studies on the temperature dependence of electric ... · studies on the temperature dependence of...

Revista Brasileira de Ensino de Fısica, v. 33, n. 4, 4602 (2011)www.sbfisica.org.br

Studies on the temperature dependence of electric conductivity for

metals in the Nineteenth Century:

a neglected chapter in the history of superconductivity(Estudos sobre a dependencia com a temperatura da condutividade eletrica de metais no seculo XIX:

um capıtulo menosprezado na historia da supercondutividade)

Simon Reif-Acherman1

Escuela de Ingenierıa Quımica, Universidad del Valle, Cali, ColombiaRecebido em 9/9/2011; Aceito em 11/11/2011; Publicado em 5/12/2011

Two different lines of research had significant contributions to the discovery of superconductivity: the lique-faction of gases and the studies of the temperature dependence of the electrical conductivity, or resistance, ofpure metals and alloys. Different publications have described and discussed the achievements in the first oneof these subjects. The second subject had not received, however, the same attention. This article tries to fillthis gap by presenting an account showing details of the evolution of the ideas, the first essentially experimentalcontributions to the subject and their corresponding responsible persons.Keywords: superconductivity, electrical resistance, temperature, dependency relation, history, metals, alloys.

Duas diferentes linhas de pesquisa deram significativa contribuicao a descoberta da supercondutividade: aliquefacao de gases e os estudos da dependencia da condutividade ou resistencia eletrica com a temperatura, emmetais puros ou ligas. Diferentes artigos descrevem e discutem as conquistas da liquefacao ao passo que a segundanao recebeu, contudo, a mesma atencao. Este artigo busca preencher esta lacuna, apresentando um historicodetalhado da evolucao de ideias, das primeiros resultados experimentais e dos pesquisadores nelas envolvidos.Palavras-chave: supercondutividade, resistencia eletrica, dependencia com a temperatura, historia da super-condutividade em metais e ligas.

1. Introduction

The traditional accounts about the discovery of super-conductivity, whose first century is commemorated thisyear, show it as a consequence, in some way acciden-tal, of the experimental researches on the liquefactionof the by then so called ‘permanent’ gases. A previousarticle on this subject is mainly focused on the histor-ical evolution of these events [1]. This conception is,however, historically incomplete, since parallel achieve-ments developed in a different line of research madeequally significant contributions to the identification ofthe new phenomenon. The necessity for disposing of ap-propriate thermometric instruments for the each timemore extreme and limited regions of low temperaturein order to replace those, by then, unpractical gaseousones, forced the carrying out of researches focused onthe application of different physical principles and ma-terials in order to fill this objective. The studies onthe electrical conductivity, or resistance, of pure metalsand alloys and their temperature dependence aroused

the interest of scientists of different nationalities in thesecond half of the nineteenth century and the first halfof the twentieth century, and contributed not only tothe understanding of the electrical properties of thosematerials but also to the proposal of several theoreticalmodels on electric conduction. The purpose of this ar-ticle is to expose an account of the more relevant factsrelated with this second line of knowledge, including de-tails of the first essentially experimental contributionsto the subject and their corresponding responsible per-sons.

2. The concept of electrical conductiv-ity in the eighteen century and thefirst studies on its dependence withtemperature

Although the first real theoretical advancement onelectrical conductivity of metals came with the Ger-man physicist Paul Karl Ludwig Drude (1863-1906) by

1E-mail: [email protected].

Copyright by the Sociedade Brasileira de Fısica. Printed in Brazil.

4602-2 Reif-Acherman

putting forth his famous free electron theory [2], theestablishment of electricity as an imponderable elasticfluid transferable from one body to another had beendiscovered around one hundred and eighty years be-fore by the British scientist Stephen Gray (1666-1736),sweeping so away the old idea of an electrical effluviainseparably attached to a body in which they were ex-cited [3,4]. Stimulated by the reading of the accountsof the physicist and compatriot his Francis Hawksbee(1666-1713) [5,6], and after some experiences on relatedsubjects as assistant to the also British natural philoso-pher Jean Theophilus Desaguliers (1683-1744), Gray, adyer by profession and an amateur naturalist by in-clination, carried out in 1720 a series of experimentsusing a hemp thread that allowed him to demonstratethat electricity could be conducted by some materialsfor distances as great as 233 m, while others did notconduct electricity at all [7]. Although initially almostignored, the early Gray’s ideas on electrical communi-cation came to the fore nine years later, and became ofthe public domain with a new publication in 1731 [8].

No further significant progress was made on thissubject until 1734, when the French scientist and Su-perintendant of the Jardins du Roi, Charles Francois deCisternay du Fay (1698-1739), suggested the existenceof two kinds of electric fluid, vitreous and resinous,which could be separated by friction and neutralizedeach other when they combined [9]. The so-called “two-fluid” theory of electricity proposed by du Fay, basedon experiments with the attraction and repulsion of dif-ferent electrified substances, was later contrasted withthat of “one-fluid” theory suggested by the Americanscientist Benjamin Franklin (1706-1790), which consid-ered only one fluid either present, positively or neg-atively charged [10]. With the classification of sub-stances as conductors or insulators and the establish-ment of the electricity flow direction from positive tonegative, the basis for the behavior of the new prop-erty was ready.

It is the British natural philosopher Joseph Priest-ley (1733-1804) the first in trying, although with greatimperfections, the estimation of electrical conductivityin metals by using static electricity. He determined therelative scale of conduction power between two met-als by measuring the amount of fine test melted af-ter passing similar discharges through wires of identi-cal length and diameter [11]. The first notice about thedependence of electrical conduction with temperature,however, is very probably due to the British scientistHenry Cavendish (1731-1810). Accurate measurementshe did in 1776 of relative resistances of an iron wireand solutions of common salt allowed him to identifybetter conduction powers for warmer solutions than forcolder ones [12]. The first more reliable measurementsfor metals with voltaic electricity are attributable tothe British chemist Humphry Davy (later Sir) (1778-1829), who carried out researches in 1821 by which notonly clearly proved the differences existing between the

conducting power of different materials and its depen-dence with temperature, but also found the relationof this power to the other physical variables such asweight, surface and length of the conducting body, aswell the conditions of electro-magnet action [13]. Work-ing as nearly as possible with similar wires (diameterbeing more than one-tenth of an inch and lengths ofthree inches) of platinum, silver wire, copper, tin, iron,lead, gold and palladium, Davy found much greater dif-ferences in the behavior of different materials than heinitially expected, and, over all, what he considered themost remarkable result, which was the significant varia-tion of the corresponding conducting powers with tem-perature, being lower in some inverse ratio as the tem-perature was higher. One year before the publication bythe German physicist Georg Simon Ohm (1789-1854) ofthe well-known mathematical theory of the galvanic cir-cuit, and based on the Davy’s work, the French scientistAntoine Cesar Becquerel (1788-1878) compiled in 1826a list of conductive powers of nine metals (relative tothat of cooper), which was considered as a referencework and used as a guide on the subject for severaldecades [14].

3. The first analytical relations of de-pendence

The first mathematical relation for the temperature de-pendence of electrical conductivity was established bythe Russian physicist and Professor at the University ofSaint-Petersburg, Emil Khristianovich Lenz (HeinrichFriedrich Emil) (1804-1865) (Fig. 1), widely known bythe discovery of two fundamental physical laws on thephenomena of induction and the thermal action of acurrent (the latter now better known as Joule’s law)[15]. After finishing some electromagnetic experimentson the influence of various factors in the induction ofthe electrical currents by magnets, and before startingthose that led him to the establishment of the law thatbears his name, Lenz was involved in studies on theelectrical resistance and conductivity in metals. In anarticle published in 1832 [16] he revealed how the lec-ture of a paper written by the Italian physicist LeopoldoNobili (1784-1835) and his countryman, the science ad-ministrator Vincenzo Antinori (1792-1865), on the elec-trical phenomena produced by a magnet [17], suggestedhim the idea for the new subject of research. The paperdescribe the way they used for determining the orderin which four different metals (cooper, iron, antimonyand bismuth) were adapted to produce the electric cur-rent by magnetism. The Lenz’s exact words were: “it isparticularly striking that the order is the same as thatwhich these metals occupy, also, in reference to theircapacity of conducting electricity, and the idea sud-denly occurred to me whether the electromotive powerof the spirals did not remain the same in all metals;and whether the stronger current in the one metal did

Studies on the temperature dependence of electric conductivity for metals in the Nineteenth Century 4602-3

not arise from its being a better conductor of electric-ity than the others. With this in view, I examined fourmetals, cooper, iron, platinum and brass” [16].

Figure 1 - Emil Khristianovich Lenz.

In a later paper, read before the Academy of St. Pe-tersburg on June 7, 1833, Lenz revealed details of hisresearch. A pair of identical spirals were built for eachmetal under investigation and connected in series into asingle circuit whose free ends were joined by cooper leadwires to a galvanometer very similar to that invented byNobili. By using a circuit with an electromotive forcewhich was free of the uncertainty implied by the inter-nal resistance of the battery, Lenz was able to find theelectric conductivity of each one of the studied metalsat different temperatures and found with considerabledegree of accuracy the magnitude of their respectivechanges with this variable. The ballistic method basedon the original conception of an instantaneous, impact-like effect of induction current he employed for mea-suring this and other electric and magnetic quantities,allowed him to determine values at between six andtwelve different temperatures for, initially, silver, cop-per, brass, iron and platinum [18], and sometime later,gold, lead and tin too [19]. According to the particu-lar analytical style that characterized his research anddifferenced it from that of most of contemporaneouscolleagues, Lenz worked the whole set of experimentalvalues with the assistance of mathematical methods,mainly that of least squares, looking for the establish-ment of a general quantitative relation between bothvariables. The relation he found for this specific casewas (using his own notation)

γn = x + yn +zn2 ,

where γn represented the electrical conductivity at atemperature n, x the conductivity at 0 ◦C in the Reau-mur scale, and y and z two particular coefficients foreach specific substance (Table 1).

Table 1 - Lenz’s specific coefficients for electrical conductivity ofeight metals. Credit: Ref. [19].

Lenz determined as well the ranges in which the for-mulas could be utilized for each one of the studied met-als. Researches carried out more than a decade later bythe German physicist and mathematician Johann Hein-rich Muller (1809-1875) showed a favorable comparisonbetween the results found by application of these for-mulas and the experimental values [20].

The next essay on the subject was carried out morethan a decade later by the third son of the previ-ously mentioned A.C. Becquerel, the French physicistAlexandre-Edmond Becquerel (1820-1891) (Fig. 2),more known by his studies on solar radiation and onphosphorescence. The author did not make, however,any reference to the Lenz’s work, and the research in-cluded not only the effect of heating on the electricalconductivity for a larger number of metals, but also forsome liquids and solutions.

The apparatuses he used for the study incorporateseveral changes in order to improve the accuracy regard-ing that used by Lenz, and are schematically shown inFig. 3 [21]. A first step for the evaluation of the temper-ature influence on the conduction power was its deter-mination at a reference value (around 12.75 ◦C). Thecorresponding device included (Fig. 3a) a differentialgalvanometer having two separate wires in its coil (oneof them of the metal to be studied) and placed on theboard SS’, a couple FF’ formed by one cylinder of amal-gamated zinc immersed in a saturated sodium chloridesolution and other of cooper in a solution of sulphate ofthe same metal, an early version of a Wheatstone rheo-stat DEE’D’ for the introduction of a conductor wirein the circuit, and a device RAA’R’ where the wirewhose conductivity was to be determined was placed.


If the wires was be made of two different metallic con-ductors of equal conducting power connecting the polesof the same galvanic pair or battery, and so that bothcurrents shall be in opposite directions through the gal-vanometer, the needle of the latter would be stationary,and this became the test for the equality of the conduc-tion powers of the two metals. A quantity denominatedequivalent of resistance must to be determined in termsof a number of divisions in the rheostat for a definitelength of wire of the metal to be studied. The rheo-stat was made to furnish a measure of the resistance toconduction of a given length of wire, and on this waythe length of the other wire must to be conditioned ac-cording its conduction power in order to maintain theequilibrium of the needle. If the nature of the connec-tions remaining the same, the apparatus was arrangedso that scarce any change could be made in either cir-cuit, beyond that of the length of the wire, and thecorresponding variations in the length of the wire un-der study could be read off in a graduated scale.

Figure 2 - Alexandre-Edmond Becquerel.

The study of the effect of temperature included asimple arrangement (Fig. 3b), in which the wire underinvestigation was putted around a metallic tube CD toform a helix whose convolutions were not touching, andintroduced along with the bulb of a thermometer intoa bath of oil. Two thick connecting parts of cooper,whose resistance to electrical conduction could be ne-glected regarding that of the wire, were connected withthe extremities of the latter in the bath, and the wholearrangement was then immersed in a water bath. The

increase of the equivalent of resistance in the wire due toheating it from the ambient temperature to the boilingpoint could be then accurately measured by allowingthe heated bath to cool gradually. The obtained re-sults allowed Becquerel to conclude that the increaseof resistance by unitary change of temperature (dr/dt)was a characteristic constant for each metal studied.Although without the primary purpose for explicitlyestablish an analytical equation for estimating conduc-tivities, Becquerel arranged the results as a function ofboth, the so called coefficient of the increment of resis-tance (dr/dt/ resistance at 0 ◦C) and temperature,

R = R0 (1 + at) ,

where R0 represents the electrical resistance of themetal at 0 ◦C. The Table 2 presents the coefficientshe estimated for a number of metals.

Figure 3 - Becquerel’s equipment. Credit: Ref. [21].

A few time later, in the second semester of 1848, theIrish astronomer and physicist, Rev. Dr. Thomas Rom-ney Robinson (1792-1882), made a contribution to thesubject, which have been almost ignored by historians.Unsatisfied as he was, on one side with the imperfectstate of the rheometric knowledge and the unsteady ac-tion of the batteries implied in the experiments carriedout by Davy, and with the range of temperature coveredby the researches of both, Lenz and Becquerel, (littleabove of that of boiling water) on the other, Robinsonmeant to find a more general relation between conduc-tivity and temperature based on his strong belief abouta close relation between it and the molecular forces andthe structure of matter. The main difference in theequipment used was the inclusion of a pyrometer tomeasure the temperature by expansion of a wire of thematerial to be investigated [22]. Although he appar-ently identify the analytical expression


Table 2 - Becquerel’s coefficients of increment of resistance forseveral metals. Credit: Ref. [21].

R = R0 + bT,

(where R0 was the resistance at 0 ◦C, b its change forone degree) as the more appropriate to represent theresults of his experiments, Robinson also understoodthat it was required to introduce corrections due to theheating effect of the current on the rheostat and resis-tance coils by which they were measured. The formulato which he finally arrived, whose results showed closeagreement with the experimental values, would be

R = R0 + bT − cR2I2,

where I is the electric current. The coefficients a, b andc, specific again for each substance, could be determinedby minimum squares techniques or ordinary eliminationon the basis of experimental values of successive trials.The initial promising results showed for platinum wiresof different thickness quickly became strongly limited.The possibility to extend these experiments to othermetals was minimized because of the difficulty to findany determination of similar expansions to that got-ten for platinum, with the only exceptions of iron andcopper. The oxidation in the pyrometer of the firstof these metals did not permit, however, to get con-sistent results. Cooper also oxidized, but the film ofthe oxide acted as a coating and protected the interior,prevented changes in the diameter of the wire for tem-peratures below 480 ◦C. With results for only platinumand cooper, the research had not important diffusionamong the then scientific community.

4. Arndtsen, Siemens and the improve-ments of accuracy and coverage

The separate works on the subject by the Norwegianneurophysiologist, physicist, and professor at the Uni-versity of Christiania, Adam Frederik Oluf Arndtsen

(1829-1919) (Fig. 4) and the German Ernst WernerSiemens, complete this first chapter of the history. Re-garding the first, it was very probably that his early in-terests on phenomena related with nerve conductivityand transmission, and in general on the uses of elec-tricity in medicine in general, motivated him to carryout researches on the electrical resistance in metals atdifferent temperatures. Knowledgeable, as he was, ofthe Lenz’s work, the primary objective Arndtsen hadwith the experiments was to eliminate some sourcesof error he indentified in previous researches, in orderto improve the accuracy of the by then known results.These mistakes were mainly focused in the significantinfluence the contact between the wire and the warmliquid had, specially at high temperatures, on the con-ductivity measurements. With this purpose in mind,Arndtsen modified twice the arrangements used by hispredecessors by working first in his native land, andlater at Gottingen in the laboratory of one of his pro-fessors, the German physicist Wilhelm Eduard Weber(1804-1891).

Figure 4 - Adam Frederik Oluf Arndtsen. Credit: Courtesy ofJustervesenet (Norwegian Metrology Service).

In order to make the above mentioned corrections,the first arrangement included the covering of themetallic wire L with silk, its winding up around a testtube of a little diameter, and the soldering of the freeends of two thick and short cooper wires ab and bc(with lengths appropriately conditioned as it is exposedabove) completed with caps fully filled with mercury.The new disposition was then placed into other widerglass test tube provided with a thermometer and closedwith corks, and the whole device was immersed in a wa-ter or oil bath carefully kept at constant temperature.The whole assembly was coupled to a simple Wheat-stone’s differential galvanometer AA and the rheostatR as the basic elements of the circuit. The essential dif-


ferences of the second arrangement regarding the firstone were the introduction not only of a previously cali-brated copper wire ce placed on a board R and coupledto the motor B for carry out the rheostat function, butalso of a differential galvanometer A with multipliers aand b and the respective reel M in the assembly of thewhole equipment. This latter modification had as ob-jective to amplify in the scale F the effect of the current,further deflecting the needle m, improving so the accu-racy of sensitivity, and, as consequence, the accuracyof measurements [23]. Both arrangements are shown inthe Fig. 5.

To the only metals studied in the first series ofexperiments, cooper and platinum, Arndtsen subse-quently added silver, aluminum, brass, iron, lead, andthe alloy argentan, or German silver, composed this lat-ter by nickel, copper and zinc. The experiments showeda proportional resistance increasing with temperaturefor most of the metals under investigation, it meant sil-ver, copper, aluminium and lead, confirming so the pre-vious Becquerel’s findings. Regarding brass, argentanand iron, the changes in resistance with temperaturewere far from to be simply proportional and Arndtsendecided to use a parabolic equation of second order forrepresent the corresponding experimental data. Someof the formulas he found, valid in the range studied, 0to 200 ◦C, are shown in Table 3.

Arndtsen observed that, with the only exceptionof iron, the proportional increase in the resistance forthe six different metals investigated varied very little,and that if the resistance at the freezing point wascalled 100, the numbers representing the increase forone centigrade degree in the metals he investigated lied,again with the exception of iron, between 0.327 and0.413. This fact allowed him to speculate that if stillmore carefully investigations were carried out and ab-solutely pure metals were employed, perfectly accor-dant numbers could be obtained. This little differenceled the German physicist and mathematician RudolfJulius Emanuel Clausius (1822-1888) to suggest a verysimple and original new class of relation between bothvariables. After glance at the Arndtsen’s results, andwithout an apparent connection in his mind with any

theoretical consideration, Clausius observed that theyvery closely approached the coefficients of expansion[24]. By leaving of consideration the quadratic memberoccurring in iron and taking the mean of the whole ofthe first coefficients, he obtained the following expres-sion for the resistance at the temperature t as a functionof the resistance at the freezing point Rf

R = Rf (1 + 0.00366 t) .

From this equation he followed that, although thenumber of metals investigated was still too small andthe agreement of the numbers too imperfect to enablehim to arrive to a “safe” conclusion, the resistance ofsimple metals in the solid state was nearly in propor-tion to the absolute temperature. Almost a quarter ofa century later, this speculation was taken up againby the Polish physicist and chemist Zygmunt FlorentyWroblewski (1845-1888), who inferred from it the factthat the electric conductivity of metals would be nullat the temperature of zero absolute. This inferencecan be considered the first explicit, although uncon-scious, reference to the phenomena what would be latercalled superconductivity. Although Wroblewski carriedout researches on this subject working with copper, thetechnical limitations by then existing only allowed himto reach temperatures of about -200 ◦C, and he wastherefore unable to establish conclusive experimentalsupport about this fact [25]. It seems that no furtherinvestigations about this relation were later proposedand the speculation did not go further away.

Table 3 - Arndtsen’s equations for electric resistance of some met-als as a function of temperature. Credit: Ref. [23].

⌋

Figure 5 - Two assemblies used by Arndtsen. Credit: Ref. [23].


About 1860 the inventor and industrialist ErnstWerner Siemens (1816-1892) (Fig. 6) investigated thelaw of change of resistances in wires by heating andproposed several equations and methods for testing re-sistances and use them for determining faults. His in-terest on the subject was not casual, but arouse asa consequence of preceding researches, mainly relatedwith electrical communication, which had allowed himto developments such as the invention of the pointertelegraph, the magneto-electric dial instrument givingalternate currents, and the instrument for translat-ing on and automatically discharging submarine cables,among others. The subject of telegraphy was closelyassociated with the then system of electrical measure-ments and with the invention of many delicate measur-ing instruments. The requirement of other standardsof measurements in order not only to some quanti-ties could be gauged, but also consistent work couldbe done, led W. Siemens and other contemporary sci-entists to the identification of a general, easily repro-ducible, and sufficiently accurate standard measure ofresistance.

Figure 6 - Ernst Werner Siemens.

W. Siemens adopted in this search the resistanceof mercury as the unit, and embarked on its more ac-curate possible experimental determination at differenttemperatures. Among the enough criteria for its choicewere facts such as that it could be easily be procuredof sufficient, almost indeed of perfect purity, the non-existence of different molecular states that could affectits conducting power, a smaller dependence of its resis-tance with temperature regarding other metals, and avery considerable specific resistance that allowed thatnumerical comparisons founded on it as a standard weresmall and convenient. As every experimenter would

then be able to provide himself with a standard measureas accurate as his instruments permit or require and tocheck the changes of resistance of the more convenientmetal standard, W. Siemens understood the necessityfor establishing a comparison between the conductingpower of mercury and some solid metals. By using iden-tical experimental procedures with all materials underinvestigation, he was able to build a table including therelative conducting power of nine metals at the tem-perature t (Table 4) [26]. The results showed very ac-ceptable agreement with those presented by Arndtsenregarding common metals in both studies.

Table 4 - Siemens’s conducting powers of nine metals at a temper-ature t compared with that of mercury at 0 ◦C. Credit: Ref. [26].

5. The researches of Augustus Mat-thiessen

The maybe most widely known and integral researchesin the nineteenth century on the electric conductivi-ties of metals and their relation with different vari-ables, including temperature, were carried out by theBritish chemist and physicist Augustus Matthiessen(1831-1870) between 1857 and 1864. It was during thestudies at Heidelberg that his interest in electrical sub-jects arose. From 1853 he spent nearly four years underthe direction of German chemist Robert Wilhelm Eber-hard Bunsen (1811-1899), isolating for the first timethe metals calcium and strontium in the pure state bymeans of electrolytic methods. The studies of the elec-trical conductivities of these metals, and later of manyothers, carried out in the laboratories of the Germanphysicist Gustav Robert Kirchhoff (1824-1887), becamethe opening to researches in the area. Kirchhoff hadmade in 1849 what can be very probably considered thefirst absolute determination of resistance, and his skills


for not merely working out the solution of each newphysical problem he faced up to after it had been so for-mulated, but also for stating it in terms of mathematics,very probably influenced the character of Matthiessen’slater investigations on conductivities and other areas.

A first paper published by Kirchhoff in Matthies-sen’s name on the electric conductivity of the twoabove mentioned metals, besides potassium, sodium,lithium and magnesium, embodied the experimentalresults obtained by Matthiessen in the physical labo-ratory [27].The required wires were formed in a devicehe designed to press out small portions of metals intothin samples by means of a steel pressure, while thedetermination of the resistances was made by using aslightly modified apparatus constructed by Kirchhoff onthe basis of the Wheatstone’s method. Other publica-tions his, including experimental data of conductivitiesfor twenty-five metals, followed this paper [28].

Almost simultaneously Matthiessen also showed in-terest in alloys made of two metals because of the mul-tiple industrial applications he predicted for them [29],and proceeded to determine not only the electrical con-ductivities of upwards of 200 alloys of variable compo-sition [30], but also their tenacities and specific gravi-ties. He decided to classify the metals employed in thedifferent alloys in order to try to state some generalrules about the behavior of their conductivities com-pared to those in individual condition. The classifi-cation included two great groups: those which, whenalloyed with one another, conducted electricity in theratio of their relative volumes, and others which, whenalloyed with one of the metals belonging to the firstclass, or with one another, do not conduct electricity inthe ratio of their relative volumes, but always in a lowerdegree than the mean of their volumes. To the firstclass belonged lead, tin, zinc, and cadmium, whereas tothe second belonged bismuth, mercury, antimony, plat-inum, palladium, iron, aluminum, gold, copper, silver,and, as he thought, in all probability most of the othermetals. The alloys were consequently divided into threegroups: those made of the metals of the first class witheach other; those made of the metals of the first classwith those of the second class, and finally those madeof the metals of the second class with each other. Thecomparison between the obtained experimental valuesand those calculated by assuming a proportional par-ticipation of each metal in the whole value accordingto its relative volume in alloys showed very acceptableagreements. Other comparison, this time between themagnitudes of the electric conductivities of the alloysand those of their constituents, allowed him too to workin the opposite way, and get information about the realnature of the alloys and to state if some chemical com-bination would really exist there or not. On the sameway, and because of the preparation of cooper of thegreatest conductivity had great practical importance inconnection with telegraphy and his results showed sig-

nificant discrepancies regarding previous similar obser-vations by different researchers, Matthiessen embarkedas well in studies about the probable influence of minutequantities of other metals, metalloids and impurities onthe quantitative magnitude of this property [31].

Matthiessen’s first researches on the influence oftemperature on the electric conducting power of metalswere published in 1862. The paper describes the ap-paratus and the corresponding procedure in the minutedetail that characterized all his scientific work [32]. Fig-ure 7a shows the disposition of the whole apparatus. Bis the trough in which the wires (soldered to two thickcopper wires, bent as shown in the figure, and endingin the mercury-cups E, which were connected with theapparatus by two other which were connected with theapparatus by two other copper wires, F ′, of the samethickness) were heated by mean of an oil-bath; C a pieceof board placed in such a manner in order to preventthe heat of the trough from radiating on the apparatus;G a cylinder glass including the normal wire solderedto the wires F ′′; H a wire of German silver stretched onthe board, I the galvanometer, K the battery, L andL′ two commutators fitting into four mercury-cups ato, and M the block to make the observations. In addi-tion, a identifies the tubes for filling the space betweenthe inner and outer troughs with oil, and d a glass tubeallowing the thermometer c to pass freely. The way asthe wire to be studied was placed on a small glass trayin the trough is shown separately in the Fig. 7b.

Matthiessen determined the conducting power ofthe wires or bars of silver, copper, gold, zinc, tin, ar-senic, antimony, bismuth, mercury, and the metalloidtellurium at about 12◦, 25◦, 40◦, 55◦, 70◦, 85◦, and 100◦C, and from the mean of the eight observations madewith each wire (four at each temperature on heating,and four on cooling), deduced the same general formulapreviously proposed by Lenz for representing its depen-dence with temperature, but determining new sets ofcoefficients for each one on the basis of the new ac-curate experimental data. Table 5 shows the mean ofthe formula found for some metal, with the conductingpower of each one taken equal to 100 at 0 ◦C. Someconclusion he arrived, by which the conducting powerof all pure metals in a solid state would seem to varyin the same extent between 0 ◦C and 100 ◦C, it meant29.307%, did not received additional experimental sup-port and consequently did not extend in the time.

Two years later he published a new article on theeffect of temperature, this time on alloys [33]. The con-clusions of the study showed great similarity in the be-havior of the alloys regarding those of the metals whichcomposed them. By using a very similar apparatus hewas able to find that the conducting-power of alloys de-creased (with exception of some bismuth alloys and fewothers) with an increase of temperature and to deducespecific equations of dependence for fifty-three alloyscomposed by two metals and three alloys composed by


three metals. The Table 6 shows the results for some al-loys of definite chemical formula; Table 7, on the otherside, shows the variation of these formulas for alloys in-cluding the same metals but different composition. Allthe values were reduced to 0 ◦C, as mentioned for puremetals.

Figure 7 - Matthiessen’s apparatus. Credit: Ref. [32].

Table 5 - Matthiessen’s analytical expressions for the relative elec-trical conductivities of ten different metals. Credit: Ref. [32].

Table 6 - Matthiessens’s analytical expressions for the tempera-ture dependence of electric conductivities of some alloys of defi-nite chemical formula. Credit: Ref. [33].

A very significant conclusion Matthiessen derivedfrom the study was the deduction of the fact that theabsolute difference between the observed and calculatedresistances of an alloy at any temperature equaled theabsolute difference between the observed and calculatedresistances at 0 ◦C. On this basis it was followed thatthe formula for the correction for temperature for aspecific alloy could be then easily be determined withonly knowing its composition and its resistance at anytemperature.

Table 7 - Matthiessen’s analytical expressions for the variation ofthe temperature dependence of electric conductivities of somealloys including the same metals with composition. Credit:Ref. [33].

6. Extension and consolidation of ananalytical relation

The investigations of Arndtsen, W. Siemens, and

Matthiessen were limited to the range of temperatures

between the freezing and boiling-points of water, and do

not comprise important metals such as platinum, which

began to be considered as the most valuable metal for

constructing pyrometric instruments. The equation, in-

cluding the coefficients determined by Matthiessen for

example, gives a close agreement with observation be-

tween the narrow limits indicated, but resulted wholly

inapplicable for temperatures exceeding 200◦ Centi-

grade, when the term t2 began to predominate and

to produce absurd values for R. This had been clear

for German born engineer Carl Wilhelm (later Charles

William) Siemens (1823-1883) (Fig. 8), who in 1860,

in the course of the testing of the electrical condition

of the Malta to Alexandria telegraph cable, its manu-

facture and submersion, identified the potential danger

of the heat that could be spontaneous generated within

a large amount of cable, either when coiled up at the

works or on board ship, due to the influence of the

moist hemp and iron wire composed its armature. In

considering the ways by which such increase of temper-

ature might happen, his attention was directed to the

importance for studying the relation between electric

conductivity and temperature. This study additionally

led some time later to made use of this relation for the

design of a new thermometer. The instrument, which

really worked as an electric thermometer, was further

perfected by C.W. Siemens and applied as a pyrometer

to the measurement of furnace fires.


Figure 8 - Wilhelm (William) Siemens.

As a consequence of this design, C.W. Siemens un-dertook to carry out a series of detailed experimentsin order to find a more widely applicable equation [34].His work was initially focused on platinum, the metalhe considered in many aspects the most suitable one forextending the enquiries to high temperatures, and thatMatthiessen had been left out of consideration in his re-searches. C.W. Siemens carried out then three series ofexperiments using equal number of different assemblies.In the first one the wire was wound upon a cylinder ofpipeclay in helical grooves to prevent contact betweenthe convolutions of the wire. This wire was then placedtogether with a delicate mercury thermometer, first ina cooper vessel contained in a bath of linseed oil, andthen in a larger vessel, packing with sand between thetwo in order to the too sudden radiation and the conse-quent change of temperature. Wire was then connectedwith a Wheatstone’s bridge and a sensitive galvanome-ter. The bath was then very gradually heated by aseries of small burners, being the resistances read off atintervals of 4 to 5 ◦C whilst the oil was kept in contin-ual motion. When the highest point had been reached,the bath was allowed to gradually cool down measure-ments were taken at the same points of temperature asbefore. This methodology was repeated several timesuntil about six readings of the resistance at each pointof temperature had been obtained. The second assem-bly (Fig. 9) replaced the wire in the pipeclay by a spiralcontained in a glass tube and hung by its leading wiresin a rectangular air chamber. The space between thewalls was filled with sand in order to insure too a verysteady temperature inside. Three mercury thermome-ters with the bulbs around the platinum coil in the same

horizontal plane were inserted through the cover of thedouble chamber. Five small burners heated externallythe box, which, together with the flames, were alwayssurrounded by a metallic screen in order to prevent ir-regular looses of heat by radiation or by atmosphericcurrents. Measurements of the resistance were thentaken at the same regular intervals of temperature pre-viously mentioned. The third assembly made use ofthe same platinum wire, with the only difference thatchamber containing the tube and wire was filled withlinseed oil.

Figure 9 - C.W. Siemens’s apparatus. Credit: Ref. [34].

As no general conclusion could be drawn from thebearing of only one metal, C.W. Siemens decided tocarry out similar researches with coils of comparativelypure cooper, fused iron (or mild steel), iron, silver andaluminum, which were in a similar way gradually heatedand cooled in metallic chambers containing the bulbsof mercury thermometers, and for higher temperaturesof air thermometers, and the electrical resistances werecarefully determined. The progressive increase of elec-trical resistance was thus directly compared with theincreasing volume of an incondensable gas between thelimits of 0 and 470 ◦C. The experiments were describedby C.W. Siemens in 1871 in a Bakerian lecture deliveredat the Royal Society in which he presented the possi-bility of temperature measurement by measuring thecorresponding resistance variations of a metal conduc-tor. Although a committee designated two years laterdetermined the inconvenience for to use the platinumwire proposed as a sensor by C.W. Siemens for temper-ature measurement because of a thermal hysteresis itexhibited, the investigations led to the formulation of anew formula for the electric dependence of conductiv-ity. He was convinced that the new formula should bebased upon a rational dynamic principle and the appli-cation of the mechanical laws of work and velocity tothe vibratory motions of a body which represented, ac-cording him, ‘its free heat’. If this heat was consideredto be directly proportional to the square of the veloc-ity with which the atoms vibrate and it was assumedthat the resistance which a metallic body offered to thepassage of an electric impulse from atom to atom was


directly proportional to the velocity of the vibrationsrepresenting its heat, it followed that the resistance in-creased in the direct ratio of the square root of the freeheat communicated to it. In mathematical terms, theequation should to take an initial form,

Rt = αT 1/2,

where T symbolized temperature by first time in anabsolute scale, and α a specific and experimentallydetermined coefficient for each metal in particular.C.W. Siemens analyzed however that this exclusivelyparabolic expression would make no allowance for thepossible increase of resistance due to the increasing dis-tance between adjoining articles with increase of heatand the ultimate constant resistance of the material it-self at the absolute zero. He speculated that the firstof these contributions should depend upon the coeffi-cient of expansion βT and the second one only uponthe nature of the metal. Once these contributions wereconsidered, the expression took the form

Rt = αT 1/2 + βT + γ,

where β and γ symbolized usual specific coefficients foreach metal. Table 8 shows the individual equations foreach one of the metals under consideration.

Table 8 - C.W. Siemens’s analytical expressions for the electricresistances of several metals. Credit: Ref. [34].

Improvements in the range of coverage in both di-rections of the scale of temperature of the generalforms of the relation between conductivity and temper-ature would become the last significant contributionsto the subject in the nineteenth century. The first ofthem is due to the work of the French physicist andlater Director of the Bureau International des Poids etMesures (BIPM) Justin-Mirande Rene Benoıt (1844-1922) (Fig. 10), who, with an early training in medicine,turned very quickly to studies in physics, and conductedin 1873 a series of experiments on the temperature de-pendence of electrical resistance in metals as a require-ment to receive his Doctoral es Sciences Physiques [35].By employing the differential galvanometer for measur-ing resistances, Benoit was able to determine betweenfive and eight measurements of electric resistances ofnineteen metals at equal number of different tempera-tures, covering a range that varied between the melt-ing point of ice and the boiling point of cadmium, it

meant 0 and 860 ◦C. The experimental results werenumerically treated in order to find the optimum coef-ficients for each metal by the method of least squares onthe basis of the above mentioned form of the equationoriginally proposed by Lenz. Table 9 lists the analyti-cal equations derived for all the metals included in thestudy. In the graphical results shown in the Fig. 11 forsome metals the resistance of each at 0 ◦C is supposedequal to 1, and each ordinate indicates the experimentalincrease at the corresponding temperature [36].

Figure 10 - J.-Rene Benoıt.

Table 9 - Benoit’s analytical expressions for the electric resis-tances of nineteen metals. Credit: Ref. [35].


Figure 11 - Graphical behavior of resistance according theBenoit’s results. Credit: Ref. [35].

Other extensions, this time on low temperatures,were later reported on the same line of investigationthat in the second decade of the twentieth centurywould led Kamerlingh Onnes to his important discov-ery, it means in the whole framework of the researcheson liquefaction of gases, and by using the excessive coldso produced for the determination of several proper-ties of matter. The French physicist Louis-Paul Cail-letet (1832-1913), one of the two responsible for thefirst liquefaction of oxygen, reported in 1885 the resultsof experimental measurements carried out jointly withhis colleague Edmond Bouty (1846-1922) on conduc-tivities of mercury, silver, magnesium, tin, copper, ironand platinum in the new range between 0 and -123 ◦C[37]. If it is important to remark that their experimentsproved again the regular decreasing in the electrical re-sistance with the drop in temperature for most of themetals, that the coefficient of variation was appreciablythe same for all, and that the results acceptably agreedthe general form of the analytical formulas previouslyproposed, the most relevant facts for the present historyare the speculations they venture to do on the basis ofthese results. In a short sentence concluding the paperthe authors considered that although their experimentsdo not enable them to form any precise idea of whatwould take place in those conditions as “very proba-bly that the resistance would become extremely smalland therefore the conductivity very great at temper-atures below -200 ◦C”, and what could be consideredone of the first, if not the first one, although unwittingpredictions about the existence of the phenomena of su-perconductivity, that “if the same law (that proposedaccording the Matthiessen and Benoit’s results) heldat low temperatures, the resistance of a metal, varyinglike the pressure of a perfect gas under constant vol-ume would furnish a measure of the absolute tempera-ture, and would cease to exist at absolute zero”. Thishypothesis complemented the previously mentioned byClausius, but on a slightly more supported basis.

About a decade later researches carried out by theBritish physicist James Dewar (later Sir) (1842-1923)

and John Ambrose Fleming (1849-1945) strengthenedthe information about the electrical behaviors of met-als at still lowest temperatures, thanks to the increasingavailability of each time more complete appliances forthe production of large quantities of the liquid gasesnecessary as refrigerant agents. With great experi-ence on the subject thanks to previous researchers thathad allowed him to liquefy hydrogen by first time, De-war embarked with his colleague in specific investiga-tions on the measurement of electrical conductivitiesof eight metals (nickel, tin, iron, platinum, aluminium,gold, silver and copper), seven alloys (platinoid, germansilver, platinum-iridium, platinum-silver, palladium-silver, platinum-rhodium and phosphor-bronze), andcarbon at the temperatures produced by the evapora-tion of liquid oxygen when boiling under normal or un-der reduced pressures, it means of about -200 ◦C [38].The initial research was complemented one year laterby adding other metals (palladium, zinc, lead, magne-sium, cadmium and thallium) and alloys (gold-silver,aluminium-silver, aluminium-copper, manganese-steel,nickel-steel, copper-manganese, titanium-aluminium,silverine and copper-nickel-aluminium) in the wholestudy [37]. Figure 12 shows some of the preliminary re-sults. The experimental results showed that the order ofthe conductivity of the metals at very low temperatureswas different from the order at ordinary temperatures,but what was more important, after extrapolate theirdata they dared to speculate that “the electric specificresistance of all pure metals will probably vanish at theabsolute zero of temperature” [39].

Figure 12 - Dewar’s electrical conductivities of some metals atlow temperatures. Credit: Ref. [38].


7. Concluding remarks

Several factors influenced the scientific studies on thetemperature dependence of the electric conductivity ofmetals in the nineteenth century. The curiosity arisenfor the still new science of electricity that character-ized many subjects related with this discipline was veryquickly complemented by interactions with other sci-ences, as for example medicine, and the usefulness thatthe results provided for the technological developmentsin emerging communication systems, the design of in-struments for measure temperature, and the establish-ment of a standard unit of resistance. But while thesemotivations were diverse, the experimental methodol-ogy used along the full century was not so different.The introduction of the differential galvanometer byBecquerel and Wheatstone bridge in the first half ofthe century for the measuring of resistances became themaybe only significant modifications in the methodol-ogy followed by the different scientists involved in thesubject, and the fact that the various results only cor-respond each other in an approximate way was not dueto the diversity of apparatuses employed but circum-stances such as the purity of the materials used, the pro-cedure by which the corresponding wire was built andthe accuracy of the measurements, among others. Thegeneral dependence equation between resistance andtemperature established by Lenz about the first thirdof the century was basically retained and the exten-sion in the number of metals included in the study, theaccuracy and the coverage of temperatures would be-come the main modifications and the facts that helpedto consolidate the relation.

The fact that the different involved researchersmostly worked with the same metals was not a merelycoincidental matter. Criteria for the selection of thematerials to be studied included, besides the obviousavailability, conditions of the highest possible purity,relative good conducting power, and scientific and in-dustrial usefulness in electrical and non-electrical areas.The weighted consideration of all these criteria pro-vided good reasons for the joint study of their respec-tive physical, thermal and electrical behaviors. Threemetals, copper, aluminium, and platinum, become goodexamples. Because their high electrical conductivitiesand the ease with which copper could be drawn intorod and flexible and easily soldered wire this metal be-came in great demand. It was known, however, thatthis electrical conductivity varied with the presence ofeven small various impurities, and very few of its com-mercial grades reached the required standard of purity.The fire-refined copper was too poor an electrical con-ductor, but this did not matter for most of the usualnon-electrical applications, such as the manufacture ofdomestic pots and pans, sheathing of ships’s bottomsand fireboxes for locomotives; for electrical applica-tions, however, it mattered very much. The appearing

of a patent for the electrolytic refining of cooper in 1865in order to replace the old fire-refining methods notonly allowed precious metals to be recovered efficientlyand economically, but provided a means of producingthe desirable very pure copper. The introduction ofthe dynamo in the second half of the nineteenth cen-tury favored impetus in the production of both, copperand lead, being the electrical industry the greatest forthese two metals, and in to a lesser extent practicallyall other non-ferrous metals. Aluminium is other caseto mention. Nor Lenz nor Becquerel included it in thelist of the metals to be studied, and the determina-tion of its power conduction only aroused the interestof the scientific community in the second half of thecentury. The finding of a possibility by which it couldbecome a challenger to copper in the field of electricalconductivity and for a number of other uses previouslytraditional the latter metal propelled increased interestin the evaluation of its properties and a later phenom-enal rise in its production. Platinum, for mentioningthe third example, was not only important in the nine-teenth century because the property that would led itto be used in the resistance thermometer and subse-quently to bridge the gap between scales and to estab-lish as a new one in the each time greatest range oftemperatures. Other properties such as its expansionwith heat as glass did, which allowed wires to be sealedinto glass tubes or vessels to carry an electric current,its high resistance to caustic substances even at hightemperatures and its inertness to react with most of el-ements and compounds, made of it a valuable materialin the chemical and physical laboratories from beforethe coming of the stainless steel.

Kamerlingh Onnes discovered the phenomenon ofsuperconductivity on April 8, 1911. In no one of thedifferent related publications that preceded the discov-ery, nor in his Nobel Lecture in 1913 he referred to theresearches by Lenz, Arndtsen, Matthiessen, Benoit, theSiemens’s brothers, or to whatever those by the othernames mentioned along this article. The only referenceshe occasionally did to Cailletet and Dewar were relatedwith the apparatus or procedures that these scientistsfollowed along their experiments on liquefaction. Al-though there is not historical evidence about the factthat Kamerlingh Onnes had information or not aboutthe researches who preceded him in the study of elec-trical properties at low temperatures, and no one of theexperiments carried out by the Dutch physicist seemedto have require of the utilization of analytical relationsfor the calculation of electrical conductivities or resis-tances, it is evident that the full knowledge he had onthe temperature dependence of electrical conductivitiesof metals in the full range must to be based to a greatextent in the lecture of the respective publications.

The developments of the relation between electri-cal conductivity and temperature for metals, as manyothers of the discoveries in electricity in the nineteenth


century, favored significant improvements in other spe-cific areas besides the later well-known discovery ofsuperconductivity, as it was, for example, thermom-etry. The invention of resistance thermometers deci-sively made the establishment of reliable standards ofelectrical units much easier and allowed accurate mea-surements of especially by then high temperatures. Al-though not so quickly, the phenomena of superconduc-tivity also found commercial use. In the same way that,for example, the electromagnet invented by the Britishphysicist William Sturgeon (1783-1850) and later devel-oped by American physicist Joseph Henry (1797-1878),quickly found application in the developing heavy in-dustries, that the recognition by the Estonian-Germanexperimental physicist Thomas Seebeck (1770-1831) ofthe fact that the flow of an electrical current could beregulated by heat marked not only the beginning of thestudy of thermoelectricity but also played an importantrole in the design of superconductors in the late twenti-eth century, or that the independent discoveries of theconversion of temperature differences directly into elec-tricity, the presence of heat at an electrified junctionof two different metals, and the heating or cooling ofa current-carrying conductor with a temperature gra-dient by the French physicist Jean Charles AthanasePeltier (1785-1845), Seebeck, and the mathematicalphysicist and engineer William Thomson, 1st BaronKelvin (1824-1907), respectively, brought about thephenomena of thermoelectric effect and found wide uti-lization in power generation and refrigeration, amongothers, the progressive understanding of the propertiesof superconducting materials had allowed their prac-tical application in areas such as power transmission,superconducting magnets in generators, energy storagedevices, particle accelerators, levitated vehicle trans-portation, rotating machinery, and magnetic separa-tors. If the whole research program on liquefaction ofgases from middle of the nineteenth century suppliedthe thermal frame that favored the discovery of super-conductivity, the amazing amount of available experi-mental data of the temperature dependence of the elec-trical conductivities for metals, the continuously im-proved methodologies for the respective studies, and theanalysis of the observed tendencies were the responsibleof the not so much accidental discovery of this phenom-ena.

Acknowledgments

I thank Mr. Thomas Framnes, Advisor of communica-tion matters for Justervesenet (Norwegian MetrologyService), for supply the photograph of Adam FrederikOluf Arndtsen.

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