The change in the elasticity of a copper wire with current and external heating

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations 1914 The change in the elasticity of a copper wire with current and external heating Homer Levi Dodge State University of Iowa This work has been identified with a Creative Commons Public Domain Mark 1.0. Material in the public domain. No restrictions on use. This dissertation is available at Iowa Research Online: Recommended Citation Dodge, Homer Levi. "The change in the elasticity of a copper wire with current and external heating." PhD (Doctor of Philosophy) thesis, State University of Iowa, Follow this and additional works at:

2 Thesis presented to the FACULTY OF THE GRADUATE COLLEGE of the STATE UNIVERSITY OF IOWA in partial fulfillment of the requirements for the Degree of Doctor of Philosophy July, 1914 Part I The Change in the Elasticity of a Copper Wire with Current and External Heating. Part II The Change in the Elasticity of an Iron Wire with Current and External Heating.

3 TH E CHANGE IN T H E ELA STICITY OF A C O PPER W IR E W ITH C U R REN T AND EX TER N A L HEA TIN G. B y H. L. D o d g e. [Reprinted from the P h y s i c a l R e v i e w, N.S., Vol. II., No. 6, December, 1913.]

4 (Reprinted from the Physical Review, N.S., Vol. II., No. 6, December, ] T H E CHANGE IN T H E ELA STICITY OF A CO PPER W IR E W IT H CU R REN T AND E X T E R N A L H EATING. B y H. L. D o d g e. ' I ^HE present investigation consists of determinations of Young s modulus of a specimen of copper wire at various tem peratures between 20 C. and 150 C. with the object of ascertaining whether or not heating by an electric current has any effect other than th at caused by the accompanying increase of tem perature, and also to learn certain facts regarding the tem perature effect itself, concerning which there seems to be considerable doubt. P r e v i o u s R e s u l t s u p o n t h e E f f e c t o f C u r r e n t H e a t i n g. Wertheim1 reported a decrease in Young s modulus caused by current and believed this decrease to be independent of any tem perature effect, a conclusion not sufficiently justified as he assumed the heating effect of the current negligible. Edlund2 made allowance for the tem perature effect, and concluded th at current, except for the accompanying tem perature change, does not affect Young s modulus. Streintz3 made observations of the torsion modulus at room tem perature and at C. The following figures represent the percentage change of elasticity caused by the current, correction being made for the tem perature effect: Brass (a) : Q>), ; copper, 0.0; silver, + 3.9; iron, + 3.1; steel, Mebius4 found the effect due to current in the case of steel, iron, brass, and silver rods to be extremely small. Miss Noyes5 studied steel, silver, and copper wires and found th at the current heating caused a uniform decrease in Young s modulus which could be entirely accounted for as a temperature effect. W alker6 employed the same experimental methods as Miss Noyes, but found very irregular changes with steel, soft iron, platinum, and copper, which could not be accounted for by temperature and which differed greatly with increasing and decreasing 1 Ann. de Chim. et de Phys., 12, 610, Annal. d. Phys., 129, 15, 1866; 131, 337, Annal. d. Phys., 150, 368, Oefvers. af k. Vet. Akad. Forhandl., 681, 1887; B e ib l. 12, 678. P h y s. R e v., 2, 279, 1895; 3, 433, Proc. R oy. Soc. Edin., 27, 343, 1907.

5 432 H. L. DODGE. [ S eco n d LSe r ie s. current. A survey of previous work leaves a serious doubt as to the effect of current heating, and this doubt a critical study serves to increase. P r e v i o u s R e s u l t s u p o n t h e C h a n g e o f Y o u n g s M o d u l u s w i t h T e m p e r a t u r e. The investigations th at have been carried on to determine the change of Young s modulus with tem perature are so extensive th at the results with copper only can be considered. These are however representative of the results for other metals. Shakespeare1 has found a decrease of Young s modulus for copper of 3.6 per cent, on heating from 130 C. to ioo C. Miss Noyes2 made observations at various temperatures up to 150 C. and reports a uniform decrease of the modulus of 0.13 per cent, and 0.07 per cent, per degree for two samples of wire. Gray, Blyth, and Dunlop3 also were able to make observations at intermediate temperatures up to ioo C. They also report a uniform decrease, which for two samples was per cent, and 0.04 per cent, per degree respectively. On the other hand Slotte s4 observations at intervals over a range of io C. to 70 C. upon two samples of copper wire showed a decrease of Young s modulus with increase of tem perature which was not uniform but became less rapid with one sample and more rapid with the other as the temperature increased. An increasing rate of change is also indicated by the results of W ertheim6 a t 150 C., 100 C., and at 200 C., the change being much greater for the upper interval. In this connection the work of Pisati,6 Kohlrausch and Loomis,7 and of Slotte8 upon the torsion modulus is of interest. They found the rate of decrease of the modulus greater as the tem perature was raised. This is suggestive as it is highly probable th at the general nature of the elastic changes is similar for the two moduli. These results leave no doubt th at increase of temperature causes a decrease of Young s modulus, but there is no conclusive evidence as to the exact nature of the decrease. S c o p e ' o f W o r k. In view of the facts which have been cited it was decided to attem pt an investigation of the effect of current upon Young s modulus, accompanied by a parallel investigation of the tem perature change produced by an 1 Phil. M ag., 47, Loc. cit. 2 Proc. R oy. Soc., 67, 180, A cta Soc. Scien. Fennicse, Vol. 26, * Loc. cit. 4 N u ovo Cimento, 4, 152, 1878; 5, 34, 135, Annal. d. Phys., 141, 481, A cta Soc. Scien. Fennicse, Vol. 35, 1908.

6 V ol. I I.1 N o. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 433 external source of heat. Examination of the previous work led me to believe th at the desideratum was not a hastily made series of observations upon a number of metals but rather thorough and extended observations upon a single metal. Consequently this report is confined to results with copper although work is under way with other metals. A review of the literature made clear th at the causes of inaccurate results in the past have been chiefly a lack of mechanical perfection in the apparatus and insufficient attention to the distribution of tem perature. In none of the work upon the effect of current has there been any knowledge of the differences in tem perature along the wire or any effective attem pt made to secure a uniform distribution. The apparent crudity of the apparatus th at is here described is the result of an attem pt to keep every part of the apparatus as simple as possible and to refrain from unwarranted refinements. Each source of error has been considered in relation to the others and the effectiveness' of the apparatus is best judged from the consistency of the results th at have been obtained. D e s c r i p t i o n o f t h e A p p a r a t u s. In order to prevent convection currents and consequent non-uniformity of heating necessarily accompanying vertical suspension the wire was mounted horizontally. The mechanical features of the apparatus (Fig. i) may be considered independently of the heating box. The wire is Fig. 1. T he apparatus, showing m ethod of suspending the test specimen. suspended between a bar (b) and a pulley (p) which are in turn supported by a heavy cast iron base, bolted to the carriage of the dividing engine. The wire is stretched by the weights Wi and W 2. Current is led in at the points (d) through the mercury cups (c), the wire being insulated at (a) and at (b). Three copper-constantan thermo-couples (t) of No. 36 wire are for tem perature measurements. The weight W\ is kept upon the wire continually and is heavy enough to stretch the wire almost straight. The weight W2 is added gradually and w ithout jar by a simple

7 4 3 4 H. L. DODGE. ECOND S e r i e s. apparatus operated by a foot lever. The elongation of the wire is measured with two micrometer microscopes attached to the bed of the dividing engine. These are focused upon bright scratches on the wire, made visible by incandescent lamps. The heating apparatus (Fig. 2), although supported by the cast-iron base, is mechanically entirely independent of the wire. It m ust not only furnish a means of heating the wire externally but also must retain the heat when the current is passed through the wire itself. The base (0), bottom piece (5), and back (z>) are covered with asbestos and fastened together. The asbestos-covered front (h), which has two windows of mica (m) for observing the wire, and the glass cover (n) are held together by clamps easily removed. The glass tubes (k) are large enough to give sufficient clearance to the wire (w) but small enough to prevent convection or other air currents. Zigzagging back and forth across the bottom piece (s) is a heating wire of German silver through which a current can be Fig. 2. H eating box surrounding the test specimen. sent. This heating box proved to be one of the three im portant features of the apparatus and its simple form in no way indicates the difficulty of securing a reasonably even tem perature distribution. This fact is very suggestive in connection with the results of former investigations in which average tem perature only was known, there being no information concerning the tem perature distribution. The use of thermocouples which could be slipped to different portions of the wire revealed surprising inequalities of temperature. Even after uniformity of heating had been secured with the external source it was necessary to still further alter the box before a satisfactory distribution could be obtained with internal or current heating. A t the highest temperature employed the maximum variation of tem perature over the portion of the wire under observation was less than 150 C. A second feature of importance is the free suspension of the wire. The possibility of error due to contact of the wire with rigid portions of the apparatus is eliminated by permitting it to touch nothing except the thermo-couples which are of fine flexible wire. Consequently the specimen hangs freely in the form of a flat catenary. The elongation

8 Vol. II.l N o. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 435 caused by the straightening of the catenary on the application of the additional stretching weight is negligible, being about i / ioo of the smallest reading of the micrometer microscope. The third feature is also mechanical. It is the pulley which changes the direction of the applied force, which m ust be transm itted without gain or loss resulting from friction or change of leverage. Fig. 3 shows its construction and suggests the method of centering the axis. The pulley was tested at different posi- Fig. 3. Side view of pulley and section along A -B. tions at various times during the progress of the work and found to introduce no appreciable error. M e t h o d o f D e t e r m i n i n g T e m p e r a t u r e o f S p e c i m e n. When the wire is heated by the external source it is of uniform tem perature throughout its cross section and of the same tem perature as the surrounding air. Under these conditions the thermo-couples which have already been mentioned are a perfectly satisfactory means of measuring its temperature. In the case of internal or current heating there is an increase of tem perature toward the center, resulting in a number of effects, change of resistance, thermal conductivity, etc., each of which has its influence upon the current distribution and in turn upon the temperature distribution. The average tem perature of the wire is of course a function of the surface tem perature and of the current, but for evident reasons the thermo-couples do not give the surface tem perature of the wire when the wire itself is the source of heat. Measurement of tem perature by change of length caused by thermal expansion has proved to be the most accurate and convenient method. Blondlot1 has shown conclusively for several pieces of brass and one of German silver th at current has no direct effect upon the dimensions of 1 Journal de Phys., [i], 8, 122, 1879.

9 436 H. L. DODGE. [Se c o n d LSe r i e s. a metal carrying a current. This has also been shown by Righi1 for four wires whose composition is not given. There is no reason to believe that copper should be peculiar in showing this effect. In fact our own experience and the persistency with which our results for Young s modulus at any tem perature as determined by this method remain the same, no m atter w hat may be the source of heat, is in itself proof that current has no direct effect upon the length of the wire. In using change of length as an indication of tem perature account must be taken of the change caused indirectly by the effect of temperature upon Young s modulus. Thermo-couple readings and length observations were taken for all work with external heating. W ith internal heating length observations were made and the tem perature determined by comparison with the other results. The thermo-couples were connected to a sensitive Siemens and Halske galvanometer by a three-way switch and were calibrated by direct comparison with an accurate thermometer. W ith current heating the central portions of the wire tend to lengthen more than the outer portions which are at a lower tem perature and it is assumed th at the actual lengthening so averages this effect as to be an indication of the average temperature. It is also worthy of notice that the contribution to Young s modulus will be different for the different portions, the value observed being an average of the moduli of the various circular layers making up the cross section of the wire. There is of course a similar averaging of temperature and modulus along the length of the wire. N a t u r e o f t h e T e s t s. Three sections of commercial copper wire were tested, all from the same piece obtained from the Driver-Harris Wire Co., Harrison, N. J. The purity of the specimen was determined electrolytically, with results of per cent, and per cent. As the second was the more accurate we may take ±.01 as the purity of the specimen. There was no trace of either silver, lead, or iron. The coefficient of linear expansion was Specimen No. 2 was 0.81 mm. in diameter. The portion under observation was 50.7 cm. long. The other samples were of similar dimensions. A weight of 2,109 grams was kept upon the wires continually. The modulus was determined by measuring the elongation produced by an additional weight of 2,252 grams. The elongation was observed with a microscope, the micrometer head of which can be read to 1/50 revolution, corresponding to mm. stretch. A t room tem perature the stretch amounted to about.02 mm. N u o v o Cimento, [3], 7, 116, 1880.

10 V ol N o CHANGE IN THE ELASTICITY OF A COPPER WIRE. 437 Currents as high as 15 amperes were used. The accuracy of the work is. of a high degree. The error in the determination of Young s modulus is about 1 per cent. A greater accuracy may prove desirable if small peculiar effects appear with other metals, but the present apparatus is sufficiently accurate to determine the general nature of the changes in the modulus. Each determination of Young s modulus as represented by a point on the curves or a value in the tables is the result of ten or more separate measurements taken so as to eliminate any error caused by a slight drift in temperature. Generally a half hour or more was required for the temperature to reach a sufficiently steady state. After the preliminary work the greater part of the observations consisted of series of determinations with increasing or decreasing tem perature over a range of 20 C. to 150 C. P r e l i m i n a r y T e s t s. The possible ways in which current may affect elasticity are so numerous th at a determination of Young s modulus at a given tem perature is of no value unless interpreted in connection with the whole thermal history of the wire. Since the essential part of this investigation is the comparison of observations taken under as nearly similar thermal conditions as possible, except for the difference in time and in the source of heat, an elimination as far as possible of any other than pure temperature effects is desirable. If this is impossible a thorough understanding of the nature of the other effects is essential. In order to eliminate the well-known permanent changes accompanying extreme temperatures the treatm ent of the wire after its first heating and stretching was confined to a tem perature range of 20 C. to 150 C. In order to find out how consistent was its behavior within this range and under the various conditions of treatm ent a great deal of preliminary work was necessary. This showed th at there are no sudden changes in the elastic state of the wire, th at the rapidity of heating and cooling had little if any effect upon the changes in elasticity, and th at the length of time the wire was held at a given temperature had no great effect. As explained later, permanent or history effects were found, but for any series of readings these changes were insignificant, the value of Young s modulus returning at the close of any day s observations to practically its original value. T hat history effects could be eliminated and the elasticity of the wire made independent of treatm ent and a function of tem perature only is illustrated in Fig. 4, Series 5. Observation 15 is almost identical with 8, and 16 and 17 are nearly the same as the first observations, although the wire had meantime been heated and cooled twice.

11 438 H. L. DODGE. [Se c o n d LSe r i e s. In order to learn whether or not at any given temperature the value of Young s modulus is dependent upon the manner of heating, the observations of Table I. were made. The shifting from one method of heating to another was done without permitting much alteration in the temperature of the wire. T a b l e I. Showing Constancy of Young's Modulus under Different Conditions of Heating, Temperature Remaining the Same. M ethod of H eating. V ariation in Length, Mm. Variation in Stretch, Mm amperes, alternating cu rren t amperes, direct current External, direct current External, alternating current amperes, direct cu rren t The greatest variation in length is.0065 mm. or 0.14 revolution of the micrometer head. This corresponds to a temperature variation of less than one degree Centigrade. The greatest variation in stretch is.0014 mm. This corresponds to only 0.03 revolution and is about the experimental error. These results show clearly th at at this temperature, which was approximately n o C., the stretch modulus is independent of the source of heat. These preliminary investigations and others which need not be described showed the behavior of copper to be very consistent and are the justification for the taking of more extended series of observations and the comparison of results secured at different times. T e s t s u p o n S p e c i m e n N o. 2. After specimen No. 2 was placed in the apparatus it was heated to a high tem perature and stretched to remove the kinks. Afterward it was never heated above 150 C. The four series of readings composing Fig. 4 were taken after the wire had been heated by both methods a total of about 50 hours and after about 500 applications of the stretching weight. If such a thing were possible as a state in which all changes in elasticity, except those caused by temperature could be eliminated, this treatm ent should have secured the result. As far as possible the figures have been made self-explanatory. Certain additional information which is characteristic of all the work is given in Tables II. and III. Series 4 shows a series of observations in which the heating was entirely external. In this as well as in the other three series of Fig. 4 dotted points represent observations taken while the

12 Vol. II.l N o. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 439 Fig. 4. Results of tests upon specimen N o. 2, showing effect of internal and external heating. T a b l e II. Data for Series 5, Wire 2, External Heating. Obs. No. Time. Tem p. Stretch (Revs, of Micr. Screw ). Y oung s M odulus X io-u D ynes per Cm2. 1 9:00 A.M. 18 C : : : : : :00 P.M : : : : : : : : : :

13 44 0 H. L. DODGE. [Se c o n d LSe r i e s. T a b l e III. Data for Series 7, Wire 2, Internal Heating. Obs. No. Time. Temp. Current, Amperes. Stretch (Revs, of Micr. Screw). Young s M odulus X io-11 Dynes per Cm :30 P.M. 21 C :15 A.M : :05 P.M : : : : : : :30 27 OJO : : : : : tem perature was being raised by steps and the crossed points those when the tem perature was being lowered. Particular attention is called to points 2 and 3, the second of which was taken after the temperature had been maintained for twelve hours. They show th at the length of time the wire was kept at the high tem perature had no effect upon its elasticity. The proximity of points 8 and 1 shows the elimination of history effects and permanent changes. Two days later Series 5 was secured, which yields results identical with those of Series 4, showing th at the work of one day can be repeated at a later time. Further proof of the absence of history effects is afforded by the positions of points 14, 15, 16, 17, and 18 relative to observations taken a t earlier times at the same temperatures. The fact th at points 5, 6, and 7 taken with increasing temperature fall on the same curve as points 9, 10, and 12 taken with decreasing temperature shows the absence of any hysteresis effects. Series 6 was taken three days later, followed the next day by Series 7. The procedure was the same as before except for the difference in the manner of heating. In Series 4 and 5 the wire was heated externally by means of the heating wire on the bottom of the box enclosing it. In Series 6 and 7 the wire was heated by an electric current in the wire itself. The results of Series 6 and 7 show the absence of hysteresis effects and the elimination of history effects the same as with external heating. The fact th at the variation of the curves forming Fig. 4 is less than would

14 Vol. II.1 N o. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 441 be expected from the experimental error shows th at one is justified in taking these results as an indication of tem perature effect alone and is justified in comparing the results of different days with different methods of heating. T e s t s u p o n S p e c i m e n N o..3. A third sample of the same wire was next placed in the apparatus in order to confirm the results obtained with the former specimen, to attem pt still other variations in the therm al treatm ent and to secures the complete elastic history of a specimen. The results are given in Figs. 5, 6, and 7. Upon these curves appear every observation th at was made with the third specimen, not one having been discarded. Fig. 5. Complete elastic history of specimen No. 3. The curves are those of Figs. 6 and 7, the Roman numerals corresponding to the series numbers. First Changes in Elasticity. The specimen was made as free from kinks as possible and placed in the apparatus. Observation i, Fig. 5, was at room temperature. The wire was then heated externally to about 1250 C. and cooled. Observation 2 shows no change. Heating by 17 amperes current to about the same tem perature brought a slight increase in the modulus as indicated by observation 3. There was very little increase in length during this treatm ent, as the additional weight was not applied at high temperatures.

15 442 H. L. DODGE. [Se c o n d LSe r i e s. It was anticipated th at continued application of the additional weight while the wire was hot would remove any kinks in the wire, cause an increase in length and a change in the modulus. The wire was heated by 17 amperes current and the weight applied a number of times. On Fig. 6. Results of tests upon specimen No. 3 with different thermal treatment, showing history effect, change of Young s modulus with temperature, and absence of any effect peculiar to current heating.

16 V ol. II.1 N o. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 443 cooling an increase of length of about 0.2 mm. was found and an increase of Young s modulus as indicated by observation 4. The wire was again heated to 1250 C. and Young s modulus measured at this temperature, resulting in observation 5. The tem perature was then increased to about 150 C. and the additional weight applied about thirty times, resulting in observation 6. Cooling to 1220 C. gave observation 7, and to 28 C., observation 8. It was believed th a t a sufficiently steady state had been secured to justify the trial of a series of readings and a comparison of points 6, 7, and 8 with reference to later observations shows this to have been the case. It is highly probable th at the increase in Young s modulus due to this particular treatm ent was caused as much by the mechanical stretching and straightening of the wire as by the thermal treatm ent, although the latter was undoubtedly essential to the securing of the steady state. Discussion of Fig. 6.- Following the work just described came eight days of testing under a variety of conditions. Fig. 6 shows the results and has been made practically self explanatory. The order in which the observations at the different tem peratures were taken and the manner of heating were varied in a number of ways in order to catch any possible changes caused by treatm ent. Series 1 is with external heating, increasing temperature. Series 2, first part, was taken in exactly the same manner and the results show th at for external heating a sufficiently steady state had been reached so th at only small permanent changes were to be anticipated. The second part of Series 2 was taken in exactly the same manner except for the change in the manner of heating, the external heating having been changed to internal by means of the current. No difference is observed. The following day a series was taken in a similar way except that the observations were made with decreasing temperature. The nature of the tem perature change remains the same and a slight permanent increase appears. In Series 4 the systematic heating and cooling over the whole tem perature range was not followed, but no peculiar effects were observed. During the following night the wire lay unstretched and it is possible th at this had some influence in causing the permanent increase of elasticity observed the next day. Series 5 is the result of heating and cooling with internal heating and Series 6 is for the same treatm ent with external heating. No hysteresis effect appears nor does there appear any difference due to method of heating. Discussion of Series 7. Series 7 is the most interesting single set of observations, and was taken in order to compare the two methods of heating without permitting the elapse of several hours or allowing an

17 444 H. L. DODGE. [Se c o n d LSe r i e s. appreciable change of temperature. At each temperature at which observations were taken, the change in heating was made gradually, w ithout permitting the tem perature of the wire to change. Observation I was a t room tem perature. Observation 2 was with current heating. W ithout permitting more than a few degrees variation in temperature the current in the wire was decreased while th at in the heater was increased. Observation 3 was with external heating. The temperature was then increased and observation 4 taken. Again the method of heating was gradually changed until observation 5 was secured with internal heating at practically the same temperature. In the same way 6 and 7; 8 and 9; 10 and 11 were taken. The results show in a striking manner th at the changes accompanying current heating are only tem perature effects. The tests of the tenth day with internal heating gave Series 8. In any single series of this group the permanent changes with treatm ent do not appear prominent. B ut a comparison of the eight curves, Fig. 5, reveals a gradual increase of Young s modulus from day to day. This was caused undoubtedly by the continued application of the additional weight which caused a very small gradual stretching. Effect of the Period of Rest. Two days after the observations of Series 8 a measurement was taken at room tem perature after which the wire was undisturbed for 106 days. This last observation appears with Series 9, Fig. 7, and a comparison with point 1 shows a slight recovery of Fig. 7. Results of tests upon specimen No. 3 after 106-day rest. the wire during the long rest. Nine other observations were then taken with an idea of determining whether or not the modulus would remain low upon heating. This proved to be the case both for external and current heating as is clearly brought out by comparison with the dotted line which is the Series 8 curve. Two days later, as shown by Series 10, further heating and testing brought the specimen back to its former state

18 Vo l. II. 1 No. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 445 for low temperatures although a t high temperatures greater values of Young s modulus were observed than ever before. Too much stress must not be laid upon these slight changes in the wire. The difference between Series 9 and Series 8 is small and may have its origin in a slight change in the working condition of the apparatus caused by its period of idleness. The im portant fact is th at no great change occurred and the wire was in practically the same condition as when left. The explanation of the difference in slope in some of the curves is th at the experimental error is of about the am ount of the variation. The total change in Young s modulus over the entire tem perature range is only 10 per cent, and the difference in stretch which this represents corresponds to less than one revolution of the micrometer head. In order to show this variation the scale to which Young s modulus is plotted has to be so large th at the errors of observation become appreciable. When the magnitude of the probable error is taken into consideration the consistency of the curves taken under such a variety of conditions is remarkable. C o n c l u s i o n s. The following conclusions apply to the sample of copper wire th at has Teen studied. I am of the opinion th at other specimens of copper will yield results differing only in the magnitude of the changes, and believe that the results are very suggestive of the effects th at can be expected in other metals. But work with iron wire now under way and certain results of other investigations to which reference is made later makes me feel th at too great caution cannot be exercised in making general conclusions from observations upon particular samples. From the preliminary observations and the tests upon specimens Nos. 2 and 3 we reach these conclusions: 1. A copper wire can be brought to a steady elastic state in which the stretch modulus becomes a function of temperature. In the present instance it was brought about by repeated stretching and heating and cooling over a range of temperature of 20 C. to 150 C. The preliminary tests show th at the rate at which the heat was applied or at which the wire was cooled, the length of time the temperature was maintained, and the thermal route by which a given tem perature was reached had no apparent effect upon the value of the modulus at any given temperature. These same facts are brought out still more convincingly by the extended work upon specimens 2 and 3, which also show th at permanent changes in the modulus can be practically eliminated by a relatively small amount of heating and stretching, which if continued for a longer time renders them negligible.

19 4 4 6 H. L. DODGE. [Se c o n d - [Se r i e s. 2. Heating by an electric current has no effect other than th at caused by the accompanying temperature. This was proved for one temperature by the results of Table I. and at a number of different temperatures by the work of Series 7, Wire 2, shown in Fig. 6, in which the heating was alternately by current and the external source. Further proof with step by step heating is also furnished by the identical nature of the results recorded in the four curves of Fig. 4, two curves of which are for current and two for external heating. Conclusive evidence is afforded by the long series of experiments carried out upon the third specimen, in which every possible way of varying the methods of heating was attem pted without detecting any difference in the results. 3. Young s modulus of a copper wire decreases with increase of tem perature at an increasing rate. In the case of the specimen studied, the am ount of decrease a t different temperatures in terms of per cent, of the value of the modulus at 20 C. is as follows: 40 C., 0.6 per cent.; 60 C., 1.7 per cent.; 8o C., 2.9 per cent.; xoo C., 4.6 per cent.; 120 C., 7.0 per cent.; 140 C., 10.0 per cent. At 20 C. the modulus of the sample in the steady elastic state was 11.5 X io 11 dynes per cm2. The true nature of the tem perature change was first shown by the work with specimen 2 as represented by the curves of Figs. 4 and was fully substantiated by the further work with specimen 3 which yielded identical results. 4. Heating and repeated stretching increases Young s modulus. As is shown by the results with specimen 3 there is an apparent increase of about 5 per cent, caused by the first four heatings and the accompanying stretching, which is thought to be due in part to the straightening out of the kinks. B ut there was a further increase of 2 per cent., which was a true history effect, although caused probably as much by the repeated stretching as by the heating. C o m p a r i s o n w i t h R e s u l t s o f O t h e r s. As has already been stated previous results upon the effect of current do not agree. A comparison of these with the present work will not be attem pted as the degree of accuracy in the latter is far greater. The conclusion th at there is no effect of current upon copper other than th at caused by tem perature can be accepted to an accuracy of less than 1 per cent. An interesting comparison regarding the history effect and the magnitude of change with tem perature is furnished by the work of Shakespeare,1 1Loc. cit.

20 V ol. II.1 No. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE. 447 who used interference methods to determine the modulus at 130 C. and at xoo C. He does not compute the value of the modulus but gives the change from 130 C. to ioo C. as 3.6 per cent. For this range the present specimen shows a change of 5 per cent. Shakespeare also found that the modulus increased with continued heating and cooling, until a permanent state was reached. The first heating produced a sudden increase of several per cent, which was followed by a gradual change. Nine heatings produced a total increase of 12 per cent. The permanent change described in this paper was of the same kind and amounts to 7 per cent. In the following comparison of results upon the tem perature effect the bracketed figures are taken from our own curves. A t 20 C. our value of Young s modulus was 11.5 X io 11 dynes per cm2. Miss Noyes1 found the modulus of a specimen of copper to be a t 20 C. This and another specimen tested a t tem peratures up to 150 C. gave a uniform decrease of the modulus which computed for 20 C. to 140 C. gives a change of 8.5 per cent, and 16 per cent, respectively [10 per cent.]. At C. Gray, Blyth, and Dunlop2 found the modulus of a sample of commercial copper to be and of hard drawn electrolytic copper at 19.5 C. to be They made tests over a range of ioo C. and reported a uniform rate of decrease which computed for 20 C. to ioo C. gives for the two samples changes of 1.2 per cent, and 3.4 per cent, respectively [4.6 per cent.]. Slotte3 found for two specimens changes of 6.6 per cent, and 4.2 per cent, respectively [1.5 per cent.], for a tem perature increase from 20 C. to 6o C. The moduli at 20 C. were respectively 12.4 and The more im portant point is th at he did not find a uniform rate of change. The modulus of the former specimen decreased at an increasing rate while the latter shows a decrease at a decreasing rate. Decrease of the modulus a t an increasing rate is also indicated by the work of W ertheim.4 If his results a t 150 C., 100 C., and at 200 C. are plotted and a smooth curve drawn it is almost identical with our own curves, except th at the values are about 10 per cent, lower. Regarding the nature of the change observations on the torsion modulus are valuable although too great stress must not be placed on them. Kohlrausch and Loomis5 made observations upon copper a t various temperatures. They found an increasing rate of change as the tem perature increased. Computed for 20 C. to ioo C. the change is 4.2 per cent. [4.7 per cent.], and for 20 C. to 140 C. 7.5 per cent. [10 per cent.]. Slotte6 has also made a study 1 Loc. cit. * Loc. cit. 2 Loc. cit. 6 Loc. cit. 2 Loc. cit. 2 Loc. cit.

21 4 4 8 H. L. DODGE. [Se c o n d LSe r i e s. of the torsion modulus of copper and finds the same increasing rate of change. Corresponding values from his work are 5.9 per cent, and 8.3 per cent. The results th at have been cited must be considered from two standpoints, first as to the general nature of the changes of Young s modulus, whether uniform or otherwise, and secondly, regarding the numerical values. Examination of the methods of those who have reported a uniform decrease shows th at their work was not of, sufficient accuracy to have detected the variation from a linear relation found by others. We are not certain how much importance should be attached to the work of Slotte upon Young s modulus. He worked also with aluminum, iron, and platinum as well as copper and found a decreasing rate of change. None of these results seem to have been repeated.. The torsion modulus can be determined to a much higher degree of accuracy and Slotte s recent work upon the torsion modulus of all these metals shows an increasing rate of change. Since the evidence th at is available points toward a similarity in the nature of the tem perature change of the two moduli this raises a question as to whether Slotte s former results upon Young s modulus are a true tem perature effect. W ith the results of Wertheim and of Slotte upon one specimen agreeing with our own and the work of Kohlrausch and Loomis and of Slotte upon the torsion modulus showing the same general type of change, I believe th at the conclusion th a t Young s modulus of copper decreases with increase of tem perature a t an increasing rate has sufficient corroboration. A comparison of the numerical values of Young s modulus and of the tem perature coefficient, ample allowance being made for experimental error, leaves no doubt as to the importance of chemical purity, method of preparation, and size of specimen. It is possible th at samples of copper may be found th at will show effects peculiar to current heating, or will not give modulus-temperature curves of the simple form th at I have found,, b ut I am inclined to believe the main differences will be found in the magnitude of the coefficients. Undoubtedly further work will reveal some relation between the chemical composition, the coefficient of linear expansion, the electrical conductivity, and other physical constants, and the value of Young s modulus and its rate of change with tem perature. Investigation is under way upon other metals in order to study the effect of current, to determine the tem perature coefficient of Young s modulus, and to study the relation between the temperature changes of the two elastic moduli.

22 V o l. I I.l No. 6. J CHANGE IN THE ELASTICITY OF A COPPER WIRE In conclusion I wish to acknowledge indebtedness to the staff of the physical laboratory of the State University of Iowa for their interest in the work and especially to Professor G. W. Stewart for suggesting the problem and to Professor J. N. Pearce, of the department of chemistry, for the chemical analysis. P h y s ic a l L a b o r a t o r y S t a t e U n i v e r s it y o f I o w a, August, 1913.

23 THE PHYSICAL REVIEW A JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS Conducted by THE AMERICAN PHYSICAL SOCIETY BOARD OF EDITORS F r e d e r i c k B e d e l l, Managing Editor J. S. A m e s K. E. G u t h e J. C. M cl e n n a n W. F. M a g i e R. A. M i l l i k a n E. F N i c h o l s B. O. P e i r c e C. A. S k i n n e r J. Z e l e n y Annual Subscription, throughout the Postal Union, $6.00 Single Copies, postpaid, $.60 Subscriptions should be sent to T h e P h y s i c a l R e v i e w, 41 North Queen Street, Lancaster. Pa., or Ithaca, N. Y. Two volumes of T h e P h y s i c a l R e v i e w are published annually, these volumes beginning in January and July, respectively, and containing six numbers each. A limited number of complete sets of the R e v i e w, both First and Second Series, will be supplied at the price of $3.00 per volume for all volumes, carriage extra. When they can be furnished without breaking a set, separate back volumes will be supplied at the same price, and single back numbers will be mailed to any address in the Postal Union at the price of $.60 per copy. First Series. From July 1, , to January 1, 1913, the R e v i e w was conducted by Edward L. Nichols, Ernest Merritt and Frederick Bedell, with the financial support of Cornell University. During this period thirty-five volumes were issued, constituting the First Series. The first four volumes of the First Series were issued annually; subsequent volumes were issued semi-annually. Second Series. On January first, 1913, the Review was transferred to the American Physical Society. A second series was then begun, the January, , number being designated Volume I., Number 1, Second Series. (An announcement of this transfer will be found on the first page of the new series.) F o r a d v e r tis in g r a te s, a d d r e s s T h e P h y s i c a l R e v i e w, Ithaca, N. Y. C h a n g e o f c o p y in s ta n d in g a d v e r tis e m e n ts s h o u ld b e s e n t d ir e c t t o t h e p r in te r s, T h e N e w E r a P r i n t i n g Co., Lancaster, Pa. Contributors to the R e v i e w are referred to page two of the advertisements for further information. Permission is given to republish any article appearing in the R e v i e w, provided proper credit is given. Address correspondence to THE PHYSICAL REVIEW, Ithaca, N. Y., U. S. A.

24 Part II The Change in the Elasticity of an Iron Wire with Current and External Heating.

25 To the Members of the Examining Committee: As it is expected that Mr. Dodge's thesis will be published in the near future, I have permitted him to submit it to you in manuscript form. The original drawings will of course be sent to the printer and cannot be bound with the manuscript. Chairman.

26 1 THE CHANGE IN THE ELASTICITY OE AN IRON WIRE WITH CURRENT AND EXTERNAL HEATING. By H. L. Dodge. The effect of current and external heating upon the Young's m&dulus of a copper wire was described in a previous number of the Physical Review1. The present paper deals with a similar investigation of an iron wire, the more ffl&rked changes being an increased temperature range, namely 20 C. to 475 C. and slightly greater accuracy. For a detailed description of the apparatus and method og making the determinations the former paper should be consulted. Improvements in Apparatus and Method. Mention cannot however be omitted of certain changes which have resulted in greater accuracy. Attention was called in the previous paper to the desirability of having the specimen of wire free from mechanical interference between the two points of suspension. The only interference in the case of copper wire was the three thermo-couples of fine wire which did ndit seem to cause any inaccuracy in the results. Some changes in the method of measuring the tempefature have made these unnecessary and in the present apparatus tjje specimen of wirehangs absolutely free. As before, the temperature of the wire is determined by its change in length with increase of temperature. In the former paper the justification and advantages of this method were explained. The same statements apply in the present instance as the only changes have been in the process of finding the relation between temperature and length. This was found as follows. 1 Phys. Rev., N.S., 2, 431, 1913.

27 2 A thermo-couple was carefully calibrated by means of a thermometer. It was then attached to the wire at the middle point and the relation between the temperature of this point and the length determined. As all Se points of the wire were not at the same temperature it wt?.s necessary to find the relation between the average temperature and the temperature of the middle point. The heating box was maintained at a constant temperature of about 350 C. and a large number of thermo-couple readings taken at various points on the wire. This resulted Ant only in an established relation between the average temperature of the wire and its length but also gave complete information concerning the temperature distribution. Uhder the above conditions the maximum variation of the temperature along the wire was about 40 C. while the error in the measurement of the average temperature was probably not more than 10 C, At lower temperatures the accuracy is of course greater, the error amounting to but one or two gegrees at or near room temperature and perhaps five degrees at 150 C, At higher temperatures the possibility of error is of course greater amounting to about 20 C. at 475 C. The curve representing the relation between change of length and temperature was plotted and found to be a straight line within the limits of accuracy of the temperature measurements. The increase in length between 20 C. and 475 C., corrected for the stretch caused by the decrease in the modulus, was 3.67 mm. As the wire was 57.6 cm. between points of observation the mean temperature coefficient of expansion proves to be with a possible error of five per cent. Considerably increased accuracy has been secured in the measurement of the stretch and consequently the modulus with the present apparatus by the use of new microscopes and micrometer slides with screws accurate to,001 mm.

28 3 ^he Specimen. The sample of wire upon which the tests were made was obtained from the Driver-Earris Wire Co., Harrison, N. J. ( The chemical analysis of the wire will be secured and inserted at this point.)

29 The ynean ^ coefficient of expansion between 20 C. and * c 475 C. is 14 x 10 per degree Centigrade to an accurac y of 4 about 5 per cent. The wire is.82 mm. in diameter. The portion between the points of observation was 57.6 cm. long. A weight of 2,109 grams was kept unon the wire continually, the modulus being determined by measuring the elongation produced by an additional weight of 2,252 grams. Certain additional facts regarding the loading, current, number of readings, time between readings, duration of tests, etc. appear in Table I which contains the complete data of a characteristic series of observations with current heating. The other series differ materially only in method of heating or temperature range. Eature of the Tests. The preliminary observations made while the wire was being straightened and brought to a cyclic state revealed striking irregularities in its behavior. At first increase of temperature increased the modulus, but this effect soon disappeared. Continued heating and testing gradually increased the modulus. This was probably due largely to stretching ana straightening. Both current and external heating were employed and no effect characteristic of the method of heating could be detected. After a number of cycles of heating and cooling accompanied by stretching the wire was brought to a cyclic state and the more extended tests made. The first group of observations were with a temperature range of 20 C. to >00 C. The tests were with both external and internal heating and increasing and decreasing temperature and were so arranged as to reveal if possible any effects peculiar to the method of heating or the thermal route by which any

30 5 temperature was reached. later the temperature range was extended to 450 Q. and to 475 G. and similar series of tests made. A few characteristic results are shown in Figs. 1, 2 and 3, Lr: explanation^)! which follow* Explanations of the Curves. ( Figs. 1, 2 and 3 represent graphically certain of the results that have been obtained. Table I contains the complete data for Series 9, Fig.2. The dat^ for the other curves do*. not differ materially in general character. In every case th dotted points represent determinations of the modulus with increasing temperature and the crosses those with decreasing temperature. Nearly all the points are the fesult of ten or more observations. ±sx±hx When the terms "external'1 and "internal" heating are employed the former indicates that the wire was heated by means of a heating element of Uichrome wire extending along the bottom of the enclosing box, while the latter term refers to heating by means of an electric current passing through the specimen itself. In all of the statements regarding the absence of certain effects it should be understood that this refers to effects amounting to one per cent or more. The presant apparatus cannot detect variations in the modulus of a less amount. of the work can best be judged from the curves. The accurac y change in the modulus from 18 to 19 corresponds to a difference in stretch of only.007 mm. I,. xhe first four series cover^a temperature range of 20 c. to 300 C. with both external and internal heating and showed a practically linear relation between loung's modulus and temperature. Series 5, Fig. 1, was with external heating,

31 increasing and decreasing temperature. Series 6 and 8 are plotted 6 together, ^hey were with internal heating, increasing and decreasing temperature. fi'he results of the first eight series show that for temperatures below 300 C. the elasticity is a definite function of temperature, independent of manner of heating and free from any hysteresis effects. It was next thought desirable to extend the temperature range by a considerable amount and to repeat the tests in various orders to ascertain whether the same relations held for a greater range of tem«*. * perature. Upon heating above 300 S. a very ragid decrease of the r 1 modulus was discovered, the rate of decrease becoming very marked at about 450 C. The results are shown in Fig. 1, Series 9. At this temperature the wire stretched about one fourth of a millimeter, approximately.05 per cent of its length. When the elastic limit is exceeded there should be an increase of the modulus for all temperatures. The next observation at room temperature showed an increase,from 18.5 to 19.2 or 2.6 per cent. The increase of the modulus for other temperatur as well can be aeen from Fig. 2. The first three series of observations of Fig. 2 give the temperature variation of Young s modulus with external heating. Series 11 shows the type of curve, and the return of the modulus to the same value after a day of heating and stretching. Series 12 was taken under similar conditions. By yielding the same results it proves the total disappearance of all history effects except the very gradual increase of the modulus with continued heating and stretching. As the observations for decreasing temperature in the last two series were few, ^eries 13 was made in order to learn whether the curve with decreasing temperature is the same as with increasing temperature. The results indicate the absence of any hysteresis effect. In order that the various series in this and the other figures may be more easily compared the curve which appears was drawn to fit a composite of them all Its shape

32 is exactly the stone in every case the only difference being that it is gradually raised to correspond to the general increase of the modulus as the work progressed. All of the observations so far had been made with the wire enclosed in an asbestos board heating box so that the currents used in the wire and the heating element might be as low as possible. Walker'*' has found a great difference between the effects of internal and external heating, dependent in part upon the current density. He interprets these results as caused by the magnetic effect of the current, the maximum field which he secures having an average value of 31 gausses. Then Series 19 was taken an attempt was made to find this effect in case it were associated with residual magnetism. Between the first two observations of this series ( Pig. 2) the wire was subjected for an instant to a current corresponding to an average fiftld of 50,gausses. The difference in the two plotted points is but a fraction of the experimental error, ileither this test nor any of the other results up to this time gave any suggestion of the effect Walker reports, ft,* It seemed desirable however to employ as large 'currents as possible in an attempt to bring out the effect. Accordingly the cover of the box enclosing the wire was removed giving the air free access. Series 21, Pig. 3, is the result, the maximum current being 9 amperes, corresponding to a current density of 17 ampefes per square millimeter and an average field of 29 gausses, or purposes of comparison Series 22 was taken with external heating, the slight tendency of the readings to fall lower ( less than.001 mm. difference in the actual measurements) being probably due ir entirely to the experimental 1 Proc. Hoy. Soc. Edin.,31,186; 1910.

33 errors caused by the fact that the main part of the apparatus was much hotter in the latter case. ij0 indication of the effects reported by Walker is to be found. Comparison With the Results of Others. The earlier work1 upon the effect of an electric current upon Young's modulus is of very questionable value. Reference will be,, 2 Miss Noyes made only to the more recent work of Walker and Lliss Iloyes. found no effect peculiar to current in the case of piano wire but her work was not of sufficient accurac y to have revealed even a relatively large difference. 3 Walker on the otherhand, taking measurements with what appears to be a considerably greater accurac y -^6u a <4 striking differehces of large magnitude. There are several points concerning even his most recent work that make one seriously question whether the results which he secured are attributable to the causes to which they are assigned, A lengthy discussion of kizxxsx Walker's work is out of place at this time but two or three xxiixts differences in our results may be of interest. Walker worked over a temperature range of to 125 C., finding in the oase of iron wire a maximum value of the modulus at about 50 C., the value at 125 C. being about the same as at 20 C. Employing different loads he finds that the is z c ss maximum treoroacoo- hoi-ght with the heavier loads amountixng p to 11 per cent for 18 kg. per ansxfo: square millimeter only.5 per cent for 32 kg. ner square millimeter. The load and

34 9 which I have employed is only 8.2 kg. per square millimeter. It would seem as if some trace of '"alker's maximum ought to have appeared hut in my results there has been no indication of any such effect. Walker ^ also studied the effect of variation,of load while keeping the current constant at a certain value, ^or some reason the results are now interpreted in terms of field intensity produced in the wire although formerly the effect of the current was regarded as one of temperature. The fields employed vary from.7 p u M to 31.9 gausses, skb*±xgxihrger The modulus is larger for small loads, the difference being the greatest for fields of intermediate values, amounting to 12 per cent for a field strength of 9 gausses. In my own work the field strength is 3.25 times the current in amperes. It -var&ed therefore from 0 to 29 gausses and since the external heating was sometimes used in conjunction it was-not always the same for the same temperature. In no instance have I been able to detect any effect peculiar to the current or its accompanying magnetis field qnd any variation amounting to more than one per cent would have been observed. Concerning the effect of magnetization upon Young s modulus a great deal of work has been carried on. The more important results have been those of 2 3 a Honda and Terada, Rensing, Stevens, 2 Phil. Mag., 13, 36; Annal. d. Phys., 14, 363 ; Phys. Rev., O.S., 11,95; 1900/

35 1 0 1 ^ Brackett, and Bock. An effect has been observed but in every case it was small amounting to less than one half per cent. As far as these results.xxshcsoy roomcgga which are for longitudinal and not circular magnetisation, and my own can be compared to those of»*alker there is flat contradiction. In the near future x hope to have more data as a basis for comparison. The differences may of course be due entirely to an inherent difference in the samples of wire. 1 Phys. Rev., O.S.,5, 257; Annal. d. Phys., 54, 442; 1895.

36 11 -he results of the Curlier investigations of the temperatute coefficient of Young's modulus of an iron wire were over rather limited temperature ranges and were subject to considerable errear. Wertheim 1 found a maximum in the neighborhood of 100 Q. followed by a rapid decrease up to 200 C. Kupfer 1 employing a method of bending rods found for severalmetals^a decrease of elasticity with increase of temperature.

37 1 2 nore recently Gray, Blyth, and Dunlop,'*' 2 3 Katzenelsohn, and Shakespeare have worked at room temperature and at or about 100 G. and found a decrease in the modulus of iron wire per 100cC. of 1.36, 2.33, and 1.6 per cent respectively, H The bracketed figures here and following are results taken from my own work for corresponding temperatures. But little work has been done at intermediate temperatures. The work of Miss Noyes 4 is not sufficiently accurate to have detected other than a linear relation had it existed. She finds for four samples of piano wire with moduli of about 20.3 an average decrease of the modulus of 4,6 per cent ner 100 C.

38 13 On he o herhand Pisati finds for both iron and steel a decrease of the modulus at an increasing rate for a temperature range up to 300 C. His value of the modulus for steel is Heating from 25 C. to 300 C. produces a decrease of 6.3 per cent. Por iron the modulus was 21.43, the decrease, 12 per cent, j f 2 Walker found the modulus of a piece of soft iron wire to be at 17.5 C. and with ordinary heating h x e x x up to 129 C.^a uniform decrease amounting to 3.7 per cent, * The results of Pisati, Gray, Blyth, and Dunlop, 5 6 Kohlrauoch and Loomis, and Sfotte upon the torsion modulus of iron are of interest showing as they do a decrease of the modulus with increase of temperature, the decrease in nearly every case becoming more rapid at the higher temperatures. 4 lluovo Cimento, (3), 4, 152; Proc. Roy. Soc. Edin., 28, 652; loc. cit. 4 loc. cit. 3 Annal. d. Phys., 141, 481; Acta. Soc. Scien. Fennicae, 35,1908.

39 Discussion of Errors* 14 At the lower temperatures the most important source of error is the measurement of the modulus. For temperatures below 350 C. the influence of the temperature upon the modulus is so small that errors in temperature are negligible in comparison. Above 350 C. the temperature effect becomess greater and greater and the e.rrors in the temperatute are the more important. Even with the measurement of the stretch made with micrometer slides accurate to.001 mm. it is impossible to be from any single determination below 350*0.,to a greater accuraccy than one per cent. In some eases the results vary as much as two per cent. At 350 C* a change in the temperature of 0*0. would be necessary to produce a change of one per cent in the modulus. At this temperature the measurement of the average temperature is accurate to about 10*0. which is entirely sufficient for the purposes of this investigation. Above 350 C. the error in the modulus becomes greater amounting to three or four percent at 475*C. Over this range the rate of change of the modulus with temperature is so rapid that the errors in the modulus are now negligible in comparison with ±khs3 x±h the temperature error which may be as great as 20 C. at 475 C.

40 The errors in the modulus are errors of observation and in the plotting of the curves tend to cancel each other. The change of length can be observed to an accuracy corresponding to a temperature difference of one eigmi of a degree. The temperature error is therefore due entirely to the difficulty of determi ning the relation between change of length and temperature, on account of a i w t i ia uncertainty as to whether give the true temperature of the wire. the thermo-couples It is probable that this error is not more than 5fC. at 150 C., 10 C. at 350 C., and 20 C. at 475 C. and I am of the opinion that it is considerably less. If we were-to consider the curves as moved, first, with a x e x ±±k *± motion up and down a distance corresponding to one per cent of the modulus and second, with a motion to the right and left corresponding^0 jthxgflft twenty degrees variation in temperature, the true position v,e U of the curve would fall^within the area covered. As explained in a previous section of this paper there is a variation of temperature along the wire amounting to 40 C. at 350 C.. Consequently at any given feverage temperature the value of the modulus is the average of the moduli of elements of length some of which are at temperatures lower and some at temperatures higher than the average. In the case of current heating the variation along the wire is less but a variation in the cross section is introduced. It is assumed that the change of length averages the variation in temperature of the different layers as welljas the variation along the length. It should be noted that the value of the modulus is a similar average of the moduli of the different layers as welljas the different elements of length.

41 Except for the fact that sudden changes in the modulus,or in the slope of the curve^peculiar to some definite temperature would he concealed by this averaging these factors are negligible in comparison with the errors already discussed* Attention has asaretidy been called to the effect of magnetisation on the modulus and mention is now made of ±kzx magnetostriction, the cooling of the wire on application of the weight, and the apparent increase in length of the wire accompanying the straightening of the catenary only to call attention to the extreme smallness of these effects and the fact that they may be entirely neglected in this investigation*

42 Summary. The results of the tests that have been made upon this sample of iron wire may be summarized as follows: (1) The sample showed very erratic changes in elasticity when fifst heated. (2) By continued heating and stretching it was brought to a cyclic condition, or steady elastic state, in which Young s modulus becomes a function of temperature. This was secured first for a temperature range of 20cC. to 300 C., and later for a range extending to 475 G. (3) Continued heating and stretching gradually increased the modulus, the effect being probably caused largely by the stretching. (4) Bxcept for the small gradual increase above mentioned, the modulus of the wire was independent of history, the thermal route by which any temperature w?.s reached having no apparent &ff&e±xuxhxx±hs: influence upon the value of the modulus. (5) Heating by an electric current has no effect other than that caused by the accompanying temperature. This is in dierect contradiction to the work of Walker. She very small changes in the modulus caused by magnetization reported by other investigators would not have been detected by this apparatus. (6) The Young's modulus of the iron wire decreased with increase of temperature at an increasing rate, - -he modulus decrease slowly and almost uniformly up to a temperature of about 300 C. Then the rate of decrease beccgne becoming very steep at 475 C. more and more rapid, the curve The following table is compiled from the various results.

43 Table II. Change of Young's Modulus of Iron Wire with Increase of Temperature. Temperature Modulus x 10 1 i dynes per cm. d.e*lo" Total decrease^ A T per cent of E at 20*0. 20* * (7) The values of the modulus are accurate to one per cent for temperatures between and 350 C. At 475*0. the error may amount to three or four per cent. Below 350*0. the temperature error is negligible in comparison to the error in the modulus. At 350*0. it may amount to 10 C. At higher temperatures the error is greater and of more importance on account of the more rapid decrease of the modulus. At 475 C. it is possible that the error may be as much as 20*0.

44 iron (8) The above results while applying to but one sample of/wire when considered in the light of other investigations appear to be characteristic and I should expect to find very similar effects with other samples of iron. In conclusion I wish to acknowledge indebtedness to the staff o! the physical laboratory of the State University of Iowa for their interest in the work and especially to Professor Stewart for suggesting the problem. Physical Laboratory^ State University of Iowa, duly, 1914.

45 F i g. 1

46 F i g. 2

47 F i g. 3

48 1 6 Table I Data for Series 19, Internal Heating. Length of wire Diameter of wire 57.6 cm..82 mm. Ohs. Ho. Unvarying load 2109 g. Added load 2252 g. 5otal load per sr. mm. i. 8.2 kg. Time Temp. Stretch Current ilo. of Obs. 1 9; 30 A.M. 220 C : : : : : :50 P.M : :00 282, : : : : : : : : : : : n Young's Modules x 10 dynes per cm.^

49 Qbs. Mo. Time Temp. stretch Current No. of Obs. -1] Young's Modulus x 10 dynes per cm.^ 21 9: : : : :

50 1 8 Titles of figures. Fig. 1. Change of Young's modulus with temperature, two ranges. Fig. 2. Change of Young's modulus with increasing and decreasing temperature, internal and external heating. F ig. 3. Comparison of results with external heating and internal heating by.the largest possible currents.