On the Influence of Temperature on the Electric Conducting Power of Metals

I. On the Influence of Temperature on the Electric Conducting Power of Metals. By Augustus Matthiessen, F.R.S., and Moritz von Bose. Received December 5, 1861,—Read January 16, 1862. The results obtained by different observers in their researches on the influence of temperature on the electric conducting power of metals do not agree at all together. The differences in their results may be partly owing to their not having tested pure metals, and partly to their not having taken into consideration the fact that, when a wire of a pure metal is heated for the first time to 100° C., an alteration in the conducting power of the wire is observed on its again being cooled; in fact, it is necessary to keep the wire for several days at 100° before its conducting power, on again being cooled, becomes constant. In the experiments we are about to detail we have taken great care to employ only pure metals, as well as a method and a disposition of the apparatus with which great accuracy could be obtained. The method employed for the determination of the resistances is fully described in the 'Philosophical Magazine' for February 1857. Fig. 1 shows the disposition of the apparatus. B is the trough in which the wires were heated: these were soldered to two thick copper wires F (4–5 millims. thick), bent as shown in the figure, and ending in the mercury-cups E, which were connected with the apparatus by two other copper wires, F', of the same thickness. C is a piece of board placed in such a manner as to prevent the heat of the trough from radiating on the apparatus. The mercury-cups O are made of small blocks of wood, through which holes are bored just large enough to take the thick wires, and to the bottoms of which blocks amalgamated copper plates are fastened. Now it is clear that if the ends of the thick copper wires are filed flat, and well amalgamated, and the mercury-cups are filled with mercury, this method of connexion may be looked upon as a soldering of the copper plates to the wires, or, in other words, as a perfect connexion; for the wires may be removed as often as required, and on replacing them the same resistance is always observed. The wires F", to which the normal wire (in the glass cylinder G) is soldered, are also 4–5 millims. thick. The reason why such thick wires were chosen was to make any difference in their resistance, caused by the change of temperature in the room or by the heating of the ends in the oil-bath, so small that no correction was necessary. This was proved to be the case by the following experiment:—After having soldered a wire in the trough to the ends of the thick copper wires, and determined its resistance with the normal wire generally used, the wire F' at e was heated with the 6-Bunsen burner much above 100° C., and the resistance of the circuit was again determined whilst the wire was at that temperature, when it was found to have increased only 0·08 per cent.; we did not, therefore, consider it necessary to make any correction for the increase of resistance caused by the heating of the ends of the thick wires in the trough. The resistance of the copper wires was determined at the ordinary temperature, and brought into calculation without further correction. Before the commencement of each series, all the ends of the wires dipping into the mercury-cups were carefully re-amalgamated. L, L' are the two commutators fitting into four mercury-cups at o. The wire stretched on the board H is of german silver instead of copper, as was formerly described; its half-length was 4550 millims. The length of the board is about 1500 millims.; the wire, therefore, was wound backwards and forwards several times on the one side; this is not visible in the figure. By using normal wires of different resistances, and by choosing proper lengths of the wire to be tested, it was always possible to begin the observations with the block M within 100 millims. of the middle of the wire. Great care was taken to lift the block M off the wire when it was moved, in order to prevent as much as possible its wearing. It may be mentioned that, although we generally worked with only one of the commutators, and therefore mostly used the one half of the wire, the zero-point of the wire only varied, during the whole of the experiments, which have taken almost a year to carry out, 3 millims. The zero-point was always determined before each series was begun. The distance the block M was moved when the resistance of a wire was determined, first at $0^\circ$ and then at $100^\circ$, was, for pure metals in a solid state, about 800 millims., or about 8 millims. for $1^\circ$. As, however, the movement of the block M of 1 millim. caused a deflection of the needles of the galvanometer I of $20^\circ$ to $30^\circ$, it is evident, with the apparatus employed, that the differences in the resistance of a wire to values less than those corresponding to $0^\circ\cdot1$ C. can be accurately determined. Our results, moreover, prove this to be the case, as in many instances the difference between the observed and calculated conducting powers for the whole series do not amount to values equal to $0^\circ\cdot1$ to $0^\circ\cdot2$ C. The trough B is a double one, the space between the inner and outer one being 20 millims. The dimensions of the inner trough were 400 millims. long, 80 millims. wide, and 80 millims. deep. Through the ends of both two holes of about 20 millims. wide were made, in which good corks were fitted, and through these passed the thick copper wires F; and also at one end a glass tube d, wide enough to allow the thermometer c to pass freely. A piece of india-rubber tubing, fitting over the glass tube d, and tightly round the thermometer, closed the tube, but allowed the thermometer to be moved either backward or forward with great ease. The tubes a are for filling the space between the inner and outer troughs with oil. The wire to be tested lay in the trough, as shown in fig. 2, on a small glass tray, made by splitting a glass tube longitudinally, thereby preventing any possibility of its touching the trough, and also guarding it from being moved by the stirrer. A second trough, of somewhat smaller dimensions, was also used. The use of an oil-bath for heating the wires has been objected to by a former observer*; it was therefore necessary to determine experimentally whether there was any real reason for the objection or not. He states that, as oil conducts electricity better on being heated than when cold, the differences between the conducting powers of cold and hot oil will materially affect the values obtained for the resistances of wire which had been determined at different temperatures in that liquid. In order to test the accuracy of this assertion, two copper plates of about 150 millims. diameter were connected, the one with the galvanometer, the other with a single Bunsen's cell; and to complete the circuit, this was connected with the galvanometer. A piece of filtering-paper, moistened with the olive-oil used, was placed between the copper plates, and these were pressed together with a weight. On completing the circuit not the slightest deflection of the needles was observed; the copper plates were then heated to above $100^\circ$ C., and still no deflection was visible. To show that the connexions were good, a drop of water was put on the oiled paper; and immediately the needles of the galvanometer were sent with great violence to the stops. This proves that although oil may --- * Arndsten, Poggendorff's 'Annalen,' vol civ. p. 1. have a higher conducting power when hot than cold, yet in either case it is so infinitely small, that it cannot influence the results obtained in the manner just described. Again, it was proved in a former research* that the formula for the correction of conducting power for temperature of a wire, deduced from the observations made in an oil- or air-bath, were exactly the same. Thus the formula obtained for an annealed wire of the gold-silver alloy heated in the oil-bath was \[ \lambda = 15.052 - 0.01074t + 0.00000714t^2, \] and that for the same wire heated in an air-bath was \[ \lambda = 15.059 - 0.01077t + 0.00000722t^2. \] As, however, more accurate results may be obtained by experimenting in an oil- than in an air-bath, on account of the wires taking more readily the temperature of the bath, and of their being more rapidly cooled if heated by the current passing through them, we have chosen this manner of heating the wires in preference to the other. As oil, and more especially oil when hot, attacks most wires to a degree which would render the observations valueless, we were obliged to varnish them. The best varnish for the purpose is a solution of shell-lac in alcohol. For instance, a hard-drawn copper wire, not varnished, loses in conducting power after having been heated in an oil-bath to 100°, but if varnished, increases. To show that varnishing has no effect on the results, we give in Table I. the conducting power of a hard-drawn gold wire, first not varnished, and then varnished. Each result is the mean of two observations. ### Table I. | T | Conducting power. | Difference. | Conducting power. | Difference. | |-------|-------------------|-------------|-------------------|-------------| | | Observed. | Calculated. | Observed. | Calculated. | | 15°30 | 72.697 | 72.705 | 13°85 | 73.120 | | 30°55 | 68.806 | 68.879 | 30°95 | 68.756 | | 48°65 | 64.659 | 64.717 | 49°55 | 64.523 | | 69°55 | 60.409 | 60.423 | 68°40 | 60.636 | | 83°25 | 57.915 | 57.906 | 84°55 | 57.704 | | 99°85 | 55.151 | 55.174 | 98°70 | 55.346 | | 84°55 | 57.704 | 57.680 | 84°90 | 57.645 | | 70°80 | 60.224 | 60.184 | 70°25 | 60.318 | | 50°85 | 64.239 | 64.239 | 51°20 | 64.149 | | 30°95 | 68.746 | 68.782 | 30°60 | 68.886 | | 16°80 | 72.343 | 72.316 | 17°85 | 72.111 | The formula deduced from the observations, and from which the conducting powers were calculated, was \[ \lambda = 76.838 - 0.27973t + 0.0006285t^2. \] The thermometers used were:—1. One divided into degrees, each of which was 3.5 * Philosophical Magazine for February 1861. millims. long. With very little practice the temperature could be read off to 0°·1 C. with accuracy. This thermometer was calibrated by ourselves, and afterwards compared with a normal thermometer from Kew Observatory, for which we were indebted to the kindness of Mr. Balfour Stewart. The corrected readings of our thermometer agreed perfectly with those of the Kew thermometer. 2. A normal thermometer from Messrs. Negretti and Zambra, divided into 0°·2 C. This was compared with the Kew thermometer and found to be correct. The boiling- and freezing-points of the thermometers were taken at intervals, and the necessary corrections made. As the light in the room where the experiments were made came from above, and as the thermometers lay horizontally in the trough, by placing the eye in a position so that the division on the thermometer covered its reflexion on the column of mercury, all error of parallax was avoided. The thermometers were always read off with the help of the magnifying glass A through the oil in the glass tube d, so that the whole of the column of mercury had very nearly the temperature of the bath. The normal wires were made of annealed german silver, and their resistances determined by comparing them with a hard-drawn wire of the gold-silver alloy*. They were soldered to two thick copper wires, varnished, and when used placed in the cylinder G, filled with oil, in which a thermometer hung. The temperature of the oil was taken immediately after each observation, and the conducting power of the normal wire corrected by the use of the formula \[ \lambda = 7·803 - 0·0034619t + 0·0000003951t^2, \] which was found by the determination of the conducting powers, at different temperatures, of a piece of wire from the same coil as that from which the normal wires were cut. In this paper we have taken as unit the conducting power of a hard-drawn silver wire at 0° C. = 100 (that of the hard-drawn gold-silver alloy at 0° being = 15·03), in order to be able to compare at sight the present determinations with those made by one of us a short time ago†. Before beginning a series, as already stated, all the ends of the wires dipping in the mercury-cups were re-amalgamated, and the zero-point of the scale redetermined. The current from the cell D was only allowed to pass through the apparatus for a second or two at a time, for fear of heating the wires, &c. From 0° to 100° seven intervals were chosen at which observations were made, viz. 12°, 25°, 40°, 55°, 70°, 85°, 100°. With a little practice the flames of the 6-Bunsen burner could be regulated so as to come within a degree or two of the above temperatures. For about five minutes before, and whilst making the observations, the oil in the trough was stirred, one observer being at the trough whilst the other determined the resistances. Four observations at each interval were generally made on heating the wire to 100°, and again four at each interval on cooling (where this was not the case it will be mentioned with the series). * Philosophical Magazine, February 1861. † Philosophical Transactions, 1858 and 1860. To save space, the mean only of the eight observations will be given, as otherwise the number of figures would be very great. Table I. may be taken as a fair example of the results obtained. The formulæ from which the conducting powers have been calculated is \[ \lambda = x + yt + zt^2, \] where \( \lambda \) is the conducting power at \( t^\circ \) C., \( x \) the conducting power at 0°, and \( y \) and \( z \) constants. The values for \( x \), \( y \), and \( z \) were deduced from the mean of the observations by the method of least squares. We will now proceed to the experiments made with each metal, making at the same time a few remarks on their purification, &c., and then see what general laws and conclusions we may draw from the results obtained. Silver. Purified by precipitating nitrate of silver with hydrochloric acid, and reducing the washed chloride with pure carbonate of sodium. Wires 1, 2, and 3 were of different preparations. Table II. gives the results obtained with these wires. ### Table II. | | First wire. | Second wire. | Third wire. | |------------------|-------------|--------------|-------------| | | Hard drawn. | Annealed. | Hard drawn. | Annealed. | Hard drawn. | Annealed. | | Length | 1546 millims.| 1535 millims.| 1753 millims.| 1741 millims.| 1962 millims.| 1953 millims.| | Diameter | 0·462 millim.| 0·462 millim.| 0·596 millim.| 0·596 millim.| 0·448 millim.| 0·648 millim.| | Conducting power found before heating the hard-drawn wires | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | | Conducting power after being kept at 100° for 1 day | 97·645 at 15·4 | 103·528 | 95·112 at 16·0 | 101·149 | 94·053 at 16·0 | 99·800 | | Ditto, for 2 days | 98·138 at 16·2 | 104·364 | 96·618 at 15·6 | 102·585 | 95·241 at 15·4 | 100·839 | | Ditto, for 3 days | 98·913 at 15·6 | 104·951 | 101·544 at 16·8 | 108·303* | 96·337 at 16·0 | 102·223 | | Ditto, for 4 days | 99·837 at 16·0 | 106·091 | 102·237 at 16·0 | 108·714 | 96·671 at 17·6 | 103·178 | | Ditto, for 5 days | 99·212 at 18·4 | 106·377 | 101·427 at 19·2 | 109·152 | 97·917 at 15·6 | 103·747 | | Ditto, for 6 days | 99·586 at 17·4 | 106·380 | 101·750 at 18·6 | 109·262 | 97·669 at 17·4 | 104·168 | | | | | | | 97·322 at 18·2 | 104·100 | The means of the conducting powers found for each of the following temperatures were— * During the day the temperature of the oil increased, by mistake, to 130°. ### TEMPERATURE ON THE ELECTRIC CONDUCTING POWER OF METALS. | T. | First wire, hard drawn. | Second wire, hard drawn. | Third wire, hard drawn. | |----|-------------------------|--------------------------|------------------------| | | Conducting power. | Conducting power. | Conducting power. | | | Observed. | Calculated. | Observed. | | | Calculated. | Difference. | Calculated. | | | | | Difference. | | 11°00 | 102·238 | 102·272 | 12°20 | | 26°17 | 96·710 | 96·645 | 23°70 | | 38°25 | 92·490 | 92·505 | 41°70 | | 55°40 | 87·130 | 87·149 | 56°20 | | 68°85 | 83·389 | 83·374 | 68·90 | | 84°00 | 79·540 | 79·572 | 85·45 | | 101°30| 75·831 | 75·813 | 99·20 | | | | | 78·073 | | | | | 78·103 | | | | | 98·60 | | T. | First wire, annealed. | Second wire, annealed. | Third wire, annealed. | |----|-----------------------|------------------------|-----------------------| | | Conducting power. | Conducting power. | Conducting power. | | | Observed. | Calculated. | Observed. | | | Calculated. | Difference. | Calculated. | | | | | Difference. | | 11°30 | 103·391 | 103·404 | 8°00 | | 24°25 | 98·589 | 98·576 | 24°35 | | 41°85 | 92·520 | 92·530 | 38°05 | | 56°45 | 88·006 | 87·965 | 55·17 | | 67°75 | 84·670 | 84·714 | 68·22 | | 83°65 | 80·562 | 80·554 | 83·62 | | 98°80 | 77·046 | 77·042 | 100·00 | | | | | 78·319 | | | | | 78·331 | | | | | 100·00 | The formulæ deduced from the observations, from which the conducting powers were calculated, were— For first wire (hard drawn) . \( \lambda = 106·651 - 0·40948t + 0·0010370t^2 \). For first wire (annealed) . \( \lambda = 107·880 - 0·40698t + 0·0009601t^2 \). For second wire (hard drawn) \( \lambda = 108·928 - 0·42389t + 0·0011407t^2 \). For second wire (annealed) \( \lambda = 109·802 - 0·43138t + 0·0011667t^2 \). For third wire (hard drawn) \( \lambda = 104·209 - 0·39124t + 0·0010133t^2 \). For third wire (annealed) \( \lambda = 106·088 - 0·40160t + 0·0010235t^2 \). From the above Table it will be seen that, after heating a silver wire to 100° C. for some days, its conducting power is increased almost to the same extent as if it had been annealed, and that wires 1 and 2 were not completely hard drawn. On comparing the difference in the conducting powers produced by annealing the wires, we find for wire 3 it is only 6 per cent., whereas for wire 2 it is almost 10 per cent., taking the conducting power of the hard-drawn silver wire = 100. In a former research * this difference was found to be— 1. Hard drawn . . . . 95·28 at 14°0 Reduced to 0°. Annealed . . . . 103·98 at 14°8 109·98 2. Hard drawn . . . . 95·36 at 14°6 100·78 Annealed . . . . 103·33 at 14°6 109·20 * Philosophical Transactions, 1860. These values have been reduced by using a formula which is the mean of the six deduced from the experiments; for although there is a difference in the formula obtained for the annealed and hard-drawn (or rather partially annealed) wires, yet it is so small that they may be considered the same, more especially as the difference between the one obtained for the different wires is far greater. Taking the mean of the above values, and assuming the influence of temperature on the conducting power of hard-drawn and annealed wires to be the same, we find the following formulæ: For hard-drawn wires \( \lambda = 100 \cdot 00 - 0 \cdot 38287t + 0 \cdot 0009848t^2 \). For annealed wires \( \lambda = 108 \cdot 574 - 0 \cdot 41570t + 0 \cdot 0010624t^2 \). **Copper.** Wires 1 and 2 were of the same piece of electrotype copper prepared for us by Dr. H. Müller at Messrs. De la Rue and Co.'s. Wire 3 was cut off a piece of commercial electrotype copper from the same source. Table III shows the results obtained with these wires. ### Table III. | | First wire. | Second wire. | Third wire. | |------------------|-------------|--------------|-------------| | | Hard drawn. | Annealed. | Hard drawn. | Annealed. | | Length | 2262 millims.| 2245.5 millims.| 1753 millims.| 1738 millims.| 1476 millims.| 1461 millims.| | Diameter | 0.691 millim.| 0.691 millim.| 0.598 millim.| 0.598 millim.| 0.537 millim.| 0.537 millim.| | Conducting power found before heating the hard-drawn wires | 95.672 at 10°-6 | Reduced to 0°. | 99.526 | 94.355 at 15°-0 | Reduced to 0°. | 100.021 | 92.568 at 20°-6 | Reduced to 0°. | 100.327 | | Conducting power after being kept at 100° for 1 day | 96.824 at 9°-9 | 99.943 | 94.965 at 13°-2 | 99.971 | 93.863 at 19°-0 | 100.461 | | Ditto, for 2 days | 96.750 at 11°-8 | 101.097 | 94.880 at 14°-2 | 100.268 | 93.720 at 18°-0 | 100.563 | | Ditto, for 3 days | 96.914 at 12°-2 | 101.418 | 94.501 at 15°-9 | 100.524 | 93.434 at 19°-0 | 100.645 | | Ditto, for 4 days | 97.950 at 9°-8 | 101.671 | 94.153 at 17°-2 | 100.656 | 93.278 at 19°-6 | 100.708 | | Ditto, for 5 days | 98.437 at 8°-7 | 101.682 | 95.570 at 14°-4 | 101.074 | 92.865 at 20°-6 | 100.649 | | Ditto, for 6 days | ............ | ............ | 94.327 at 18°-2 | 101.230 | 92.738 at 21°-1 | 100.705 | | Ditto, for 7 days | ............ | ............ | 96.575 at 12°-7 | 101.469 | The means of the conducting powers found for each of the following temperatures were— | T. | First wire, hard drawn. Conducting power. | Difference. | Second wire, hard drawn. Conducting power. | Difference. | Third wire, hard drawn. Conducting power. | Difference. | |----|------------------------------------------|-------------|------------------------------------------|-------------|------------------------------------------|-------------| | | Observed. Calculated. | | Observed. Calculated. | | Observed. Calculated. | | | 16°86 | 95·473 95·467 +0·006 | 19°17 94·359 94·334 +0·025 | 12°65 95·769 95·739 +0·030 | | 29°88 | 91·063 91·002 +0·061 | 30°95 90·187 90·208 −0·021 | 25°61 91·061 91·076 −0·015 | | 51°03 | 84·235 84·315 −0·080 | 48°53 84·518 84·544 −0·026 | 39°52 86·415 86·456 −0·041 | | 69°52 | 78·997 79·044 −0·047 | 69°22 78·640 78·634 +0·006 | 53°92 82·069 82·090 −0·021 | | 83°77 | 75·413 75·347 +0·066 | 83°77 75·015 74·968 +0·047 | 69°90 77·798 77·741 +0·057 | | 98°60 | 71·829 71·838 −0·009 | 99°00 71·532 71·562 −0·030 | 84°87 74·172 74·142 +0·030 | | | | | | | | | | T. | First wire, annealed. Conducting power. | Difference. | Second wire, annealed. Conducting power. | Difference. | Third wire, annealed. Conducting power. | Difference. | |----|----------------------------------------|-------------|----------------------------------------|-------------|----------------------------------------|-------------| | | Observed. Calculated. | | Observed. Calculated. | | Observed. Calculated. | | | 17°00 | 95·535 95·567 −0·032 | 18°96 94·987 94·959 +0·028 | 13°45 96·954 96·934 +0·020 | | 29°63 | 91·291 91·239 +0·052 | 31°86 90·424 90·449 −0·025 | 26°15 92·246 92·260 −0·014 | | 50°23 | 84·687 84·726 −0·039 | 52°05 83·974 84·003 −0·029 | 39°35 87·727 87·753 −0·026 | | 69°60 | 79·223 79·209 +0·014 | 70°27 78·836 78·829 +0·007 | 55°50 82·675 82·722 −0·047 | | 83°42 | 75·636 75·638 −0·002 | 83°81 75·428 75·377 +0·051 | 69°90 78·742 78·656 +0·056 | | 99°39 | 71·891 71·893 −0·002 | 99°57 71·757 71·784 −0·027 | 84°67 75·047 74·988 +0·059 | | | | | | | | | The formulæ deduced from the observations, from which the conducting powers were calculated, were— For first wire (hard drawn) . . . \( \lambda = 101·645 - 0·37963t + 0·0007844t^2 \). For first wire (annealed) . . . \( \lambda = 101·791 - 0·37959t + 0·0007921t^2 \). For second wire (hard drawn) . . . \( \lambda = 101·614 - 0·39806t + 0·0009546t^2 \). For second wire (annealed) . . . \( \lambda = 102·143 - 0·39629t + 0·0009179t^2 \). For third wire (hard drawn) . . . \( \lambda = 100·620 - 0·39885t + 0·0010236t^2 \). For third wire (annealed). . . . \( \lambda = 102·243 - 0·40850t + 0·0010228t^2 \). The observations made with wires 1 and 2 were as follows: two at each interval on heating and two on cooling; again, two on heating and two on cooling, as shown in Table I. On looking at the above, we observe that wire 1, after having been kept at 100° for several days, increased in conducting power almost to the same extent as if it had been annealed, wire 2 partially so, and wire 3 hardly at all. The annealing took place in a glass tube heated with a 4-Bunsen burner, whilst a current of hydrogen passed through it. Here, again, as in the case of the silver wire, we may assume that the formulæ of the hard-drawn and annealed copper wires are the same. In a former research* pure copper was found to conduct— Reduced to 0°. 1. 93·00 at 18·6 99·877 2. 93·46 at 20·2 100·980 3. 92·02 at 18·4 99·824 4. 92·76 at 19·3 99·886 5. 92·99 at 17·5 99·453 * Philosophical Transactions, 1860. The difference found between the conducting powers of hard-drawn and annealed wires was — 6. Hard drawn . . . . . . 95·31 at 11·0 Reduced to 0°. Annealed . . . . . . . 97·83 at 11·0 99·435 7. Hard drawn . . . . . . 95·72 at 11·0 102·065 Annealed . . . . . . . 98·02 at 11·0 99·864 These values have been reduced to 0° as follows: take for instance the first, 93·00 at 18°·6. The mean of the six formulæ obtained for copper (see Table XV.) is \[ \lambda = 100 - 0·38701t + 0·0009009t^2; \] and calculating the conducting power for 18°·6 by this formula, we find it equal to 93·114. Now \[ \frac{93·00}{93·114} = 0·99877; \] and if all the terms of the above formula be multiplied by this number, we deduce a formula by which the above value can be reduced. All the reductions given in this paper of former determinations were made in this manner, using the formulæ given in Table XV. The reductions to 0° in the Tables were made in a like manner, the only difference being that the formulæ found for the respective wires were used instead of the mean. Taking the mean of all the values found for copper, and using the mean for the formulæ given in Table XV., we find as the formula for correction of the conducting power for temperature of A hard-drawn wire \( \lambda = 99·947 - 0·38681t + 0·0009004t^2 \) An annealed wire \( \lambda = 102·213 - 0·39557t + 0·0009208t^2. \) The values given as first term in the formulæ were found as follows: on referring to the paper* from which the conducting powers of copper were taken, it will be seen that each of them is the mean of three determinations. The reduced values therefore of 1 to 5, the mean of 6, hard drawn, and 7, hard drawn, and the mean of the first determinations of the three wires given in Table III., were added together, and the mean taken as the conducting power of a hard-drawn copper wire at 0° C. For the annealed, the percentage differences of the values of 6, hard drawn and annealed, 7, ditto, and of the first determinations of the three wires in Table III. and the annealed ones, were added together, and the mean added to the value found for the hard-drawn wire (as a percentage amount). All the formulæ given as end-result with each metal have been constructed in this manner. Gold. Purified as described in the Philosophical Transactions, 1860, p. 175. Wires 1, 2, and 3 were of different preparations. The results obtained with these wires are given in Table IV.* * Philosophical Transactions, 1860. ### Table IV. | | First wire. | Second wire. | Third wire. | |------------------|-------------|--------------|-------------| | | Hard drawn. | Annealed. | Hard drawn. | Annealed. | Hard drawn. | Annealed. | | Length | 2214 millims.| 2200 millims.| 837 millims.| 759·6 millims.| 742·5 millims.| | Diameter | 0·759 millim.| 0·759 millim.| 0·467 millim.| 0·434 millim.| 0·434 millim.| | Conducting power found before heating the hard-drawn wires | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | | Conducting power after being kept at 100° for 1 day | 73·239 at 13·2 | 76·821 | 72·550 at 15·1 | 76·561 | 67·530 at 30·8 | 77·229 | | Ditto, for 2 days | 72·746 at 15·2 | 76·854 | 73·359 at 12·6 | 76·733 | 71·868 at 19·4 | 77·223 | | Ditto, for 3 days | 72·751 at 15·1 | 76·832 | | | 71·854 at 20·1 | 77·405 | | Ditto, for 4 days | | | | | 72·191 at 19·0 | 77·457 | | | | | | | 72·396 at 18·0 | 77·394 | The means of the conducting powers found for each of the following temperatures were— | T. | First wire, hard drawn. | Second wire, hard drawn. | Third wire, hard drawn. | |----|-------------------------|--------------------------|-------------------------| | | Conducting power. | Conducting power. | Conducting power. | | | Observed. | Calculated. | Observed. | | | Difference. | | Calculated. | | 15·95 | 72·567 | 72·536 | +0·031 | 13·36 | 73·222 | 73·212 | +0·010 | 12·44 | 73·854 | 73·841 | +0·013 | | 30·76 | 68·798 | 68·828 | -0·030 | 24·79 | 70·329 | 70·325 | +0·004 | 23·27 | 70·965 | 70·975 | -0·010 | | 50·06 | 64·392 | 64·410 | -0·018 | 40·80 | 66·515 | 66·544 | -0·029 | 39·42 | 67·002 | 67·013 | -0·011 | | 69·75 | 60·397 | 60·385 | +0·012 | 55·65 | 63·306 | 63·312 | -0·006 | 55·47 | 63·441 | 63·448 | -0·007 | | 84·31 | 57·742 | 57·722 | +0·020 | 69·52 | 60·528 | 60·531 | -0·003 | 70·56 | 60·455 | 60·435 | +0·020 | | 99·27 | 55·248 | 55·263 | -0·015 | 84·12 | 57·905 | 57·854 | +0·051 | 84·79 | 57·904 | 57·893 | +0·011 | | | 100·00 | 55·203 | | 55·232 | -0·029 | 99·00 | 55·635 | 55·647 | -0·012 | First wire, annealed. | T. | Conducting power. | At the commencement of the determinations this wire was torn away from its place by the stirrer. | |----|-------------------------|---------------------------------------------------------------| | 14·92 | 74·020 | 73·992 | +0·028 | 14·10 | 74·327 | 74·293 | +0·034 | | 30·05 | 70·039 | 70·068 | -0·029 | 26·31 | 71·067 | 71·095 | -0·028 | | 48·87 | 65·575 | 65·611 | -0·036 | 40·51 | 67·582 | 67·621 | -0·039 | | 69·90 | 61·220 | 61·191 | +0·029 | 53·72 | 64·645 | 64·628 | +0·017 | | 82·82 | 58·811 | 58·768 | +0·043 | 70·17 | 61·229 | 61·220 | +0·009 | | 99·62 | 55·915 | 55·948 | -0·033 | 85·36 | 58·422 | 58·388 | +0·034 | | | 99·80 | 56·029 | | 56·056 | -0·027 | The formulæ deduced from the observations, from which the conducting powers were calculated, were— For first wire (hard drawn) . . . \( \lambda = 76·838 - 0·27973t + 0·0006285t^2 \). For first wire (annealed) . . . \( \lambda = 78·161 - 0·28935t + 0·0006664t^2 \). For second wire (hard drawn) . . . \( \lambda = 76·786 - 0·27549t + 0·0005995t^2 \). For third wire (hard drawn) . . . \( \lambda = 77·343 - 0·29043t + 0·0007200t^2 \). For third wire (annealed) . . . \( \lambda = 78·231 - 0·28849t + 0·0006564t^2 \). The observations made with wire 1 (hard drawn) are given in Table I., those of the same wire (annealed) were made in the same manner. Here we find no permanent change in conducting power with wire 1, after being kept at 100° for several days, and only a very slight increase with wires 2 and 3. The formulae for the hard-drawn and annealed wires agree so closely that they may also, as with silver and copper, be considered the same. In the paper just alluded to, the conducting power of pure gold was found— | | Reduced to 0° | |---|---------------| | 1. | 72·68 at 19·3 | | | 77·966 | | 2. | 73·08 at 23·3 | | | 79·524 | | 3. | 73·27 at 13·8 | | | 77·053 | | 4. | 73·99 at 15·1 | | | 78·178 | The difference between hard-drawn and annealed wires was— | | Reduced to 0° | |---|---------------| | 5. | Hard drawn | | | 74·20 at 14·8 | | | 78·313 | | Annealed | 75·53 at 15·2 | | | 79·833 | | 6. | Hard drawn | | | 73·78 at 15·5 | | | 78·067 | | Annealed | 75·18 at 15·8 | | | 79·635 | Taking the mean of the values as with copper, the following formulae were deduced for the correction of conducting power for temperature: For hard-drawn wires \( \lambda = 77·964 - 0·28648t + 0·0006582t^2 \). For annealed wires \( \lambda = 79·327 - 0·29149t + 0·0006697t^2 \). **Zinc.** Zinc free of arsenic was purified by distillation. All pressed wires. In Table V. the results obtained are given. **Table V.** | | First wire. | Second wire. | Third wire. | |---|-------------|--------------|-------------| | Length | 502·2 millims. | 394 millims. | 372 millims. | | Diameter | 0·588 millim. | 0·513 millim. | 0·519 millim. | | Conducting power found before heating the wires | 26·744 at 23·1 | 26·903 at 18·5 | 26·835 at 18·0 | | Reduced to 0° | 29·093 | 28·836 | 28·639 | | Ditto, after being kept at 100° for 1 day | 26·695 at 23·7 | 27·081 at 17·5 | 26·784 at 18·5 | | Reduced to 0° | 29·103 | 28·919 | 28·636 | | Ditto, for 2 days | 26·980 at 18·5 | 28·919 | 26·885 at 17·4 | | Reduced to 0° | 28·632 | The means of the conducting powers found for each of the following temperatures were— The formulae deduced from the observations, from which the conducting powers were calculated, were— For first wire . . \( \lambda = 29.114 - 0.10727t + 0.0002372t^2 \). For second wire . . \( \lambda = 28.881 - 0.10949t + 0.0002616t^2 \). For third wire . . \( \lambda = 28.649 - 0.10424t + 0.0002182t^2 \). No permanent alteration in the conducting power takes place after heating the wires for several days to 100°. The value formerly found for the conducting power of zinc (precipitated galvanoplastically, fused and pressed) was— Reduced to 0°. 27.39 at 17°. 29.220. Treating these values as before, we find the formula for zinc to be \( \lambda = 29.022 - 0.10752t + 0.0002401t^2 \). **Cadmium.** The metal was purified as described in the Philosophical Transactions, 1860, p. 177. The wires were pressed. Table VI. shows the results. **Table VI.** | Length | First wire. | Second wire. | Third wire. | |--------|-------------|--------------|-------------| | | 625 millims.| 559 millims.| 439 millims.| | Diameter | 0.641 millim.| 0.678 millim.| 0.684 millim.| The means of the conducting powers found for each of the following temperatures were— | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | |----|------------------|-------------|----|------------------|-------------|----|------------------|-------------| | | Observed. Calculated. | | | Observed. Calculated. | | | Observed. Calculated. | | | 8°87 | 23-327 23-329 | -0.002 | 8°89 | 23-374 23-400 | -0.026 | 14°60 | 21-849 21-859 | -0.010 | | 20°75 | 22-351 22-338 | +0.013 | 21°59 | 22-280 22-270 | +0.010 | 22°05 | 21-318 21-310 | +0.008 | | 34°47 | 21-241 21-255 | -0.014 | 36-37 | 21-075 21-059 | +0.016 | 39-65 | 20-072 20-061 | +0.011 | | 49°38 | 20-138 20-150 | -0.012 | 48-52 | 20-157 20-146 | +0.011 | 54-45 | 19-065 19-067 | -0.002 | | 63°39 | 19-188 19-186 | +0.002 | 62-90 | 19-171 19-162 | +0.009 | 68-10 | 18-179 18-194 | -0.015 | | 77°74 | 18-292 18-268 | +0.024 | 80-00 | 18-109 18-131 | -0.022 | 81-20 | 17-393 17-397 | -0.004 | | 93°55 | 17-325 17-339 | -0.014 | | | | 89-90 | 16-896 16-888 | +0.008 | The formulæ deduced from the observations, from which the conducting powers were calculated, were— For first wire . . \( \lambda = 24.100 - 0.088554t + 0.0001740t^2 \). For second wire . \( \lambda = 24.240 - 0.096753t + 0.0002548t^2 \). For third wire . \( \lambda = 24.974 - 0.078004t + 0.0001147t^2 \). The values obtained for the alteration in the conducting power of these wires after heating them for several days to 100°, have unfortunately been lost. It may, however, be stated that the differences were very small, and that there was a loss in conducting power. The conducting power of cadmium was found in the paper already referred to— Reduced to 0°. \( 22.10 \) at \( 18.8 \) \( 23.678 \). Deducing the formula for cadmium in the manner before described, we find \( \lambda = 23.725 - 0.087476t + 0.0001797t^2 \). Pure cadmium, when heated to about 80°, becomes exceedingly brittle, in fact it may be powdered in a hot mortar with great ease. We should not have been able to carry out the determinations if the wires had not been varnished, as the movement of the oil by the stirrer would have caused them to fall to pieces. It is worthy of remark that this change in the molecular arrangement of the wires does not make itself apparent in the conducting power to any very marked extent. **Tin.** Purified by dissolving commercial tin in nitric acid, and reducing the washed oxide by heating it with lampblack. Pressed wires were used. Table VII. gives the results. ### Table VII. | | First wire. | Second wire. | Third wire. | |------------------|-------------|--------------|-------------| | Length | 279 millims.| 375 millims.| 315 millims.| | Diameter | 0.559 millim.| 0.634 millim.| 0.729 millim.| | Conducting power found before heating the wires | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | | 10.970 at 18.2 | 11.710 | 11.532 at 18.1 | 12.324 | | Ditto, after being kept at 100° for 1 day | 11.124 at 19.4 | 11.926 | 11.442 at 19.1 | 12.273 | 12.285 at 18.2 | 13.108 | | Ditto, for 2 days | 10.852 at 27.0 | 11.956 | 11.448 at 18.6 | 12.257 | 12.291 at 18.4 | 13.124 | | Ditto, for 3 days | 10.835 at 28.0 | 11.980 | 11.444 at 18.4 | 12.264 | 12.296 at 18.4 | 13.129 | The means of the conducting powers found for each of the following temperatures were— The formulæ deduced from the observations, and from which the conducting powers were calculated, were— For first wire . \( \lambda = 11.9613 - 0.042902t + 0.00007422t^2 \). For second wire \( \lambda = 12.2419 - 0.044965t + 0.00008213t^2 \). For third wire . \( \lambda = 13.1186 - 0.046561t + 0.00007206t^2 \). We see from the results that wires 1 and 2 decrease to a small extent in conducting power, whereas wire 3 increases slightly after being heated to 100°. The conducting power of tin was found— Reduced to 0°. 11.45 at 21° and calculating the formula of tin as before, we find \( \lambda = 12.366 - 0.044554t + 0.00007588t^2 \). Lead. Purified by reducing by heat the twice recrystallized acetate. Wires 1 and 2 were pressed; wire 3 drawn. No permanent alteration in the conducting power of the wires was observed after they had been kept at 100° for two days. Table VIII. shows the results. **Table VIII.** | Length | First wire. | Second wire. | Third wire. | |--------|-------------|--------------|-------------| | | 416 millims.| 453 millims.| 389 millims.| | Diameter | 0.669 millim.| 0.698 millim.| 0.959 millim.| The means of the conducting powers found for each of the following temperatures were— | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | |----|-------------------|-------------|----|-------------------|-------------|----|-------------------|-------------| | | Observed. | Calculated. | | Observed. | Calculated. | | Observed. | Calculated. | | 14°55 | 7.9365 | 7.9336 | +0.0029 | 14°50 | 7.8685 | 7.8653 | +0.0032 | 15°40 | 7.9038 | 7.9022 | +0.0016 | | 25°40 | 7.6129 | 7.6152 | -0.0023 | 25°50 | 7.5336 | 7.5392 | -0.0056 | 26°20 | 7.4967 | 7.4968 | -0.0001 | | 40°30 | 7.2036 | 7.2071 | -0.0035 | 40°37 | 7.1405 | 7.1397 | +0.0008 | 39°60 | 7.1309 | 7.1324 | -0.0015 | | 54°80 | 6.8423 | 6.8420 | +0.0003 | 54°80 | 6.7789 | 6.7775 | +0.0014 | 54°60 | 6.7565 | 6.7585 | -0.0020 | | 70°33 | 6.4881 | 6.4863 | +0.0018 | 69°63 | 6.4392 | 6.4370 | +0.0022 | 69°70 | 6.4205 | 6.4187 | +0.0018 | | 84°52 | 6.1964 | 6.1929 | +0.0035 | 84°80 | 6.1189 | 6.1218 | -0.0029 | 84°40 | 6.1250 | 6.1229 | +0.0021 | | 99°35 | 5.9159 | 5.9189 | -0.0030 | 100°10 | 5.8388 | 5.8381 | +0.0007 | 98°85 | 5.8642 | 5.8658 | -0.0016 | The formulæ deduced from the observations, from which the conducting powers were calculated, were— For first wire \( \lambda = 8.3882 - 0.032346t + 0.00007540t^2 \). For second wire \( \lambda = 8.3147 - 0.032055t + 0.00007307t^2 \). For third wire \( \lambda = 8.2925 - 0.032468t + 0.00008011t^2 \). The value found for the conducting power of lead was Reduced to 0°. \( 7.77 \) at \( 17^\circ \) \( 8.304 \). Treating the mean of the values as above, the formula is \( \lambda = 8.318 - 0.032237t + 0.00007608t^2 \). Arsenic. Purified by sublimation. Small bars were cut from a comparatively solid piece and soldered to two copper wires; on account of the extreme brittleness of arsenic, the bars were placed in glass tubes closed at the ends with gypsum, through which the copper wires passed. As these were dried in a water-bath for several days, no permanent alteration of the conducting power of the bars was found after being heated in the oil-bath for two days. The values found for the conducting power of arsenic agree as well as could be expected, considering the bars were made by hand, and the metal somewhat porous. The difficulty of obtaining bars of metal of sufficient length is so great that we have been contented with two series. These are given in Table IX. **Table IX.** | Length | First bar | Second bar | |--------|-----------|------------| | | 50.4 millims. | 55.5 millims. | | Diameter | 0.93 millim. | 1.01 millim. | The means of the conducting powers found for each of the following temperatures were— | T. | Conducting power | Difference | T. | Conducting power | Difference | |----|------------------|------------|----|------------------|------------| | | Observed. | Calculated. | | Observed. | Calculated. | | 14.20 | 5.0203 | 5.0180 | +0.0023 | 13.50 | 4.0051 | 4.0037 | +0.0014 | | 25.30 | 4.8007 | 4.8008 | -0.0001 | 24.50 | 3.8371 | 3.8450 | -0.0079 | | 37.80 | 4.5710 | 4.5736 | -0.0026 | 40.15 | 3.6367 | 3.6311 | +0.0056 | | 55.00 | 4.2854 | 4.2906 | -0.0052 | 55.55 | 3.4447 | 3.4341 | +0.0106 | | 70.00 | 4.0767 | 4.0722 | +0.0045 | 69.90 | 3.2559 | 3.2628 | -0.0069 | | 85.30 | 3.8810 | 3.8764 | +0.0046 | 82.50 | 3.1144 | 3.1221 | -0.0077 | | 101.00 | 3.7005 | 3.7041 | -0.0036 | 99.80 | 2.9485 | 2.9435 | +0.0050 | The formulæ deduced from the observations, and from which the conducting powers were calculated, were— For first bar \( \lambda = 5.3168 - 0.021874t + 0.00005848t^2 \). For second bar \( \lambda = 4.2078 - 0.015506t + 0.00002843t^2 \). Taking the mean of the conducting powers at $0^\circ$, we deduce the formula for the correction of conducting power for temperature to be $$\lambda = 4.7623 - 0.018571t + 0.00004228t^2.$$ **Antimony.** Purified by twice recrystallizing commercially pure tartrate of antimony and potassium, reducing by heat and re-fusing with antimonic acid. As antimony is so very brittle, it was not possible to manipulate with it in form of wire, it was therefore fused in the bowl of a tobacco-pipe, and when liquid allowed to run into the stem. After breaking off the bowl, the ends of the pipe were made so hot that the metal melted, and clean copper wires were pushed into the liquid metal, which on solidifying held them fast. The free ends of the copper wires were then soldered to the thick ones in the trough. Unfortunately in each case the copper wires in the pipe-stem became loose after heating for two or three days, and had to be therefore resoldered, so that no reliable determinations could be made as to the effect of heating to $100^\circ$ for several days on the conducting power. It may be stated that the three wires lost in conducting power; but to what extent, we are of course not in a position to say. As the diameter of the pipe-stem could not be accurately determined, and as it could not be ascertained whether there were cavities in the wires (caused by contraction on cooling and crystallization) or not, the first observed conducting power was taken equal to 100. Table X. shows the results. **Table X.** The means of the conducting powers found for each of the following temperatures were— | T. | First wire. Conducting power. | Second wire. Conducting power. | Third wire. Conducting power. | |--------|-------------------------------|--------------------------------|-------------------------------| | | Observed. Calculated. Difference. | Observed. Calculated. Difference. | Observed. Calculated. Difference. | | 10-00 | 100-000 100-052 -0-052 | 8-40 100-000 99-999 +0-001 | 13-80 100-000 99-901 +0-099 | | 26-35 | 94-062 93-910 +0-152 | 25-60 93-947 93-850 +0-097 | 22-30 96-378 96-514 -0-136 | | 40-40 | 88-982 89-089 -0-107 | 42-45 88-139 88-329 -0-190 | 38-65 90-552 90-527 +0-025 | | 54-55 | 84-633 84-664 -0-031 | 57-80 83-707 83-731 -0-024 | 53-50 85-671 85-692 -0-021 | | 70-65 | 80-126 80-152 -0-026 | 69-45 80-691 80-517 +0-174 | 69-65 81-118 81-082 +0-036 | | 83-50 | 77-071 76-953 +0-118 | 86-85 76-138 76-159 -0-021 | 84-45 77-480 77-454 +0-026 | | 99-40 | 73-430 73-484 -0-054 | 101-25 72-922 72-953 -0-031 | 98-80 74-448 74-480 -0-032 | The formulæ deduced from the observations, from which the conducting powers were calculated, were— For first wire $\lambda = 104.095 - 0.41487t + 0.0010755t^2.$ For second wire $\lambda = 103.190 - 0.38721t + 0.0008748t^2.$ For third wire $\lambda = 105.801 - 0.44541t + 0.0012995t^2.$ The observed conducting powers in this and the foregoing Table do not agree so well with the calculated as the others, on account of the temperature of the bath never being exactly the same as that of the wire; for in the one case the heat had to traverse the glass tube filled with air, in the other the thickness of the pipe-stem, before reaching the metal. The conducting power of antimony was found equal to \[ 4.29 \text{ at } 18^\circ \quad \text{Reduced to } 0^\circ. \quad 4.6172 \] Using this value as before described, we obtain a formula for antimony where \[ \lambda = 4.6172 - 0.018389t + 0.00004788t^2. \] **Bismuth.** Purified by reducing the basic nitrate of bismuth with lampblack. Table XI. gives the results. The wires were pressed. ### Table XI. | | First wire. | Second wire. | Third wire. | |------------------|-------------|--------------|-------------| | Length | 117 millims.| 121.4 millims.| 42.5 millims.| | Diameter | 0.596 millim.| 0.596 millim.| 0.217 millim.| | Conducting power found before heating the wires... | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | | 1.1787 at 16.6 | 1.2517 | 1.1036 at 18.8 | 1.1773 | | Conducting power after being kept at 100° for 1 day... | Reduced to 0°. | Reduced to 0°. | Reduced to 0°. | | 1.3599 at 17.6 | 1.4494 | 1.3110 at 19.0 | 1.3995 | | Ditto, for 2 days... | 1.3595 at 18.2 | 1.4521 | 1.3121 at 19.0 | 1.4006 | | Ditto, for 3 days... | 1.3624 at 18.0 | 1.4541 | 1.3096 at 19.9 | 1.4023 | The means of the conducting powers found for each of the following temperatures were— | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | |----|-------------------|-------------|----|-------------------|-------------|----|-------------------|-------------| | | Observed. | Calculated. | | Observed. | Calculated. | | Observed. | Calculated. | | 9.20 | 1.4059 | 1.4058 | +0.0001 | 9.60 | 1.3654 | 1.3641 | +0.0013 | 9.40 | 1.4129 | 1.4128 | +0.0001 | | 26.15 | 1.3226 | 1.3226 | 0.0000 | 24.00 | 1.2909 | 1.2935 | -0.0026 | 25.65 | 1.3329 | 1.3339 | -0.0010 | | 39.50 | 1.2609 | 1.2614 | -0.0005 | 38.75 | 1.2297 | 1.2287 | +0.0010 | 43.05 | 1.2551 | 1.2538 | +0.0013 | | 57.25 | 1.1863 | 1.1858 | +0.0005 | 55.80 | 1.1591 | 1.1593 | -0.0002 | 57.45 | 1.1913 | 1.1912 | +0.0001 | | 68.95 | 1.1397 | 1.1397 | 0.0000 | 68.90 | 1.1058 | 1.1050 | +0.0008 | 71.60 | 1.1315 | 1.1328 | -0.0013 | | 84.35 | 1.0833 | 1.0833 | 0.0000 | 84.00 | 1.0478 | 1.0474 | +0.0004 | 88.60 | 1.0671 | 1.0666 | +0.0005 | | 96.35 | 1.0428 | 1.0429 | -0.0001 | 95.90 | 1.0036 | 1.0042 | -0.0006 | The formulæ deduced from the observations, by which the conducting powers were calculated, were— For first wire \( \lambda = 1.4535 - 0.0052883t + 0.00001060t^2 \). For second wire \( \lambda = 1.4049 - 0.0047972t + 0.000006453t^2 \). For third wire \( \lambda = 1.4603 - 0.0051286t + 0.000007737t^2 \). From the above we see how bismuth increases in conducting power after being kept at 100° for one day. This increment is so rapid that it may be followed for the first two hours from five to five minutes. Wire 1 altered by one day’s heating 16 per cent.; wire 2, 19 per cent.; and wire 3, 12 per cent. Wires 1 and 2 were cut from the same piece. This behaviour explains why the conducting power of bismuth wires varies so much: for in the paper so often here alluded to, the maximum difference between twelve wires was found to be 22 per cent. In pressing the wires the heat applied to the press is never constant; so that, if pressed very warm, wires of high conducting power would probably be the result. The conducting power of bismuth was found equal to Reduced to 0°. \( 1.19 \) at \( 13.8^\circ \) \( 1.2484 \) Taking the mean of the values as before, we find the formula for bismuth to be \( \lambda = 1.2454 - 0.0043858t + 0.000007134t^2 \). Mercury. Purified by allowing a solution of subnitrate of mercury to stand over the metal for several weeks, during which time it was often well shaken up with it. The determinations were made in a calibrated thermometer-tube, to the ends of which wide glass tubes (13 to 14 millims. wide) were fused and bent, as shown in fig. 3. Mercury prepared at different times was used for the determinations. For the experiments, the tube was filled with hot mercury, and its resistance was determined when cold. This was twice repeated; and the resistance being found the same each time, it was assumed that the tube filled in this manner did not contain air-bubbles; this is also proved by the close agreement of the formulæ found in the two cases for the variation of the conducting power at higher temperatures; for if in either case air-bubbles had been present, the formulæ must have differed to a much greater extent, as it can scarcely be assumed that in the two cases the bubbles were equal in bulk. The mercury was connected with the apparatus by amalgamated copper wires (4 to 5 millims. thick). Table XII. shows the results obtained. The means of the conducting powers found for each of the following temperatures were— | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | |----|------------------|-------------|----|------------------|-------------| | | Observed. | Calculated. | | Observed. | Calculated. | | 0 | 1·6521 | 1·6530 | 0 | 1·6529 | 1·6533 | | 20·55 | 1·6276 | 1·6272 | 20·95 | 1·6272 | 1·6268 | | 40·45 | 1·6003 | 1·6011 | 39·92 | 1·6010 | 1·6018 | | 59·82 | 1·5750 | 1·5746 | 60·40 | 1·5741 | 1·5738 | | 79·78 | 1·5465 | 1·5462 | 80·70 | 1·5454 | 1·5450 | | 99·90 | 1·5162 | 1·5164 | 99·30 | 1·5174 | 1·5177 | The formulæ deduced from the observations, by which the conducting powers were calculated, were— For the first series \( \lambda = 1·6530 - 0·0012240t - 0·000001434t^2 \). For the second series \( \lambda = 1·6533 - 0·0012370t - 0·000001297t^2 \). The value found for the conducting power of mercury was Reduced to 0°. 1·63 at 22·8° 1·6588 Taking the mean of the values as before, we find the formula for mercury to be \( \lambda = 1·656 - 0·0012326t - 0·000001368t^2 \). Tellurium. Purified by dissolving the commercial metal in aqua regia, evaporating to dryness with excess of carbonate of sodium, fusing the residue, which was dissolved in water, and nitrate of barium added to precipitate any selenium present. The filtrate was evaporated to dryness with hydrochloric acid in excess, the residue dissolved in water, and precipitated by sulphurous acid. On account of the low conducting power of tellurium, small bars of about 15 millims. in length and 3–5 millims. in diameter were used for the experiments. Bars I. and II. are of the same preparation. As the bars could not be accurately measured, we have called the first observed conducting power 100 in each case. Table XIII. gives the results. ### Table XIII. | Conducting power found before heating the bar to 100° | Bar I | Bar II | Bar III | |------------------------------------------------------|-------|--------|---------| | Ditto, after being kept at 100° for 1 day | 79·145 at 15·4 | 86·50 at 13·0 | 83·16 at 12·6 | | Ditto, for 2 days | 45·449 at 16·0 | 76·51 at 13·6 | 69·23 at 14·1 | | Ditto, for 3 days | 22·378 at 16·0 | 70·43 at 16·4 | 61·25 at 16·9 | | Ditto, for 4 days | 16·129 at 15·0 | 65·68 at 16·6 | 54·92 at 17·2 | | Ditto, for 5 days | 8·068 at 15·2 | 61·68 at 16·8 | 50·69 at 17·8 | | Ditto, for 6 days | 6·989 at 15·0 | 56·85 at 17·2 | 46·11 at 16·6 | | Ditto, for 7 days | 5·781 at 14·2 | 54·88 at 16·6 | 42·35 at 16·4 | | Ditto, for 8 days | 4·830 at 15·5 | 51·33 at 16·1 | 38·64 at 15·8 | | Ditto, for 9 days | 4·621 at 16·8 | 46·27 at 15·6 | 35·31 at 16·2 | | Ditto, for 10 days | 4·302 at 15·3 | 45·26 at 16·2 | 33·50 at 16·4 | | Ditto, for 11 days | 4·181 at 15·0 | 42·10 at 16·6 | 30·97 at 16·8 | | Ditto, for 12 days | 4·1371 at 16·1 | 3·7662 | 29·98 at 18·2 | | Ditto, for 13 days | 4·0844 at 14·6 | 3·7646 | 28·21 at 15·6 | | Ditto, for 14 days | | 37·72 at 17·1 | 26·73 at 16·8 | | Ditto, for 15 days | | 35·35 at 15·4 | 23·68 at 15·4 | | Ditto, for 16 days | | 32·23 at 15·6 | 19·43 at 16·0 | | Ditto, for 17 days | | 29·92 at 17·0 | 16·65 at 17·6 | | Ditto, for 18 days | | 28·11 at 17·6 | 14·43 at 17·0 | | Ditto, for 19 days | | 26·25 at 16·2 | 12·59 at 16·4 | | Ditto, for 20 days | | 25·54 at 13·0 | 11·68 at 14·4 | | Ditto, for 21 days | | 24·12 at 13·4 | 10·34 at 13·6 | | Ditto, for 22 days | | 23·29 at 12·8 | 9·32 at 13·6 | | Ditto, for 23 days | | 22·00 at 13·6 | 8·64 at 14·1 | | Ditto, for 24 days | | 21·45 at 14·1 | 7·92 at 13·8 | | Ditto, for 25 days | | 20·86 at 14·6 | 7·36 at 14·6 | | Ditto, for 26 days | | 20·17 at 15·8 | 6·97 at 14·2 | | Ditto, for 27 days | | 19·74 at 16·0 | 6·66 at 14·8 | | Ditto, for 28 days | | 19·68 at 13·0 | 6·52 at 15·8 | | Ditto, for 29 days | | 19·65 at 12·2 | Reduced to 0° | | Ditto, for 30 days | | 19·633 at 12·0 | 6·35 at 15·8 | | Ditto, for 31 days | | 19·633 at 11·9 | 6·04 at 12·0 | | Ditto, for 32 days | | 20·137 | Reduced to 0° | | Ditto, for 33 days | | | 5·6134 | The means of the conducting powers for each of the following temperatures were— | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | T. | Conducting power. | Difference. | |----|-------------------|-------------|----|-------------------|-------------|----|-------------------|-------------| | | Observed. | Calculated. | | Observed. | Calculated. | | Observed. | Calculated. | | 10·40 | 3·9566 | 3·9575 | 3·70 | 19·976 | 19·972 | 4·20 | 5·6646 | 5·6797 | | 25·25 | 4·5212 | 4·5240 | 11·80 | 19·650 | 19·660 | 22·80 | 6·7456 | 6·7392 | | 38·85 | 5·3940 | 5·3846 | 22·40 | 19·477 | 19·466 | 39·40 | 8·6703 | 8·5781 | | 55·10 | 6·9089 | 6·9060 | 29·40 | 19·468 | 19·473 | 53·90 | 10·8480 | 10·9426 | | 70·45 | 8·7006 | 8·9019 | 29·40 | 19·468 | 19·496 | 69·50 | 14·2472 | 14·3441 | | 83·10 | 11·0316 | 11·0018 | 34·60 | 19·546 | 19·544 | 83·60 | 18·4043 | 18·2406 | | 99·40 | 14·3690 | 14·3764 | 39·70 | 19·689 | 19·653 | 98·80 | 23·3209 | 23·3769 | -0·0009 +0·0028 -0·0005 -0·0028 +0·0002 -0·0117 +0·0077 -0·019 The formulæ deduced from the observations, and from which the conducting powers were calculated, were— For first bar . . . . . . . \( \lambda = 3.7619 + 0.011614t + 0.0006598t^2 + 0.000002994t^3 \). For second bar to 29.4 . . . \( \lambda = 20.162 - 0.055338t + 0.001085t^2 \). For second bar from 29.4 to 100 \( \lambda = 20.014 - 0.029569t + 0.00009390t^2 + 0.000010635t^3 \). For third bar . . . . . . \( \lambda = 5.5752 + 0.019274t + 0.0013235t^2 + 0.000003088t^3 \). From the above Table we learn that tellurium behaves in a very different manner from the other metals; for it will be seen how very much the conducting power decreases after it has been heated to 100° for some days, and how different is the time required before the conducting power of the different bars becomes constant, or, in other words, until the heating of the bars to 100° causes no further permanent alteration in the conducting power. Bar I. required 13 days; bar II. 32; bar III. 33. The first observed conducting power being taken equal to 100, bar I. is reduced to 4, bar II. to 19.6, and bar III. to 6. If we now look at the determinations of the conducting power at different temperatures of the three bars, we are struck at the great want of concordance in the results. With the first series we observe that the conducting power increases rapidly as the temperature rises; with the second it decreases with the rise of temperature to 29°.4, from which point it increases rapidly, as with bar I.; the third behaves as the first. Bar I. showed no apparent difference in crystalline structure after being heated; it was thought very probable that the crystalline structure might have been altered by heating, and thus caused the enormous change in conducting power. The three bars, when first heated, behaved as metal to 70° or 80°, that is to say, they lost in conducting power up to that temperature, where it then began to increase. The temperature of this turning-point became lower after each day's heating, until, as in bars I. and II., it is below the lowest temperature at which observations were made. The behaviour, therefore, of tellurium is intermediate between that of the metal and that of the metalloid; for, according to Hittorf*, selenium increases rapidly in conducting power with the temperature. Graphite and gas-coke† behave in the same manner; and Becquerel‡ found that gases when heated conduct better than when cold. From these facts we learn another marked difference in the physical properties of the metals and metalloids, viz. that the metals lose in conducting power with an increase of temperature, whereas under the same circumstances the metalloids gain. In order to be better able to compare the results obtained with the pure metals, we give the following Tables. Table XIV. contains all the formulæ deduced from the observations by the method of least squares, with the conducting power of each metal taken = 100 at 0°; Table XV. the mean of the formulæ found for each metal. * Poggendorff’s ‘Annalen,’ vol. lxxxvi. p. 214. † Philosophical Transactions, 1858, p. 386. ‡ Ann. de Chim. et de Phys. (iii.) vol. xxxix. p. 388. ### Table XIV. | Metal | Annealed | Hard drawn | |-----------|----------|------------| | Silver | λ = 100 - 0.38287t + 0.0009848t² | λ = 100 - 0.38394t + 0.0009723t² | | Copper | λ = 100 - 0.38701t + 0.0009009t² | λ = 100 - 0.38915t + 0.0010472t² | | Gold | λ = 100 - 0.36745t + 0.0008443t² | λ = 100 - 0.37047t + 0.0008274t² | | Zinc | λ = 100 - 0.36871t + 0.0007575t² | λ = 100 - 0.36851t + 0.0006757t² | | Cadmium | λ = 100 - 0.39915t + 0.0010511t² | λ = 100 - 0.39826t + 0.0010364t² | | Tin | λ = 100 - 0.36029t + 0.0006136t² | λ = 100 - 0.36383t + 0.0004593t² | | Lead | λ = 100 - 0.38553t + 0.0008788t² | λ = 100 - 0.38966t + 0.0008879t² | | Arsenic | λ = 100 - 0.41141t + 0.0011000t² | λ = 100 - 0.38756t + 0.0009146t² | | Antimony | λ = 100 - 0.37524t + 0.0008477t² | λ = 100 - 0.37647t + 0.0008340t² | | Bismuth | λ = 100 - 0.34146t + 0.0004593t² | λ = 100 - 0.35216t + 0.0005728t² | | Mercury | λ = 100 - 0.074047t + 0.00008672t² | λ = 100 - 0.074820t + 0.00007844t² | ### Table XV. | Metal | Annealed | Hard drawn | |-----------|----------|------------| | Silver | λ = 100 - 0.38287t + 0.0009848t² | λ = 100 - 0.38394t + 0.0009723t² | | Copper | λ = 100 - 0.38701t + 0.0009009t² | λ = 100 - 0.38915t + 0.0010472t² | | Gold | λ = 100 - 0.36745t + 0.0008443t² | λ = 100 - 0.37047t + 0.0008274t² | | Zinc | λ = 100 - 0.36871t + 0.0007575t² | λ = 100 - 0.36851t + 0.0006757t² | | Cadmium | λ = 100 - 0.39915t + 0.0010511t² | λ = 100 - 0.39826t + 0.0010364t² | | Tin | λ = 100 - 0.36029t + 0.0006136t² | λ = 100 - 0.36383t + 0.0004593t² | | Lead | λ = 100 - 0.38553t + 0.0008788t² | λ = 100 - 0.38966t + 0.0008879t² | | Arsenic | λ = 100 - 0.41141t + 0.0011000t² | λ = 100 - 0.38756t + 0.0009146t² | | Antimony | λ = 100 - 0.37524t + 0.0008477t² | λ = 100 - 0.37647t + 0.0008340t² | | Bismuth | λ = 100 - 0.34146t + 0.0004593t² | λ = 100 - 0.35216t + 0.0005728t² | | Mercury | λ = 100 - 0.074047t + 0.00008672t² | λ = 100 - 0.074820t + 0.00007844t² | From the last Table we see how closely the values found for the constants \( y \) or \( z \) agree together; and to show this more clearly, the conducting powers calculated from these formulæ for 0°, 20°, 40°, 60°, 80°, and 100° are given in Table XVI., together with values calculated from the mean of all the formulæ. Again, in Table XVII., we give the conducting power of the metals compared with hard-drawn silver wire at $0^\circ=100$, first at $0^\circ$ and then at $100^\circ$, and, lastly, taking silver at $100^\circ=100$. From these Tables we think we may deduce the law, that all pure metals in a solid state vary in conducting power between $0^\circ$ and $100^\circ$ to the same extent, more especially as we find that wires of one and the same metal show almost the same differences as were found between the mean results obtained for the different metals. In Table XVIII. two examples of this are given. In Table XIX. the resistances of the copper wires 1, 2, and 3, and those calculated from the mean of all the formulae, are given; we do this to show that the resistance of a wire does not increase in direct ratio to the temperature (as stated by some experimenters in this direction), but, on the contrary, the formula for correction of the resistance of a wire for temperature is \[ r = x + yt + zt^2, \] and not \[ r = x + yt. \] **Table XIX.** | First wire, hard drawn. | First wire, annealed. | Second wire, hard drawn. | Second wire, annealed. | |-------------------------|-----------------------|--------------------------|------------------------| | T. | Resistance. | Increase of resistance for 1°. | T. | Resistance. | Increase of resistance for 1°. | T. | Resistance. | Increase of resistance for 1°. | T. | Resistance. | Increase of resistance for 1°. | | 0 | 98·382 | ...... | 0 | 98·241 | ...... | 0 | 98·412 | ...... | 0 | 97·902 | ...... | | 16·86 | 104·74 | 0·3771 | 17·0 | 104·67 | 0·3782 | 19·17 | 105·98 | 0·3948 | 18·96 | 105·28 | 0·3891 | | 29·88 | 109·81 | 0·3825 | 29·63 | 109·54 | 0·3813 | 30·95 | 110·88 | 0·4028 | 31·86 | 110·59 | 0·3982 | | 51·03 | 118·72 | 0·3985 | 50·22 | 118·08 | 0·3950 | 48·53 | 118·32 | 0·4102 | 52·05 | 119·08 | 0·4069 | | 69·52 | 126·59 | 0·4057 | 69·60 | 126·23 | 0·4021 | 69·22 | 127·16 | 0·4153 | 70·27 | 126·85 | 0·4119 | | 83·77 | 132·60 | 0·4085 | 83·42 | 132·21 | 0·4072 | 83·77 | 133·31 | 0·4166 | 83·81 | 132·58 | 0·4138 | | 98·60 | 139·22 | 0·4142 | 99·37 | 139·10 | 0·4112 | 99·00 | 139·80 | 0·4181 | 99·57 | 139·36 | 0·4164 | | Third wire, hard drawn. | Third wire, annealed. | Resistance calculated from the mean of the six formulæ found for copper. | Resistance calculated from the mean of all the formulæ. | |-------------------------|-----------------------|-------------------------------------------------|--------------------------------------------------| | 0 | 99·384 | ...... | 0 | 97·806 | ...... | 0 | 100 | ...... | 0 | 100 | ...... | | 12·65 | 104·42 | 0·3981 | 13·45 | 103·14 | 0·3966 | 20 | 107·97 | 0·3985 | 20 | 107·76 | 0·3880 | | 25·61 | 109·82 | 0·4075 | 26·15 | 108·41 | 0·4055 | 40 | 116·33 | 0·4082 | 40 | 115·91 | 0·3977 | | 39·52 | 115·72 | 0·4134 | 39·35 | 113·99 | 0·4113 | 60 | 124·98 | 0·4163 | 60 | 124·36 | 0·4060 | | 53·92 | 121·85 | 0·4167 | 55·50 | 120·95 | 0·4170 | 80 | 133·69 | 0·4211 | 80 | 132·92 | 0·4115 | | 69·90 | 128·54 | 0·4171 | 69·90 | 127·00 | 0·4176 | 100 | 142·22 | 0·4222 | 100 | 141·46 | 0·4146 | | 84·87 | 134·82 | 0·4175 | 84·67 | 133·25 | 0·4186 | 99·92 | 140·94 | 0·4159 | 99·05 | 139·32 | 0·4190 | The calculations from a formula of four or more terms, as \[ \lambda = x + yt + zt^2 + at^3, \] agree better with the observed values than that of three. An example of this is shown in Table XX., where the formulæ, deduced from observations made with a hard-drawn wire (of course previously heated to 100° for several days), of three and four terms, with the differences, are given. The formula of three terms, deduced from the observations, was \[ \lambda = 99.137 - 0.37675t + 0.0008728t^2; \] and that of four terms \[ \lambda = 99.307 - 0.39301t + 0.0012318t^2 - 0.000002193t^3. \] From the above it will be seen how much better the observed values agree with the formula of four terms. We have, however, contented ourselves with a formula of three terms, as the conducting powers calculated from it agree with those observed to values corresponding to \(0^\circ.1\) or \(0^\circ.2\), and as the calculations for a formula of four terms would have increased the labour of the research to a very great extent. But it may be asked how it happens that the formulæ obtained for wires of one and the same metal vary so much, in fact, show differences almost equal to the mean of those deduced for the different metals? That this is not due to errors of observation we have repeatedly satisfied ourselves; for compare only the formulæ of the hard-drawn (or rather partially annealed) and the annealed wires, and see how well they agree with each other. It appears, however, to be probably due to the molecular arrangement of the wires being different in each case. Take, for instance, the copper wires experimented with: wire 1 increased in conducting power by heating to \(100^\circ\) for several days, almost to the same extent as if it had been annealed, wire 2 partially so, and wire 3 hardly at all; and here it may be mentioned that silver and copper wires become softer and lose their elasticity, whereas gold does not seem to be annealed at all after having been kept at \(100^\circ\) for several days. Again, take cadmium, where we know that the wires become brittle and crystalline at \(80^\circ\), and we find the formulæ vary more than those of any other metals; and, lastly, look at the results obtained with bismuth and tellurium, and there can be little doubt that the reason why the formulæ of the wires and bars of the same metal do not agree together is that the molecular arrangement is different in each; and that this is the cause of the differences in the formulæ, we may also assume from the fact that, when the wires on being heated do not at all or only to a very slight degree permanently alter in their conducting power, when cooled again, then the formulæ of wires of the same metal agree very closely with each other. Compare, for instance, those of lead, tin, mercury, &c. | T | Conducting power. | Calculated from formula of three terms. | Difference. | Conducting power, calculated from formula of four terms. | Difference. | |------|-------------------|----------------------------------------|-------------|----------------------------------------------------------|-------------| | | Observed. | | | | | | 16.9 | 95.169 | 95.134 | +0.035 | 95.166 | +0.003 | | 30.1 | 88.537 | 88.588 | -0.051 | 88.534 | +0.003 | | 49.5 | 82.610 | 82.627 | -0.017 | 82.605 | +0.005 | | 69.0 | 77.320 | 77.297 | +0.023 | 77.304 | -0.014 | | 82.8 | 73.976 | 73.926 | +0.050 | 73.966 | +0.010 | | 97.9 | 70.579 | 70.619 | -0.040 | 70.580 | -0.001 | The mean of the conducting powers given in the Tables agrees very well with the mean of the former determinations made with wires of metals of different preparation to that of those used for the experiments described in this paper. The following questions have suggested themselves during the foregoing investigation, the answers to which we reserve for ourselves. It is intended to make them the subjects of short communications, which from time to time will be laid before the Royal Society: 1. Will a hard-drawn wire become partially annealed by age? and, on the other hand, will an annealed wire become partially hard drawn? 2. Will bismuth or tellurium return to their original conducting power in time, or by exposure to intense cold? 3. Whether by heating tellurium or any of the metals to a higher temperature than $100^\circ$ we should not arrive at the same result in a much shorter time. 4. What are the thermo-electric properties of bismuth, antimony, tellurium, &c. after being kept at $100^\circ$ for several days? will they not have altered? It is remarkable that bismuth, which stands at one end of the thermo-electric series, should gain in conducting power after heating for some days, and that antimony and tellurium, at the other end of the series, should lose, the one slightly, the other, with a much higher thermo-electric number, to a very great extent. 5. Will tellurium conduct better in a melted state than the solid? 6. What law do the alloys follow as regards the influence of temperature on their conducting power?