276.] MEASUREMENT OF CONDUCTIVITY. 555 which it will heat to redness: the same quantity of electricity is transmitted in equal intervals of time through wire of the same temperature, whether it be a centimetre only or a metre or more in length: but the increased length which the stronger current will ignite measures the increase in tension of the electric discharge. Dr. Siemens has constructed a thermometer depending on the diminution of the conductivity of a platinum wire by a rise of temperature (Proc. Roy. Soc. 1871, xix. 443). The conductivity of the different metals for electricity varies nearly in the same order as their conductivity for heat; but it is remarkable that charcoal, though so bad a conductor of heat, transmits electricity with great facility. The measurement of the conductivity of solids and of liquids for electricity has occupied the attention of many distinguished philosophers. An ingenious method was proposed many years ago by Becquerel, who constructed a differential galvanometer, in which the needles were surrounded by two insulated copper wires of equal length and diameter; they were coiled in the usual way, and formed two independent circuits, so that the galvanometer had four terminations instead of two. When two perfectly equal currents were transmitted, one through each wire in opposite directions, they exactly neutralized each other in their effect upon the needle, which therefore remained stationary; but if either current preponderated, a corresponding deviation of the needle was occasioned. To use the instrument, a small voltaic combination was connected with the galvanometer, two wires passing from each pole, so as to divide the current into two exactly equal portions, one being transmitted through one of the coils, the other through the second coil in the opposite direction. Wires of the different metals were then introduced into the two circuits. If into either circuit a conductor of inferior power were introduced, the current in that circuit was proportionately diminished, and the needle was disturbed; but the equilibrium could be restored by increasing the length of the wire in the other circuit; then by comparing the lengths of the two wires thus introduced, their relative conductivity could be inferred. By means of this instrument, conjoined with the use of Wheatstone's rheostat, Ed. Becquerel was enabled to measure the conductivity of a number of wires of different metals with precision (Ann. Chim. Phys. 1846 [3], xvii. 242). The relative conductivities of the wires were obtained by ascertaining the lengths of the rheostat wire, which was required to restore the equilibrium, when wires of different metals were employed. In fig. 229 is exhibited the arrangement adopted 556 ELECTRIC CONDUCTIVITY OF METALS. [276. in these experiments. G is the differential galvanometer with its four wires, 1 and 3 being the terminations of one coil, 2 and 4 those of the other coil; H, a voltaic pair; R, the rheostat; and w, the metallic wire the resistance of which is to be measured. This wire is stretched and insulated between two binding clamps, A and B; ss, is a copper scale, with linear subdivisions for measuring the length of the wire which is included in the circuit; D is a sliding FIG. 229. Ᏼ B clamp of copper, which can be made to move in either direction along the scale s, and can be connected with w, at any desired point, by the clamp at D. Suppose the resistance of a certain length of the wire w is to be measured. The current from н is divided into two portions so as to send each in opposite directions through the galvanometer. One half of the battery current is made to pass along the wire ƒ ƒ ƒ, up the clamp D, and through part of the wire w; the other half is transmitted through the rheostat, in the direction shown by the arrows. By coiling or uncoiling the wire of the rheostat, the two circuits are rendered exactly equal, so that the needle of the galvanometer shall stand at o°. Now, if D be unclamped, and it be caused to slide through a definite distance, say 300mm. towards B, the equilibrium of the galvanometer will be destroyed; since the resistance in w is increased, whilst that in the rheostat remains unaltered; but by uncoiling the wire of the rheostat, additional resistance can be introduced into the circuit of which it forms a part; the equilibrium may thus be again restored, and the resistance of 300mm. of in will be given by counting the number of coils of the rheostat required. The comparative resistances of any number of different wires introduced at w may thus be readily ascertained. The following table exhibits the conductivities of wires of equal length and diameter of various metals as determined by this process. The mercury was placed in a glass tube of uniform diameter. It These metals were carefully purified and well annealed. was found that annealed metals conducted better than those which 276.] ELECTRIC CONDUCTIVITY OF METALS. 557 had not undergone this process. If hard drawn silver, for instance, have a conductivity of 100, the same wire when annealed will have a conductivity of 108:57 (Matthiessen). The effect even of a moderate elevation of temperature in reducing the conductivity for the time being is very considerable, as will be evident by comparing the second column of figures in the table with the first. Electric Conductivity of Metals. (E. Becquerel, Ann. Chim. Phys. 1846 [3], xvii. 266.) The measurement of electric conductivity may be attained more simply by the use of the instrument known as Wheatstone's bridge, combined with a single galvanometer of ordinary construction. This method is now extensively employed for the measurement of the conductivities of wires for telegraphic purposes (Phil. Trans. 1843, 323). The principle of the instrument will be understood with the aid of the following diagram: 558 WHEATSTONE'S BRIDGE. [276. Upon a slab of mahogany, m m, are fastened four stout copper wires, c a, cb, z a, z b, the extremities of which are attached to binding-screws. The binding-screws z and c are to be connected with the electrodes of a voltaic combination, v; the screws a and b are to be attached to the terminal wires of the galvanometer, g. Suppose, first, the four wires to be of equal length and thickness, and to be continuous; perfect equilibrium would in this case be established in the galvanometer, how powerful soever the current from the battery, and the needle would remain at zero: for the two currents, z bg a c and z a gb c, are exactly equal, and both tend to pass in opposite directions through the galvanometer; the tensions at a and b are equal, and the needle is consequently unaffected. But if a resistance be interposed in either of the four wires, the equilibrium of the needle is disturbed. Suppose, then, that the copper wire cb be divided at ef; the current from c will now pass entirely through the continuous wire ca; at a it will become divided, part passing through the wire a z, and a smaller portion through the galvanometer and the wire bz, which offers a greater resistance than the wire a z alone. If the interval at ef be completed by a conductor, such as a mile of copper wire of which the resistance is to be measured, a smaller amount of the current will traverse the wire cefb than will pass along c a, and a proportionate amount of the current will pass through the galvanometer; but if now a resistance equal to that of the wire at ef be introduced at hi, the amount of electric tension at a and b will again become equalized, and the needle will remain stationary. By means of the resistance coils and rheostat, a known amount of resistance expressed in terms of the standard agreed upon, can be introduced at hi, and so the resistance of the wire at ef may be exactly determined in terms of this interposed resistance. Various modifications of the form of this apparatus may be used, and many precautions are needed to ensure the greatest attainable accuracy. A modification of this method was applied by Matthiessen (Phil. Mag. 1857 [4], xiii. 81) in his researches upon the conductivities of wires of various metals (Phil. Trans. 1858, 383; 1862, 1; 1863, 369). He considers the metals in the first of the two following tables to have been chemically pure. The wires of the oxidizable metals were obtained by forcing them through an opening in a steel plate, by strong pressure, the wire as it was formed being received into a vessel filled with naphtha. Matthiessen and Von Bose conclude from these experiments that the law of decrease of electric conductivity is the same for all metals, and it will be at once apparent that the relative conductivities of the metals continue to be the same with trifling variation, whether they be compared at o° or at 100° C., as will be evident by comparing the first and third columns of figures with each other. The numbers given for palladium, platinum, cobalt, iron, and nickel are calculated as on pure specimens from experiments upon specimens of these metals known to be slightly impure. In the table which follows, the metals were commercially pure, but the conductivity, when not absolutely accurate, is probably below the truth, as the addition of a second metal always diminishes the conductivity. Matthiessen finds that scrupulous attention to the purity of the metals is essential. The presence of 25 per cent. of phosphorus in copper reduced the conductivity of a specimen of the pure metal from 100 to 7.78. A mere trace of arsenic in the copper reduced it from 100 to 60, and the presence of a little suboxide |