodes.

These researches confirm the statement of Faraday * that the electric tension (see Art. 48) required to cause a disruptive discharge to begin at the electrified surface of a conductor is a little less when the electrification is negative than when it is positive, but that when a discharge does take place, much more electricity passes at each discharge when it begins at a positive surface. They also tend to support the hypothesis stated in Art. 57, that the stratum of gas condensed on the surface of the electrode plays an important part in the phenomenon, and they indicate that this condensation is greatest at the positive electrode.

• Exp. Res., 1501.

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