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LONDON, EDINBURGH AND DUBLIN
JOURNAL OF SCIENCE.
XIII. On the Electric Conducting Power of the Metals of the Alkalies and Alkaline Earths. By A. MATTHIESSEN, Ph.D.*
[With a Plate.] THE THE electric conducting power of one of these metals, potas
sium, was determined by Becquerel about thirty years ago t; he found its ratio to that of silver to be 107:100, whereas according to my experiments this ratio appears to be 22:6: 100. He, however, is not sufficiently explicit in the description of the method he employed for one to ascertain the cause of this great difference in our restits. Latterly, after my experiments on the alkaline metals were finished and the results already printed I, M. Lamy S published a notice on the electric conducting power of potassium and sodium, wherein he only states the place in the series these two metals take compared with those whose conducting powers are already decided; in this respect his results agree with mine.
For these experiments I employed wires formed by pressure. The press consisted of a small block of steel, the section of which (Plate I. fig. 1) shows it of its natural size. In the hole, which ends in a fine round opening, the metal is placed, and the steel piston being fitted on, the press is fixed between two small iron bars, which are then placed in a vice. Potassium, sodium and lithium, on account of their strong tendency to oxidation, were pressed immediately in a trough filled with rock-oil, the oil
* Communicated by the Author.
Phil. Mag. September 1856.
having been previously boiled in small portions at a time with metallic sodium to make it perfectly dry and free from oxygen. Fig. 2 shows the process of pressing the wires. Here we have the vice and the iron bars mentioned above, the latter connected at the upper end in such a manner as to permit the pressure of the vice to act on the steel press which is held between them at the lower end within the trough of rock-oil; the bar which is in contact with the block of the press has an aperture through which the wire can pass.
As soon as the wire appears it is laid hold of with pincers and inserted in a wire-holder, consisting of two pieces of hard brass whose extremities are riveted at one end to a thick copper wire, and press together at the other, as shown in fig. 3; the copper wire is bent and fixed in the block of wood i, fig. 2. The wire-holder was moved back and the wire increased until it had attained the desired length, when it was cut off from the press and fastened in the second wire-holder, the press and bars being removed. In the trough a plate of glass was supported in such a position that the wire lay upon it, in order to prevent the latter from distending through the effect of its own weight: this precaution was especially necessary with potassium, on account of the warmth of the weather in which the experiments were made. To prevent as much as possible the absorp
. tion of the oxygen of the air by the rock-oil, a plate of glass was placed over the trough as soon as the second end of the wire was secured: fig. 4, representing a section of the trough, shows how this plate was supported, allowing at the same time the free movement of the wire-holders.
As wires of calcium, strontium, and magnesium cannot be obtained without the aid of heat, a glassblower's gas-lamp was brought to bear on the press whilst under pressure between the jaws of the vice; a layer of asbestos placed between the press and retaining bars prevented these from conducting the heat away. With this arrangement I have even been able to press tellurium, antimony, and bismuth wires, to whose conducting powers I shall shortly return.
The calcium and strontium wires were pressed into a tube filled with rock-oil, which was held before the opening of the press, so that the metal had only the distance of a few millimetres to pass through the air; in the case of magnesium the rock-oil was not necessary. As soon as the wires had attained their desired length in the tubes, they were removed into the trough of rock-oil mentioned above, where the wires were taken out of the tubes, scraped at the ends, and fastened in the wireholders as before described.
The method by which the electrical resistance was determined was that given by Mr. Wheatstone, modified by the use of an apparatus constructed by Prof. Kirchhoff. The principle of Mr. Wheatstone's method is as follows When four wires form the four sides of a quadrilateral figure, with one of the diagonals of which a battery is connected, and with the other a galvanometer, if no current be indicated by the latter, the resistances of the four sides are proportional. Suppose, then, the first of these wires to be of the metal whose resistance is sought; the second, a chemically pure silver wire; and the third and fourth, parts of a copper wire stretched on a strip of wood, and separated from each other by a block of lead with a shield of copper on one side, which moves along the wood, keeping the edge of the copper in contact with the wire, and that a wire of the same metal connects this shield with the galvanometer. Then if no current passes through the latter, we have the ratio of the electric resistances of the wire under observation, and the normal silver wire identical with that of the parts of the copper wire divided by the shield, which is easily read off by means of a scale affixed to the wood.
The arrangement of the apparatus is shown in fig. 5. The strip of wood, A, about 4 inches wide and 1 inch thick, has two binding screws, a and d, at its middle point; these hold the two ends of a copper wire about 1 millim. thick and nearly twice the length of the wood, on the surface of which it is stretched, passing round the pegs s and s' at the extremities; on the wood is fixed a scale, by means of which the length of the two parts of the wire divided by the shield may be read off; the shield, b, is connected with the galvanometer, g, by a spiral wire. At the point c in the copper wire near the binding screw a, a wire is sol. dered on, of which one end dips in the quicksilver cup g, and the other is connected with one pole of the battery K; a similar wire is soldered on at the point d near the screw a', the one end dipping in the cup d, and the other passing to the second pole of the battery: in the same snall block of wood in which are the cups g and d', are two others, e and f, forming with the others the four corners of a square. With f one end of the normal silver wire is connected; this wire, wound round a piece of wood, is immersed in the cylinder N filled with rock-oil; both of its ends are soldered to thick copper wires, the one going to f and the other to h. Two copper wires connect the cups e and h with the cups i and k, in which the wire-holders are fastened. From h another wire goes to the galvanometer. Above the block of wood containing the cups e f g g' is another small block, through which are passed two wires twice bent at right angles, so that the four ends fit in the cups below. With this arrangement we can connect either fg and eg' together, or eg and fg. At each of these positions of the commutator a quadrilateral figure of the
nature before specified is formed, whose angular points are c and d', the point of contact of the copper shield, and the quicksilver cup h. By altering, therefore, the position of the commutator, the relative position of the silver wire and the wire whose resistance we want is exchanged. In the scăle on the wood the zeropoint is equally distant from c and d'; each division is 6.75 millims.; the length of the wire from the zero-point to c or dis 170-5 such divisions.
Let l represent this number, L, the number indicated by the scale at the point of contact by the copper shield for the position of the commutator numbered 1, and L, for the position 2 of the commutator; then we have the ratio of the resistances of that branch containing the silver wire to that containing the wire in the trough
1-L 1+La Let n represent the resistance of the silver wire, w that of the wire under observation, a that of the wires making up the firstmentioned branch with the silver wire, and b that of those completing the second branch; then w+b 1+L
1-L nt a l-Li' 1+ LE In order from this formula to calculate w for the observed values of L, and Lą, on the supposition that n is known, it was only necessary to determine a and b by preliminary experiments. This was done as follows :- In the place of wires of potassium, sodium, &c., under the same circumstances, silver wires from the same piece as the normal wire were fastened; let w' and w" be the resistances of two such wires, and L', and Il", the corresponding values of Lj; then W+b 1+1,
and nta I-L, nta l-I'i Taking the unit of electrical resistance to be that of 1 millim. of the normal silver wire, we then call the values of n, u', w" the lengths expressed in millimetres of the wires whose resistances they represent, and from the two equations we can calculate the values of a and b. For the experiments with potassium, sodium and lithium, these values were
n=500:9, w=492-4, W=594.2. These numbers express in millimetres the lengths of these three wires, from each of which 4 millims. having been subtracted to allow in the first case for the soldering on, for the others for
the fastening in the wire-holders, we had
I',= -3.15, 1/",=11.55, from which we find
For the experiments with calcium, strontium and magnesium, another normal wire and other connecting wires were used; here we had therefore other values for n, a and b.
When the resistance, w, is known in terms of our unit of resistance, we can determine the ratio we require as follows:-Let , be its conducting power, L its length in millimetres, & its diameter, r the diameter of the normal silver wire, and s the conducting power of silver at the temperature at the time the observation was made, determined by a thermometer placed in the rock-oil contained in the cylinder N; then
Taking the conducting power of silver at 0° C. = 100, then, according to Lenz's formula*, it is at t C.,
s=100-0-292547 +0.0003776to. L was determined after the observation had been made by means of a beam-compass, d was found by measuring the fine opening of the press under the microscope. Lead wires pressed cold showed the same diameter as the opening of the press; we can therefore take it for granted that it was the same with potassium, sodium and lithium wires; with the hot-pressed wires, calcium, strontium and magnesium, the diameter was measured directly under the microscope whilst the wire lay in rock-oil : here we found the diameter inconstant, and always smaller than the opening of the press; the mean of the diameters of the two ends was therefore taken and brought into calculation.
The results which were obtained with the different wires now follow. In the first two columns are the values of L, and L, of which the arithmetical mean was taken; the third gives the temperature t of the normal silver wire; the fourth the temperature T of the wire in the trough; the fifth the diameter & in millimetres; the sixth the length L, also in millimetres; and the seventh the conducting power à for the temperature T. The values of n, a, b, and r are also annexed.
* Poggendorff's Annalen, vol. xxxiv. p. 433.