LIBRARY OF THE UNIVERSITY OF CALIFORNIA. GIFT OK Class Relations between Length, Elasticity, and Magnetization of Iron and Nickel Wires. DISSERTATION. SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY, FOR THE DEGREE OF DOCTOR OF PHILOSOPHY, BY EDSON F. GALLAUDET. 1.896. WASHINGTON, D. C. '. GIBSON BROS., PRINTERS AND BOOKBINDERS. It has long been known that magnetic metals change their di- mensions when magnetized. Begun by Joule 7 , the study of these changes has taken the attention of many careful investiga- tors, whose work, especially that of Bidwell 3 , has established the following facts with regard to the phenomena observed. HISTORICAL SUMMARY. Iron. If subjected to an increasing magnetic field, iron at first elongates in a direction parallel to the direction of its mag- netization, more rapidly than in proportion to the magnetizing field, reaches a maximum length, and then contracts nearly in proportion to the magnetizing field, to less than its original length. As the strength of the field is greatly increased, the contraction shows signs of reaching a limit, which was reached by one of Bidwell's 311 specimens at about H = 1250. The absolute value of the change in length varies with different specimems, but is qualitatively the same in all. If tension 1 12 is applied to the iron, the initial elongation is decreased, and a great enough tension destroys it entirely, making the initial phenomenon a contraction. Hardening^ 1 12 decreases the elongation, and increases the con- traction. Annealing 3f also diminishes the initial elongation, and increases the final contraction. Nickel is found, by Bidwell, to contract from the start, ap- proaching a minimum length rather sooner than iron, i. e., at about If= 900 c. g. s., for a particular specimen 311 . Tension 3 ' 1 diminishes the contraction in weak fields. In fields of strength greater than 140 or 150, magnetic contraction is in- creased by tension, up to a critical value, depending on the strength of the field, and diminished by greater tension. FAULTS OF PREVIOUS WORK. In all but one 13 " of the investigations made prior to last winter, a relation between change in length and magnetizing field only 144002 has been given. This fact led last year to the investigation of Dr. More 1 - in this laboratory, who got curves between change in length of an iron wire and magnetization. In order to get the change in length due to the magnetization alone, he considered the metal as under a mechanical stress 8 equal T>2 to , and therefore having suffered a purely mechanical con- O7T J5 2 traction proportional to 6 - . He therefore measured Young's O/T modulus, and the induction J5, deduced this mechanical contrac- tion, and added it with positive sign, to his curves between change in length, and / the magnetization. It was known that Young's modulus 4 ' l5 for iron changed when the iron was mag- netized, but Dr. More showed that he could neglect the small correction due to this cause, when the tension in the wire was small. His curves for the wire, under the minimum tension used, are given below. The upper one is intended to show the rela- tion between change in length and magnetization alone, and is j> obtained by applying the g- correction to the lower one, which is the uncorrected relation as observed. Both curves show that as the magnetization increases, the length increases, at first slowly, then more rapidly, reaching a maximum shortly before saturation, when the wire begins suddenly to contract quite rapidly, and the curve falls in an almost vertical straight line. jfi The correction merely raises the curve, without changing its o~ general shape. There is, however, considerable doubt :>l> as to the propriety of this correction. The careful work of Bidwell principally, and the results to be given presently, show that the contraction of iron, after satura- tion is reached, is, for a time at least, proportional to the mag- netizing force. Bidwell's experiments with very strong fields "' also show that the contraction approaches a limiting value asymptotically. In other words, the retraction curve, after saturation, is first a de- scending straight line, and then becomes curved with its concave I > side upward. The curve of plotted to //, constantly rises, but ~ is convex upward where the retraction curve is straight, and con- cave upward where the inductions are large. If, therefore, that part of the change in length, which is not due to the magnetiza- J5 2 tion, were a contraction proportional to ^ , the contraction that immediately follows saturation, should be less than proportional to the field ; i. e., that part of the contraction curve that imme- diately follows saturation, should be concave upward, while ex- periment shows it to be straight. Also, for very strong fields, J? 2 the rapid increase in - should make the contraction more rapid than in proportion to the field ; i. e., the contraction curve should finally curve downward. The work of Bid well, already cited, shows the reverse to be the fact. Finally, if the change in length were due to change in I and in , Dr. More's curve, as cor- rected, should come to an end at a point given by the maximum elongation as ordinate, and maximum magnetization as abscissa. In reality his curve falls almost perpendicularly just before reach- ing the point where it should end, showing that after the metal is nearly saturated, the change in length is independent of both JM the magnetization and of . It seems, therefore, reasonable to J5 2 assume that the change in length is also independent of ^- before o/r this point is approached. OBJECT OF INVESTIGATION. The following investigation was undertaken at the suggestion of Dr. Ames, with the original purpose of studying iron, nickel, cobalt, and bismuth, and in the hope that a tabulation of Young's modulus, along with induction, permeability, field strength, and magnetization, as well as the change in length of each, would show enough connection between some of these quantities, to explain the phenomena. It was, however, impossible to get bis- muth and cobalt in the form of wire ; hence the investigation is con- fined to iron and nickel. Also, on account of the many set-backs in getting the apparatus to work satisfactorily in its necessary surroundings, and owing to the short time available, it has been 6 possible to investigate only one specimen of each metal. This is especially to be regretted, since the results differ unexpectedly, and in an important manner from any given by previous investi- gators. DESCRIPTION OF APPARATUS AND METHOD OF OBSERVATION. The apparatus was the same as that used by Dr. More last year, and is shown in figures 1 and 2. The wire was encased in a brass tube a, Fig. 1, open at the upper end and closed at the lower end by a brass plug b. At the top was a bracket c supporting a lever d, and a projecting arm e. The wire experimented on passed up through the brass plug b, in which it was tightly fastened by a set-screw, was held concentric in the tube by a loosely-fitting cork/, in the open end of the tube, carried tightly screwed to it immediately above the cork, a brass hook g, and finally passed to the support above, thus carrying the load of the tube and bracket. The hook g, screwed to the wire, made a knife-edge connection with the short arm of the lever f?, which was supported on knife edges by the bracket c. The projecting arm e of the bracket passed out under and parallel to the long arm of the lever d, and had its extremity bent up, so that this extremity and the upper surface of the end of the lever lay near together and in the same plane when at rest. A small brass table h furnished with three legs made of needle points about 3 mm. apart, was placed on the end of the lever, so that two of its legs rested in a scratch in the lever, while the third leg rested on the raised extremity of the'project- ing arm of the bracket. This little three-legged table carried a bit of plane glass mirror, in which a vertical scale was observed by means of a telescope. It is evident that any change in the length of the part of the wire between the set-screws in the plug b and the hook #, must change the inclination of the lever d and tilt the mirror at h. If L = length of long arm of lever, / = length of short arm of lever, d = distance from one leg of brass table to line joining other two bearing on lever end, D distance from scale to mirror, I ! i i i ? i i i i | i i 1 1 i 1 bH i ; 1 1 i 1 i i 1 1 i 1 1 Ui i i UI i LJ i i 1 1 i i i ! F I then the multiplying power of the apparatus is X 2 Z = 11.67 cm. J = 0.477 d = 0.3365 D = 147.6 therefore multiplying power is 11.67 X 147.6 X 2 _ ^ All X .3365 Hence Scal r e ' ives the actual changes in the length of the wire. It was possible, under good conditions, to read the scale to one-tenth of a millimeter, corresponding to an actual change in length of 0.000000466 cm. The length of the wire between fastenings = 70 cm. It was therefore possible to de- tect, with a fair degree of certainty, changes in the unit length as small as 0.000,000,006,6, or one part in 150,000,000. The hollow brass tube a, containing the wire, and supported by it, was placed inside a vertical solenoid a, Fig. 2, considerably greater in length than the tube itself, thus bringing the set- screws in b and y, Fig. 1, well within the magnetic poles of the wire studied. The wire of the solenoid was wound on a brass tube, inside which another brass tube was placed, thus forming a jacket between the wire of the coil carrying the magnetizing current, and the suspended tube containing the specimen studied. A stream of cold water was kept flowing in this jacket, so that it took some time for the heating of the current to affect the read- ing in the telescope. The strength of the field was 45.7 c. g. s. per ampere. For weak fields the magnetizing current was meas- ured by a Weston mil-ammeter, and regulated by a water and copper sulphate resistance. For strong fields, the current was measured by a Weston ammeter of greater capacity, reading to hundredths of an ampere, and was regulated by an iron wire re- sistance. The current was obtained from the storage cells of the laboratory, and could be kept very constant. The induction in the wire was measured by the method of in- creasing reversals. In the case of the iron, a paper cylinder, wound with two hundred turns of fine copper wire connected with a Rowland- d'Arsonval galvanometer, was slipped over the wire, and placed midway between the ends of the tube a, Fig. 1. For the nickel, instead of using the paper cylinder, a thin coating of sealing-wax was first applied, over which were wound four hundred turns of fine silk-covered wire, connected with the galvanometer. After each set of induction measurements, the galvanometer was calibrated by means of a long solenoid wound on a wooden core, and carrying a secondary coil of two hundred turns. The mean area of the secondary coil upon the wire was carefully measured and the section of the wire, whence the in- ductions were calculated in the usual manner. The lower end of the wire studied, was provided with a weight-carrier , Fig. 2, so that weights could be added and measurements taken of Young's modulus. The stretching weight, or rider c, weighing 46.9 grams, consisted of a piece of brass tubing about 3 cm. in diameter, and the same in length. One side was cut axially, so that it could be applied without re- moving the weight-carrier. Two loops of copper wire were soldered to opposite sides of this rider, and through these passed light wire hooks suspended by strings which passed through two small pulleys, one on each side of the stretched wire, and about 1.5 cm. from it. Above the pulleys the strings were united into a single one d, and carried to the table where the readings were taken, and there fastened. The length of this string was such that when it was fully extended, the rider was supported by the weight-carrier, and the supporting hooks just swung free of the side loops. When it was desired to remove the rider, the string d was drawn aside, and held by a tack in the table, which kept the rider freely suspended, about 3 mm. above the weight- carrier. Great difficulty was experienced in getting trustworthy results from an apparatus of such delicacy. The induction measure- ments could be made at any time, but the length and modulus measurements had to be made between two and four in the morning, when the traffic of the city was less than at any other time, and even then, the effect of the March winds upon the building was a sore trial to the patience. A very important source of error was, of course, found to be that due to the heat- ing of the current in the coil. It was finally found necessary to read only instantaneous changes of length, both for the elon- gation curve, and for the change in Young's modulus. In measuring Young's modulus there seemed to be an instan- taneous elongation upon applying the rider, followed more or less continuously by a slow increase in the reading, showing an apparent viscosity of the metal. On account of the heating, it was impossible to wait for the modulus reading to become con- stant, but the instantaneous elongation was guessed at as nearly as possible and though, of course, much too small to give the usual value of Young's modulus, and also too irregular to be of any quantitative value, was still near enough what it should have been to show the approximate position of the modulus curve. In any case, whatever the modulus curve may be, the elongation and retraction curve seems to be independent of it, so that accuracy in this respect is not vital. It was also the ex- ception to have the apparatus free from vibrations, though its supports rested in boxes of sawdust e, Fig. 2, and the whole was placed on brick piers built up from the ground. But fortunately the night on which the first iron curve was taken was unusually quiet, and all the conditions most favorable, as the results seem to show, since a smooth curve can be drawn through nearly all the points obtained. The wires were annealed before being set up, and demagnetized by an alternating current before each set of measurements. The elongation curves were taken as follows : A reading was taken through the telescope, the magnetizing current then in- creased a small amount, and another reading taken immediately. The process was then repeated without turning off the current, and carried from zero current to between 6 and 7 amperes, or a field of about 300. [The current had to be turned off twice dur- ing each set of measurements, to allow a change in the voltage applied, which, on account of high resistance of the solenoid and the low resistance of the rheostats obtainable, had to be varied between 20 and 100 volts. No harmful effects on the results could be detected.] No readings could be repeated, since the alternator supplying the current, used to demagnetize the wire, was not kept running at night. Two sets of curves were taken, the first when the wire carried only the weight of the apparatus, giving a tension of 53 kg. per sq. cm. in the case of the iron, and 10 of 30 kg. per sq. cm. in case of the nickel, the second when the load on the wire was increased to 323 kg. per sq. cm. in the iron, and to 179 kg. per sq. cm. in the nickel. The temperature re- mained fairly constant somewhere in the neighborhood of 9 C. KESULTS. I. Iron. Tension = 53 kg. per sq. cm. The iron wire was one of ordinary commercial iron, number 19 Stubs' gauge, diameter = .106 cm. The elongations are given in Table I and plotted to // in Plate I, and to /in Plate V. Values of Young's modulus are given in Table la and plotted to //in Plate I, and to /in Plate V. All the magnetic quantities are given in Table Ib and plotted to // in Plate I, and to / in Plate V. a.) Elongation: The elongation curve for the iron wire given in Table aud Plate I is the most suggestive of any of those taken. It is peculiar in showing an initial contraction. A glance at the curve is a much better description than can be put into words. It will be noticed that the initial contraction, while increasing, increases more rapidly than in proportion to the magnetizing force, and reverses quite abruptly at the value of /fat which the magnetiza- tion curve begins to be convex upward, and at which the perme- ability also changes abruptly from an increase to a decrease. The length begins at this point to increase quite rapidly, but less than in proportion to //. After regaining the original length, the wire continues to elongate to a maximum, and then contracts again in the way observed by Bidwell, More, and others. This curve is the last and best of four sets of measurements, which, for various reasons, had to be discarded, but in all of which the initial contraction was observed. This initial contraction can be very satisfactorily explained on the well-known theory that particles of the metal rotate when the metal is magnetized. The last part of this curve seems to show that the wire suffers a contraction directly proportioned to H after saturation is reached. It has been assumed, therefore, that the change in 11 length is equal to the change produced by the magnetization alone, plus a constant times H ' or, expressed in symbols, where ? is the slope of the straight part of the curve and is negative. To separate out that part of the elongation due to the magnetization alone we have If each ordinate of Table I is increased by fH, we obtain Table V. the results of which are plotted in Fig. 3. A relation between elongation and magnetization is taken from this curve as in Table VI and plotted in Fig. 4. b.} Change in Young's modulus. The points of the curve are seen to be a good deal scattered, but serve well enough the purposes of this paper. There is a total increase of about 30%, the maximum being reached at about saturation, followed by a decrease to nearly the original value at H = 100. A comparison between the curves for Young's modulus and for elongation, seems to show that they are not connected. II. Iron. Tension = 323 kg. per sq. cm. Same wire as in I. The elongations are given in Table II and plotted to ZTin Plate II. Values of Young's modulus are given in Table Ha and plotted to 77 in Plate II. All the magnetic quantities are given in Table lib and plotted to If in Plate II. a.) Elongation. This elongation curve adds nothing, except that a small in- crease in the tension of the wire almost annuls the initial con- traction, increases the elongation and final contraction. b.) Young's modulus. This, as might be expected, shows a greater change under the increased load, the percentage increase being about the same, but the final value only about 80% of the original value. 12 III. Nickel Tension = 30 kg. per sq. cm. Wire obtained from Eimer & Amend, of New York. Number 15 American gauge, diameter = .143 cm. Elongations are given in Table III and plotted to //in Plate III, and to /in Plate VI. Values of Young's modulus are given in Table Ilia and plotted to //in Plate III, and to /in Plate VI. All the magnetic quantities are given in Table III/> and plotted to // in Plate III, and to / in Plate VI. a.) Elongation: The wire increased in length, at first more rapidly, then more slowly than in proportion to the magnetizing field, reaching a maximum length just before the point of maximum permeability. Contraction then began, soon bringing the wire to its original length, and continued much more rapidly than in the iron, and in proportion to 'the magnetizing force, until saturation \vas aj. preached, when the decrease in length began to be less than in proportion to the magnetizing force, and so continued till the end of the experiment at about //= 300. The curve, however, offers no opportunity for the separation of the part of the elongation due to magnetization alone, from that part due to the magnetizing force. />.) Young's modulus. The modulus curve shows an increase of about '26% with the maximum nearly coincident with maximum elongation, followed by a gradual decrease to about 80% of its original value. This curve, though it suggests that the change in Young's modulus may be due to the change in the molecular arrangement, never- theless shows that the change in length is not at all due to the change in the modulus. For while an increase in the modulus might cause contraction, it certainly could not cause expansion, and similarly, a decrease in Young's modulus might cause expan- sion, but not contraction. IV. Nickel. Tension = 179 kg. per sq. cm. Same wire as in III. Elongations are given in Table IV and plotted to 7/in Plate IV. Values of Young's modulus are given in Table IVa and plotted to H in Plate IV. 13 All the magnetic quantities are given in Table IV b and plotted to H in Plate IV. a.) Elongation. The small increase in the tension of the wire seems to cause a decrease in the initial expansion, quite analogous to the decrease in the initial contraction in the case of iron. BidwelFs 3d work on the effect of tension in the contraction of nickel shows that in strong fields, as the tension is increased, the contraction at first increases and then decreases, which is analogous to the in- crease and subsequent decrease in the elongation of iron pro- duced by increasing tension. b.} Young's modulus. The modulus curve does not seem to be materially altered by the increased tension. DISCUSSION OF RESULTS. I. Iron. The curves of Plate I and Fig. 3 afford a striking veri- fication of Weber's 10 theory that the molecules of iron rotate when magnetized, which has been elaborated by Maxwell and Ewing, and indicate that this rotation is the common cause of both the magnetization and elongation. Thus, suppose the metal to be made up of or to contain small particles of oblong shape, and magnetized in the direction of their length. Take any plane section of the wire at right angles to its axis : If there is no magnetization of the iron, the particles in this section may be supposed to be pointing in all directions, thus magnetically neutralizing one another. Now, suppose that all these particles, with their directions kept unchanged, are moved so that their south poles coincide. There will thus be formed a spherical pencil of rays, each ray a small magnet, with the south poles at the center and the north poles in the surface, as in the figure, where all the south poles are at o and the north poles as at a, 6, c, d. If a magnetizing force is now applied in the direction of the arrow, the particles, radii in the figure, will 14 rotate, as shown. If the ends of the particles are in some way connected to the metal, this rotation should produce a change in the thickness of the section proportional to the sum of the changes in the cosines of the angles made by the particles with the axis. For a weak field the rotations should be small, but those par- ticles that originally pointed downward, as o a, o b, should turn more than those in the upper hemisphere, since in the lower hemisphere the turning moments increase as the particles turn, while in the upper hemisphere they decrease. The change in the arithmetical value of the cosines in the lower hemisphere is negative, but of those in the upper positive. Hence a small magnetizing force should produce a contraction of the wire. Also, on account of the increasing moments in the lower hemisphere, the wire should contract more rapidly than in proportion to the magnetizing force, until what might be called the "average parti- cle," has passed the horizontal position, when the sign of the change's in length should abruptly reverse, and the wire elongate, gradually approaching a maximum length which should be reached at satu- ration, when the particles are supposed to have become parallel. If the above is correct, it should be possible to find a connection between the elongation and magnetization curves. This cannot be done, of course, without knowing something not only of the shape of the particles, but, also, of the law by which they r turning. But a comparison between the two curves can be made thus : Consider the part of the magnetization curve that is con- cave upward, i. e. 9 from H = to H = 2.45. It is evident that before that magnetization is reached that corresponds to Jf== 2.45, /increases more rapidly than in proportion to II. Now, in the theory given above, each particle is supposed to turn under the influence of a magnetizing force and contribute to the total mag- netization an amount proportional to the change in the cosine of the angle formed by it with the perpendicular. If the particle is below the horizontal, it will turn under an increasing moment, and the change in magnetization, due to it, will be greater than in proportion to the turning force. If the particle is above the horizontal, the change in magnetization due to it will be less than in proportion to the turning force. Conversely, since the mag- netization up to H = 2.45 increases more rapidly than in propor- 15 tion to the magnetizing force, the average motion of the particles musi be below the horizontal. But the contribution of each par- ticle to the change in length, is also given by the change in the cosine of its angle, is negative if the particle is below, positive if above the horizontal. Hence the magnetization curve, if plotted with its sign changed, as far as H = 2.45 should resemble the elongation curve up to that point. Now consider the magnetiza- tion curve between H == 2.45 and H = 2.93. This part is quite straight, which shows that the change in magnetization is pro- portional to the force, i. e., that the average motion of the parti- cles is in the horizontal. But here the positive changes in the cosine just balance the negative changes, and we should get no change in length. Continuing from H = 2.93 the magnetization curve is convex upward, showing that the average motion of the particles is above the horizontal. Hence the elongation curve and magnetization curve should be similar beyond H = 2.93. If I' = the value of I at H = 2.45, and I" the value of I at H= 2.93, the comparison curve already carried to 11= 2. 93 might be continued from this point by plotting ordiuates equal to I I" T. Now, the elongation, when the average motion is above the horizontal, should be very much greater than the con- traction taking place when the average motion is below the hori- zontal, since in the former case a majority of the particles work together. The elongation ordinates should be therefore prob- ably anywhere from two to five or six times greater than the contraction ordinates. If they are taken twice as great, and the comparison curve is continued from H ' = 2.93, by plotting ordi- nates given by 2 ( I I"} I', we get the curve given in Table VII and Fig. 5. The similarity between this curve and the elongation curve is evident enough to make it seem probable that if we knew the law by which the particles resisted turning, we could, without any guess-work, construct from the magneti- zation curve one that would approximate very closely to the elongation curve. It seems, therefore, that the elongation curve of Plate I proves quite clearly that the initial contraction, elonga- tion, and magnetization are all due to the same cause, namely, the actual rotation of particles in the metal. The straight part of the curve does not seem to suggest any specific positive conclusion, except that already given, that the 16 part of the contraction not due to the magnetization is pro- portional to H up to a certain limit. Some negative conclu- sions, however, are quite evident. The* strain in the metal pro- duced by the magnetic field, after saturation, cannot be like an ordinary mechanical one, for since, within the elastic limit, strains are proportional to stresses, the curve should continue straight for the strongest fields attainable with a solenoid, or if it curved at all it should be concave downward. Bidwell has shown 1 " 1 , how- ever, that after a certain strength of field has been passed, the contraction is less than in proportion to the field, and for the specimen he used, ceased entirely at about // = 1250, the curve beyond this point being horizontal. To conclude, therefore, the initial contraction and subsequent elongation may be explained as due to the rotation of particles in the iron, and the final con- traction, whatever may be its cause, is not an ordinary mechani- cal strain, and is not, as one would expect from the equations of Maxwell, and from experiments on magnetic tractive force", pro- J5 2 portional to & . o~ The effects of a small increase in tension, upon the elongation due to magnetization, as shown in Plate II, namely, decrease in the initial contraction and increase in the elongation, are what one would expect, if there is any looseness of the particles, as must be the case, if they can rotate. It is, however, hard to see why tension should increase the final contraction. II. Nickel: The explanation of the elongation curves for nickel, Plates III and IV, is not so easy as in the case of the iron. If the particles were flattened instead of elongated, in the direction of their magnetic axes, their rotation would combine with the contraction proportional to the field to make up the curve as far as T= 90. Since, however, the ultimate effect of the rota- tion would be contraction, and what might be called the magnetic elastic limit, is approached so early, it would be impossible to separate out the change due to the rotation alone, for compari- son with the magnetization curve. The effects of a small increase in the tension of the wire, namely, decrease in the initial expansion, and, according to Bid- well, increase in the final contraction, seem to complete the analogy between the phenomena shown by iron and nickel, provided the particles of the latter are flattened in the direction of their mag- netic axes. DISCREPANCIES BETWEEN THESE RESULTS AND THOSE OF OTHERS. . In the case of iron, it has been impossible to find in the work of other investigators, any mention of an initial contraction, like that shown in Table and Plate I. Similarly in the case of nickel, it has been impossible to find any record of an initial elongation like that shown in Table and Plate III. In the figures given by More, in his work on iron, the weakest field used is 4.6, at which strength of field, tke iron wire of Plate I has more than regained its original length. It is, however, hard to see why these initial effects are not re- corded in the extensive work of Bidwell. Many of his tables show initial fields weak enough to produce the initial contraction in iron, and initial expansion of nickel. His remarks on the peculiarities shown by annealed speci- mens ;if of iron, suggest that the annealing to which the speci- mens examined in this paper were subjected, put them in a con- dition to show the unusual initial effects, and that if Bidwell had given more attention to his annealed specimens, and examined them with weaker fields and lighter loads, the initial contraction of iron, and expansion of nickel, would not have escaped his notice. The results for iron, shown in Tables and Plate I, are also shown in Plate V, but plotted to magnetization instead of mag- netizing field. The great differences between the elongation curve and the unconnected curve of Dr. Moie, already given, are obvious, and illustrate what variations may be shown by two different specimens, though studied with the same apparatus. Plate V shows better, perhaps, than Plate I how greatly the change in length is affected by the magnetizing field, after the change due to the magnetization has practically ceased. Plate VI shows the results for nickel of Tables and Plate III, plotted to I instead of //, but does not seem to throw any additional light upon the matter. 18 SUMMARY OF RESULTS. Iron. Phenomena observed. 1. The wire showed an initial contraction when magnetized, contracting more rapidly than in proportion to the magnetizing field. At about the point where the magnetization increases most rapidly and the permeability is greatest, this contraction ceased and the wire began to expand more slowly than in pro- portion to the magnetizing field, till a maximum length was reached in the neighborhood of saturation. The wire then con- tracted in direct proportion to the magnetizing field, up to // = 250, where the experiment was brought to an end. 2. The instantaneous modulus of elasticity was found to in- crease over 30%, reaching a maximum at saturation, but de- creased again to nearly its original value at about //= 300. 3. A small increase in the tension of the wire reduced the initial contraction, did not appreciably change the percentage increase in the modulus, but the final decrease in the modulus left it at only about 80% of its original value. CONCLUSIONS. 1. The initial decrease in the length of the wire and the elon- gation, are explained as due to the rotation of particles in the metal. 2. The final contraction is not an ordinary mechanical strain, is not proportional to ^- , but is proportional to the magnetiz- O/T ing field. 3. The change in the modulus seems to have nothing to do with the change in length. Nickel. Phenomena observed. 1. The nickel wire, when magnetized, increased in length, at first more rapidly, then more slowly than in proportion to the magnetizing field, reaching a maximum length just before the point where the permeability was greatest. Contraction then began, soon bringing the wire to its original length, and con- 19 tinued much more rapidly than in the iron, and in proportion to the magnetizing force, until saturation was approached, when the decrease in length began to be less than in proportion to the magnetizing force, and so continued till the experiment was ended at about H = 300. 2. The instantaneous modulus of elasticity increased about 26%, reaching a maximum at about the same field as that of the maximum elongation, and then fell to 80% of its original value at about //== 300. 3. A small increase in the tension of the wire reduced the original expansioD, the increase in the modulus was about 23%, and its final value 88% of its original value. CONCLUSIONS. 1. The results for nickel are not so easily explained as those for iron. They do not, however, conflict at all with those for iron, but confirm, though not very definitely, the conclusions drawn therefrom. 2. The change in the modulus does not seem to have anything to do with the change in length. I ought to say that the conclusions drawn in this paper are entirely my own, and must not be taken as involving the opinion of any one connected with this University. In closing, I would express most hearty thanks to Dr. Ames for his kindness and help throughout this work, and to Prof. Eowland for his consideration and suggestions. EDSON F. GALLAUDET. JOHNS HOPKINS UNIVERSITY, May, 1896. TABLE I. Iron. Tension in wire = 53 kg. per sq. cm. H ^xlO> H xir z x 10 " 1.1 3.99 11.70 57.91 66.29 5.99 1.64 6.66 13.58 58.57 82.74 20.63 2.24 10.65 14.52 58.57 94.63 43.93 3.02 21.30 17.33 58.57 105.60 63.23 3.34 20.63 18.51 58.57 118.86 - 89 . 86 3.66 13.98 i 23.31 58.57 136.23 124.47 3.93 7.32 27.84 57.24 158.17 - 171.06 4.20 .67 33.00 54.58 191.10 - 236.3 6.35 -f 32.62 36.75 51.25 224.46 299.53 7.22 39.27 41.33 45.93 251.43 352.78 8.91 47.92 46.95 37.27 10.29 53.92 54.86 25.96 TABLE la. Values of the modulus of elasticity. * *L x 10 19 = M al H 7 Y'X 10 ia =Jf ill H ^x 10"= M al 2.89 2.79 26.57 3.37 128.00 3.72 4.02 2.7!) 41.28 3.40 150.04 3.80 4.98 2.84 47.13 3.47 165.49 3. / H B /> 1 .9 193 214 15.3 22.83 15351 672 1220 1.2 268 223 21 28.89 15565 539 1236 1.5 367 245 29 34.41 15840 460 1258 1.8 516 287 41 38.4 16002 417 1270 2 6G3 331 53 41.37 16021 387 1272 2.2 900 409 71 47 64 16175 340 1283 2.3 1087 473 86 52.71 16334 310 1296 2.4 1446 603 115 60.44 16514 273 1309 2.51 2835 3129 225 64.73 16586 256 1315 2.7 5554 2057 442 68.57 16630 243 1319 2.826 7571 2679 602 74.97 16873 225 1337 3.2 10641 3325 847 81.14 16880 208 1337 4.43 12437 2808 989 89.60 17115 191 1335 5.49 13288 2421 1057 99.66 17374 174 1375 6.86 13815 2014 1099 125.26 17841 142 1410 8.14 14058 1727 1118 151.09 18280 121 1443 10.06 14393 1431 1145 178.23 18329 103 1444 12.43 14651 1179 1165 205,03 18793 92 1479 15.54 14905 959 1185 228.57 18942 83 1489 19.02 15217 800 1209 299.44 19571 65 1534 TABLE II. Wire under tension of 323 kg. per sq. cm. H x Lt H ^xlO- Ll H %* 1.05 .67 10.93 72.55 69.94 17.97 1.23 .67 12.75 72 . 55 80.46 38.61 1.51 1.33 14.31 75.21 100.12 79.21 1.87 1.33 16.09 73.88 110.17 - 103.84 2.51 -f 32 62 18.70 64.56 124.80 137.12 3.11 59.90 ... 57.91 142.63 - 181.71 3.70 65.23 29. '53 56.58 166.40 - 235.62 4.30 69.89 35.89 44.60 201.15 - 312.17 5.94 71.22 40.00 41.27 246.86 - 392.05 6.35 69.89 45.72 28.62 269.72 445.30 7.45 9.14 69.89 72.55 53.76 64.41 17.31 3.99 f 22 TABLE Ha. Values of modulus of elasticity. H ^ x 10" = M al H ^x!0=Jf H ^x 10" = M al 2.88 7.74 33.28 10.47 113.38 11.56 3.66 9.44 36.98 10.33 121.60 10.46 5.03 9.68 44.25 11.06 131.66 10.06 7.45 9.33 52.62 10.76 143.09 10.06 9.13 9.00 58.47 11.39 157.26 8.60 12.02 9.68 65.24 11.91 174.64 8.60 15.04 9.68 68.57 11.73 197.49 7 67 18.38 9.68 79.09 11.91 211.66 7.74 23.64 9.68 85.94 12.49 237.72 8.15 27.93 9.80 103.05 12.10 301.73 7.45 TABLE Ub. H B /* I H B /J- / .8 168 210 13.3 12.71 14(599 1157 1169 1 214 214 17 15.77 14892 944 1184 1.3 293 225 23 20.43 15197 744 1208 1.5 353 235 28 27.02 15552 576 1235 1.7 429 252 34 31.91 156HO 491 1245 1.9 524 276 42 39.27 15799 402 1254 2.1 666 317 53 48.92 16174 331 1283 2.3 962 418 76 55.43 16267 293 1990 2.42 1824 754 145 66.04 16433 249 1302 2.70 5952 2204 473 75.43 16545 219 1311 2.88 8106 2815 645 91.43 16954 185 1342 3.11 10858 3491 864 116.57 17417 149 1377 3.22 11901 3696 947 141.72 17852 126 1409 4.57 13093 2865 1042 172.57 18148 105 1430 6.33 1M905 2197 1106 215.32 18607 86 1464 7.8*4 14162 1806 1126 222.86 18872 85 1484 10.38 14561 1403 1158 297.15 19420 65 1522 23 TABLE III. Nickel. Tension in wire = 30 kg. per sq. cm. fir H ^ x 10* J.J H 77 x 1Q8 H z x 1Q8 .59 .67 11.02 46.59 64.37 679.59 .78 .67 12.89 51.92 70.40 779.44 1.05 1.33 14.22 52.58 87.77 992.43 1.37 2.00 16.23 48.59 101.94 - 1152.2 2.10 6.00 18.83 35.28 119.32 - 1333.2 3.38 12.65 22.26 1 33 146.74 1660.7 4.57 18.64 27.29 60.57 170.52 - 1848.4 5.12 19.97 32.50 133.79 ^06.17 2061.4 5.48 21.30 35.89 185.71 242^29 - 2234.5 6.35 26.63 42.97 - 320.16 315.44 2488.7 7.54 33.28 49.69 - 433.32 9.23 41.27 58.52 566.44 TABLE Values of the modulus. H ^x IQ 11 = M TT ^x!0" = Jf H -f x 10 n = M al al al 6.92 13.71 8.65 100.11 7.50 .23 7.40 18.20 8.72 116.57 7.80 1.01 7.53 23.68 8.55 139.89 7.36 1.69 7.87 32.18 8.40 175.09 5.94 2.38 7.97 39.41 8.33 211.20 6.09 3.29 8.17 45.53 8.22 233.15 6.04 4.21 8.28 52.94 8.36 278.86 5.76 5.99 8.43 63.96 8.25 329.15 5.64 7.41 8.51 69.94 8.17 10.15 8.65 84.57 7.72 TABLE III&. H B V / H B > 1 1 24 24 1.8 31.91 2711 85 213 2 48 24 3.6 37.58 2997 80 236 3 74 25 5.6 45.99 3362 73 264 4 105 26 8 54.86 3662 67 278 5 149 30 11.4 66.88 3969 59 311 5.5 174 32 13.4 77.26 4245 55 332 6.13 246 40 19 97.83 4556 47 355 6.99 293 42 23 129.37 4942 38 383 8.23 405 49 32 142'. 4 5064 36 392 9.28 485 52 38 173.49 5305 31 408 10.65 604 57 47 212.12 5495 26 ! 420 15.22 1220 80 96 221.20 5635 25 431 20.8 1882 91 148 242.29 5633 23 429 25.69 2313 90 182 290.29 6787 L>0 437 TABLE IV. Wire under tension of 179 kg. per sq. era. H ^xlO< _// H %xIO- H *>' .23 .67 9.10 23.96 67.89 7",7.r, .73 .67 12.98 19.30 87.77 - 1052.3 1.14 2.00 16.32 4.66 121.14 1398.5 1.83 6.66 20.62 34.61 148.57 - 1667.4 2.83 8.65 27.-J-.I 114.49 181.95 - 1940.3 3.61 10.65 30.03 170.4 212.12 2149.9 4.53 12.65 37.17 278.9 242.29 2372.3 5.99 17.97 45.30 397.4 288 2579.9 7.04 21.30 57.56 579.1 25 TABLE IVa. Values of the modulus. TJ r H al H ^x 10 12 = M al H 1 , x 10 12 = M al 3.38 4.98 4.09 66.97 3.73 .46 3.49 6.17 4.09 78.17 3.35 .91 3.67 7.86 4.05 86.40 3.55 1.37 3.87 9.28 4.21 109.26 3.11 1.83 3.97 11.89 4.17 134.86 3.30 2.29 3.90 14.54 4.29 156.35 3.11 2.74 4.01 18.24 4.52 192.00 3.30 3.20 4.09 30.04 4.09 223.55 3.30 3.66 4.13 40.46 3.90 274.29 2.84 4.11 4.13 53.21 3.55 TABLE IVft. H 13 1 J - / H B /->- / 2 52 26 4 18.29 1451 79 114 3 80 27 6.1 22.86 1866 82 147 4 117 29 9 32.69 2479 76 195 5 159 32 12.2 40.69 2860 70 224 6 207 35 16 49.69 3209 65 251 6.86 253 37 19.6 59.34 3501 59 274 7.77 333 43 26 73.6 3887 53 303 8.69 397 46 31 87.32 4185 48 326 10.06 484 48 38 97.37 4357 45 339 10.97 564 51 44 116.34 4530 39 351 11.89 676 57 53 143.09 4945 35 382 12.8 788 62 62 192.46 5330 28 409 14.63 1036 71 81 240 5564 23 424 16 1196 75 94 333.72 5904 18 443 26 TABLE V. Elongations of Table I due to magnetization alone. 1.98. H -^ x 10" ^ x io 8 + rn H X Xl 8 ^ x 10" + /-// L L 1.1 3.99 1.81 23.21 58.57 104.80 1.65 6.66 3.40 27.84 57.24 112.45 2.24 10.65 6.21 33.00 54.58 120.03 3.02 21.30 15.31 36.75 51.25 124.13 3.34 20.63 14.01 41.33 45.93 127.90 3.66 13.98 6.72 46.95 37.27 130.38 3.93 4.20 7.32 .67 + .47 4- 7.66 54.86 66.29 25.96 5.99 134.76 137.46 6.35 + 32.62 45.21 82.74 20.63 143.46 7.22 39.27 53.59 94.63 43.93 143.75 8.91 47.92 65.59 105.60 63.23 146.20 10.29 53.92 74.33 118.86 89.86 145.87 11.70 57.91 81.11 136.23 - 124.47 145.71 13.58 58.57 85.50 158.17 - 171.06 142.63 14.52 58.57 87.37 191.10 236.30 142.70 17.33 58.57 92.94 224.46 299.53 145.63 18.51 58.57 95.28 251. 4:j 352.78 145.86 I TABLE VI. / ?. 7 ^xlO Li / 20 2 560 12 1180 88 40 4 710 14 1220 103.2 70 6 770 15.5 1258 121.6 100 7.2 840 16.8 1296 134.2 130 7.6 870 14.7 1337 141.1 160 7.8 910 8 1360 144 190 8 950 1400 144.2 220 8.4 1000 14 1534 144.2 330 9.4 1060 34 450 10.5 1100 52 27 TABLE VII. H a = I H a = 2 (I I") I' 1 18 1 650 1.5 24 11.8 770 2 53 16.5 830 2.3 86 19 868 2.45 150 40 990 ... a = 2(7 I"} I' 100 1180 2.93 150 180 1350 3.04 10 3.2 " 130 3.6 270 r = iso 4.5 450 /" = 700 28 PLATES AND DIAGRAMS. Plate 1. Iron. Curves of change in length, magnetization, permeability, induction, and Young's modulus, all plotted to H. Tensile stress 53 kg. per sq. cm. Plate I. Enlarged. Enlargement of first part of elongation and magne- tization curves of Plate I. Plate II. Iron. Curves of change in length, magnetization, permeability, induction, and Young's modulus, plotted to H. Tensile stress = 323 kg. per sq. cm. Plate III. Nickel. Curves of change in length, magnetization, induction, permeability, and Young's modulus, plotted to H. Tensile, stress = 30 kg. per sq. cm. Plate IV. Nickel. Curves of change in length, magnetization, induction, permeability, and Young's modulus, plotted to H. Tensile stress = 179 kg. per sq. cm. Plate V. Iron. Curves of change in length, permeability, Young's mod- ulus, and magnetizing field, plotted to /. Tensile stress = 53 kg. per sq. cm. Plate VI. Nickel. Curves of change in length, permeability, Young's modulus, and magnetizing field, plotted to /. Tensile stress = 30 kg. per sq. cm. Figure 3. Iron. Curve of change in length due to magnetization alone, plotted to H. Tensile stress = 53 kg. per sq. cm. First part enlarged. Figure 4. Iron. Curve of change in length due to magnetization alone, plotted to magnetization. Tensile stress = 53 kg. per sq. cm. Figure 5. Comparison curve, constructed from magnetization curve of Plate I, and plotted to H, showing similarity to elongatian curve of Fig. 3. yj| y iji j||t|f tiff "\8 R A *y UNIVERSITY or l\K \ 3. M. XcM ~/c -20 tcro 7*- fn 9n> /en a. ( | Tiq 5 J : _ ^r ^ - ^-r- - ^ ' ^ > ^^ ,X ^ / / ?n I . 3s* In I -/n / . - J l> - c f c 6 c / t :> ' " ' w / c / It / 7* / t / >1^ / it / >o ' ' r >f REFEBENCES. 1. Barrett, a) Nature 1882, Vol. 26, p. 585. b) Phil. Mag. 1874, Vol. 47, p. 51. 2. Berget. Comp. Rend. 1892, Tom. 115, p. 722. 3. Bidwell. a) Proc. Roy. Soc. 1885, Vol. 38, p. 265. b) " " " " 1886, Vol. 40, pp. 109, 257. c) " " " 1888, Vol. 43, p. 407. d} " " " 1890, Vol. 47, p. 469. e) " " " 1892, Vol. 51, p. 495. /) " " ' " 1894, Vol. 55, p. 228. g} " " " 1894, Vol. 56, p. 94. h) Phil. Tran. Roy. Soc. 1888, Vol. 179A, p. 205. 4. Bock. Wied. Ann. 1895, Vol. 54, p. 442. ' 5. Chree. a) Phil. Tran. Roy. Soc. 1890, Vol. 181, p. 339. b) Nature 1896, Vol. 53, p. 269, 365, 533. 6. Jones, a) Phil. Mag. 1895, Vol. 39, p. 254. b) " " 1896, Vol. 41, pp. 153, 454. 7. Joule. Phil. Mag. 1847, Vol. 30, p. 76, 225. 8. Knott. Phil. Mag. 1894, Vol. 37, p. 141. 9. Lochner. Phil. Mag. 1893, Vol. 36, p. 498. 10. Maxwell. Elec. and Mag. Vol. 2, Chap. 6. 11. Mayer, a) Phil. Mag. 1873, Vol. 45, p. 350. b) " " 1873, Vol. 46, p. 177. 12. More. Phil. Mag. 1895, Vol. 40, p. 345. 13. Nagaoka. a) Phil. Mag. 1894, Vol. 37, p. 131. b) " " 1896, Vol. 41, p. 454. c) Wied. Ann. 1894, Vol. 53, p. 487. 14. Mary C. Noyes. Physical Review 1896, Vol. 3, p. 432. 15. J. J. Thomson. Appl. Dyu. to Ph. and Chem. BIOGRAPHICAL SKETCH. Edson Fessenden Gallaudet was born at Washington, D. C., April 21, 1871. Entered the Hartford Public High School in 1885, graduating in 1889. In fall of that year entered Yale Uni- versity, in the Academic Department ; graduated in 1893. In fall of 1893 entered upon graduate work at Johns Hopkins Univer- sity, where he studied till June, 1896. Best known as the second son of E. M. Gallaudet, President of the Columbian Institution for the Deaf and Dumb, Washington, D. C. OFTH1 UNIVERSITY 1VERSITY OF CALIFORNIA LIBKAK'Y, BEEKELEY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW V Books not returned on time are subject to a fine of J50c per volume after the third day overdue, in< to $1.00 per volume after the sixth day. 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