VARIATION OF ELECTRICAL RESISTANCE IN THE MAGNETIC FIELD BY WILLIAM HOWARD SANDERS A.B. University of Illinois, 1920 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS IN PHYSICS IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS, 1922 URBANA, ILLINOIS Digitized by the Internet Archive in 2015 https://archive.org/details/variationofelectOOsand UNIVERSITY OF ILLINOIS THE GRADUATE SCHOOL Ju ne — 1 92-. 1 HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY_ ..WILLIAM -HO-WAI RS ENTITLED J I _ILECxR T CAL ^FSJTTA "I."..: L,jL^ir;Ti c f r eld Uj ■ BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE DEGREE OF &AHIZR HT A £ Recommendation concurred in* Committee on Final Examination* •Required for doctor’s degree but not for master’s 4S8980 CONTENTS I Origin and Scope 1 II Historical Review of Experimental Study 2 III Theoretical Treatments 11 IV Suggestive Experiments, Their Bearing on the Theory 16 V Experimental Work Here 19 VI Discussion 25 Bibliography 27 Table 1 Observations on the Resistance Change of #40 B & S Copper Wire in a Transverse Magnetic Field 29 Table 2 Summary of Measurements of the Resistance Change of #40 B & S Copper Wire in the Magnetic Field 30 Figure la, lb Variation of Electrical Resistance of #40 B & S Copper Wire in the Magnetic Field 31 ■ ORIGIN AND SCOPE During the course of an investigation by Professor A. P. Carman on the resistance of a metallic conductor in the field of a rotating magnet, question arose as to the value of the resistance change caused by the stationary magnetic field alone. A short search through the literature on this subject showed that this phe- nomenon, although quite well known, has been studied quantitatively in the case of only a few elements, particularly iron, nickel, and bismuth. For the nonmagnetic metals such as gold, silver, copper, and platinum the results of comparatively few measurements are avail- able. The present work deals with the development of a method for the determination of resistance change in both transverse and longi- tudinal magnetic fields and with measurements made on copper. The experimental arrangements were adapted particularly for the study of such metals in wire form subjected to magnetic! fields of 2 to 16 kilogausses. The measurements were in all cases made at room tem- perature, about 21°C. ' .. ' . . - 1 - 2 II HISTORICAL REVIEW OF EXPERIMENTAL STUDY The possibility of a change in electrical resistance result- ing from the action of a magnetic field was perhaps first suggested by the experiment of Maggi (1) who believed that he had established a change in the thermal conductivity of an iron disk in a magnetic field. In the year 1824 both Abraham (2) and Fischer (3) reported experiments on the electrical conductivity of magnetized iron. Their results were conflicting and were furthermore of little weight since they used friction or influence machines as a source of cur- rent and had no accurate method for resistance measurement. Edlund (4), in 1854, was probably the first to employ a method sufficiently sensitive to obtain definite results. He applied a longitudinal magnetic field to iron wire and made his resistance determinations with a Wheatstone net work. He detected no change, perhaps because the field which he applied was not sufficiently strong. The existance and magnitude of the effect were finally estab- lished beyond doubt in 185G by Professor William Thomson (5), later Lord Kelvin. He worked with nickel and iron, applying both longi- tudinal and transverse magnetic fields. The most significant advance to be noted in his experimental arrangement is the care in securing close temperature control. Both the iron and the standard resistance were surrounded by liquid baths. The magni- tude of the change in resistance was found to be about l/3,000 of the normal resistance. Also, the conductivity was greater along than across the lines of magnetization. No estimate is given of . 3 the strength of the magnetic field applied. The next experiments reported are those of Beetz (6) in 1866. His results were of little quantitative value but the work offers a suggestion which has been followed by later investigators. Beetz used iron wire in a longitudinal field and measured both the change in length and the change in resistance. Working about ten years later, Adams (7) also studied iron. He placed bars of the metal inside a solenoid, thus securing longi- tudinal magnetization and found that the resistance change was pro- portional to the square of the magnetizing current, or that the AR ratio Tg was approximately constant. For large values of i, how- ever, the ratio tended to decrease in value. Auerbach (8) in per- forming similar experiments measured the temperature of the speci- men by means of a thermocouple to determine the necessary tempera- ture correction and also measured the magnetic moment of the iron for the various fields applied. He found that the change in resis- tance was proportional to the moment of magnetization rather than , AR to the field, thus explaining the drop in value of Adams’ ratio “ for large values of i, for saturation values of the field. Goldhammer (9) reported in 1887 and 1889 study of quite an ex- tensive series of metals, including bismuth, nickel, tellurium, antimony, cobalt, and iron. He deposited the metals electro lyti- cally on glass, using only a thin film. One of the chief objects of this arrangement v/as the avoidance of internal stress in the metal as a result of magnetization. Both longitudinal and trans- verse fields were employed. Goldhammer' s results were similar to those of Adams and Auerbach; R = A K 2 R c , as he put it, A being a constant characteristic of the metal and K its magnetizing factor. & ' 4 In the study of later progress it is probably best to take advantage of the classification used by Koenigsberger , who has written the section on metallic conduction in Graetz’ Handbuch der Elektricit&t und des Magnetismus. The matter is therefore divided into three groups, accordingly as it pertains to material which is (1) ferromagnetic, (2) strongly diamagnetic or weakly ferro- magnetic, (3) paramagnetic or weakly diamagnetic. In the first v group are nickel, iron, and cobalt; in the second are bismuth, an- timony, tellurium, and graphite; in the third gold, silver, copper, cadmium, platinum, and palladium. In the case of ferromagnetic materials the difference between the effect of a transverse and that of a longitudinal field is most marked. Iron and nickel are the elements which have received the greatest amount of attention. There is some discrepancy betv/een results obtained by different experimenters here, particularly for the action in a transverse field. The discrepancy seems to be due as much to difference in the nature of specimens observed as to experimental error. The results of most investigators indicate that a longitudinal field causes an increase in resistance and that this increase in resistance approaches a limiting value for high fields. In the transverse field the resistance first rises to a maximum and then decreases to a value less than that for zero field. Among the most important experiments on iron in a transverse magnetic field are those of Grunmach and Weidert (10), d* Ago s tiro (11), Alpheus W. Smith (12), and Heaps (13). Grunmach and Weidert used samples of pure iron wire and of piano w r ire . In every case except one they found an initial increase in resistance which reached a maximum in a field of the order of 2 kilogausses. A sub- J ~ 5 sequent decrease in the higher fields reduced the resistance below its initial value. D’Agostino used both wire and bands of iron. In the specimens which he had the initial increase in resistance did not appear, the change being from the beginning a decrease. This was also the behavior of one sample observed by Grunmach and Weidert. Smith and Heaps have both found about the same action that Grunmach and Weidert reported, an initial increase and a sub- sequent decrease to a value even below that in zero field. Work on nickel in a transverse field has been carried on by Williams (14), Knott (15), and by Blake (16) in addition to those mentioned above in connection with measurements on iron. Nickel also shows the initial increase and following decrease. The data of Blake, which are the most accurate yet obtained, show that in the temperature range from -190°C to 186°C the decrease is much greater than the temporary increase. In a longitudinal field the resistance of nickel and of iron increases, rising rapidly to a maximum. There is no subsequent . drop as in the case of the transverse field. In the few cases where a decrease was reported, it has been shown that this was the result of inaccurate alignment of the specimen so that there was a transverse component of magnetization to which the decrease was due. Among the best experiments here are those of Williams (14), Blake (IS), Knott (15), Heaps (13), and Alpheus W. Smith (12). Cobalt although also a member of this group has been subjected to comparatively little study. One of the chief difficulties here lies in the obtaining of a sample of a high degree of purity. The effect of a slight impurity on the electrical conductivity of a metal is well known. On such an electromagnetic phenomenon as this - • . r . - • • ‘ • * . . r It ' ! . 6 the effect of impurities is even more disturbing. Grunmach and Weidert (10) found that cobalt also showed the behavior character- istic of ferromagnetic elements, the decrease in the transverse magnetic field. Their results indicated a possibility of a slight initial rise but did not confirm it. In the longitudinal field the resistance of cobalt increases similarly to that of iron and nickel. In the group of strongly diamagnetic and weakly ferromagnetic materials bismuth occupies by far the most prominent place. In fact, this element has received more attention than any other in this group or the other groups. Bismuth is unique in the magni- tude of its change in resistance in the magnetic field. The effect is an increase in both the longitudinal and the transverse fields. The variation of the change with temperature is also unusually great. The work of Lennard (18) who used spirals, measuring the resistance change for both direct and alternating currents, is par- ticularly important. His experiments showed that the resistance change as measured by alternating current is different from that measured by direct current. This difference is a function of the magnetic field, reversing sign at about 6 kilogausses. Among the best quantitative work on bismuth is that of Henderson (IS) and Blake (16). Both used fields well above 30 kilogausses and made their measurements over a considerable temperature range. Antimony', tellurium and graphite have also received consider- able attention. All exhibit an increase in resistance for both the transverse and the longitudinal field. One of the chief facts that renders the results on these first two metals interesting is the disparity between the ratio of the resistance change in them to that in bismuth and the corresponding relation for the Hall effect. f " : ‘ - » 0 £Mtj a , 7 since the change in resistance is sometimes viewed as a manifesta- tion of the Hall effect. Work on graphite has been suggested partly by its negative temperature coefficient of resistance and partly by the possibility of investigating the effect of crystal structure. In this connection the work of de Haas (20) on antimony and that of Roberts (21) on graphite is important. i The paramagnetic and weakly diamagnetic materials, nearly all of them good conductors, show a much smaller change in resistance in the magnetic field than do the elements of either of the other groups. In every result that has been confirmed, the change is an increase, usually slightly greater in the transverse than in the longitudinal field. The generalization of Goldhammer that the dia- magnetic elements show a greater resistance alteration than do the paramagnetic elements holds fairly well. For any one metal, vari- ations are dependent upon the magnetic susceptibility of the sample used. D'Agostino (11) was the first to make fairly accurate mea- surements on a large number of substances . His work included cadmi- um, zinc, gold, palladium, mercury, silver, copper,. and platinum as well as invar, manganin, and german silver. For platinum and the three alloys he reported a decrease. This has not been confirmed. In gold, silver, and copper, the change was too slight to be deter- mined by his method. Later- work by Grunmach and Weidert (10) and by Heaps (13) indicates that these three metals as well as platinum all increase slightly in resistance. Heaps’ measurements are valu- able particularly in the comparison offered of the transverse and the longitudinal effects. The work of d'Agostino and of Grunmach and Weidert was confined to changes in the transverse field. Kam- merlingh Onnes and Hof (22), and Beckman (23) have carried out a . - - - - - 8 large number of measurements with such metals at the very low tem- peratures of from 2°K to 25°K. In regard to liquids the results are not yet beyond question. Measurements on mercury and molten bismuth have been made by Drude and Nernst (24) and later by Berndt (25). The first investigators found a slight increase in resistance of the order of 0.2 % for both bismuth and mercury. However, the effect in bismuth was much smaller than that for the same sample when solid and that in mercury varied greatly with the current through the bridge. It was suggest- ed that this change in resistance was not of the same nature as that found in solid conductors but might be the result of electrodynamic action on the fluid conductor. Des Coudres (26) has suggested that the magnetic field may cause turbulent motion in the fluid if it is contained in a tube having bends, as was the case here. The result- ing energy consumption would be manifested as an increase in resis- tance. The pinch effect noted by Hering (27) would result in an increase in resistance, but it is doubtful whether it would be of sufficient magnitude to be effective at such lew current densities as are used in measurement. Berndt (25), in connection with mea- surements on a number of electrolytes, observed also mercury and molten bismuth, the latter however being 75 0 above the temperature at which Drude and Herns t (24) worked. He too employed capillary tubes but of much smaller diameter than those used by Drude and Nernst. The object in reducing the diameter was to prevent as far as possible turbulent motion of the fluid. In a transverse field of 3 kilogausses the resistance of mercury remained constant to less than l/2, COO %, so Berndt reported. In a longitudinal field of 1 kilogauss he gives l/20,000 % as the upper limit of any change. - ’ 9 None was actually detected In either case. To bismuth only the transverse field of 3 kilogausses was applied. The upper limit giv- en for any possible change in resistance here is l/660 %. Berndt’s work appears to have been very carefully done and in the absence of better data his conclusion that liquid metallic conductors show no resistance change, within the limits indicated, must be accepted. It should be added that his measurements on electrolytes, including solutions of iron, nickel, bismuth, and copper compounds all indi- cated that any resistance change occurring must be less than l/250 %> Transverse fields of 3 kilogausses and longitudinal fields of 1 kilogauss were applied. In the work w T ith electrolytes alternating current was used. The resistance change of copper in a field of 10 kilogausses is about 0.003$, so that if that of electrolytes varied as much as is the case with copper, Berndt would not have detected it . In general, the three groups of metals are quite distinct. The ferromagnetic group is characterized by the decrease in resistance in moderate and high transverse fields and by the limitation of re- sistance increase in the longitudinal field. Except for bismuth, the strongly diamagnetic and weakly ferromagnetic materials exhibit a smaller change in resistance and do not show the great decrease in resistance in strong transverse fields. The paramagnetic and weakly diamagnetic elements show the least change in resistance. The difference in longitudinal and transverse effects is less in these metals too. For the ferromagnetic elements the longitudinal resistance effect is proportional to the square of the magnetiza- tion. For the second group, the square relation is not so satisfac- tory. The metals of the last group exhibit a change in both trans- - * * . ■ 10 verse and longitudinal fields which, for the smaller field values, is fairly well represented as AR p T = A H • For large values of H the correspondence between this equation and experimental results is not so good. In fact, the variation there seems to be more nearly as the first power of H. 11 III THEORETICAL TREATMENTS Present theories of metallic conduction hardly explain in a convincing manner the variation of resistance with temperature and pressure over the range covered by experimental data. A satisfac- tory theoretical explanation of the resistance changes here dis- cussed is therefore hardly to be expected. Most theories now supported place the burden of conduction on the electron. Corbino (28) and his co-workers in Italy have re- tained the older idea of two types of ions, one bearing a positive charge and the other a negative. Mathematically their theory is much like those more widely accepted. With the two carriers, how- ever, they have the advantage of a larger number of equations and arbitrary constants so that the theoretical deductions may be made to conform to more diverse experimental results. For instance, the reversal of sign of the Hall effect in some metals may be explained. Aside from the initial postulate of both positive and negative car- riers, the assumptions made in developing this theory are practical- ly the same as those for the more widely held electron theories, and on the whole, experimental evidence seems to point more clearly to the single negative carrier. The pioneer attempt to give an explanation of the increase in resistance in a magnetic field was that of Sir J. J. Thomson (29) in 1900. He assumed that in the normal state electrons were moving freely about at random w r ithin the metal, as do the molecules of a gas in a container. When an electric force was applied, there was set up a drift which constituted the current. The resistance is . ■ 12 supposed to be the result of collisions between the electrons and the molecules of the metal. In the magnetic field the path of a moving electron is altered and as a result of this the resistance changes. In order to get the right sign for the change it is ne- cessary to assume that the collisions between electrons and atoms are greatly influenced by the charges borne by the electrons. The expression given is where T is the mean free period of an electron. Such an explanation is evidently inadequate; no indication is given of a variation of the resistance change in ferromagnetic materials from that in para- magnetic materials or of the difference between solid and liquid conductors . Lorentz assumed that the collisions between electrons and atoms were like those between hard, elastic spheres, as in the ki- netic theory of gases, and was able to work out the explanation of some thermoelectric phenomena. E. P. Adams (30) has extended this line of thought by applying it to J. J. Thomson's consideration of resistance change. Another modification made by Adams is that he assumes not only the change in path of the moving electron but also a change in the molecular configuration of the metal which be- comes an additional factor operating to change the resistance. His expression for the resistance change in a transverse field is then The sign of the effect -will evidently depend on the relative magni- ' fl*. k tude of the change in free time resulting from alteration in molec- ular arrangement. Using Grunmach and Weidert’s data (10), Adams In this case, however, AT is more complex. The alteration in molec- ular configuration is effective as in the transverse field. Besides this, the spiral path of a moving electron about the lines of mag- netization also influences T. According to Adams’ development the difference between the transverse and the longitudinal effect in an isotropic medium should be given by the equation Noting that in the paramagnetic and in many diamagnetic ele- ments the difference between the transverse and longitudinal effects is very small, C. W. Heaps (13) has presented still another modifi- cation of the theory to make it accord with this fact. In so doing he has employed and extended somewhat the equations given by Town- send (31) for the drift of electrons under the action of mutually perpendicular electric and magnetic fields. Assuming the current to flow along one axis of the coordinate system, say, the x axis, a magnetic field parallel to the z axis will result in the building up of an electric field parallel to the y axis. This potential difference along the y axis is then the Hall effect; Townsend had ignored it in his consideration of the problem, being interested chiefly in the current flow itself. Heaps included in his consid- eration the potential thus built up along the y axis and its effect calculated T to be about 3*10“^ second and about 2.5*10”' J For the longitudinal field his analysis gives AR _ AT R T ■ . - « ■ 14 on the motion parallel to the x axis. With this change, the devel- opment indicates that the electron flow is not affected by the mag- netic field; that is, the action of the magnetic field on the mov- ing electrons does not result in a change of resistance. The ex- pression for the current with or with out the field is then where n is the number of electrons per unit volume. Changes in re- sistance must therefore be the result of variations in E x , T, or n caused by the field applied. Experiments by Roberts (21) on crystalline graphite, de Haas (20) on antimony, and Heaps (13) on bismuth, graphite, and cadmium indicate that the relative directions of the magnetic field and the current have little or no effect on the resistance change. The effect of the field is therefore probably confined to changes in T and in n. The general expression given for the resistance change in the magnetic field then becomes AR _ n 0 T 0 _ R nT 1 where n 0 and T 0 are the values for zero magnetic field. Both n and T are supposed to be functions of unknown form of H. The various theories advanced offer none too good an oppor- tunity for experimental test. The results of Thomson (29) and Adams (30) as well as those of Gans (32) and Livens (33) all indicate that ~ should be proportional to the factor (Jj) ^ T 2 H 2 or to the e 2 i 2 factor (“) (^) H 2 , substituting l/v for T, where 1 is the mean AR free path and v the mean velocity. From this, — should be propor- ■ . 15 tional to the square of the field. This might have been antici- pated at once from the symmetry of the action, since reversal of current or field has no effect. Another possibility of experimental test appears in the same factor. The mean free path, 1, is proportional inversely to the A>H absolute temperature, 0. As a result, — should be proportional to ft e-» Experimental results show with a fair approximation a variation in resistance according to the law Y - A H 2 . The variation of resistance change with temperature does not follow the theoretical prediction. ' - ■ . 16 IV SUGGESTIVE EXPERIMENTS, THEIR BEARING ON THE THEORY It is thought worth while to mention briefly a few experiments which are of particular value for the suggestions they offer with respect to further investigation or for their bearing on the theo- retical explanations of the resistance effect. The suggestion that resistance change for paramagnetic materi- als is proportional to the square of the field strength or that f was tested carefully by Heaps (13) in observations on gold, zinc, cadmium, bismuth, tellurium, and lead sulfide in both transverse and longitudinal fields. It has been stated above that the equation holds quite well for low values of H, for high values the change is less than the equation would indicate. Opportunity to test the relation AR _3 T* B « is given by the data of Blake on bismuth and nickel at temperatures ranging from -190°C to 186°C and by the large amount of data taken at helium temperatures by Onnes and Hof (22) and by Beckman (23). The agreement with experimental results is not good over a large or over a small temperature range. The effect of crystal structure and of the orientation of the crystal in the magnetic field was studied in considerable detail by van Everdingen (34) before 1900. This line of work has been con- * S X ' - 17 tinued also by other Dutch investigators, among whom de Haas (20) has been mentioned. The resistance of bismuth crystals is normally different in two different directions and may be represented by an ellipsoid of revolution. In the magnetic field three unequal axes are necessary to show the resistance characteristics. Instead of the simple relation — = A R these expe rimenters have found that the effect for, say, crystalline bismuth, should be given as a function of the components of the field parallel to the various crystal axes. The equation is there- fore written AR R n ll ( aH ) 2+ n l2 ( bH ) 2 + n l3 ( °H) where a, b, and c are direction cosines and n-^, n-^g, and n-^ char- acteristic constants. This form has been used by van Everdingen and more recently by Borelius and Lindh (35). The experiments of de Haas (20) on antimony, Roberts (21) on graphite, and Heaps (13) on bismuth, graphite, and cadmium all reenforce the conclusion that the crystal structure of the conductor plays a very important part in resistance changes. In connection with the work on the effect of crystal structure it is perhaps well to recall the work done on liquid conductors. To the limit of accuracy of the experiment, and this was quite good, it indicated that in all these substances lacking crystalline charac- teristics the magnetic field produced no change in resistance. A very interesting set of data is that presented recently by Alpheus W. Smith (12). He measured the change of thermoelectric 18 force in the magnetic field for a wire subjected to tension of vari- ous magnitudes. Data taken by other investigators for similar ob- servations with respect to changes in resistance and changes in length are also given. The similarity of the variation of all three is striking. Heaps (13) had previously made simultaneous mea- surements of resistance and length changes for iron and nickel and pointed out the direct relation between the two effects. The work of B. C. Knott (15) on nickel subjected to the com- bined action of transverse and longitudinal fields, one of which varies periodically has been very carefully done. The immediate value of his results seems to be diminished rather than increased by the complexity of the action. i 19 V EXPERIMENTAL WORK HERE The object of the experimental investigation was, in brief, the determination of both the longitudinal and the transverse re- sistance changes in the magnetic field exhibited by metals such as copper; gold, and silver. The first problem, therefore, was the choice of a method for the accurate measurement of small resistance increments. The method employed was essentially that of the bolom- eter. A balanced Wheatstone bridge is used and the resistance changes may be measured either by the resulting galvanometer deflec- tions or by changes made in one arm of the bridge to maintain the balance. The deflection method is much more rapid than the other and is sufficiently accurate. In order to employ this method the relation between galvanometer deflections and the resistance changes which cause them must be known. This information was ob- tained by observing the change in deflection when a one ohm resis- tance in series with the sample and in the same arm of the bridge was shunted by a resistance of 1000 ohms, thus giving AR ="0 .001 ohm, very nearly. The maximum sensitiveness of the bolometer is secured when the four arms are equal and each is twice the resistance of the galva- nometer. As the result of limitation of space available for the specimen under investigation this condition was not fulfilled. The four arms were approximately equal and each was a little less than the galvanometer resistance. The material on which the observations were made was #40 B & S ■ 20 copper* wire, double silk covered. It had been purchased some years before for the construction of fine galvanometers and therefore is believed to be quite pure. This wire was wound around thin strips of mica about 6.2 mm wide and 7.6 cm long so as to be in the form of a rectangular spiral with one side 6.2 mm long and the other approximately 0.2 mm. Of the 7.6 cm length only about 1.8 cm was occupied by this winding, since the field available was circular in shape and only 2.5 cm in diameter. Five such units fastened firmly together formed a compact re- sistance of about 20 ohms. The connections were of course soldered here and at all other points possible. The extra length of the mica strips was quite convenient in handling the windings. In order to secure accurate alignment in the magnetic field this group of resistances was fastened on the shaft of a T-shaped piece of sheet brass. The plane of the mica strips was parallel to that of the shaft. Consequently, the longer dimension of the wire was parallel to the cross bar of the T and no difficulty was experienced in the adjustment either for longitudinal or transverse fields. Chiefly for the sake of thermal insulation, the resistance unit so prepared was placed in a box 8 mm square and about 5 cm high made of very thin sheet copper. The upper part of the shaft and the cross bar of the T of course projected outside. The extra space within the box was filled with paraffin poured in wliile hot and allowed to cool so that the wire was held firmly in place. Leads of #30 Ad- vance having a negligible temperature coefficient were brought out. In an early series of measurements made on copper wound on a hard rubber spool and placed directly between the circular pole- pieces for determination of the transverse effect, it was found that . . _ ' ■ . . ■ 21 the temperature variation of the sample was fairly regular. By taking deflection readings at intervals of, say, 20 seconds, with the magnetic field alternately on and off the increase in resistance due to temperature rise could be determined and correction made accordingly. Plotting deflection as ordinate and time as abscissa, two approximately parallel curves appeared, one for the resistance in the magnetic field and the other for the resistance in zero field. The slope of each curve is determined by the rate of change of tem- perature. The mean distance between the two curves, measured par- allel to the axis of ordinates, gives a measure of the resistance change caused by the magnetic field alone. Actually it is not necessary to plot the curves. The mean difference between succes- sive deflections gives the value desired. This is the method used by Grunmach and Weidert (1C) in their work on the transverse effect. Proceeding in this manner, a fairly consistent set of data on copper was obtained. The wire had been wound in bifilar fashion on the spool but there was still quite an inductive kick so that for strong fields the time between readings was increased to 30 seconds to allow the galvanometer coil to return to its normal position. When the copper specimen was replaced by one of platinum, wound similarly on a hard rubber spool, the difference between measurements made with a time interval of 30 seconds and those with an interval of 15 seconds be- came very great, amounting to as much as 50^. An extended series of observations showed that this discrepancy was the result of the irregular rate of temperature change of the sample . With the mag- net energized periodically the heat supply was of course periodic and it was as a result of this that the large difference between JAJ - 22 measurements for different time intervals appeared. In order to correct this, arrangements were made for a constant flow of kerosene through the space between the resistance and the pole pieces, the resistance now being wound on mica and enclosed in a copper box as described. With this arrangement the heat from the magnet was taken up by the liquid and carried away. Preliminary trials showed that fluctuations in the temperature of the oil might easily cause as much trouble as the irregular rate of change it was desired to avoid. As a partial correction for this, the oil was passed through a spiral of small brass tubing immersed in a large tub of water at room temperature . Slow changes in the temperature of the sample could hardly be prevented but they were made quite regular. Difficulty with this gradual change was greatly reduced by the use of a second resistance of copper in an arm of the bridge adjacent to the sample. This second copper resistance also was placed in the bath of flowring oil. The other two arms of the bridge then were made up of two Otto Wolff resistance boxes with a slide wire between them for convenience in balancing. In preparing for a series of observations great care was taken that the many disturbing influences affecting the resistance of the coil might come to an equilibrium before measurements were begun. To this end the oil flow was started at least 30 minutes before the first reading. The bridge current too was allowed to pass for some time before beginning the run and continuously during its course. The magnet was energized at the regular time intervals for several periods before any measurements were made. The galvanometer circuit was closed continuously so that no difficulty with thermal electro- motive forces in it was experienced. During the time the current , • ■ ' 23 through the magnet was changing, about 5 seconds, the galvanometer leads were short circuited by a copper-contact key to prevent large deflections resulting from the current induced. With the preliminaries finished, the procedure was quite simple, consisting only of deflection readings from the galvanom- eter at 20 second intervals, with the field on and off for alternate periods of 20 seconds beginning and ending immediately after a read- ing. The sensitiveness was determined before and after such a run by a series of observations of the change in deflection resulting from a change of 0.001 ohm in the X branch. In Table 1 there are given two typical sets of observations, the first for the determination of sensitiveness and the s econd for measurement of the change in a field of about 11 kilogausses. The first column, D, gives the scale reading; the second, AD, is the difference between one reading and that preceding it; and the third, Aq, is the difference of AD from its mean. Using the sum of the values of A? the probable error in the mean value of AD is calcu- lated (36). Variations in the value of AD are the result mainly of small rather rapid changes in temperature of the specimen. These appear to be wholly irregular and so their effect can be eliminated by making a number of observations and taking the mean. For values of -AD greater than the variation this is satisfactory. A summary of the data taken on the #40 copper is given in AR Table 2. The last column in each case gives the value of — - (= A) RH^ which should be approximately constant if the equation AR p — = A H 2 is to represent the variation of resistance. The agreement for the - 24 case of the transverse field is considerably better than that for the longitudinal field. In both cases there seems to be a definite change in the value of A as the field increases. Study of other specimens will be required, however, before it can be stated whether this is actually the case and to determine the character of the variation if it actually exists. The mean values for the constants are A x = 2.40-KT 7 A t = 2.86-10” 7 . These values are for the field strength in kilogausses. Using the _ i 3 o gauss as the unit the factor is 1C instead of 10 . A slight correction might be applied to these values because of the fact that the wire was in the form of a rectangle and the mea- surements were made with the longer side parallel or perpendicular to the lines of force. However, the ratio of the longer to the shorter side was 52:1 and as the difference bet?feen the two con- stants is small, the correction is less than the experimental error. _ 25 VI DISCUSSION In continuing the experimental investigation measurements should he made on other samples of copper, as well as on gold, sil- ver, platinum, tungsten, and other metals. If the results of such further measurements establish a change in the value of A in the equation AR R = A H‘ as H increases, it may be well to divide the measurements into two groups, the first covering the lower range of values of H up to 10 or 12 kilogausses and the second range for values of H up to about 50 kilogausses. This arrangement of the work would permit of great- er accuracy at both extremes and would lessen the difficulties met in securing the necessary temperature control. It has been suggested that the crystal structure influences greatly the resistance change. A sample in the form of wire, as a result of the drawing process, would not be expected to be strictly isotropic. Some indication of the effect of the structure might be gathered from observations on films formed by electrodeposition and films formed by sputtering in a vacuum. The latter would be par- ticularly interesting since it has been fairly well established that when such a film is first formed, there is no crystalline structure. Perhaps even more important would be a repetition of Berndt's experiments on mercury, using fields of 10 kilogausses or more . - . 26 The study of bismuth or the ferromagnetic elements is equally important but is better treated as a separate field of investigation. This discussion would be incomplete without full acknowledge- ment of the interest and aid of Professor A. P. Carman who has directed the work. 27 BIBLIOGRAPHY (1) Maggi, Archiv des Sci. Phys . et Nat. v. 14, p . 132 (2) Abraham, Archiv f. d. gesammte Naturlehre (Kastner) III, 426 (3) Fischer, " " " " " III, 421 (4) Edlund, Ann. d. Phys. u. Chemie 169, 315, 1854 (5) W. Thomson, Phil. Trans. 146, 649, 1856 (6) Beetz, Pogg. Ann. 128, 193, 1866 (7) Adams, Proc . Roy. Soc . 23, 533, 1874-5 Phil. Mag. (5) 1, 153, 1876 (8) Auerbach, Wied. Ann. 5, 289, 1878 (9) Goldhammer, Wied. Ann. 31, 360, 1887 Wied. Ann. 36, 807, 1889 (10) Grunmach and Weidert , Ann. Phys. 22, 141, 1907 (11) d'Agostino, Rend. Accad. Lincei 8, 531, 1908 (12) Alpheus W. Smith, Phys . Rev. 19, 285, 1922 (13) Heaps, Phil. Mag. 22, 900, 1911 Phil. Mag. 24, 813, 1912 Phys. Rev. 6, 34, 1915 " " 10, 366, 1917 " " 19, 7, 1922 (14) Williams, Phil. Mag. 4, 430, 1902 Phil. Mag. 6, 683, 1903 " " 9, 77, 1905 (15) Knott, Edin. Phil. Soc. Proe . 33, 200, 1913 Edin. Phil. Soc. Trans. 61, 39, 1904 (16) Blake, Ann. Phys. 28, 449, 1909 (17) Hurion, C. R. 100, 348, 1885 (18) Lermard, Wied. Ann. 39, 619, 1890 (19) Henderson, Phil. Mag. 38, 488, 1894 (20) de Haas, Konink. Akad . Wetensch, Amsterdam 16, 1110, 1914 (21) Roberts, Ann. d. Phys. 40, 467, 1913 (22) K. Onnes and Hof, Comm. Leiden Nr. 142, 1914 Akad. Wet. Amsterdam, February 1914 Versl. Akad. Wet. Amsterdam 23, 493, 1914 (Onnes and Beckman) Comm. Leiden Nr. 129 a, c; 130 a, c; 132 a, b, c, d; 1912 (23) Beckman, Comm. Leiden. Lab. Suppl. 40, Juni 1915 (24) Drude and Nernst, Wied. Ann. 42, 568, 1891 (25) Berndt, Ann. Phys. 23, 932, 1907; Journ. Phys. 7, 221, 1908 (26) Des Coudres, Berl . Phys. Gs . Vh. 10, 50, 1891 (27) Hering, (Northrup) Phys. Rev. 24, 476, 1907 (28) Corbino, Nuovo Cimento (6) 16, 185, 1918 (Trabacchi) Nuovo Cimento (6) 12, 177, 1916 (Trabacchi) Atti. Accad. Lincei 18, 137, 1919 (Freda) Nuovo Cimento (6) 12, 177, 1916 (29) J. J. Thomson, Rapp, Congr. intern. Physique 3, 138, 1900 (30) E. P. Adams, Phys. Rev. 24, 428, 1907 (31) Townsend, Electricity in Gases (Oxford, 1915) p. 100 (32) Gans, Ann. Phys. 20, 293, 1906. (33) Livens, Phil. Mag. 30, 256, 1915 (34) van Everdingen, Archives Neerlandaises 4, 371, 1901 Archives Neerlandaises 5, 453, 1901 " " 6, 294, 1901 28 (35) Borelius and Lindh, Ann. Phys . 53, 97, 1917 (36) Goodwin, Precision of Measurements and Graphical Methods (McGraw-Hill, 1913) p. 19 General reviews giving also a bibliography of portions of the literature are: Zahn, Jahrb. f. Rad. 5, 166, 1908 J. Clay, Jahrb. f. Rad. 12, 273, 1915 The sections on this topic in the handbooks of Wiedemann, Winckelman, and Graetz Baedeker, Elektrische Erscheinungen in Metallischen Leitern (Vieweg, 1911). * ■ Table 1 OBSERVATIONS ON THE RESISTANCE CHANGE OF #40 B & S COPPER WIRE IN A TRANSVERSE MAGNETIC FIELD Sensitivity R =-0.001 ohm Time interval, 20 seconds D, mm 39.8 AD ^2 8.8 31.0 0.5 40.0 31.2 0.7 4.1 30.9 0.4 40.0 30.9 0.4 8.6 31.4 0.9 38.5 29.9 0.6 8.1 30.9 0.1 40.4 31.7 1.2 10.8 29.6 0.9 40.0 29.2 1.3 7.7 32.3 1.8 39.0 31.3 0.8 10.6 28.4 2.1 41.0 30.4 0.1 Mean value of AD — 30.5 mm. The probable error in AD is 0.20 mm, or 0.1%. Magnet Energized for Alternate Readings i = 5.30 amp. H = 11.1 kilogausses D, mm 10.3 AD ^2 29.8 19.5 2.2 7.2 22.6 0.9 26.2 21.9 0.2 4.1 22.1 0.4 26.0 21.9 0.2 4.0 22.0 0.3 24.7 20.7 1.0 2.0 22.7 1.0 24.3 22.3 0.6 2.1 22.1 0.4 24.1 22.0 0.3 4.0 20.1 1.6 25.9 21.9 0.2 4.1 21.8 0.1 26.0 21.9 0.2 2.3 23.7 2.0 Mean value of AO — 21.7 mm. The probable error in AD is 0.21 mm or 1^. , ■ ' . . 50 Table 2 SUMMARY OF MEASUREMENTS OF THE RESISTANCE CHANGE OF #40 B & S COPPER WIRE IN THE MAGNETIC FIELD In a Longitudinal Magnetic Field H AD AR AR AR kilogausses mm. ohms • 10“ R 10 -5 RH 2 4.64 3.9 1.22 6.1 2.84 7.04 8.1 2.53 12.7 2.56 9.82 13.8 4.31 21.6 2.24 12.8 23.2 7.25 36.3 2.22 16.4 The mean 38.4 value 12.0 ° r *i * 60.0 is 2.40-10" 7 2.32 In a Transverse Magnetic Field H AD AR -4 AR kilogausses mm. ohms • 10 R 10 “S RH 2 5.5 5.5 1.76 8.8 2.89 8.4 13.0 4.28 21.4 3.06 11.1 21.7 7.14 35.7 2.90 12.9 29.0 9.26 46.3 2.79 15.0 37.3 11.9 59.5 2.65 The mean value of A + ( = *”^c) is t RH 2 ' 2.86-10 “ 7 ♦ , . I FIGURE VARiAIlOk -TANC& FIELD umvhtiXLM& aknkrfkVI I II ill B11VJ 4 - i ?: 4 -