On the Influence of Temperature on the Electric Conducting-Power of Alloys
Author(s)
Augustus Matthiessen, Carl Vogt
Year
1864
Volume
154
Pages
35 pages
Language
en
Journal
Philosophical Transactions of the Royal Society of London
Full Text (OCR)
IV. On the Influence of Temperature on the Electric Conducting-Power of Alloys. By Augustus Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary's Hospital, and Carl Vogt, Ph.D.
Received June 11,—Read June 18, 1863.
The influence of temperature on the electric conducting-power of the pure metals in a solid state has been proved to be very great*, and as very little is as yet known with regard to the influence of temperature on the electric conducting-power of alloys, we undertook this research in order, if possible, to discover the law which regulates this property.
For the sake of clearness, we have thought it advisable to divide this subject into four parts, and they will be treated of in the following order:
1. Experiments on the influence of temperature on the electric conducting-power of alloys composed of two metals.
2. Experiments on the influence of temperature on the electric conducting-power of some alloys composed of three metals.
3. On a method by which the conducting-power of a pure metal may be deduced from that of the impure one.
4. Miscellaneous and general remarks.
I. Experiments on the Influence of Temperature on the Electric Conducting-power of Alloys composed of two Metals.
It will be as well to mention that, from the few experiments already published on the influence of temperature on the conducting-power of alloys, we had at the commencement of the research some idea of the law which regulates this property, and having found after a few experiments our supposition confirmed, we were able to shape the course we intended to pursue, in such a manner as to curtail the number of alloys to be experimented with. Thus, with the alloys made of the metals lead, tin, cadmium, and zinc with one another, instead of using the alloys
\[ \text{Pb}_6\text{Sn}, \text{Pb}_4\text{Sn}, \text{Pb}_2\text{Sn}, \text{Pb Sn}, \text{Pb Sn}_2, \text{Pb Sn}_4, \text{Pb Sn}_6, \]
and testing in the same manner the tin-cadmium, tin-zinc, cadmium-zinc alloys, we only used the following,
\[ \text{Sn}_6\text{Pb}, \text{Sn}_4\text{Cd}, \text{Sn}_2\text{Zn}, \text{Pb Sn}, \text{Zn Cd}_2, \text{Sn Cd}_4, \text{Cd Pb}_6, \]
thus forming a mixed but complete series. Other groups of alloys have been treated in
* Philosophical Transactions, 1862, p. 1.
a similar manner. The reason for grouping alloys made of different metals under different heads has already been elsewhere discussed*. It has also been only considered necessary to experiment on one wire of each alloy, as the results obtained agree, in most cases, very closely with those calculated, and as it has been proved by a few determinations, which are given in Table I., that the same values were obtained for the percentage decrement in the conducting-power of the alloy between $0^\circ$ and $100^\circ$, when series of determinations were made with two wires of the same alloy.
### Table I.
| Alloy | Volumes per cent. | Percentage decrement observed between $0^\circ$ and $100^\circ$. |
|-----------------------|-------------------|---------------------------------------------------------------|
| Gold-copper (hard drawn) | 98-63 of Au | 21-87 |
| Gold-copper (hard drawn) | 98-38 | 21-75 |
| Gold-silver † (hard drawn) | 52-08 | 6-50 |
| Gold-silver (hard drawn) | 52-08 | 6-48 |
| Gold-silver (annealed) | 52-08 | 6-72 |
| Gold-silver (annealed) | 52-08 | 6-70 |
| Gold-silver (annealed) | 52-08 | 6-71 |
| Gold-silver (annealed) | 79-86 | 10-15 |
| Gold-silver (annealed) | 79-86 | 10-21 |
| Tin-cadmium | 23-50 of Sn | 28-89 |
| Tin-cadmium | 23-50 | 29-08 |
The method and apparatus employed for the determination of the conducting-power at different temperatures was the same as that described and used for the experiments on the pure metals†. We have, however, in many cases only taken observations at three intervals, as we found that almost the same formula was deduced from observations made at three different temperatures as from seven, especially when the temperature of the second observation was the mean of the other two; now as three or more observations were made at each interval, it was easy to obtain the wished-for temperature as the mean of several determinations. Thus the formulæ deduced for correction of conducting-power for temperature of the alloy Cd Pb$_6$ were—
From seven observations . . . $\lambda = 9\cdot287 - 0\cdot032501t + 0\cdot00006743t^2$,
From three observations . . . $\lambda = 9\cdot286 - 0\cdot032450t + 0\cdot00006683t^2$.
Again, those deduced for the alloy Sn$_2$ Zn were—
From seven observations . . . $\lambda = 16\cdot876 - 0\cdot065544t + 0\cdot0001471t^2$,
From three observations . . . $\lambda = 16\cdot899 - 0\cdot065790t + 0\cdot0001454t^2$,
where $\lambda$ represents the conducting-power at $t^\circ$ C.
We have here taken, as in former papers, the conducting-power of a hard-drawn silver wire at $0^\circ=100$ as defining our unit. The normal wires were made of german silver, the resistances of which were determined by comparing them with the gold-silver alloy‡; the conducting-power of a hard-drawn wire of which is equal to $15\cdot03$ at $0^\circ$.
* Philosophical Transactions, 1860, p. 162.
† Ibid. 1862, p. 1.
‡ Philosophical Magazine for February 1861.
Table II. contains the conducting-powers, specific gravities, and equivalents of the metals used for making the alloys. These values are those which have been used in calculating the results given in this paper.
| Metal | Conducting-power at 0° | Specific gravity | Equivalent |
|------------------------|------------------------|------------------|------------|
| Silver (hard drawn) | 100·00 | 10·468 | 108·0 |
| Silver (annealed) | 108·57 | | |
| Copper (hard drawn) | 99·95 | 8·350 | 31·7 |
| Gold (hard drawn) | 77·96 | 19·263 | 157·0 |
| Gold (annealed) | 79·33 | | |
| Zinc | 29·02 | 7·148 | 39·6 |
| Cadmium | 23·72 | 8·655 | 56·0 |
| Palladium (hard drawn) | 18·45 | 11·500 | |
| Platinum (hard drawn) | 17·99 | 21·400 | |
| Iron (hard drawn) | 16·81 | 7·730 | |
| Nickel | 13·11 | 8·50 | |
| Tin | 12·36 | 7·294 | 58·0 |
| Thallium | 9·16 | 11·900 | |
| Lead | 8·32 | 11·376 | 103·7 |
| Bismuth | 1·245 | 9·822 | 208·0 |
Tables III., IV., V., and VI. contain the results obtained with the alloys belonging to the different groups. The alloys marked thus (†) are those which were made and used for former experiments; in all cases, however, fresh wires were made. All the rest have been re-made and analyzed. In Table III. the results are given which were obtained with some alloys made of those metals which, when alloyed with one another, conduct electricity in the ratio of their relative volumes; in Table V. those with some alloys of those metals which, when alloyed with one another, do not conduct electricity in the ratio of their relative volumes, but always in a lower degree than the mean of their volumes; in Table IV. those with some alloys made with the metals belonging to the alloys given in Table III. with those in Table V.; and in Table VI. those with some alloys whose places in the foregoing Tables we have not yet been able to assign.
### Table III.
1.
†Sn₆ Pb, containing 16·04 volumes per cent. of lead.
Length 435·5 millims.; diameter 0·793 millim.
Conducting-power found before heating the wire 11·782 at 13·7 Reduced to 0°*.
Ditto, after being kept at 100° for 1 day 12·052 at 9·3 12·494
Ditto, for 2 days 12·088 at 9·1 12·522
| T. | Conducting-power. | Observed. | Calculated. | Difference. |
|----|-------------------|-----------|-------------|-------------|
| 16·03 | 12·043 | 12·033 | ±0·010 |
| 24·56 | 11·371 | 11·381 | -0·010 |
| 39·27 | 10·760 | 10·768 | -0·008 |
| 55·00 | 10·168 | 10·165 | +0·003 |
| 67·93 | 9·720 | 9·716 | +0·004 |
| 84·93 | 9·175 | 9·165 | +0·010 |
| 98·87 | 8·757 | 8·766 | -0·009 |
λ = 12·510 - 0·048619t + 0·0001087t².
* These and all similar values were reduced to 0° as described in the paper "On the Influence of Temperature on the Electric Conducting-power of the Pure Metals;" Philosophical Transactions, 1862, p. 10.
2.
†Sn₄ Cd, containing 83·10 volumes per cent. of tin.
Length 285 millims.; diameter 0·417 millim.
Conducting-power found before heating the wire 14·259 at 6·8 Reduced to 0°.
Ditto, after being kept at 100° for 1 day 14·207 at 6·2 14·569
Ditto, for 2 days 14·072 at 7·7 14·517
| T. | Conducting-power. | Observed. | Calculated. | Difference. |
|----|-------------------|-----------|-------------|-------------|
| 8·72 | 13·986 | 13·985 | +0·001 |
| 25·52 | 13·069 | 13·092 | -0·003 |
| 39·50 | 12·419 | 12·423 | -0·004 |
| 54·96 | 11·770 | 11·761 | +0·009 |
| 69·40 | 11·218 | 11·217 | +0·001 |
| 84·02 | 10·733 | 10·740 | -0·007 |
| 98·85 | 10·333 | 10·330 | +0·003 |
λ = 14·487 - 0·059047t + 0·0001720t².
### Table III. (continued).
#### 3.
†Sn₂Zn, containing 77·71 volumes per cent. of tin.
Length 276·5 millims.; diameter 0·555 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 16·89 | 16·89 | +0·000 |
Ditto, after being kept at 100°
for 1 day
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 16·89 | 16·89 | +0·000 |
Ditto, for 2 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 16·89 | 16·89 | +0·000 |
\[ \lambda = 16·876 - 0·065544t^2 + 0·000147t^3. \]
#### 4.
†Pb Sn, containing 53·41 volumes per cent. of lead.
Length 359 millims.; diameter 0·844 millim.*
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 10·073 | 10·071 | +0·002 |
\[ \lambda = 10·423 - 0·039433t^2 + 0·00008775t^3. \]
#### 5.
†Zn Cd₂, containing 26·06 volumes per cent. of zinc.
Length 577 millims.; diameter 0·629 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 24·774 | 24·774 | +0·002 |
Ditto, after being kept at 100°
for 1 day
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 25·101 | 25·101 | +0·002 |
Ditto, for 2 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 24·916 | 24·916 | +0·002 |
\[ \lambda = 25·906 - 0·098065t^2 + 0·0002072t^3. \]
* The reason why here and in some cases in the following Tables no determinations of the effect of heating the wire on its conducting-power are given, is that the wire unfortunately, from some cause or another, became unsoldered after it had been heated to 100° for one or more days.
### Table III. (continued).
#### 6.
†Sn Cd₄, containing 23·50 volumes per cent. of tin.
Length 512·5 millims.; diameter 0·670 millim.
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 12·57 | 21·096 | 21·086 | +0·010 |
| 25·55 | 20·068 | 20·084 | -0·016 |
| 40·20 | 19·033 | 19·037 | -0·004 |
| 54·30 | 18·127 | 18·113 | +0·014 |
| 69·33 | 17·219 | 17·220 | -0·001 |
| 80·96 | 16·589 | 16·594 | -0·005 |
| 91·30 | 16·086 | 16·084 | +0·002 |
\[ \lambda = 22·123 - 0·085159t^2 + 0·0002082t^3. \]
#### 7.
†Cd Pb₆, containing 10·57 vols. per cent. of cadmium.
Length 224 millims.; diameter 0·644 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 9·068 | 9·068 | 9·264 |
Ditto, after being kept at 100°
for 1 day
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 9·490 | 9·490 | 9·574 |
Ditto, for 2 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 9·039 | 9·039 | 9·285 |
Ditto, for 3 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 8·964 | 8·964 | 9·285 |
\[ \lambda = 9·287 - 0·032501t^2 + 0·00006743t^3. \]
### Table IV.
#### 1.
†Pb₂₀Ag₁ containing 94·64 volumes per cent. of lead.
Length 372 millims.; diameter 0·704 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 8·508 | 8·508 | 8·938 |
Ditto, after being kept at 100°
for 1 day
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 8·578 | 8·578 | 9·060 |
Ditto, for 2 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 8·640 | 8·640 | 9·096 |
Ditto, for 3 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 8·731 | 8·731 | 9·238 |
Ditto, for 4 days
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 8·700 | 8·700 | 9·236 |
\[ \lambda = 9·244 - 0·033467t^2 + 0·00007360t^3. \]
### Table IV. (continued).
#### 2.
†Pb Ag, containing 46·90 volumes per cent. of lead.
Length 267 millims.; diameter 0·584 millim.
Conducting-power found before heating the wire Reduced to 0°.
13·009 at 14·9 13·391
Ditto, after being kept at 100°
for 1 day 13·072 at 15·9 13·482
Ditto, for 2 days 13·087 at 15·1 13·477
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| 14·10 | 18·099 | 13·100 | -0·001 |
| 24·70 | 12·841 | 12·837 | +0·004 |
| 39·88 | 12·478 | 12·477 | +0·001 |
| 54·61 | 12·141 | 12·146 | -0·005 |
| 70·05 | 11·818 | 11·818 | 0·000 |
| 83·88 | 11·546 | 11·542 | +0·004 |
| 99·37 | 11·250 | 11·251 | -0·001 |
\[ \lambda = 13·464 - 0·26424t + 0·00004174t^2. \]
#### 3.
Pb Ag₂, containing 30·64 volumes per cent. of lead.
Length 373 millims.; diameter 0·634 millim.
Conducting-power found after heating the wire for 2 days... Reduced to 0°.
21·186 at 16·1 21·874
Ditto, for 3 days 21·160 at 16·5 21·863
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| 16·82 | 21·191 | 21·190 | +0·001 |
| 24·93 | 20·811 | 20·813 | -0·002 |
| 39·48 | 20·236 | 20·232 | +0·004 |
| 54·17 | 19·669 | 19·669 | 0·000 |
| 69·78 | 19·089 | 19·098 | -0·009 |
| 84·27 | 18·602 | 18·593 | +0·009 |
| 100·00 | 18·069 | 18·071 | -0·002 |
\[ \lambda = 21·866 - 0·043636t + 0·00005686t^2. \]
#### 4.
†Sn₁₂ Au, containing 90·32 volumes per cent. of tin.
Conducting-power found before heating the wire Reduced to 0°.
7·9495 at 11·8 8·2418
Ditto, after being kept at 100°
for 1 day 7·9479 at 13·0 8·2702
| T. | Conducting-power. |
|----|------------------|
| 14·0 | 7·9224 |
| 57·0 | 6·9935 |
| 100·0 | 6·2676 |
\[ \lambda = 8·2687 - 0·025501t + 0·00005490t^2. \]
#### 5.
†Sn₅ Au, containing 79·54 volumes per cent. of tin.
Length 222 millims.; diameter 0·599 millim.
Conducting-power found before heating the wire Reduced to 0°.
4·8386 at 14·3 5·0427
Ditto, after being kept at 100°
for 1 day 4·8432 at 14·6 5·0518
Ditto, for 2 days 4·8741 at 13·0 5·0608
| T. | Conducting-power. |
|----|------------------|
| 14·0 | 4·8593 |
| 57·0 | 4·3212 |
| 100·0 | 3·9009 |
\[ \lambda = 5·0599 - 0·014776t + 0·00003186t^2. \]
#### 6.
Tin-copper alloy, containing 93·57 volumes per cent. of tin.
Length 274·5 millims.; diameter 0·667 millim.
Conducting-power found before heating the wire Reduced to 0°.
11·264 at 18·1 12·034
Ditto, after being kept at 100°
for 1 day 11·498 at 16·9 12·231
Ditto, for 2 days 11·445 at 18·3 12·237
Ditto, for 3 days 11·549 at 16·3 12·259
Ditto, for 4 days 11·571 at 16·3 12·282
Ditto, for 5 days 11·558 at 17·1 12·304
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| 13·58 | 11·622 | 11·618 | +0·004 |
| 24·70 | 11·242 | 11·242 | 0·000 |
| 38·91 | 10·679 | 10·688 | -0·009 |
| 54·96 | 10·109 | 10·111 | -0·002 |
| 70·29 | 9·615 | 9·609 | +0·006 |
| 85·68 | 9·160 | 9·152 | +0·008 |
| 99·40 | 8·777 | 8·784 | -0·007 |
\[ \lambda = 12·299 - 0·045304t + 0·00008997t^2. \]
#### 7.
Tin-copper alloy, containing 83·60 volumes per cent. of tin.
Length 201 millims.; diameter 0·581 millim.
Conducting-power found before heating the wire Reduced to 0°.
12·119 at 15·7 12·764
Ditto, after being kept at 100°
for 1 day 12·264 at 15·3 12·900
Ditto, for 2 days 12·389 at 15·3 12·031
Ditto, for 3 days 12·420 at 14·7 13·038
Ditto, for 4 days 12·384 at 15·7 13·043
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| 8·27 | 12·688 | 12·689 | -0·001 |
| 25·28 | 12·009 | 12·002 | +0·007 |
| 39·43 | 11·460 | 11·470 | -0·010 |
| 54·31 | 10·943 | 10·949 | -0·006 |
| 70·13 | 10·444 | 10·437 | +0·007 |
| 84·18 | 10·032 | 10·022 | +0·010 |
| 99·28 | 9·607 | 9·614 | -0·007 |
\[ \lambda = 13·042 - 0·043382t + 0·00006924t^2. \]
### Table IV. (continued).
#### 8.
**Tin-copper alloy, containing 14·91 vols. per cent. of tin.**
Length 141 millims.; diameter 0·501 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 16·58 | 8·8565 8·8560 +0·0005 |
| 34·85 | 8·7687 8·7692 -0·0005 |
| 56·33 | 8·6684 8·6693 -0·0009 |
| 77·40 | 8·5753 8·5737 +0·0016 |
| 99·48 | 8·4754 8·4760 -0·0006 |
\[ \lambda = 8·9364 - 0·004889t^2 + 0·00002626t^3. \]
#### 9.
**Tin-copper alloy, containing 12·35 vols. per cent. of tin.**
Length 429 millims.; diameter 0·627 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. |
| 11·0 | 10·1386 |
| 55·5 | 9·8710 |
| 100·0 | 9·6526 |
\[ \lambda = 10·212 - 0·006804t^2 + 0·00001210t^3. \]
#### 10.
**Tin-copper alloy, containing 11·61 vols. per cent. of tin.**
Length 322·5 millims.; diameter 0·524 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·43 | 12·058 12·057 +0·001 |
| 23·40 | 11·990 11·991 -0·001 |
| 40·35 | 11·852 11·853 -0·001 |
| 54·75 | 11·737 11·736 +0·001 |
| 69·78 | 11·619 11·617 +0·002 |
| 84·66 | 11·499 11·500 -0·001 |
| 98·70 | 11·391 11·391 0·000 |
\[ \lambda = 12·186 - 0·008468t^2 + 0·00003700t^3. \]
#### 11.
**Tin-copper alloy, containing 6·02 vols. per cent. of tin.**
Length 210 millims.; diameter 0·458 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 17·23 | 19·484 19·484 0·000 |
| 24·03 | 19·355 19·354 +0·001 |
| 40·03 | 19·050 19·052 -0·002 |
| 55·47 | 18·771 18·769 +0·002 |
| 69·70 | 18·511 18·513 -0·002 |
| 83·16 | 18·279 18·276 +0·003 |
| 98·87 | 18·004 18·006 -0·002 |
\[ \lambda = 19·820 - 0·019729t^2 + 0·00001397t^3. \]
#### 12.
**Tin-copper alloy, containing 1·41 vol. per cent. of tin.**
Length 599 millims.; diameter 0·449 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| Ditto, for 4 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·53 | 60·470 60·455 +0·015 |
| 24·68 | 59·011 59·029 -0·018 |
| 39·03 | 56·897 56·900 -0·003 |
| 54·98 | 54·681 54·686 -0·005 |
| 68·73 | 52·924 52·906 +0·018 |
| 84·25 | 51·036 51·041 -0·005 |
| 99·70 | 49·334 49·336 -0·002 |
\[ \lambda = 62·997 - 0·168556t^2 + 0·0003163t^3. \]
#### 13.
**Tin-silver alloy, containing 96·52 vols. per cent. of tin.**
Length 304 millims.; diameter 0·478 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 11·12 | 11·983 11·971 +0·012 |
| 24·90 | 11·353 11·364 -0·011 |
| 39·40 | 10·751 10·768 -0·017 |
| 54·60 | 10·193 10·189 +0·004 |
| 69·81 | 9·676 9·657 +0·019 |
| 84·88 | 9·178 9·177 +0·001 |
| 99·68 | 8·743 8·751 -0·008 |
\[ \lambda = 12·488 - 0·047691t^2 + 0·0001023t^3. \]
### Table IV. (continued).
#### 14.
**Tin-silver alloy, containing 75·51 vols. per cent. of tin.**
Length 273 millims.; diameter 0·467 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 11·53 | 13·651 | 13·646 | +0·005 |
| 25·51 | 12·955 | 12·958 | -0·003 |
| 40·26 | 12·283 | 12·283 | 0·000 |
| 55·86 | 11·700 | 11·708 | -0·008 |
| 69·58 | 11·099 | 11·099 | 0·000 |
| 84·98 | 10·572 | 10·561 | +0·011 |
| 99·48 | 10·103 | 10·108 | -0·005 |
\[ \lambda = 14·250 - 0·053772t + 0·0001219t^2. \]
#### 15.
**Zinc-copper alloy, containing 42·06 vols. per cent. of zinc.**
Length 296·6 millims.; diameter 0·516 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·72 | 21·807 | 21·801 | +0·006 |
| 23·75 | 21·562 | 21·564 | -0·002 |
| 39·28 | 21·116 | 21·118 | -0·002 |
| 54·38 | 20·693 | 20·698 | -0·005 |
| 69·31 | 20·300 | 20·297 | +0·003 |
| 84·63 | 19·897 | 19·898 | -0·001 |
| 99·43 | 19·527 | 19·526 | +0·001 |
\[ \lambda = 22·274 - 0·030601t + 0·00002980t^2. \]
#### 16.
**Zinc-copper alloy, containing 29·45 vols. per cent. of zinc.**
Length 190 millims.; diameter 0·381 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 13·47 | 21·704 | 21·702 | +0·002 |
| 24·07 | 21·413 | 21·416 | -0·003 |
| 39·21 | 21·020 | 21·017 | +0·003 |
| 53·65 | 20·647 | 20·647 | 0·000 |
| 69·03 | 20·268 | 20·269 | -0·001 |
| 83·71 | 19·915 | 19·916 | -0·001 |
| 98·97 | 19·565 | 19·564 | +0·001 |
\[ \lambda = 22·076 - 0·028100t + 0·00002745t^2. \]
#### 17.
**Zinc-copper alloy, containing 23·61 vols. per cent. of zinc.**
Length 265 millims.; diameter 0·379 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·97 | 27·719 | 27·714 | +0·005 |
| 23·80 | 27·408 | 27·412 | -0·004 |
| 39·28 | 26·828 | 26·829 | -0·001 |
| 54·82 | 26·259 | 26·262 | -0·003 |
| 68·66 | 25·777 | 25·772 | +0·005 |
| 83·75 | 25·258 | 25·256 | +0·002 |
| 98·22 | 24·774 | 24·776 | -0·002 |
\[ \lambda = 28·345 - 0·040104t + 0·00003839t^2. \]
#### 18.
**Zinc-copper alloy, containing 10·88 vols. per cent. of zinc.**
Length 449 millims.; diameter 0·448 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 14·33 | 45·912 | 45·912 | 0·000 |
| 23·71 | 45·050 | 45·056 | +0·006 |
| 39·80 | 43·638 | 43·648 | -0·010 |
| 54·32 | 42·442 | 42·440 | +0·002 |
| 69·48 | 41·246 | 41·245 | +0·001 |
| 84·38 | 40·145 | 40·134 | +0·011 |
| 99·85 | 39·100 | 39·109 | -0·009 |
\[ \lambda = 47·267 - 0·096627t + 0·0001433t^2. \]
#### 19.
**Zinc-copper alloy, containing 5·03 vols. per cent. of zinc.**
Length 642 millims.; diameter 0·479 millim.
Conducting-power found before heating the wire Reduced to 0°.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·17 | 58·522 | 58·494 | +0·028 |
| 23·57 | 57·277 | 57·301 | -0·024 |
| 40·03 | 55·071 | 55·093 | -0·022 |
| 54·91 | 53·211 | 53·213 | -0·002 |
| 67·88 | 51·679 | 51·664 | +0·015 |
| 84·15 | 49·856 | 49·839 | +0·017 |
| 99·45 | 48·228 | 48·243 | -0·015 |
\[ \lambda = 60·697 - 0·14995t + 0·0002486t^2. \]
### Table V.
#### 1. Gold-copper alloy, containing 98·63 volumes per cent. of gold (hard drawn).
Length 1121·5 millims.; diameter 0·582 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·52 | 53·972 53·980 -0·008 |
| 25·10 | 52·676 52·653 +0·023 |
| 39·74 | 50·684 50·715 -0·031 |
| 55·66 | 48·739 48·740 -0·001 |
| 69·83 | 47·106 47·092 +0·014 |
| 85·00 | 45·451 45·443 +0·008 |
| 95·35 | 43·986 43·994 -0·008 |
\[ \lambda = 56·232 - 0·14916t + 0·0002616t^2. \]
#### 2. Gold-copper alloy, containing 91·66 volumes per cent. of gold (hard drawn).
Length 450 millims.; diameter 0·501 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| Ditto, for 4 days | |
| T. | Conducting-power. |
|----|-------------------|
| 13·0 | 15·880 |
| 56·0 | 15·356 |
| 100·0 | 14·837 |
\[ \lambda = 16·024 - 0·011997t + 0·00001291t^2. \]
#### 3. Gold-silver alloy, containing 79·86 volumes per cent. of gold (hard drawn).
Length 605·7 millims.; diameter 0·704 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| Ditto, for 4 days | |
| T. | Conducting-power. |
|----|-------------------|
| 11·45 | 21·013 21·030 +0·001 |
| 26·04 | 20·698 20·701 -0·003 |
| 40·04 | 20·391 20·392 -0·001 |
| 55·26 | 20·065 20·064 +0·001 |
| 67·73 | 19·806 19·802 +0·004 |
| 84·13 | 19·463 19·464 -0·001 |
| 98·45 | 19·175 19·176 -0·001 |
\[ \lambda = 21·293 - 0·023166t + 0·00001691t^2. \]
* The conducting-power of these wires did not alter after being kept at 100° for one day.
### Table V. (continued).
#### 4. Gold-silver alloy, containing 79·86 volumes per cent. of gold (annealed *).
Length 596 millims.; diameter 0·704 millim.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 7·64 | 21·342 21·341 +0·001 |
| 25·27 | 20·920 20·924 -0·001 |
| 40·71 | 20·570 20·572 -0·002 |
| 54·61 | 20·265 20·264 +0·001 |
| 70·35 | 19·930 19·928 +0·002 |
| 85·25 | 19·622 19·622 0·000 |
| 99·50 | 19·338 19·339 -0·001 |
\[ \lambda = 21·527 - 0·024475t + 0·00002500t^2. \]
#### 5. Gold-silver alloy, containing 19·86 volumes per cent. of gold (hard drawn).
Length 161·5 millims.; diameter 0·351 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| Ditto, after being kept at 100° for 1 day | |
| Ditto, for 2 days | |
| T. | Conducting-power. |
|----|-------------------|
| 13·02 | 21·838 21·833 +0·005 |
| 23·90 | 21·620 21·625 -0·005 |
| 38·03 | 21·355 21·359 -0·004 |
| 54·42 | 21·158 21·056 +0·002 |
| 68·95 | 20·795 20·794 +0·001 |
| 82·37 | 20·557 20·555 +0·002 |
| 98·15 | 20·279 20·280 -0·001 |
\[ \lambda = 22·085 - 0·019538t + 0·00001173t^2. \]
#### 6. Gold-silver alloy, containing 19·86 volumes per cent. of gold (annealed *).
Length 161·5 millims.; diameter 0·351 millim.
| T. | Conducting-power. |
|----|-------------------|
| 14·95 | 21·629 21·627 +0·002 |
| 24·56 | 21·437 21·430 -0·003 |
| 40·83 | 21·335 21·327 -0·002 |
| 55·38 | 21·059 21·055 +0·004 |
| 69·06 | 20·806 20·805 +0·001 |
| 84·78 | 20·527 20·528 -0·001 |
| 97·53 | 20·299 20·300 -0·001 |
\[ \lambda = 22·125 - 0·020097t + 0·00001419t^2. \]
### Table V. (continued).
#### 7.
Gold-copper alloy, containing 19·17 volumes per cent. of gold (hard drawn).
Length 534 millims.; diameter 0·550 millim.
Conducting-power found before heating the wire Reduced to 0°.
20·300 at 12·2 20·504
Ditto, after being kept at 100° for 1 day 20·295 at 12·0 20·517
for 2 days 20·287 at 12·4 20·505
| T. | Conducting-power. | Difference. |
|----|-------------------|-------------|
| | Observed. | Calculated. |
| 13·40 | 20·972 | 20·378 | -0·006 |
| 24·38 | 20·088* | 20·088 | 0·000 |
| 40·01 | 19·838 | 19·824 | +0·014 |
| 55·03 | 19·569 | 19·573 | -0·004 |
| 70·11 | 19·325 | 19·328 | -0·003 |
| 84·98 | 19·088 | 19·092 | -0·004 |
| 99·87 | 18·865 | 18·861 | +0·004 |
\[ \lambda = 20·513 - 0·017718t + 0·00091170t^2. \]
#### 8.
Gold-copper alloy, containing 0·71 volume per cent. of gold (hard drawn).
Length 1049 millims.; diameter 0·366 millim.
Conducting-power found before heating the wire Reduced to 0°.
79·884 at 15·3 84·008
Ditto, after being kept at 100° for 1 day 80·389 at 14·3 84·264
for 2 days 80·014 at 15·5 84·200
for 3 days 79·844 at 16·6 84·322
| T. | Conducting-power. | Difference. |
|----|-------------------|-------------|
| | Observed. | Calculated. |
| 17·27 | 79·709 | 79·670 | +0·039 |
| 23·98 | 77·952 | 77·962 | -0·010 |
| 39·55 | 74·154 | 74·212 | -0·058 |
| 54·26 | 70·294 | 70·913 | -0·019 |
| 69·29 | 67·920 | 67·879 | +0·041 |
| 83·86 | 65·213 | 65·175 | +0·038 |
| 98·78 | 62·645 | 62·677 | -0·032 |
\[ \lambda = 84·322 - 0·27999t + 0·0006162t^2. \]
#### 9.
Platinum-silver alloy, containing 19·65 volumes per cent. of platinum (hard drawn).
Length 169 millims.; diameter 0·518 millim.
Conducting-power found before heating the wire Reduced to 0°.
6·6565 at 18·0 6·6960
Ditto, after being kept at 100° for 1 day 6·6616 at 17·9 6·7008
for 2 days 6·6654 at 17·2 6·7031
| T. | Conducting-power. |
|----|-------------------|
| | Observed. |
| 8·27 | 6·6850 |
| 54·00 | 6·5876 |
| 99·90 | 6·4957 |
\[ \lambda = 6·7032 - 0·0022167t + 0·00001394t^2. \]
#### 10.
Platinum-silver alloy, containing 5·05 volumes per cent. of platinum (hard drawn).
Length 708 millims.; diameter 0·626 millim.
Conducting-power found before heating the wire Reduced to 0°.
17·812 at 16·9 18·031
Ditto, after being kept at 100° for 1 day 17·801 at 17·1 18·036
| T. | Conducting-power. |
|----|-------------------|
| | Observed. |
| 3·0 | 17·920 |
| 54·5 | 17·319 |
| 100·0 | 16·767 |
\[ \lambda = 18·045 - 0·013960t + 0·0001183t^2. \]
#### 11.
Platinum-silver alloy, containing 2·51 volumes per cent. of platinum (hard drawn).
Length 381·5 millims.; diameter 0·451 millim.
| T. | Conducting-power. |
|----|-------------------|
| | Observed. |
| 13·0 | 31·173 |
| 56·0 | 29·550 |
| 100·0 | 28·068 |
\[ \lambda = 31·640 - 0·039363t + 0·00003642t^2. \]
#### 12.
Palladium-silver alloy, containing 23·28 volumes per cent. of palladium (hard drawn).
Length 520 millims.; diameter 0·802 millim.
Conducting-power found before heating the wire Reduced to 0°.
8·4936 at 10·0 8·5214
Ditto, after being kept at 100° for 1 day 8·5147 at 10·0 8·5426
for 2 days 8·5062 at 9·1 8·5305
for 3 days 8·4918 at 8·6 8·5157
for 4 days 8·4868 at 10·0 8·5146
| T. | Conducting-power. |
|----|-------------------|
| | Observed. |
| 11·0 | 8·4846 |
| 55·5 | 8·3577 |
| 100·0 | 8·2256 |
\[ \lambda = 8·5152 - 0·0027644t - 0·000001313t^2. \]
#### 13.
Copper-silver alloy, containing 98·35 volumes per cent. of copper (hard drawn).
Length 1198 millims.; diameter 0·572 millim.
Conducting-power found before heating the wire Reduced to 0°.
86·674 at 9·5 89·544
Ditto, after being kept at 100° for 1 day 88·210 at 6·5 90·202
for 2 days 87·336 at 9·3 90·165
| T. | Conducting-power. | Difference. |
|----|-------------------|-------------|
| | Observed. | Calculated. |
| 10·48 | 86·919 | 86·846 | +0·073 |
| 25·27 | 82·583 | 82·634 | -0·051 |
| 39·57 | 78·763 | 78·861 | -0·098 |
| 53·96 | 75·317 | 75·361 | -0·044 |
| 69·73 | 72·007 | 71·868 | +0·139 |
| 85·12 | 68·875 | 68·802 | +0·073 |
| 98·35 | 66·348 | 66·442 | -0·094 |
\[ \lambda = 90·021 - 0·31050t + 0·0007193t^2. \]
### Table V. (continued).
#### 14.
Copper-silver alloy, containing 95·17 volumes per cent. of copper (hard drawn).
Length 929 millims.; diameter 0·489 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 78·165 at 16·0 | 82·300 |
| Ditto, after being kept at 100° | |
| for 1 day | 78·286 at 14·3 |
| for 2 days | 78·102 at 15·9 |
| Ditto, for 3 days | 77·666 at 17·8 |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·43 | 78·226 78·219 +0·007 |
| 24·26 | 76·066 76·059 +0·001 |
| 39·16 | 72·601 72·616 -0·015 |
| 54·62 | 69·301 69·312 -0·011 |
| 69·48 | 66·406 66·393 +0·013 |
| 83·53 | 63·885 63·866 +0·019 |
| 99·00 | 61·319 61·343 -0·014 |
\[ \lambda = 82·207 - 0·26728t + 0·0005711t^2. \]
#### 15.
Copper-silver alloy, containing 77·64 volumes per cent. of copper (hard drawn).
Length 623 millims.; diameter 0·374 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 66·807 at 14·6 | 69·811 |
| Ditto, after being kept at 100° | |
| for 1 day | 66·601 at 17·3 |
| for 2 days | 66·550 at 17·2 |
| Ditto, for 3 days | 66·707 at 17·0 |
| Ditto, for 4 days | 66·694 at 17·6 |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. Difference. |
| 15·15 | 67·155 67·192 -0·037 |
| 24·21 | 65·433 65·410 +0·023 |
| 39·48 | 62·583 62·565 +0·018 |
| 54·90 | 59·873 59·894 -0·021 |
| 69·48 | 57·557 57·556 +0·001 |
| 84·28 | 55·375 55·365 +0·001 |
| 99·90 | 53·259 53·262 -0·003 |
\[ \lambda = 70·328 - 0·21351t + 0·0004271t^2. \]
#### 16.
Copper-silver alloy, containing 46·67 volumes per cent. of copper (hard drawn).
Length 1256 millims.; diameter 0·437 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 72·036 at 14·2 | 74·940 |
| Ditto, after being kept at 100° | |
| for 1 day | 73·170 at 14·6 |
| for 2 days | 73·653 at 12·6 |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. |
| 15·0 | 73·529 |
| 56·5 | 65·449 |
| 100·0 | 58·894 |
\[ \lambda = 76·240 - 0·21375t + 0·0004030t^2. \]
#### 17.
Copper-silver alloy, containing 8·25 volumes per cent. of copper (hard drawn).
Length 2328 millims.; diameter 0·525 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 78·323 at 9·0 | 80·284 |
| Ditto, after being kept at 100° | |
| for 1 day | 78·855 at 8·5 |
| for 2 days | 78·398 at 10·2 |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. |
| 13·0 | 87·015 |
| 56·0 | 69·301 |
| 100·0 | 61·949 |
\[ \lambda = 80·628 - 0·22196t + 0·0003518t^2. \]
#### 18.
Copper-silver alloy, containing 1·53 volume per cent. of copper (hard drawn).
Length 2139 millims.; diameter 0·542 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 94·554 at 8·8 | 97·708 |
| Ditto, after being kept at 100° | |
| for 1 day | 95·314 at 9·0 |
| for 2 days | 94·968 at 9·9 |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. |
| 10·0 | 94·940 |
| 55·0 | 82·126 |
| 100·0 | 72·146 |
\[ \lambda = 98·172 - 0·033024t + 0·0006998t^2. \]
#### 19.
Iron-gold alloy, containing 27·93 volumes per cent. of iron (hard drawn).
Length 145 millims.; diameter 0·758 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 2·5815 at 14·6 | 2·7160 |
| Ditto, after being kept at 100° | |
| for 1 day | 2·6193 at 14·4 |
| for 2 days | 2·6309 at 14·2 |
| Ditto, for 3 days | 2·6286 at 14·4 |
| T. | Conducting-power. |
|----|-------------------|
| | Observed. Calculated. |
| 15·0 | 2·6239 |
| 57·5 | 2·2732 |
| 100·0 | 1·9926 |
\[ \lambda = 2·7645 - 0·0096586t + 0·00001940t^2. \]
The conducting-power of a second wire was found 2·6177 at 14·6 Reduced to 0°. 2·7451
### Table V. (continued).
#### 20.
Iron-gold alloy, containing 21·18 volumes per cent. of iron (hard drawn).
Length 184 millims.; diameter 0·943 millim.
Conducting-power found before heating the wire 1·9299 at 14° Reduced to 0°.
| T. | Conducting-power |
|----|------------------|
| 14° | 1·9822 |
| 57° | 1·7951 |
| 100° | 1·7010 |
\[
\lambda = 2·0632 - 0·0061367t + 0·000002515t^2.
\]
The conducting-power of a second wire was found 1·8745 at 17° Reduced to 0°.
#### 21.
Iron-gold alloy, containing 10·96 volumes per cent. of iron (hard drawn).
Length 226 millims.; diameter 0·470 millim.
Conducting-power found before heating the wire 2·3450 at 15° Reduced to 0°.
| T. | Conducting-power |
|----|------------------|
| 15° | 2·3573 |
| 56° | 2·3138 |
| 100° | 2·2798 |
\[
\lambda = 2·3708 - 0·0011555t + 0·0000002454t^2.
\]
The conducting-power of a second wire was found 2·2397 at 17° Reduced to 0°.
#### 22.
Iron-copper alloy, containing 0·46 volume per cent. of iron (hard drawn).
Length 578·5 millims.; diameter 0·358 millim.
Conducting-power found before heating the wire 38·315 at 9° Reduced to 0°.
| T. | Conducting-power |
|----|------------------|
| 9° | 38·283 |
| 55° | 36·739 |
| 100° | 34·533 |
\[
\lambda = 39·894 - 0·061958t + 0·00008346t^2.
\]
### Table VI.
#### 1.
†Phosphorus-copper, containing 2·5 per cent. by weight of phosphorus (hard drawn).
Length 124 millims.; diameter 0·355 millim.
Conducting-power found before heating the wire 7·2993 at 12° Reduced to 0°.
| T. | Conducting-power |
|----|------------------|
| 12° | 7·3391 |
| 34° | 7·2606 |
| 56° | 7·1963 |
| 77° | 7·1243 |
| 99° | 7·0517 |
\[
\lambda = 7·3900 - 0·0035194t + 0·000001062t^2.
\]
#### 2.
†Phosphorus-copper, containing 0·95 per cent. by weight of phosphorus (hard drawn).
Length 265·5 millims.; diameter 0·396 millim.
| T. | Conducting-power |
|----|------------------|
| 11° | 23·028 |
| 24° | 22·637 |
| 39° | 22·209 |
| 54° | 21·785 |
| 69° | 21·407 |
| 84° | 21·017 |
| 99° | 20·673 |
\[
\lambda = 23·368 - 0·030873t + 0·00003836t^2.
\]
#### 3.
†Arsenic-copper, containing 5·4 per cent. by weight of arsenic (hard drawn).
Length 225 millims.; diameter 0·289 millim.
Conducting-power found before heating the wire 6·3518 at 9° Reduced to 0°.
| T. | Conducting-power |
|----|------------------|
| 9° | 6·3742 |
| 31° | 6·3230 |
| 54° | 6·2707 |
| 75° | 6·2232 |
| 98° | 6·1703 |
\[
\lambda = 6·3989 - 0·0023880t + 0·0000006331t^2.
\]
### Table VI (continued)
#### 4. Arsenic-copper, containing 2.8 per cent. by weight of arsenic (hard drawn).
| Length | Conducting-power found before heating the wire | Reduced to 0° |
|--------|-----------------------------------------------|--------------|
| 547 mm | 12-2980 at 8° 9 | 12-3787 |
| Ditto, after being kept at 100° for 1 day | 12-2648 at 9° 5 | 12-3507 |
| Ditto, for 2 days | 12-2369 at 11° 9 | 12-3443 |
#### 5. Arsenic-copper, containing traces of arsenic (hard drawn).
| Length | Conducting-power found before heating the wire | Reduced to 0° |
|--------|-----------------------------------------------|--------------|
| 381 mm | 58-680 at 16° 4 | 61-255 |
| Ditto, after being kept at 100° for 1 day | 58-924 at 14° 5 | 61-207 |
| Ditto, for 2 days | 59-286 at 12° 7 | 61-295 |
| Ditto, for 3 days | 59-013 at 14° 1 | 61-236 |
### Table VII
| Alloy | Volumes per cent. | Conducting-power | Formulae for the correction of the conducting-power for temperature. |
|-------|------------------|------------------|---------------------------------------------------------------|
| Sn₈ Pb | 83-96 of Sn | 11-582 | 12-423 | λ = 12-002 - 0.046645z + 0.0001042z² |
| Sn₄ Cd | 83-10 of Sn | 14-459 | 14-658 | λ = 14-558 - 0.059337z + 0.0001728z² |
| Sn₃ Zn | 77-71 of Sn | 16-504 | 16-991 | λ = 16-747 - 0.065044z + 0.0001460z² |
| Pb Sn | 53-41 of Pb | 9-855 | 10-423 | λ = 10-139 - 0.038358z + 0.0000836z² |
| Zn Cd | 26-06 of Zn | 25-405 | 25-834 | λ = 25-619 - 0.096978z + 0.0002049z² |
| Sn Cd | 23-50 of Sn | 21-194 | 22-123 | λ = 21-658 - 0.083367z + 0.0002038z² |
| Cd Pb | 10-57 of Cd | 9-047 | 9-264 | λ = 9-155 - 0.032041z + 0.00006547z² |
### Table VIII
| Alloy | Volumes per cent. | Conducting-power | Formulae for the correction of the conducting-power for temperature. |
|-------|------------------|------------------|---------------------------------------------------------------|
| Lead-silver | 94-64 of Pb | 8-823 | 8-938 | λ = 8-880 - 0.032149z + 0.00007070z² |
| Lead-silver | 46-90 of Pb | 12-071 | 13-391 | λ = 12-731 - 0.021986z + 0.00003947z² |
| Lead-silver | 30-64 of Pb | 21-874 | | λ = 21-874 - 0.043652z + 0.00005687z² |
| Tin-gold | 90-32 of Sn | 8-2418 | | λ = 8-2418 - 0.025418z + 0.00005472z² |
| Tin-gold | 79-54 of Sn | 4-5500 | 5-0427 | λ = 4-7963 - 0.014000z + 0.00003020z² |
| Tin-copper (hard drawn) | 93-57 of Sn | 12-034 | | λ = 12-034 - 0.044328z + 0.00008112z² |
| Tin-copper (hard drawn) | 83-60 of Sn | 12-764 | | λ = 12-764 - 0.039476z + 0.00006063z² |
| Tin-copper (hard drawn) | 14-93 of Sn | 8-823 | 8-938 | λ = 8-823 - 0.034326z + 0.00002593z² |
| Tin-copper (hard drawn) | 11-35 of Sn | 10-154 | | λ = 10-154 - 0.006705z + 0.00001232z² |
| Tin-copper (hard drawn) | 11-61 of Sn | 12-102 | | λ = 12-102 - 0.0083587z + 0.00003674z² |
| Tin-copper (hard drawn) | 6-02 of Sn | 19-750 | 19-682 | λ = 19-716 - 0.019695z + 0.00003902z² |
| Tin-copper (hard drawn) | 1-41 of Sn | 62-463 | | λ = 62-463 - 0.16713z + 0.0003136z² |
| Tin-silver | 96-52 of Sn | 12-378 | 12-390 | λ = 12-384 - 0.047293z + 0.0001014z² |
| Tin-silver | 75-51 of Sn | 13-547 | 13-866 | λ = 13-706 - 0.051730z + 0.0001172z² |
| Zinc-copper (hard drawn) | 42-06 of Zn | 21-793 | | λ = 21-793 - 0.029395z + 0.00002162z² |
| Zinc-copper (hard drawn) | 29-45 of Zn | 21-708 | | λ = 21-708 - 0.027632z + 0.00002698z² |
| Zinc-copper (hard drawn) | 23-61 of Zn | 28-298 | | λ = 28-298 - 0.040039z + 0.00003832z² |
| Zinc-copper (hard drawn) | 10-88 of Zn | 46-934 | | λ = 46-934 - 0.095947z + 0.0001423z² |
| Zinc-copper (hard drawn) | 5-03 of Zn | 60-376 | | λ = 60-376 - 0.14916z + 0.0002473z² |
* Philosophical Transactions, 1860, p. 166.
### Table IX
| Alloy | Volumes per cent. | Conducting-power | Formulae for the correction of the conducting-power for temperature |
|------------------------------|-------------------|------------------|---------------------------------------------------------------------|
| Gold-copper (hard drawn) | 98-63 of Au | 56-122 | λ = 56-122 - 0-14887λ + 0-0002511λ² |
| Gold-copper (hard drawn) | 81-66 of Au | 16-083 | λ = 16-083 - 0-012041λ + 0-000001296λ² |
| Gold-silver (hard drawn) | 79-86 of Au | 21-393 | λ = 21-393 - 0-023212λ + 0-00001694λ² |
| Gold-silver (annealed) | 79-86 of Au | 21-527 | λ = 21-584* - 0-024539λ + 0-00002506λ² |
| Gold-silver (hard drawn) | 52-08 of Au | 15-030 | λ = 15-030 - 0-010120λ + 0-000003697λ² |
| Gold-silver (annealed) | 52-08 of Au | 15-080 | λ = 15-080 - 0-010864λ + 0-000007457λ² |
| Gold-silver (hard drawn) | 19-86 of Au | 21-305 | λ = 21-684 - 0-019185λ + 0-000001529λ² |
| Gold-silver (annealed) | 19-86 of Au | 22-125 | λ = 21-746* - 0-019753λ + 0-000003395λ² |
| Gold-silver (hard drawn) | 19-17 of Au | 20-514 | λ = 20-514 - 0-017718λ + 0-000001170λ² |
| Gold-copper (hard drawn) | 071 of Au | 84-008 | λ = 84-008 - 0-27895λ + 0-0006139λ² |
| Platinum-silver (hard drawn) | 19-65 of Pt | 6-6960 | λ = 6-6960 - 0-0022143λ + 0-000001383λ² |
| Platinum-silver (hard drawn) | 5-09 of Pt | 18-031 | λ = 18-031 - 0-0163949λ + 0-00001182λ² |
| Platinum-silver (hard drawn) | 25-1 of Pt | 3-540 | λ = 3-540 - 0-0036858λ + 0-000002142λ² |
| Palladium-silver (hard drawn)| 29-5 of Pd | 8-5214 | λ = 8-5214 - 0-005686λ + 0-000007156λ² |
| Copper-silver (hard drawn) | 98-39 of Cu | 89-544 | λ = 89-544 - 0-30886λ + 0-00005717λ² |
| Copper-silver (hard drawn) | 95-12 of Cu | 82-300 | λ = 82-300 - 0-26758λ + 0-000002426λ² |
| Copper-silver (hard drawn)† | 77-64 of Cu | 69-311 | λ = 69-311 - 0-21194λ + 0-000002426λ² |
| Copper-silver (hard drawn)† | 46-67 of Cu | 74-940 | λ = 74-940 - 0-21011λ + 0-000003961λ² |
| Copper-silver (hard drawn)† | 8-25 of Cu | 80-284 | λ = 80-284 - 0-22101λ + 0-000003503λ² |
| Copper-silver (hard drawn)† | 1-53 of Cu | 97-708 | λ = 97-708 - 0-32868λ + 0-000006959λ² |
| Iron-gold (hard drawn) | 27-93 of Fe | 2-7350 | λ = 2-7350 - 0-0095555λ + 0-000001919λ² |
| Iron-gold (hard drawn) | 21-18 of Fe | 1-9901 | λ = 1-9901 - 0-0059194λ + 0-000002426λ² |
| Iron-gold (hard drawn) | 10-96 of Fe | 2-3102 | λ = 2-3102 - 0-0011260λ + 0-0000002391λ² |
| Iron-copper (hard drawn) | 0-46 of Fe | 38-852 | λ = 38-852 - 0-060341λ + 0-000008128λ² |
### Table X
| Alloy | Weight per cent. | Conducting-power | Formulae for the correction of the conducting-power for temperature |
|------------------------------|------------------|------------------|---------------------------------------------------------------------|
| Phosphorus-copper (hard drawn)| 2-5 of P | 7-301 | λ = 7-322 - 0-0034870λ + 0-000001052λ² |
| Phosphorus-copper (hard drawn)| 0-95 of P | 23-920 | λ = 23-644 - 0-031283λ + 0-000003839λ² |
| Arsenic-copper (hard drawn) | 5-4 of As | 6-219 | λ = 6-296 - 0-0023492λ + 0-000006230λ² |
| Arsenic-copper (hard drawn) | 2-8 of As | 13-356 | λ = 12-867 - 0-0094757λ + 0-000005743λ² |
| Arsenic-copper (hard drawn) | traces of As | 60-854 | λ = 61-055 - 0-16134λ + 0-000002948λ² |
The values in columns A. and B. do not agree in all cases as well as might have been expected. Part of these differences are undoubtedly due to the fact that, the length of all wires made of alloys melting at a low temperature was measured after the determination had been made, as we found very great difficulty in soldering them to the thick copper wires in the trough, for, owing to their low fusing-points, the ends of the wires melted in with the solder. Now they had to be wound round a glass rod, as their length would not permit of their being experimented with in the trough without it; it is therefore probable that, on account of their softness, in unwinding and straightening them they became somewhat lengthened, which will account in a great measure for the differences.
The value given for the conducting-power of one alloy (lead-silver, containing 30-64 per cent. of lead, and corresponding to PbAg₂) in the paper already referred to is wrong.
* These values have been altered to the same extent as those given in column B. for the hard-drawn wires, in order that the effect of annealing may remain the same.
† The alloys of these metals formerly tested do not quite correspond in composition to those here given, and therefore the values then found for their conducting-powers are not quoted above. They agree, however, very closely with those in column B.
We not only used part of the same alloy employed for the former determinations, but also made and analysed a fresh quantity, and found the values for the conducting-power in both cases the same; the present value is therefore the correct one for the conducting-power of the alloy. The error made in the former determinations must have been that a wrong normal wire was noted down as the one with which the resistances of the wires were compared; for according to the data from which the conducting-powers were then deduced, those there given are correct.
In order to show in a clear manner the results obtained, and to explain the law which we have arrived at, we will give in the first place the following Tables:
**Table XI.**
| Alloy | Volumes per cent. | Conducting-power at 100°. | Percentage decrement. |
|----------------|-------------------|---------------------------|-----------------------|
| | | Observed. | Calculated. |
| Sn₆ Pb | 83-96 of Sn | 8-38 | 30-18 |
| Sn₄ Cd | 83-10 of Sn | 10-35 | 28-89 |
| Sn₂ Zn | 77-71 of Sn | 11-70 | 30-12 |
| Pb Sn | 53-41 of Pb | 7-16 | 29-41 |
| Zn Cd | 26-06 of Zn | 17-97 | 29-86 |
| Sn Cd | 23-50 of Sn | 15-36 | 29-08 |
| Cd Pb | 10-57 of Cd | 6-62 | 27-74 |
**Table XII.**
| Alloy | Volumes per cent. | Conducting-power at 100°. | Percentage decrement. |
|------------------------|-------------------|---------------------------|-----------------------|
| | | Observed. | Calculated. |
| Lead-silver | 94-64 of Pb | 6-37 | 28-24 |
| Lead-silver | 46-90 of Pb | 10-63 | 16-53 |
| Lead-silver | 30-64 of Pb | 18-08 | 17-36 |
| Tin-gold | 90-32 of Sn | 6-25 | 24-20 |
| Tin-gold | 79-54 of Sn | 3-70 | 18-23 |
| Tin-copper (hard drawn)| 93-57 of Sn | 8-58 | 12-72 |
| Tin-copper (hard drawn)| 85-60 of Sn | 9-39 | 18-90 |
| Tin-copper (hard drawn)| 14-91 of Sn | 6-37 | 6-142 |
| Tin-copper (hard drawn)| 12-91 of Sn | 6-70 | 6-29 |
| Tin-copper (hard drawn)| 11-61 of Sn | 11-30 | 6-347 |
| Tin-copper (hard drawn)| 6-02 of Sn | 17-89 | 6-693 |
| Tin-copper (hard drawn)| 1-41 of Sn | 48-89 | 6-978 |
| Tin-silver | 96-52 of Sn | 8-67 | 10-90 |
| Tin-silver | 75-51 of Sn | 9-71 | 23-91 |
| Zinc-copper (hard drawn)| 42-06 of Zn | 19-09 | 49-57 |
| Zinc-copper (hard drawn)| 29-45 of Zn | 19-21 | 55-89 |
| Zinc-copper (hard drawn)| 23-61 of Zn | 24-68 | 58-82 |
| Zinc-copper (hard drawn)| 10-88 of Zn | 38-76 | 65-20 |
| Zinc-copper (hard drawn)| 5-03 of Zn | 47-93 | 68-13 |
## Table XIII.
| Alloy | Volumes per cent. | Conducting-power at 100° | Percentage decrement |
|------------------------------|-------------------|--------------------------|---------------------|
| | | Observed. | Calculated. |
| Gold-copper (hard drawn) | 98·63 of Au | 43·85 | 55·33 |
| | | | 21·87 |
| | | | 22·22 |
| Gold-copper (hard drawn) | 81·66 of Au | 14·89 | 57·96 |
| | | | 7·41 |
| | | | 2·53 |
| Gold-silver (hard drawn) | 79·86 of Au | 19·18 | 58·25 |
| | | | 10·09 |
| | | | 9·65 |
| Gold-silver (annealed) | 79·86 of Au | 19·38 | {a 58·25} |
| | | | {b 60·24} |
| | | | 10·21 |
| | | | {a 9·75} |
| | | | {b 9·43} |
| Gold-silver (hard drawn) | 52·08 of Au | 14·05 | 62·55 |
| | | | 6·49 |
| | | | 6·59 |
| Gold-silver (annealed) | 52·08 of Au | 14·07 | {a 62·55} |
| | | | {b 65·00} |
| | | | 6·71 |
| | | | {a 6·59} |
| | | | {b 6·95} |
| Gold-silver (hard drawn) | 19·86 of Au | 19·88 | 67·60 |
| | | | 8·32 |
| | | | 9·62 |
| Gold-silver (annealed) | 19·86 of Au | 19·91 | {a 67·60} |
| | | | {b 72·68} |
| | | | 8·44 |
| | | | {a 8·63} |
| | | | {b 8·03} |
| Gold-copper (hard drawn) | 19·17 of Au | 18·86 | 67·68 |
| | | | 8·07 |
| | | | 8·18 |
| Gold-copper (hard drawn) | 0·71 of Au | 62·25 | 70·54 |
| | | | 25·90 |
| | | | 25·86 |
| Platinum-silver (hard drawn) | 19·65 of Pt | 6·49 | 59·31 |
| | | | 3·10 |
| | | | 3·21 |
| Platinum-silver (hard drawn) | 5·05 of Pt | 16·75 | 67·77 |
| | | | 7·08 |
| | | | 7·25 |
| Platinum-silver (hard drawn) | 2·51 of Pt | 28·07 | 69·24 |
| | | | 11·29 |
| | | | 11·88 |
| Platinum-silver (hard drawn) | 2·28 of Pd | 8·33 | 57·27 |
| | | | 3·40 |
| | | | 4·21 |
| Copper-silver (hard drawn) | 98·35 of Cu | 65·81 | 70·66 |
| | | | 26·50 |
| | | | 27·30 |
| Copper-silver (hard drawn) | 95·17 of Cu | 61·26 | 70·66 |
| | | | 25·57 |
| | | | 25·41 |
| Copper-silver (hard drawn) | 77·64 of Cu | 52·86 | 70·66 |
| | | | 24·29 |
| | | | 21·92 |
| Copper-silver (hard drawn) | 46·67 of Cu | 57·89 | 70·68 |
| | | | 22·75 |
| | | | 24·00 |
| Copper-silver (hard drawn) | 8·25 of Cu | 61·69 | 70·69 |
| | | | 23·17 |
| | | | 25·57 |
| Copper-silver (hard drawn) | 1·53 of Cu | 71·81 | 70·69 |
| | | | 26·51 |
| | | | 29·77 |
| Iron-gold (hard drawn) | 27·93 of Fe | 1·97 | 42·62 |
| | | | 27·92 |
| | | | 1·47 |
| Iron-gold (hard drawn) | 21·18 of Fe | 1·64 | 45·64 |
| | | | 17·55 |
| | | | 1·12 |
| Iron-gold (hard drawn) | 10·96 of Fe | 2·20 | 49·68 |
| | | | 3·84 |
| | | | 1·34 |
| Iron-copper (hard drawn) | 0·46 of Fe | 33·63 | 70·34 |
| | | | 13·44 |
| | | | 14·03 |
These Tables will require some explanation. Calculated conducting-power means the deduced conducting-power of an alloy, it being assumed that the conducting-power of a wire of any alloy is equal to the sum of the conducting-powers of parallel wires of the metals composing the alloy.
Under the term "calculated percentage decrement between 0° and 100°," we do not mean, as might be supposed, the mean of the percentage decrements which the component metals would suffer in their conducting-powers between 0° and 100°, and which would be, for nearly all the alloys experimented with, 29·307 per cent., inasmuch as it has been shown* that the conducting-power of most of the pure metals decreases between 0° and 100° by 29·307 per cent. (the exceptions to this law, being thallium and iron, the conducting-powers of which decrease between 0° and 100° 31·420 and 38·260 per cent. respectively†). It is therefore clear that the calculated percentage decrement in the conducting-powers between 0° and 100° of most alloys, from the above assumption, must be also 29·307 per cent. It is, however, obvious, on looking at the observed percentage decrements, that the conducting-powers of the alloys, with the exception of those given in Table XI., decrease less than 29·307 per cent. between 0° and 100°. In order to avoid repetitions, instead of the above value (29·307), we have inserted under the heading "calculated percentage decrement" that deduced from the following law:
The observed percentage decrement in the conducting-power of an alloy between 0° and 100° is to that calculated between 0° and 100° (viz. 29·307) as the observed conducting-power at 100° is to that calculated at 100°.
* Loc. cit. † Philosophical Transactions for 1863.
Or writing the above in symbols,
\[ Po : Pc :: \lambda_{100^\circ} : \lambda'_{100^\circ}, \ldots, \ldots \ldots \ldots (1) \]
where \( Po \) and \( Pc \) represent the observed and calculated percentage decrements in the conducting-power of the alloy between \( 0^\circ \) and \( 100^\circ \), and \( \lambda_{100^\circ} \) and \( \lambda'_{100^\circ} \) its observed and calculated conducting-power at \( 100^\circ \). \( Pc \) is, as just stated, equal to \( 29.307 \) in nearly all cases, the exceptions being with the thallium and iron alloys.
If the values so deduced be examined, it will be seen that those given in Table XI. for the observed and calculated percentage decrement agree very closely with each other as well as with the mean value found for the percentage decrement in the conducting-power between \( 0^\circ \) and \( 100^\circ \) of the pure metals, viz. \( 29.307 \). This is just what we expected; for these alloys conduct electricity, as will be seen from the Table, in the ratio of their relative volumes, and therefore their conducting-powers ought to decrease between \( 0^\circ \) and \( 100^\circ \) in the same percentage amount as that of the mean of their components.
On looking at Table XII., which contains the alloys made of the metals belonging to the two classes, we find that, as long as there is no change in the conducting-power of the metals lead and tin by the addition of another metal, the conducting-power of the alloy decreases between \( 0^\circ \) and \( 100^\circ \) \( 29.307 \) per cent., but the moment the alloys show a greater or smaller conducting-power than that of pure lead or tin, then the percentage decrement is less than \( 29.307 \). Again, the alloys of tin or zinc with copper containing small amounts of those metals follow approximatively the above law; and on referring to the curves* which represent the conducting-powers of these alloys, it would appear that, starting with the metal whose conducting-power is greatly altered by a small addition of a foreign metal, the above law, as just stated, is approximatively true for all alloys as far as the turning-point of the curve, and from this point there is no agreement between the observed and calculated values. The difference between these values begins to show itself in some cases much sooner than in others; thus, with tin and copper after the addition of one per cent. of the former; with zinc and copper only after more than ten per cent. of zinc has been added, and from these points it gradually increases with each addition of metal. What the exact law is which these alloys follow with regard to the property under consideration we are unable at present to state, but some of them at least show that the law we have put forth will hold good in their cases. Unfortunately the alloys of this class, containing large percentages of each metal, are exceedingly brittle and unworkable, so that no complete series of determinations with any set of alloys could be made; had we been able to do this with one or two series, we should, in all probability, have found the law which regulates the influence of temperature on the conducting-power of this group of alloys. With regard to those in Table XIII. very little need be said, for the deduced percentage decrements prove that our law holds good for most of the alloys of this group. There are nevertheless a few remarks to be
* Loc. cit.
made respecting some of the values given in this Table, namely, on those of the annealed wires. Elsewhere it has been shown that the conducting-power of hard-drawn wires of some metals is greatly altered by annealing them; with the alloys this does not seem to be the case, for the differences here are very small. On account of their smallness we have not thought it worth while to investigate this matter any further at present; for to arrive at such results as might show the connexion between the effect of annealing on the conducting-power of alloys and on that of the metals composing them, would require a long series of experiments. Although the percentage decrements in the conducting-power of these annealed wires are all somewhat higher than those of the hard drawn, yet they may be considered the same, as the percentage decrements in the conducting-power of hard-drawn and annealed wires of the pure metals vary also in a small degree, but not always in the same direction. Thus those found for silver were—
| Hard drawn | Annealed |
|------------|----------|
| 28·67 | 28·82 |
| 28·44 | 28·67 |
| 27·82 | 28·21 |
We have calculated, as will be seen in the Table, the percentage decrements in two ways:—1st (a), using for the calculations the conducting-powers of the hard-drawn, and 2ndly (b), those of the annealed metals. The values so obtained for the percentage decrement do not differ very much from one another.
In calculating the results for the iron alloys, Pc has not been taken equal to 29·307, but for each alloy Pc has had to be calculated. Thus for the 1st, iron-gold, which contains 27·93 volumes per cent. iron,
The conducting-power of 1 volume of iron may be said to lose between 0° and 100° 38·260 per cent.; therefore 0·2793 volume will lose . . . . . . 10·686
That of 1 volume of gold may be said to lose between 0° and 100° 29·307 per cent.; therefore 0·7207 volume will lose . . . . . . . . . . . . 21·122
1 volume of iron-gold alloy, containing 27·93 per cent. iron, will therefore lose 31·808
On comparing the values obtained for the conducting-powers, &c. of the iron-gold alloys, the following facts are worth mentioning,—their very low and almost identical conducting-powers, and the high percentage decrements found for the first two and the low one for the third. That there was no error in this value we convinced ourselves by remaking the alloy, which contained, according to analysis, the same percentage amount of iron as that given in the Table, and the percentage decrement in its conducting-power was found equal to 4·04. Again, an alloy, made by a well-known firm*, which gave on analysis 11·94 volumes per cent. iron, conducted at 0° 2·097, and lost between 0° and 100° 4·30 per cent. of conducting-power. Unfortunately experiments with alloys richer
* We are indebted to Messrs. Johnson, Matthey and Co., of Hatton Garden, for many of the alloys experimented with. These were the first two, iron-gold, the platinum-silver, palladium-silver, and aluminium-nickel.
in iron could not be made, owing to the brittleness of the alloys; the high percentage decrement in the conducting-power of the first two indicating something abnormal, which it would have been interesting to have followed out.
On account of the probability of the arsenic and phosphorus being chemically combined with the copper, we have not considered it worth while to calculate the percentage decrements, and therefore no Table corresponding to the last has been made for these alloys.
If the above proportion,
\[ P_0 : P_c :: \lambda_{100^\circ} : \lambda'_{100^\circ}, \ldots \ldots \ldots \ldots \ldots \ldots (1) \]
be converted into terms of resistance, the following formula is obtained,
\[ r_{100^\circ} - r_0 = r'_{100^\circ} - r'_0, \ldots \ldots \ldots \ldots \ldots \ldots (2) \]
where \( r_{100^\circ}, r_0, \) and \( r'_{100^\circ}, r'_0 \) represent the observed and calculated resistances at 100° and 0°; for
\[ \frac{P_0}{P_c} = \frac{\lambda_{100^\circ}}{\lambda'_{100^\circ}}; \]
but
\[ P_0 = 100 - \frac{\lambda_{100^\circ}}{\lambda_0} \cdot 100 = \frac{100}{\lambda_0} (\lambda_0 - \lambda_{100^\circ}), \]
and
\[ P_c = 100 - \frac{\lambda'_{100^\circ}}{\lambda'_0} \cdot 100 = \frac{100}{\lambda'_0} (\lambda'_0 - \lambda'_{100^\circ}). \]
And substituting these values in the above, we have
\[ \frac{\lambda'_0}{\lambda_0} \cdot \frac{\lambda_0 - \lambda_{100^\circ}}{\lambda'_{100^\circ}} = \frac{\lambda_{100^\circ}}{\lambda'_{100^\circ}}, \]
or
\[ \frac{\lambda_0 - \lambda_{100^\circ}}{\lambda_0 \cdot \lambda_{100^\circ}} = \frac{\lambda'_0 - \lambda'_{100^\circ}}{\lambda'_0 \cdot \lambda'_{100^\circ}}, \]
or
\[ \frac{1}{\lambda_{100^\circ}} - \frac{1}{\lambda_0} = \frac{1}{\lambda'_{100^\circ}} - \frac{1}{\lambda'_0}, \]
which is equal to
\[ r_{100^\circ} - r_0 = r'_{100^\circ} - r'_0, \ldots \ldots \ldots \ldots \ldots \ldots (2) \]
for the reciprocal values of the conducting-powers of bodies are their resistances. The formula (2) expresses the fact that the absolute difference between 0° C. and 100° C. in the resistance of an alloy is equal to the absolute difference between 0° C. and 100° C. in the calculated resistance of the alloy.
The formula (2) may be written
\[ r_{100^\circ} - r'_{100^\circ} = r_0 - r'_0, \ldots \ldots \ldots \ldots \ldots \ldots (3) \]
which is equal to saying that the absolute difference in the observed and calculated resistances at 100° C. is equal to the absolute difference between the observed and calculated resistances at 0° C. Tables XIV., XV., and XVI. contain examples of these deductions taken from the three groups of alloys, taking the resistance of silver at 0° equal to 100.
### Table XIV.
| Alloy | Volumes per cent. | \( r_{100^\circ} \) | \( r_0^\circ \) | \( r'_{100^\circ} \) | \( r'_0^\circ \) | \( r_{100^\circ} - r_0^\circ \) | \( r'_{100^\circ} - r'_0^\circ \) | \( r_{100^\circ} - r'_{100^\circ} \) | \( r_0^\circ - r'_0^\circ \) |
|---------------|-------------------|---------------------|-----------------|---------------------|-----------------|---------------------------------|---------------------------------|---------------------------------|---------------------------------|
| Sn\(_9\) Pb | 83-96 of Sn | 1193-3 | 883-3 | 1207-7 | 883-2 | 360-0 | 354-5 | 19-9 | 14-4 |
| Sn\(_9\) Cd | 83-10 of Sn | 966-2 | 686-8 | 990-1 | 699-8 | 279-4 | 290-3 | 23-9 | 13-0 |
| Sn\(_9\) Zn | 77-71 of Sn | 854-7 | 597-0 | 879-5 | 621-9 | 257-7 | 257-6 | 24-8 | 24-9 |
| Pb Sn | 53-41 of Pb | 1362-6 | 986-2 | 1387-0 | 980-4 | 410-4 | 406-6 | 9-6 | 5-8 |
| Zn Cd | 26-06 of Zn | 556-5 | 393-0 | 563-4 | 398-4 | 166-2 | 165-0 | 6-9 | 8-1 |
| Sn Cd | 23-50 of Sn | 651-0 | 461-7 | 672-0 | 474-8 | 189-3 | 197-2 | 21-0 | 13-1 |
| Cd Pb\(_9\) | 10-57 of Cd | 1510-6 | 1092-9 | 1422-2 | 1065-0 | 417-7 | 417-4 | 88-4 | 87-9 |
### Table XV.
| Alloy | Volumes per cent. | \( r_{100^\circ} \) | \( r_0^\circ \) | \( r'_{100^\circ} \) | \( r'_0^\circ \) | \( r_{100^\circ} - r_0^\circ \) | \( r'_{100^\circ} - r'_0^\circ \) | \( r_{100^\circ} - r'_{100^\circ} \) | \( r_0^\circ - r'_0^\circ \) |
|---------------|-------------------|---------------------|-----------------|---------------------|-----------------|---------------------------------|---------------------------------|---------------------------------|---------------------------------|
| Lead-silver | 94-64 of Pb | 1569-9 | 1126-1 | 1069-5 | 755-9 | 442-8 | 313-6 | 500-4 | 370-2 |
| Lead-silver | 46-90 of Pb | 940-7 | 785-5 | 248-1 | 175-4 | 155-2 | 72-7 | 692-6 | 610-1 |
| Lead-silver | 30-64 of Pb | 553-1 | 457-2 | 196-7 | 139-1 | 95-9 | 57-6 | 356-4 | 318-1 |
| Tin-copper | 93-57 of Sn | 1165-5 | 831-3 | 786-2 | 555-6 | 334-2 | 230-6 | 379-3 | 275-7 |
| Tin-copper | 83-60 of Sn | 1065-0 | 783-7 | 529-1 | 374-1 | 281-3 | 155-0 | 535-9 | 409-6 |
| Tin-copper | 14-91 of Sn | 1196-2 | 1133-8 | 162-8 | 115-1 | 62-4 | 47-7 | 1033-4 | 1018-7 |
| Tin-copper | 12-35 of Sn | 1041-6 | 985-2 | 158-7 | 112-2 | 50-4 | 46-5 | 882-9 | 873-0 |
| Tin-copper | 11-61 of Sn | 885-0 | 826-4 | 157-6 | 111-4 | 58-6 | 46-2 | 727-4 | 715-0 |
| Tin-copper | 6-02 of Sn | 559-0 | 507-1 | 149-4 | 105-6 | 51-9 | 43-8 | 409-6 | 401-5 |
| Tin-copper | 1-41 of Sn | 204-5 | 160-1 | 143-3 | 101-3 | 44-4 | 42-0 | 61-2 | 58-8 |
| Zinc-copper | 42-06 of Zn | 523-8 | 458-9 | 201-7 | 124-6 | 64-9 | 59-1 | 322-1 | 316-3 |
| Zinc-copper | 29-45 of Zn | 520-6 | 460-6 | 178-9 | 126-5 | 60-0 | 52-4 | 341-7 | 334-1 |
| Zinc-copper | 23-61 of Zn | 405-2 | 353-4 | 170-0 | 120-2 | 51-8 | 49-8 | 235-2 | 233-2 |
| Zinc-copper | 10-88 of Zn | 258-0 | 215-1 | 153-4 | 108-4 | 44-9 | 45-0 | 104-6 | 104-7 |
| Zinc-copper | 5-03 of Zn | 208-6 | 165-6 | 146-8 | 103-8 | 43-0 | 43-0 | 61-8 | 61-8 |
### Table XVI.
| Alloy | Volumes per cent. | \( r_{100^\circ} \) | \( r_0^\circ \) | \( r'_{100^\circ} \) | \( r'_0^\circ \) | \( r_{100^\circ} - r_0^\circ \) | \( r'_{100^\circ} - r'_0^\circ \) | \( r_{100^\circ} - r'_{100^\circ} \) | \( r_0^\circ - r'_0^\circ \) |
|---------------|-------------------|---------------------|-----------------|---------------------|-----------------|---------------------------------|---------------------------------|---------------------------------|---------------------------------|
| Gold-copper (hard drawn) | 98-63 of Au | 228-1 | 198-2 | 180-7 | 127-8 | 49-9 | 52-9 | 47-4 | 50-4 |
| Gold-copper (hard drawn) | 81-66 of Au | 671-5 | 621-9 | 172-5 | 122-0 | 49-6 | 50-5 | 499-0 | 499-9 |
| Gold-silver (hard drawn) | 79-86 of Au | 521-4 | 468-8 | 171-7 | 121-4 | 52-6 | 50-3 | 349-7 | 347-4 |
| Gold-silver (hard drawn) | 52-08 of Au | 711-7 | 665-3 | 159-8 | 113-0 | 46-4 | 46-8 | 551-9 | 552-3 |
| Gold-silver (hard drawn) | 19-86 of Au | 508-0 | 461-2 | 147-9 | 104-6 | 41-8 | 43-3 | 355-1 | 356-6 |
| Gold-copper (hard drawn) | 19-17 of Au | 530-2 | 487-6 | 147-8 | 104-5 | 42-6 | 43-3 | 382-4 | 383-1 |
| Gold-copper (hard drawn) | 0-71 of Au | 160-6 | 119-0 | 141-8 | 100-2 | 41-6 | 41-6 | 18-8 | 18-8 |
| Platinum-silver (hard drawn) | 19-65 of Pt | 1540-8 | 1492-5 | 168-6 | 119-2 | 48-3 | 49-4 | 1372-2 | 1373-3 |
| Platinum-silver (hard drawn) | 5-05 of Pt | 597-0 | 554-6 | 147-6 | 104-3 | 42-4 | 43-3 | 449-4 | 450-3 |
| Platinum-silver (hard drawn) | 2-51 of Pt | 356-3 | 316-1 | 144-4 | 102-1 | 40-2 | 42-3 | 211-9 | 214-0 |
What has already been said when speaking of the results contained in Tables XI., XII., and XIII., will of course apply here. In Table XIV., the values in the columns headed \( r_{100^\circ} - r'_{100^\circ} \) and \( r_0^\circ - r'_0^\circ \) do not agree in all cases; and at the first glance we should be inclined to suppose that the law was not as correct for these alloys as for those given in Table XVI.; but this is only due to slight errors in the determination of the resistances, &c., for a small percentage difference in these numbers will cause a very marked one in those under the headings \( r_{100^\circ} - r'_{100^\circ} \) and \( r_0^\circ - r'_0^\circ \). If, on the contrary, the values in the columns \( r_{100^\circ} - r_0^\circ \) and \( r'_{100^\circ} - r'_0^\circ \) in Tables XIV. and XVI. be compared with each other, it will be seen that those in Table XIV. agree together quite as well as those in
Table XVI.; and therefore, if the values in Table XIV. were smaller, those in the columns headed $r_{100^\circ} - r'_{100^\circ}$ and $r_0 - r'_0$ would agree much better together.
If
$$r_{100^\circ} - r'_{100^\circ} = r_0 - r'_0 \quad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (3)$$
be correct, we may suppose that
$$r_t - r'_t = r_0 - r'_0;$$
that is, the absolute difference between the observed and calculated resistances of an alloy at any temperature is equal to the absolute difference between the observed and calculated resistances at $0^\circ$ C.; or, in other words,
$$r_t - r'_t = \text{constant}. \quad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (4)$$
Table XVII. contains some examples which show this to be the case.
| Alloy | T. | $r.$ | $r'.$ | Difference |
|------------------------|------|------|-------|------------|
| Cd Pb$_6$ | | | | |
| | 0 | 1092-9 | 1005-0 | 87-9 |
| | 20 | 1171-0 | 1063-9 | 88-0 |
| | 40 | 1258-1 | 1164-9 | 88-2 |
| | 60 | 1358-7 | 1249-8 | 88-9 |
| | 80 | 1424-5 | 1355-8 | 88-7 |
| | 100 | 1510-6 | 1422-2 | 88-4 |
| Gold-copper, containing 0·71 volume per cent. of gold... | | | | |
| | 0 | 119-04 | 100-21 | 18-83 |
| | 20 | 127-11 | 107-98 | 19-13 |
| | 40 | 135-44 | 116-16 | 19-28 |
| | 60 | 143-92 | 124-63 | 19-29 |
| | 80 | 152-39 | 133-21 | 19-18 |
| | 100 | 160-64 | 141-76 | 18-88 |
| Gold-silver, containing 79·86 volumes per cent. of gold... | | | | |
| | 0 | 468-71 | 121-36 | 349-35 |
| | 20 | 479-00 | 130-77 | 348-23 |
| | 40 | 489-38 | 140-67 | 348-71 |
| | 60 | 499-93 | 150-92 | 349-01 |
| | 80 | 510-57 | 161-31 | 349-26 |
| | 100 | 521-30 | 171-67 | 349-63 |
The values given in the column $r$ were calculated with the help of the formulæ from Tables VII. and IX., those in the column $r'$ with that deduced for the correction of conducting-power for temperature of most of the pure metals, namely,
$$\lambda = 100 - 0.37647t + 0.0008340t^2.$$
If, now,
$$r_t - r'_t = \text{constant}, \quad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (4)$$
it is clear that we may deduce the formula for the correction of resistance or conducting-power for temperature of an alloy as soon as we know its composition and its resistance at any temperature; for, as $r'_{100^\circ}$, $r'_0$, and $r'_t$ may be calculated by means of the formula given for the correction of conducting-power for temperature for most of the pure metals, viz.
$$\lambda = 100 - 0.37647t + 0.0008340t^2*,$$
*Loc. cit.*
if the constant \( r_t - r'_t \) be determined, then
\[
r_{100^\circ} = r'_{100^\circ} + \text{constant},
\]
\[
r_t = r'_t + \text{constant},
\]
\[
r_0 = r'_0 + \text{constant};
\]
and from these terms a formula for the correction of resistance or conducting-power for temperature may be calculated, which in most cases will be found very near the truth. Thus, take, for instance, the gold-silver alloy containing 79·86 volumes per cent. gold (hard drawn), and we find
the first observed conducting-power . . . . . . 21·010 at 11°·7,
that calculated . . . . . . . . . . . . . . 78·866 at 11°·7,
hence the resistance observed is . . . . . . . . 475·96 at 11°·7,
that calculated . . . . . . . . . . . . . . 126·80 at 11°·7;
therefore \( r_t - r'_t = 349·16 \).
But the calculated resistance at . . . . . . . . 0° = 121·36,
" " " " " " " " 50° = 145·75,
" " " " " " " " 100° = 171·67,
therefore \( r \), the true resistance, will be at . . . . 0° = 121·36 + 349·16 = 470·52,
" " " " " " " " 50° = 145·75 + 349·16 = 494·91,
" " " " " " " " 100° = 171·67 + 349·16 = 521·83;
or the conducting-powers will be at . . . . . . . . 0° = 21·253,
" " " " " " " " 50° = 20·206,
" " " " " " " " 100° = 19·200.
The formula deduced from these numbers is
\[
\lambda = 21·253 - 0·021350t + 0·000008200t^2.
\]
The conducting-power, according to this formula, of the alloy at 11°·45 will be 21·010; but after having kept the alloys at 100° for three days it altered, and was found at that temperature to conduct 21·031. If the above formula be multiplied by \( \frac{21·031}{21·010} = 1·001 \), we arrive at
\[
\lambda = 21·274 - 0·021372t + 0·000008208t^2;
\]
and if the conducting-powers be calculated for the different temperatures in the following series, the difference between the observed and calculated values will be found to be very small.
| T. | Conducting-power. | Difference. |
|----|-------------------|-------------|
| | Observed. | Calculated. |
| 11°·45 | 21·031 | 21·031 | 0·000 |
| 26°·04 | 20·698 | 20·723 | -0·025 |
| 40°·04 | 20·391 | 20·421 | -0·030 |
| 55°·26 | 20·065 | 20·118 | -0·053 |
| 67°·73 | 19·806 | 19·864 | -0·058 |
| 84°·13 | 19·463 | 19·534 | -0·071 |
| 98°·45 | 19·175 | 19·250 | -0·075 |
Another example: the gold-copper alloy containing 0·71 volume per cent. gold (hard drawn) conducts 79·884 at 15°3; the formula deduced in exactly the same manner as the above was
\[ \lambda = 83·843 - 0·26810t + 0·0005152t^2; \]
and the formula deduced from this, with the help of which the following calculated values were obtained, was
\[ \lambda = 84·204 - 0·26926t + 0·0005174t^2. \]
| T. | Conducting-power. | Difference. |
|----|-------------------|-------------|
| | Observed. | Calculated. |
| 17·27 | 79·709 | 79·708 | 0·000 |
| 28·98 | 77·952 | 78·045 | -0·093 |
| 39·55 | 74·154 | 74·364 | -0·210 |
| 54·26 | 70·924 | 71·118 | -0·194 |
| 69·26 | 67·920 | 68·037 | -0·117 |
| 83·86 | 65·213 | 65·263 | -0·050 |
| 98·78 | 62·645 | 62·656 | -0·011 |
Again, let us take another example, the alloy Sn₄Cd, for which the values (Table XIV.) obtained for \( r_{100^\circ} - r'_{100^\circ} \) and \( r_0 - r'_0 \) agree worse than any other in that Table; and if the results agree, it will show that the differences in these values are, as before stated, due to errors of observation.
The first observed conducting-power was 14·259 at 6°8.
The formula deduced, as above, was
\[ \lambda = 14·641 - 0·055250t + 0·0001158t^2. \]
That deduced to calculate the conducting-powers for comparison with those observed, was
\[ \lambda = 14·455 - 0·054673t + 0·0001141t^2. \]
| T. | Conducting-power. | Difference. |
|----|-------------------|-------------|
| | Observed. | Calculated. |
| 8·72 | 13·986 | 13·968 | 0·000 |
| 25·52 | 13·086 | 13·134 | -0·045 |
| 39·50 | 12·419 | 12·473 | -0·054 |
| 54·96 | 11·770 | 11·795 | -0·025 |
| 69·40 | 11·218 | 10·211 | +0·007 |
| 84·02 | 10·933 | 10·666 | +0·067 |
| 98·85 | 10·333 | 10·166 | +0·167 |
These examples are sufficient to prove that the law we have put forth is correct for most of the two metal alloys; we might have experimented with many more alloys whose conducting-power would have followed the above law, but we thought determinations with a few members of each group of alloys would suffice to prove its correctness for most of them. We have endeavoured rather to find the exemptions to the law than to obtain a large number of results which will agree with it.
II. Experiments on the Influence of Temperature on the Electric Conducting-power of some Alloys composed of three Metals.
In the course of the foregoing experiments we were induced to try whether the influence of temperature on the conducting-power of the three metal alloys would be regulated by the above law, and Tables XVIII. and XIX. contain the results.
**TABLE XVIII.**
1. Gold-copper-silver alloy, containing 50 volumes per cent. gold, 25 copper, and 25 silver (hard drawn).
Length 341·5 millims.; diameter 0·618 millim.
Conducting-power found before heating the wire........... Reduced to 0°.
Ditto, after being kept at 100° for 1 day .................. 10·6186 at 13·7
Ditto, for 2 days .............................................. 10·5855 at 6·7
| T. | Conducting-power. | Difference. |
|----|------------------|-------------|
| | Observed. | Calculated. |
| 16·75 | 10·5627 | 10·5617 | +0·0090 |
| 33·52 | 10·4341 | 10·4346 | -0·0005 |
| 55·15 | 10·3130 | 10·3148 | -0·0018 |
| 78·35 | 10·1846 | 10·1873 | -0·0027 |
| 97·52 | 10·0857 | 10·0828 | +0·0029 |
\[ \lambda = 10·6220 - 0·005624t + 0·0000009863t^2. \]
2. Gold-copper-silver alloy, containing 40·67 vols. per cent. gold, 39·81 copper, and 19·52 silver (hard drawn).
Length 532 millims.; diameter 0·625 millim.
Conducting-power found before heating the wire........... Reduced to 0°.
Ditto, after being kept at 100° for 1 day .................. 12·007 at 15·1
Ditto, for 2 days .............................................. 11·978 at 15·5
Ditto, for 3 days .............................................. 11·914 at 15·9
| T. | Conducting-power. |
|----|------------------|
| 5·0 | 11·956 |
| 54·5 | 11·647 |
| 100·0 | 11·438 |
\[ \lambda = 12·017 - 0·0069033t + 0·00001111t^2. \]
3. Gold-copper-silver alloy, containing 3·67 vols. per cent. gold, 83·32 copper, and 13·01 silver (hard drawn).
Length 764 millims.; diameter 0·553 millim.
Conducting-power found before heating the wire........... Reduced to 0°.
Ditto, after being kept at 100° for 1 day .................. 44·820 at 18·4
Ditto, for 2 days .............................................. 42·994 at 17·1
Ditto, for 3 days .............................................. 43·047 at 17·0
| T. | Conducting-power. |
|----|------------------|
| 11·0 | 43·591 |
| 55·5 | 40·300 |
| 100·0 | 37·560 |
\[ \lambda = 44·472 - 0·081525t + 0·0001240t^2. \]
**TABLE XIX.**
| Alloy. | Volumes per cent. | Conducting-power at 100° | Percentage decrement. |
|-------------------------|-------------------|--------------------------|----------------------|
| | | Observed. | Calculated. |
| Gold-copper-silver | 50 Au | 10·14 | 62·89 |
| (hard drawn). | 25 Cu | | 5·20 |
| | 25 Ag | | 4·72 |
| Ditto | 40·67 Au | 11·52 | 64·34 |
| | 39·81 Cu | | 4·82 |
| | 19·52 Ag | | 5·25 |
| Ditto | 3·67 Au | 37·39 | 70·09 |
| | 83·32 Cu | | 15·54 |
| | 13·01 Ag | | 15·63 |
| Argentan | 12·84 Ni* | 7·46 | 44·44 |
| | 36·57 Zn | | 4·39 |
| | 50·59 Cu | | 4·93 |
* Values found by analysis. Of this wire all our normal wires were made. According to former experiments (Philosophical Transactions, 1862, p. 5), the formula for the correction of conducting-power for temperature of this alloy was
\[ \lambda = 7·803 - 0·0034619t + 0·0000003951t^2. \]
The values in Table XIX. indicate that the law will probably hold good for most of the three metal alloys.
There is, however, one of the three metal alloys which we cannot pass over unnoticed, namely, that of copper-nickel-zinc or argentan (german silver). This alloy has long been used, on account of the small effect which temperature has on its conducting-power, for making resistance coils, &c. It is a somewhat curious fact, that the conducting-power of this commercial alloy decreases less between $0^\circ$ and $100^\circ$ than almost any other alloy yet known, for in the course of this investigation we have only found the following which show a smaller percentage decrement in their conducting-power than argentan.
The conducting-power of the platinum-silver alloy, containing 19·65 volumes per cent. platinum, decreases between $0^\circ$ and $100^\circ$ 3·10 per cent.
The conducting-power of the palladium-silver alloy, containing 23·38 volumes per cent. palladium, decreases between $0^\circ$ and $100^\circ$ 3·40 per cent.
The conducting-power of the iron-gold alloy, containing 10·96 volumes per cent. iron, decreases between $0^\circ$ and $100^\circ$ 3·84 per cent.
The conducting-power of the argentan decreases between $0^\circ$ and $100^\circ$ 4·39 per cent.
III. On a Method by which the Conducting-power of a Pure Metal may be deduced from that of the Impure one.
This part of our subject is an important deduction from the law
$$P_0 : P_c :: \lambda_{100^\circ} : \lambda'_{100^\circ}; \ldots \ldots \ldots . . . . . . (1)$$
for if we consider the two last terms of the proportion, and bear in mind that a small amount of another metal has very little or no effect on $\lambda'_{100^\circ}$, when it represents the conducting-power of an alloy containing a very small percentage of the one metal, whereas it has a very considerable one on $\lambda_{100^\circ}$, we may write the proportion
$$P : P' :: M_{100^\circ} : M'_{100^\circ}, \ldots \ldots \ldots . . . . . . (5)$$
where $P$ and $P'$ represent the observed and calculated percentage decrements in the conducting-power of the impure and pure metals between $0^\circ$ and $100^\circ$, and $M_{100^\circ}$ and $M'_{100^\circ}$ their conducting-powers at $100^\circ$. $P'$ is for most metals 29·307, or we may express it as follows:
The percentage decrement in the conducting-power of an impure metal between $0^\circ$ C. and $100^\circ$ C., is to that of the pure one between $0^\circ$ C. and $100^\circ$ C. as the conducting-power of the impure metal at $100^\circ$ C. is to that of the pure one at $100^\circ$ C.
From the results given in Tables XII. and XIII., we have chosen the following alloys to show that a small amount of foreign metal has no influence on the value $\lambda'_{100^\circ}$, which may therefore be looked upon as equal to $M'_{100^\circ}$.
TEMPERATURE ON THE ELECTRIC CONDUCTING-POWER OF ALLOYS.
TABLE XX.
| Alloy | Volumes per cent. | Conducting-power at 100° |
|-----------------------|-------------------|--------------------------|
| | | Observed. | Calculated. |
| Tin-copper (hard drawn) | 1·41 of Sn | 48·89 | 69·78 |
| Zinc-copper (hard drawn) | 5·03 of Zn | 47·93 | 68·13 |
| Gold-copper (hard drawn) | 1·37 of Cu | 43·85 | 55·33 |
| Gold-copper (hard drawn) | 0·71 of Au | 62·25 | 70·54 |
| Platinum-silver (hard drawn) | 2·51 of Pt | 28·07 | 69·24 |
| Copper-silver (hard drawn) | 1·65 of Ag | 65·81 | 70·66 |
Pure copper conducts at 100° 70·27.
Pure gold conducts at 100° 55·90.
Pure copper conducts at 100° 70·27.
Pure silver conducts at 100° 71·53.
Pure copper conducts at 100° 70·27.
If now, as in the case of most commercial metals, the amount of impurity be much smaller than that in the Table, then of course its influence on the value $\lambda'_{100}$ is so small that it may be entirely disregarded.
In Tables XXI., XXII., and XXIII., we give some results obtained with impure metals, the conducting-power of the same metal in a pure state having been previously determined.
TABLE XXI.
1. Gold, containing traces of silver (hard drawn).
Length 1564 millims.; diameter 0·525 millim.
Conducting-power found before heating the wire 69·612 at 10° Reduced to 0°.
Ditto, after being kept at 100° for 1 day 70·069 at 10·4 72·578
Ditto, for 2 days 69·274 at 13·8 72·578
| T. | Conducting-power. |
|----|-------------------|
| 15·0 | 68·969 |
| 57·5 | 60·179 |
| 100·0 | 53·387 |
$\lambda = 72·548 - 0·24692t + 0·0005531t^2$.
2. Copper, containing traces of tin (hard drawn).
Length 2008 millims.; diameter 0·518 millim.
Conducting-power found before heating the wire 88·357 at 12·8 Reduced to 0°.
Ditto, after being kept at 100° for 1 day 88·690 at 12·6 92·786
Ditto, for 2 days 89·589 at 10·1 92·894
| T. | Conducting-power. |
|----|-------------------|
| 11·0 | 89·319 |
| 55·5 | 76·619 |
| 100·0 | 66·863 |
$\lambda = 92·912 - 0·33482t + 0·0007433t^2$.
TABLE XXI. (continued).
3. Copper, containing traces of zinc (hard drawn).
Length 1992 millims.; diameter 0·577 millim.
Conducting-power found before heating the wire 81·306 at 18·2 Reduced to 0°.
Ditto, after being kept at 100° for 1 day 82·185 at 12·8 86·896
Ditto, for 2 days 83·021 at 12·8 86·725
| T. | Conducting-power. |
|----|-------------------|
| 13·0 | 82·960 |
| 56·5 | 72·071 |
| 100·0 | 63·786 |
$\lambda = 86·719 - 0·29814t + 0·0006581t^2$.
4. Copper, commercial, containing traces of iron, nickel, lead, and suboxide of copper (hard drawn).
Length 2091 millims.; diameter 0·546 millim.
Conducting-power found before heating the wire 74·209 at 18·6 Reduced to 0°.
Ditto, after being kept at 100° for 1 day 74·610 at 16·2 78·350
Ditto, for 2 days 74·563 at 16·8 78·441
Ditto, for 3 days 74·283 at 18·0 78·427
| T. | Conducting-power. |
|----|-------------------|
| 12·0 | 75·668 |
| 56·0 | 66·584 |
| 100·0 | 59·351 |
$\lambda = 78·467 - 0·23396t + 0·0004780t^2$.
### Table XXI. (continued).
#### 5. Copper, commercial, containing same impurities as No. 3 (hard drawn).
Length 2246 millims.; diameter 0·549 millim.
Conducting-power found before heating the wire Reduced to 0°.
74·660 at 16·8 78·705
Ditto, after being kept at 100°
for 1 day 74·958 at 16·4 78·921
for 2 days 74·946 at 16·6 78·958
for 3 days 74·576 at 18·2 78·958
| T. | Conducting-power. |
|----|-------------------|
| 13·0 | 75·979 |
| 56·5 | 76·738 |
| 100·0 | 59·633 |
\[ \lambda = 79·155 - 0·25166t + 0·0005644t^2. \]
#### 6. Copper, commercial, containing traces of lead, iron, antimony, and suboxide of copper (hard drawn).
Length 3010 millims.; diameter 0·606 millim.
Conducting-power found before heating the wire Reduced to 0°.
89·258 at 16·7 94·896
Ditto, after being kept at 100°
for 1 day 89·241 at 17·4 95·118
for 2 days 89·524 at 16·5 95·109
| T. | Conducting-power. |
|----|-------------------|
| 10·0 | 91·849 |
| 55·0 | 78·402 |
| 100·0 | 68·324 |
\[ \lambda = 95·294 - 0·35289t + 0·0008309t^2. \]
#### 7. Silver, containing traces of lead (hard drawn).
Length 1473 millims.; diameter 0·513 millim.
Conducting-power found before heating the wire Reduced to 0°.
64·909 at 13·6 66·997
Ditto, after being kept at 100°
for 1 day 65·957 at 14·6 68·225
for 2 days 66·404 at 13·6 68·539
for 3 days 66·801 at 11·4 68·399
| T. | Conducting-power. |
|----|-------------------|
| 13·0 | 66·543 |
| 56·0 | 60·264 |
| 100·0 | 54·987 |
\[ \lambda = 68·429 - 0·16030t + 0·0002588t^2. \]
#### 8. Silver, containing traces of tin (hard drawn).
Length 2025 millims.; diameter 0·579 millim.
Conducting-power found before heating the wire Reduced to 0°.
71·427 at 13·6 73·964
Ditto, after being kept at 100°
for 1 day 72·668 at 13·8 75·287
for 2 days 72·735 at 13·7 75·338
| T. | Conducting-power. |
|----|-------------------|
| 13·0 | 72·696 |
| 57·0 | 65·305 |
| 100·0 | 59·085 |
\[ \lambda = 75·355 - 0·19437t + 0·0003167t^2. \]
#### 9. Silver, containing traces of gold (hard drawn).
Length 1780 millims.; diameter 0·648 millim.
Conducting-power found before heating the wire Reduced to 0°.
70·847 at 10·4 72·717
Ditto, after being kept at 100°
for 1 day 71·205 at 11·3 73·249
for 2 days 70·951 at 13·5 73·389
for 3 days 70·929 at 13·5 73·366
| T. | Conducting-power. |
|----|-------------------|
| 13·7 | 70·763 |
| 24·21 | 69·036 |
| 39·25 | 66·931 |
| 54·43 | 64·172 |
| 69·51 | 61·577 |
| 84·50 | 59·823 |
| 98·60 | 58·028 |
\[ \lambda = 73·336 - 0·18447t + 0·0002982t^2. \]
#### 10. Silver, containing minute traces of arsenic (hard drawn).
Length 1298 millims.; diameter 0·376 millim.
Conducting-power found before heating the wire Reduced to 0°.
85·119 at 13·0 88·931
Ditto, after being kept at 100°
for 1 day 86·795 at 9·0 89·285
for 2 days 87·881 at 7·4 89·949
for 3 days 87·091 at 10·0 89·869
| T. | Conducting-power. |
|----|-------------------|
| 11·0 | 87·029 |
| 55·5 | 76·185 |
| 100·0 | 67·767 |
\[ \lambda = 90·084 - 0·28442t + 0·0006125t^2. \]
On comparing the values in Table XXII. for the observed and calculated conducting-powers, it will be seen that those calculated for the same metal agree very closely with each other, whereas those observed vary in some cases more than 20 per cent. From Table XXIII. it is evident that the deduced value for the conducting-power of gold and silver is much higher than that found by experiment; on referring, however, to the paper on the influence of temperature on the conducting-power of metals (Table XVI.), it will be found that the percentage decrement in the conducting-power between 0° and 100° of
Silver is . . . . . 28·44
Copper is . . . . . 29·69
Gold is . . . . . 21·30
Tin is . . . . . 29·89
Lead is . . . . . 29·61
Let us now recalculate the deduced conducting-powers, using these values instead of the mean of those found for the pure metals (viz. 29·307), and we arrive at much better results. These are shown in Table XXIII.
| Metal | Impurity | Conducting-power at 0° |
|------------------------|-----------------------------------|------------------------|
| | | Observed for hard-drawn wires. | Observed for annealed wires. | Deduced from the impure metals, using the observed percentage decrements. |
| Lead | Bismuth | 8·53 | 8·32 | — | 8·65 |
| Tin | Copper | 12·19 | 12·36 | — | 12·54 |
| Gold (hard drawn) | Copper | 83·17 | 77·96 | 79·33 | 79·20 |
| Copper (hard drawn) | Tin | 100·06 | 99·95 | 102·21 | 101·91 |
| Silver (hard drawn) | Minute traces of arsenic | 112·06 | 100·00 | 108·57 | 107·43 |
* From Table XXVII. † From Table XII. ‡ From Table XIII.
The values in the last column were obtained as follows: take for instance that of gold. The mean deduced value (column 1) for its conducting-power at 0° was 83·17, under the supposition that the percentage decrement in its conducting-power between 0° and 100° was 29·307; the percentage decrement, however, found for pure gold was 28·30; we must therefore recalculate the deduced value to obtain a more concordant one, and this may be done with the help of the proportion
\[ P : P' :: M_{100°} : M'_{100°} \]
First,
\[ M_{100°} = \frac{83·17 \times 70·693}{100} = 58·80, \]
then
\[ 29·307 : 28·30 :: 58·80 : M'_{100°}; \]
ence
\[ M'_{100°} = 56·77, \]
and therefore the deduced value at 0°
\[ \frac{56·77 \times 100}{71·7} = 79·20. \]
Reducing the others in the same manner, we are struck with the coincidence of these values with those really found for the annealed wires by experiment; in fact we must assume that the values deduced for the conducting-power of metals are those of the annealed wires, even when hard-drawn ones are experimented with. What the deduced values for the conducting-power would be when using annealed wires of impure metals we are unable at present to say, for no determinations have been made in this direction.
It must be remembered that the effect of annealing on the conducting-power of alloys is very small, so that the deduced values from those found for the annealed wires would not be very different from those deduced from the hard drawn, assuming, as we have done in the former part of this investigation, that the percentage decrement in the conducting-power between 0° and 100° of hard drawn and annealed is the same.
Having thus proved that, by using the expression
\[ P : P' :: M_{100°} : M'_{100°}, \]
we may deduce the conducting-power of the pure metal from the impure one, when the observed values do not differ from those calculated by more than 20 to 30 per cent., we will now proceed to give the results of some experiments with impure metals where the conducting-power of the same metals in a pure state has not yet been determined. Tables XXIV. and XXV. contain the results.
### Table XXIV.
#### 1. Platinum, commercial (hard drawn).
Length 371 millims.; diameter 0·614 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 11·209 at 16·6 | 11·720 |
| Ditto, after being kept at 100° | |
| for 1 day | 11·919 at 15·6 |
| Ditto, for 2 days | 11·174 at 16·7 |
| Ditto, for 3 days | 11·159 at 16·8 |
| T. | Conducting-power |
|----|------------------|
| 9·0 | 11·427 |
| 54·5 | 10·172 |
| 100·0 | 9·197 |
\[ \lambda = 11·708 - 0·031875t + 0·00006762t^2. \]
#### 2. Platinum, commercial (hard drawn).
Length 209 millims.; diameter 0·243 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 11·039 at 17·0 | 11·527 |
| Ditto, after being kept at 100° | |
| for 1 day | 11·038 at 17·3 |
| Ditto, for 2 days | 11·022 at 17·6 |
| T. | Conducting-power |
|----|------------------|
| 11·0 | 11·239 |
| 55·0 | 10·072 |
| 100·0 | 9·141 |
\[ \lambda = 11·530 - 0·029721t + 0·00005827t^2. \]
#### 3. Palladium, commercial (hard drawn).
Length 167·5 millims.; diameter 0·379 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 13·230 at 18·4 | 13·991 |
| Ditto, after being kept at 100° | |
| for 1 day | 13·295 at 17·5 |
| Ditto, for 2 days | 13·322 at 16·9 |
| T. | Conducting-power |
|----|------------------|
| 8·0 | 13·645 |
| 54·5 | 11·954 |
| 100·0 | 10·658 |
\[ \lambda = 14·026 - 0·043225t + 0·00009540t^2. \]
#### 4. Palladium, commercial (hard drawn).
Length 218 millims.; diameter 0·409 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 12·091 at 17·2 | 12·678 |
| Ditto, after being kept at 100° | |
| for 1 day | 12·087 at 17·6 |
| T. | Conducting-power |
|----|------------------|
| 10·0 | 12·357 |
| 55·0 | 10·978 |
| 100·0 | 9·818 |
\[ \lambda = 12·704 - 0·035443t + 0·00007383t^2. \]
#### 5. Magnesium, commercial.
Length 717 millims.; diameter 0·497 millim.
| T. | Conducting-power |
|----|------------------|
| 15·0 | 34·912 |
| 57·5 | 30·312 |
| 100·0 | 26·922 |
\[ \lambda = 36·825 - 0·13252t + 0·0003349t^2. \]
#### 6. Magnesium (from Mr. E. Sonstadt).
Length 628 millims.; diameter 0·436 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 38·062 at 11·0 | 39·662 |
| Ditto, after being kept at 100° | |
| for 1 day | 37·963 at 12·2 |
| Ditto, for 2 days | 37·918 at 12·6 |
| T. | Conducting-power |
|----|------------------|
| 13·0 | 37·881 |
| 56·5 | 32·442 |
| 100·0 | 28·347 |
\[ \lambda = 39·765 - 0·14971t + 0·0003351t^2. \]
#### 7. Aluminium, commercial (hard drawn).
Length 1351 millims.; diameter 0·511 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 50·804 at 17·2 | 54·073 |
| Ditto, after being kept at 100° | |
| for 1 day | 51·079 at 16·4 |
| Ditto, for 2 days | 51·146 at 15·7 |
| Ditto, for 3 days | 51·035 at 16·4 |
| T. | Conducting-power |
|----|------------------|
| 13·0 | 51·910 |
| 56·0 | 44·842 |
| 100·0 | 38·938 |
\[ \lambda = 54·225 - 0·19843t + 0·0004556t^2. \]
#### 8. Aluminium, alloyed with 0·5 per cent. nickel (hard drawn).
Length 745 millims.; diameter 0·415 millim.
| Conducting-power found before heating the wire | Reduced to 0°. |
|-----------------------------------------------|----------------|
| 44·597 at 15·9 | 46·950 |
| Ditto, after being kept at 100° | |
| for 1 day | 44·786 at 15·2 |
| Ditto, for 2 days | 45·044 at 13·6 |
| T. | Conducting-power |
|----|------------------|
| 14·0 | 44·986 |
| 57·0 | 39·325 |
| 100·0 | 34·785 |
\[ \lambda = 47·071 - 0·15321t + 0·0003037t^2. \]
TABLE XXV.
| Metal | Observed percentage decrement in the conducting-power between 0° and 100° | Conducting-power at 0° |
|----------------|--------------------------------------------------------------------------|------------------------|
| | | Observed. | Calculated for the pure metal. |
| Platinum (1) | 21·45 | 11·72 | 17·79 |
| Platinum (2) | 20·73 | 11·53 | 18·28 |
| Palladium (3) | 24·01 | 18·99 | 18·35 |
| Palladium (4) | 22·09 | 12·68 | 18·54 |
| Magnesium (5) | 20·89 | 30·82 | 41·50 |
| Magnesium (6) | 28·72 | 39·66 | 46·95 |
| Aluminium (7) | 28·20 | 54·07 | 57·01 |
| Aluminium (8) | 26·10 | 46·95 | 55·12 |
Mean: 18·03
[It is scarcely necessary to add, that in the same manner as the formulæ for the correction of conducting-power for temperature may in most cases be deduced where the composition and conducting-power of an alloy at any temperature are known, that for the correction of the conducting-power for temperature of an impure metal may also be calculated, using the conducting-power of the annealed metal for $\lambda'_0$, $\lambda'_1$, $\lambda'_{100}$. This is of practical importance; for in testing copper wire for telegraphic purposes, the formula for the correction of its conducting-power for temperature may be easily deduced, of course only in cases where the conducting-power is within the limits above stated. It has already been elsewhere shown that the conducting-power of commercial metals, copper for instance, varies considerably according to the state of its purity. Thus a specimen of Rio Tinto copper was found to conduct as follows:
Length 398 millims.; diameter 0·331 millim.
Conducting-power found before heating the wire ........................................... Reduced to 0°.
Ditto, after heating to 100° for 1 day ......................................................... 13·480 at 16·6 13·622
Ditto, for 2 days ......................................................................................... 13·473 at 16·9 13·586
Ditto, for 3 days ......................................................................................... 13·442 at 14·9 13·573
Ditto, for 4 days ......................................................................................... 13·420 at 15·7 13·558
Ditto, for 5 days ......................................................................................... 13·418 at 16·0 13·558
| T. | Conducting-power. |
|----------|-------------------|
| 14·67 | 13·429 |
| 57·33 | 13·064 |
| 100·00 | 12·713 |
$\lambda = 13·558 - 0·0088326t + 0·000003844t^2$
which corresponds to a percentage decrement of only 6·23, whereas the conducting-power of pure copper decreases between 0° and 100° C. 29·69 per cent.—Feb. 1864.]
Table XXVI. contains a list of the conducting-powers of metals in a pure state. Those marked with a † are those deduced from the impure metals, and they may be called the probable values for the conducting-powers of annealed wires of the metals.
IV. Miscellaneous and general remarks.
Having thus described the results obtained in this investigation, it only remains for us to make a few general remarks on them.
1. The percentage decrement in the conducting-power of alloys between 0° and 100° is never greater than that of the pure metals composing them; for on looking at Tables XI., XII., and XIII., we only find a few cases where the observed percentage decrement is greater than that of the pure metals composing the alloy, and in these the differences are so small that they are undoubtedly due to small errors in the observations, for the differences between the percentage decrements are not greater than those obtained for different wires of the same metal.
2. The conducting-power of alloys decreases with an increase of temperature. This, however, is not strictly true for all alloys, for we already know of some where this is not the case, viz. a few of the bismuth alloys. The results of our observations are given in the following Table:
| T. | Conducting-power |
|----|------------------|
| 15°0 | 7-693 |
| 57°5 | 6-675 |
| 100° | 5-860 |
\[ \lambda = 8-101 - 0-0280217t + 0-00005619t^2. \]
The conducting-power found in a former research was ..... 7-03 at 24°0 Reduced to 0°.
---
* Philosophical Transactions, 1863.
† Ibid. 1860, p. 161.
TABLE XXVII. (continued).
3. \( \text{Bi Pb}_2 \), containing 53·74 volumes per cent. bismuth.
Length 224 millims.; diameter 0·643 millim.
| T. | Conducting-power. |
|----|-------------------|
| 96·6 | 1·8543 h m |
| 16·5 | 2·0385 1st day. |
| 12·5 | 2·0346 2nd day. |
| 12·5 | 2·0296 n m |
| 93·8 | 1·8539 > 1 10 |
| 97·0 | 1·8708 > 4 15 3rd day. |
| 12·8 | 2·0683 > 30 |
| 10·5 | 2·0277 > 1 30 |
| 97·8 | 1·8617 > 5 10 4th day. |
| 93·8 | 1·8848 > 25 |
The conducting-power found in a former research was 2·09 at 22°·2.
4. \( \text{Bi Sn}_8 \), containing 25·04 volumes per cent. bismuth.
Length 194 millims.; diameter 0·713 millim.
| T. | Conducting-power. |
|----|-------------------|
| 94·8 | 5·3564 h m |
| 88·4 | 5·4690 > 5 0 1st day. |
| 11·6 | 6·7776 > 30 |
| 7·5 | 7·6698 > 1 30 |
| 89·5 | 5·6474 > 1 30 |
| 92·9 | 5·3921 > 4 45 2nd day. |
| 12·3 | 6·7511 > 30 |
| 10·3 | 7·6086 3rd day. |
The conducting-power found in a former research was 7·82 at 24°·9.
5. \( \text{Bi}_4 \text{Pb} \), containing 90·28 volumes per cent. bismuth.
Length 90·5 millims.; diameter 0·689 millim.
| T. | Conducting-power. |
|----|-------------------|
| 10·3 | 0·5299 h m |
| 94·4 | 0·5615 > 1 50 1st day. |
| 94·1 | 0·5654 > 3 0 |
| 13·3 | 0·5439 > 1 0 |
| 10·0 | 0·5402 |
| 94·6 | 0·5682 > 2 0 2nd day. |
| 13·6 | 0·5437 > 30 |
| 6·0 | 0·5413 > 1 0 |
| 93·8 | 0·5686 > 4 0 3rd day. |
| 94·0 | 0·5682 > 0 30 |
| 9·6 | 0·5430 > 0 30 |
The conducting-power found in a former research was 0·521 at 20°·0.
These results need a little explanation; on the first two series no remarks are necessary, but on the three last we will say a few words. On experimenting with a wire of Bi Pb\(_2\) we observed nothing remarkable at first, but after making a series of observations at different temperatures up to 100°, on cooling the wire the same conducting-power was not observed for the same temperature as when heating; at first we thought this was due to the wire being badly soldered, but on resoldering it the same results were obtained. In the Table the third series will read thus: at 96°·6 the conducting-power was found 1·8543; on cooling rapidly to 16°·5 it was found equal to 2·0386; on testing it the next morning at 12°·5 it was 2·0346, showing a loss in conducting-power, for it ought to have conducted better, as the temperature is lower; on the third morning we find it still lower; and on the same day, after being kept at 100° for about 4\(\frac{1}{2}\) hours,
it, on being rapidly cooled, was 2·0683 at 12°·8, showing again an increment. On the fourth morning, at 10°·5, it was 2·0275, and after being kept for 5 hours at 100° and rapidly cooled, it was 2·0837 at 11°·7. There must be, therefore, with some of the bismuth alloys, some disturbing cause, which may act either in the one direction or the other, for on investigating the Bi Sn₈ series the opposite effect is produced. This disturbing cause may be so great that, as in the case of Bi₄ Pb, it appears as if the conducting-power increases with an increase of temperature. Other alloys of bismuth and lead, rich in bismuth, give the same results. As yet, we have not had time to investigate thoroughly this curious property of the bismuth alloys; we hope, however, to be able shortly to do so, as well as explain the reason of these remarkable exceptions to the law, that the conducting-power of alloys decreases with an increase of temperature.
3. Respecting the parts the metals take in the conducting-power of their alloys, we are at present unable to give any definite data; we did hope at one time to have deduced them with the help of the results in this memoir. It is scarcely necessary to point out that in many cases the composition of the alloy may be deduced from its conducting-power in the same manner as it may be from its specific gravity; for as
\[ Po : Pc :: \lambda_{100°} : \lambda'_{100°}, \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (1) \]
then if Po and \( \lambda_{100°} \) be determined, Pc being known (=29·307), \( \lambda'_{100°} \) can be calculated, and from it the relative amounts of the component metals for
\[ \lambda'_{100°} = \frac{xc + (100-x)c'}{100}, \]
where \( x \) represents the volumes per cent. of the one metal, \((100-x)\) those of the other, and \( c \) and \( c' \) their conducting-power at 100°.
Thus the observed conducting-power of the gold-silver alloy at 100° is 14·05, and its percentage decrement 6·49,
\[ \lambda'_{100°} = \frac{14·05 \times 29·307}{6·49} = 63·45, \]
therefore
\[ 63·45 = \frac{71·56*x + 55·90*(100-x)}{100}, \]
or
\[ 755 = 15·66x, \]
\[ 48·20 = x. \]
The amount of silver in the alloy was 47·92 volumes per cent. Again, the platinum-silver alloy, containing 19·65 volumes per cent. platinum, conducts at 100° 6·49, and loses in conducting-power between 0° and 100° 3·10 per cent.; calculating in the same manner the percentage amount of silver, we find it equal to 82·67 instead of 80·35. The values deduced for the percentage amounts only agree in a few cases well with those found by analysis, as slight errors in the determinations materially affect them; for instance, if the conducting-power of the gold-silver alloy were equal to 14·20 at 100°
* Observed conducting-power of silver and gold at 100° (Philosophical Transactions, 1862, p. 24).
instead of 14·05, the volumes per cent. of silver deduced from that value would be 52·62 instead of 48·20, the value calculated from the latter number.
4. It may be as well to state in a few words how we determine to which class a metal belongs, whether to the lead, tin, &c., or to the gold-silver, &c. class; to do this it is only necessary to alloy the metal with traces of lead, tin, &c., and if the conducting-power be equal to that of the mean of the components, we say it belongs to the lead class; if, on the contrary, the alloy has a lower conducting-power than the mean of the components, we say it belongs to the gold-silver, &c. class. These are only some of one series of alloys which have a higher conducting-power than the mean of their components, and these are the amalgams.
Table XXVIII. shows that the new metal thallium belongs to the gold-silver, &c. class.
**Table XXVIII.**
| Conducting-power found before heating the wire | Reduced to 0° |
|-----------------------------------------------|--------------|
| Ditto, after being kept at 100° | |
| for 1 day | |
| Ditto, for 2 days | |
| Ditto, for 3 days | |
| T. | Conducting-power |
|----|------------------|
| 10° | 8·196 at 12·6 |
| 55° | 8·131 at 12·6 |
| 100°| 8·097 at 9·8 |
| | 8·111 at 9·6 |
\[ \lambda = 8·355 - 0·026075t + 0·00005654t^2. \]
These alloys were not analyzed, the 5 per cent. of foreign metal being added to the thallium fused under cyanide of potassium. From the results it will be seen that they both conduct in a lower degree than the mean of their components; for both cadmium and tin conduct better than thallium, the conducting-power at 0° of cadmium being 23·72, and that of tin being 12·36.
5. In conclusion, we would point out that the law which we have deduced from our experiments only holds good in cases where the alloy may be considered a solution of one metal in the other, the metals belonging to the same class; when the alloy is composed of metals of the two classes, then the law no longer holds good (except for a few of the alloys), even if the alloy be a solution of the one metal in the other. The results which we have obtained and described in this memoir fully bear out the views put forward in a former one regarding the chemical nature of the alloys*.
* Philosophical Transactions, 1860, p. 161.