THE MAGNETIZATION OF COBALT AS A 
 FUNCTION OF THE TEMPERATURE 
 AND THE DETERMINATION OF ITS 
 INTRINSIC MAGNETIC FIELD 
 
 by 
 
 WILLIAM WARREN STIFLER 
 
 A. B. Shurlleff College, 1902 
 A. M. University of Illinois, 1008 
 
 THESIS 
 
 Submitted in Partial Fulfillment of the Requirements 
 for the Degree of Doctor of Philosophy in 
 Physics in the Graduate School of 
 the ltniversity of illinois 
 1911 
 
 Press of 
 The New Era Printing Co. 
 Lancaster, Pa. 
 1911 
 
(Reprinted from the Physical Review, Vol. XXXIII., No. 4. October, ion.) 
 
 THE MAGNETIZATION OF COBALT AS A FUNCTION OF 
 THE TEMPERATURE AND THE DETERMINATION 
 OF ITS INTRINSIC MAGNETIC FIELD. 
 
 By W. W. Stifler. 
 
 Introduction. 
 
 THOUGH cobalt has always been classed as one of the strongly 
 magnetic metals, its properties do not seem to have been studied 
 with the interest manifested in those of iron and nickel. In spite of 
 the work of E. Becquerel, 1 Pliicker, 2 Rowland, 3 Hankel, 4 H. Becquerel, 5 
 Gaiffe, 6 Trowbridge and McRea, 7 Berson, 8 Bidwell, 9 Ewing and Low, 10 
 duBois, 11 Fleming, Ashton and Tomlinson, 12 Beattie, 13 , and Nagaoka and 
 Honda, 14 until very recently the amount of real numerical data on the 
 magnetic properties of cobalt, even at ordinary temperatures, was very 
 meagre. 
 
 Within the last two years several articles have been published which 
 are of great interest from a theoretical point of view. One of these is 
 by P. Weiss 15 and gives the results of work at ordinary temperatures; 
 another is by Weiss and Kamerlingh Onnes 16 and gives the results of their 
 work at very low temperatures. In the investigation described in the 
 first of these papers, the saturation value of the specific intensity of 
 
 1 Comp. Rend., 20, pp. 1708-1711, 1845. 
 'Pogg. Ann., 91, pp. 1-56, 1854. 
 s Phil. Mag., 164, pp. 321-340, 1874. 
 •Ann. der Physik, N. F. 1, pp. 285-296, 1877. 
 
 'Ann. de Chim. et de Phys., Ser. 5, 16, pp. 227-286, 1879; Comp. Rend., 88, pp. 111-114 
 1879- 
 
 'Comp. Rend., 93, pp. 461-462, 1881. 
 
 7 Proc. Am. Acad. Arts and Sciences, 20, pp. 462-472, 1884-85. 
 
 'Journal de Physique, is, pp. 437-456, 1886; Ann. de Chim. et de Phys., Ser. 6, 8, pp. 
 433-502, 1886; Lum. Electr., 21, pp. 259-267, 1886. 
 
 'Phil. Trans. Roy. Soc. London, 179A, pp. 205-230, 1888. For cobalt see p. 215. 
 
 10 Phil. Trans. Roy. Soc. London, 180A, pp. 221-244, 1898. 
 
 "Phil. Mag., 195, pp. 293-306 and pp. 253-267, 1890. 
 
 12 Phil. Mag., 214, pp. 271-279, 1899. 
 
 "Phil. Mag., 217, pp. 642-647, 1901. 
 
 14 Phil. Mag., 220, pp. 45-72, 1902. 
 
 "Journal de Physique, Ser. 4, 9, pp. 373-393, 1910; Archives des Sciences (Geneve), 
 Ser. 4, 29, pp. 175-203, 1910. 
 
 "Journal de Physique, Ser. 4, 9, pp. 555-584, 1910; Konink. Akad. Wetensch. Amsterdam, 
 Proc. 12, pp. 649-677, 1910; Comp. Rend., 150, pp. 686-689, 1910. 
 
269 
 
 W. IF. STIFLER. 
 
 [Vol. XXXIII. 
 
 magnetization — that is, the intensity of magnetization per gram — was 
 determined. Weiss found that the law of approach to saturation at 
 1 7° C. for cobalt was given by the equation 
 
 where a is the specific intensity of magnetization. By plotting u as a 
 function of I /IP and extrapolating he found the saturation value to be 
 162 at 1 7 C. These results were confirmed by the work of Droz 1 pub- 
 lished at the same time. In the second investigation measurements were 
 taken at temperatures as low as that of liquid hydrogen. The value of 
 <r at these very low temperatures was found to be less than 163.6. 
 
 Very recently Weiss 2 has measured the specific susceptibility of cobalt 
 in the temperature interval from 1156 C. to 1302 C. using a method 
 similar to that employed by Curie in his classical researches on the 
 magnetic properties of bodies at high temperatures. 3 This article was 
 published some months after the present investigation was undertaken. 
 Weiss states that the "Curie point" for cobalt is probably in the neigh- 
 borhood of mo° C. 
 
 The recent developments of the electron theory of magnetism make 
 a knowledge of the saturation value of the intensity of magnetization as 
 a function of the temperature of great theoretical interest and the present 
 investigation was undertaken with the objects: 
 
 1. To determine the specific intensity of magnetization at various 
 temperatures up to about 1150 C; that is, to a temperature somewhat 
 above that at which spontaneous fcrro-magnetism disappears. 
 
 2. To deduce from these data the value of the intrinsic molecular 
 field of cobalt and the moment of its elementary magnet. 
 
 For this purpose, the method used by Weiss 4 seemed best adapted. It 
 consists essentially in observing the throw of a ballistic galvanometer con- 
 nected in series with a helix placed in a strong longitudinal magnetic field 
 w ben an ellipsoid of the substance to be tested is suddenly jerked out of the 
 helix. The throw of the galvanometer is then compared with that pro- 
 duced when a known current is made or broken through the primary of a 
 st.md.ird helix, the secondary of which is included in the galvanom- 
 
 1 Archives det Sciences (Geneve), Ser. 4. 20. pp. 204-224 and 290-309, 1910. 
 
 •Archives des Sciences (Geneve), Ser. 4, 31. pp. 5-19 and 89-117, 191 1. 
 
 •Ann. dr ( him. et dr I'hys., Ser. 7. ?, pp. 2K9 »".S, i R 9SI Oiuvrcs, pp. 232-334. 
 
 4 I •:• I'll'. 1 1 1. . s.-i |. ij, |>p (7i y>\. kjio; Archive* dot Science* (Geneve), Ser. 
 
 4. jv. pp. « 75-203. 1910. 
 
 10 
 
 a = 162 (1 - I. II — ), 
 
 MKTIIOI). 
 
No. 4-1 
 
 MAGNETIZATION OF COBALT. 
 
 27O 
 
 ^ — 
 
 eter circuit. The connections are shown diagrammatically in Fig. 1, 
 where C is the cobalt ellipsoid; H is the induction helix connected 
 
 in series with the controlling resistance, R', 
 the galvanometer, G, and the secondary, S, of 
 the standard helix; P is the primary of the 
 standard helix; R, the controlling resistance; 
 and A is a carefully calibrated ammeter. 
 
 The formulae for a and I by this method are 
 easily shown to be 
 
 mn'Aji - dtW) V d = R d 
 iow«(i — di\2li) d' 
 
 and 
 
 Fig. 1. 
 
 _ nm'A (I - d 1 W ) r 
 1 ~ ioVn(i - df/2h 2 ) 'd' 
 
 where A 
 
 
 area of cross section of primary of standard helix. 
 
 
 
 number of turns per cm. on primary. 
 
 N' 
 
 
 total number of turns on secondary. 
 
 h 
 
 
 length of primary. 
 
 
 
 diameter of primary. 
 
 n 
 
 
 number of turns per centimeter on H. 
 
 k 
 
 
 length of H. 
 
 di 
 
 
 diameter of H. 
 
 m 
 
 
 mass of C. 
 
 V 
 
 
 volume of C. 
 
 d 
 
 
 deflection of galvanometer when C is jerked out of H. 
 
 d' 
 
 
 deflection when current is made or broken through primary.. 
 
 V 
 
 
 current in amperes through primary. 
 
 The advantage of using a rather than I lies in the fact that <r is inde- 
 pendent of changes in density or volume due to changes in temperature. 
 The value of the field H inside the ellipsoid for an external field of H is 1 
 
 H = Ho - LI, 
 
 where L is the demagnetizing factor of fne ellipsoid. 
 
 Experimental Details. 
 Magnet. — The magnetic field was obtained by means of a large electro- 
 magnet of the duBois type. The core was approximately 10 cm. in 
 diameter. For this work it was equipped with a pair of conical pole 
 pieces 2.5 cm. in diameter at the smaller end. A hole 2.1 cm. in diameter 
 
 1 Maxwell, Treatise on Electricity and Magnetism, 3d Ed., Vol. II., §437-438, pp. 66-69. 
 
271 
 
 W. W. STIFLER. 
 
 [Vol. XXXIII. 
 
 was drilled through these to permit the ellipsoid to be withdrawn. The 
 magnet would carry 25 amperes for several minutes without undue 
 heating. For each air-gap used, the strength of the field at the center 
 was determined by means of a flip coil and ballistic galvanometer cali- 
 brated by comparison with a standard helix. The field was also measured 
 with a magnetic balance made by Weber in Zurich and practically 
 identical with the one described by Weiss. 1 The results obtained by 
 the two methods were in close agreement. For convenience, the value 
 of the field for currents from 2 to 25 amperes was determined by steps 
 of two or three amperes. From these data curves were plotted giving 
 H as a function of the current, the scale being such that I cm. was 
 equivalent to 100 or 200 lines per square centimeter. 
 
 Galvanometer. — The galvanometer used was a Leeds and Northrup 
 type H instrument. It had a resistance of 26.4 ohms, a ballistic sensi- 
 bility of 45.6 mm. per microcoulomb on open circuit with a scale distance 
 of 50 cm., and a period of 12.7 seconds on open circuit. The scale used 
 had 500 divisions in a length of 25 cm. and was made by photography 
 from a very accurate 50 cm. scale. The sensitiveness was further in- 
 creased by placing the scale at a distance of approximately three meters. 
 With this arrangement the "throw" could be read accurately to 0.5 of 
 a scale division or even less As the instrument as used was on closed 
 circuit, it was practically aperiodic, and its sensitiveness was considerably 
 reduced. 
 
 Heating Apparatus. — The induction helix was used as the core around 
 which was built up a small electric furnace to give the necessary tem- 
 peratures. For various reasons two separate pieces of apparatus were 
 built, one for the lower temperatures, the other for the higher tempera- 
 tures. 
 
 Up to 550 C. the apparatus shown in section in Fig. 2 was used. 
 The induction helix was of No. 30 bare copper wire wound on a hard 
 glass tube. The wire was held in place bycacmentium and, where neces- 
 sarv, libers of asbestos were worked in between the individual turns. 
 There were 89 turns in a length of 4 cm. 
 
 The heating coils were of No. 16 german silver wire and were insulated 
 from the induction helix by a glass tube as shown. In order to decrease 
 the temperature ^radi< nl .it the center of the induction helix, two heating 
 ( <>ilv were us< d. 'I lu- inner one was wound as regularly as possible, while 
 ilu outer one was wound closely at the ends but with the turns much 
 farther apart at the middle. The two coils were separated from each 
 
 'Journal tie I'hyniquc. .16. pp. 43»"435. I9°7- Sec nl»o L'licluiraKc Klcclriquc. 24, pp. 
 
 357 266, 1900, ami Journal da i'iiy»iquc. 20. pp- 383-390. 1900. 
 
No. 4-] 
 
 MAGNETIZATION OF COBALT. 
 
 272 
 
 other by mica. In order to reduce the magnetic effect of the heating 
 currents, the two coils were always connected so that they opposed each 
 other magnetically. By properly adjusting the currents in the two coils, 
 the temperature at the center of the helix could be made constant to 
 within 2° C. over a distance of 10 to 15 mm. The coils were packed in 
 loose asbestos, and the whole apparatus was covered with asbestos board. 
 
 Owing to the fact that at the higher temperatures saturation is reached 
 at lower fields, the apparatus used for temperatures above 550 C. was 
 
 I 3i <i Si 4., t, a, 9, id 
 
 Cm. 
 
 Fig. 2. 
 
 5, induction helix; Hi, primary heating coil; Hi, secondary heating coil; NS, magnet; 
 C. cobalt ellipsoid; AB, asbestos board; AF, asbestos fiber; GG, glass tubes; M, mica; 
 XX, galvanometer circuit. 
 
 somewhat larger though of similar design. The core of the induction 
 helix was a clear quartz tube. The helix was of No. 30 bare platinum 
 wire wound in two layers separated from each other by mica. The 
 individual turns were separated from each other by asbestos yarn. 
 Though the insulating power of this broke down considerably above 
 iooo C, actual tests showed that this did not introduce any appreciable 
 error. 
 
 The heating coils were of No. 13 nickel wire and were separated from 
 the helix by a tube of fused silica. Since nickel loses its magnetic prop- 
 erties at 360 C, no error was introduced by its use. The primary 
 heating coil was wound in two layers. Asbestos yarn was used to 
 separate the individual turns, while the layers were insulated from each 
 other by mica. The secondary heating coil consisted of one layer and 
 was wound as in the other apparatus. 
 
273 
 
 W. W. STIFLER. 
 
 (Vol. XXXIII. 
 
 Calcined magnesia contained in a porcelain ring was used as an heat 
 insulator next to the coils. Outside of this a layer of magnesia packing 
 such as is used for high pressure steam pipes was used. The whole 
 apparatus was covered with asbestos board. It is shown in section in 
 Fig. 3. The heating coils on this apparatus burned out several times 
 during the course of the experiments but they were rewound and the 
 apparatus rebuilt in substantially the same way each time. The induc- 
 tion helix was not injured in any way. 
 
 ~ • '< » » »■ »i 
 
 cm 
 
 Fig. 3. 
 
 Si. induction helix; St. fused silica tube; Hi, primary heating coil; Hi. secondary heating 
 coil; M. mica insulation; A. asbestos board; P, porcelain ring; (), quartz tube; X, galva- 
 nometer circuit. 
 
 Temperature Measurements. — Temperatures were measured with a 
 thermocouple. A Wolff potentiometer and Weston standard cell were 
 used to measure itsc.m.f., and the resistance in the galvanometer circuit 
 was adjusted so that the instrument read directly to one microvolt. 
 The method of reading and calibration was essentially that described by 
 Clement and Fgy. 1 For temperatures between ioo° C. and 420 C, a 
 copper-platinum thermocouple was used. As this has an inversion point 
 .it .,l.oin Oo C, it was not um (| below 100" ( '. It was calibrated by the 
 boiling point of water, the freezing point of zinc, and by several inter- 
 
 ' Univ. 01 III. Eng. Iixp. Station Bulletin No. 36, 1909. 
 
No. 4.] 
 
 MAGNETIZATION OF COBALT. 
 
 274 
 
 mediate points lying between 120 C. and 250 C. which were determined 
 by comparison with a carefully calibrated mercury thermometer. The 
 temperatures were read from the corresponding e.m.f.'s by a calibration 
 curve plotted to such a scale that 1 mm. corresponded to i° C. 
 
 For temperatures above 420 C, a platinum platinum-rhodium couple 
 was used. This was calibrated at the freezing points of zinc, silver, and 
 copper. From these three points the three constants of the standard 
 parabolic equation were calculated. The couple as used was easily sensi- 
 tive to 1 microvolt — equivalent to about o.i° C. — at 1100 C. The 
 temperatures as read from either couple are probably accurate at i° C. 
 
 P reparation and Mounting of the Ellipsoids. — The first samples of cobalt 
 obtained were in the form of small lumps 3 or 4 mm. in diameter. Several 
 attempts were made to fuse these into a button, using first a small assay 
 furnace and later a coke furnace. These attempts proved futile, owing 
 to the very high melting point of cobalt — 1489. 8° C. 
 
 After one or two preliminary trials, a button weighing about 200 grams 
 was prepared from the oxide by the Goldschmidt process. From this 
 two rings were turned and tested by the ring method. The tests on 
 the larger ring — No. 1 — gave values of B of only about one tenth the 
 magnitude to be expected. Annealing for several hours at white heat 
 improved this decidedly, though the results were still only about one 
 third of the accepted values. The smaller ring — No. 2 — gave similar 
 results without being annealed. Analysis showed that these samples 
 contained about 1 per cent, of aluminum. 
 
 One hundred grams of cobalt in rectangular sheets about 6 cm. X 10 
 cm. X 0.05 cm. were then obtained from Kahlbaum through Eimer and 
 Amend. Tests on a ring — No. 3 — made by building up five layers of this 
 showed that its magnetic properties were excellent (see Fig. 4). 
 
 To get this material into a form from which ellipsoids could be ground, 
 it was necessary to fuse it into a button or rod. At first this was accom- 
 plished by means of a vertical platinum resistance furnace, using a 
 maximum power consumption of approximately 2,200 watts. A No. o 
 black lead crucible, lined with a paste of 98 per cent, magnesite and 2 
 per cent, bone ash, was used. After the lining was thoroughly dry, a 
 charge of about 20 grams of metal was put in and this was covered with 
 a layer of borax glass. After several hours the cobalt fused, giving a 
 very homogeneous button about 2 cm. in diameter and 0.6 cm. thick. 
 
 An attempt to repeat the process resulted in burning out the furnace 
 before the cobalt was entirely fused. However one piece was obtained 
 from which it was possible to turn an ellipsoid. 
 
 After considerable practice it was found possible to prepare the material 
 
275 
 
 n*. ir. STIFLER. 
 
 [Vol. XXXIII. 
 
 by melting it in a fused silica tube held in an arc. Owing to the impos- 
 sibility of securing anything like uniform heating over even a short 
 distance, it was only with great difficulty that two or three rods ap- 
 proximately 0.5 cm. in diameter and 1.0 cm. to 1.2 cm. long were obtained 
 by this method. 
 
 The ellipsoids were ground from the rods on a Landis Universal 
 Grinder, using an alundum wheel with a properly shaped rim. After 
 grinding, the accuracy of the shape was tested and found to be satis- 
 factory by projecting the enlarged shadow of the ellipsoids with an 
 Edinger Drawing Apparatus. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 000 
 
 
 
 
 
 
 
 
 
 I 
 
 000 ^ 
 
 
 
 
 
 
 ,0 / 
 
 
 « 1 
 
 / 4 
 
 000 / / 
 
 rff / f, 
 
 a 
 
 . . 
 
 
 If *» 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 2 
 
 006 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 R.'nf Us : 
 
 
 
 
 
 
 /o 
 
 O06 
 
 
 
 
 
 Kig. 4. 
 
 In all, five ellipsoids of revolution, approximately 1 cm. long and 0.45 
 cm. in diameter, were prepared. Complete sets of data, however, were 
 carried out for only two. The ellipsoids were distinguished for con- 
 venience as A, B, C, D, and E. The method of preparing each is given 
 below, and a summary of their dimensions is given in Table I. 
 
 A — made from first melting in resistance furnace. C ross-section very 
 accurate. 
 
 B— made from the same button as A. Not quite as perfect cross- 
 section as A. 
 
 C— made from rod prepared by melting the metal in fused silica tube 
 h< Id in arc. Cross-section fairly accurate. 
 
 D — made from sample melted in silica tube in arc. Cross-section 
 
 fairly accurate. 
 
No. 4.] 
 
 MAGNETIZATION OF COBALT. 
 
 276 
 
 E — made from second melting in resistance furnace. Cross-section 
 fairly accurate except for very slight pit near one end. 
 
 Table I. 
 
 
 
 Mean 
 Diam. 
 
 
 Spec. 
 Grav. 
 
 Volume by 
 
 
 
 
 Length. 
 
 Mass. 
 
 Displac. of 
 Water. 
 
 Calcula- 
 tion. 
 
 e 
 
 
 A 
 
 0.9965 
 
 0.4475 
 
 0.8633 
 
 8.25 
 
 0.1047 
 
 0.1045 
 
 0.8934 
 
 1.9385 
 
 B 
 
 0.9330 
 
 0.4480 
 
 0.8412 
 
 8.24 
 
 0.1021 
 
 0.0981 
 
 0.8770 
 
 2.0890 
 
 C 
 
 0.9370 
 
 0.4110 
 
 0.6804 
 
 8.80 
 
 0.0773 
 
 0.0829 
 
 0.8986 
 
 1.8888 
 
 D 
 
 0.9960 
 
 0.4430 
 
 0.8275 
 
 8.74 
 
 0.0947 
 
 0.1023 
 
 0.8956 
 
 1.9177 
 
 E 
 
 0.9920 
 
 0.4250 
 
 0.8528 
 
 8.73 
 
 0.0977 
 
 0.0938 
 
 0.8992 
 
 1.8817 
 
 In some of the later work, C and E became more or less oxidized. 
 In each case the oxide was carefully removed with fine emery cloth and 
 the specimen was carefully polished with crocus cloth and weighed. 
 Measurements showed that the shape of the ellipsoids was not altered 
 appreciably by this process. 
 
 The reason for the low specific gravity of A and B is unexplained as yet. 
 
 A chemical analysis of the original material showed that it was 100 
 per cent, pure, with the possibility of a trace of nickel. 
 
 For temperatures below 420 C, the ellipsoids were mounted in glass 
 tubes sealed at one end. The thermocouple was inserted through the 
 other end and the junction was separated from the cobalt by a thin layer 
 of mica. As a rule the junction was about one third of the total length 
 
 (GlaSS) ~T/(S..l.n,W«x) 
 
 (Quart*) — ^p^eiSSo '~ W 
 
 Fig. 5. 
 
 of the ellipsoid from the end. For temperatures above 300 C. the end 
 of the tube through which the thermocouple was inserted was sealed 
 with sealing wax, and the whole tube was exhausted and sealed to avoid 
 oxidation of the ellipsoid. 
 
 For temperatures above 420° C. a clear quartz tube was used to hold 
 the ellipsoid. A glass tube was joined to the open end of this for con- 
 
277 
 
 W. IT'. STIFLER. 
 
 [Vol. XXXIII. 
 
 venience in exhausting. No particular difficulty was experienced in 
 making the joints air tight with sealing wax, but at the higher tempera- 
 tures the quartz devitrified upon prolonged heating and the end became 
 "chalky." In this condition it would admit air and in one or two in- 
 stances as noted above the specimens were oxidized in attempting to 
 carry out a second set of readings. Eventually it was found necessary 
 to re-seal the end of the tube and exhaust the tube anew after each set 
 of readings. Fig. 5 shows the two methods of mounting. 
 
 Procedure in Taking Readings. 
 
 The general method of taking readings was as follows. The furnace 
 was heated for several hours until thermal equilibrium was established. 
 It was found necessary to draw the heating currents from a large storage 
 battery as the variation of 0.1 ampere caused a very appreciable change 
 in temperature. For the higher temperatures heating currents of 15 to 
 20 amperes were used. When everything had reached a steady state, 
 the tube containing the ellipsoid and thermocouple was inserted. The 
 position of the tube to bring the ellipsoid into the center of the helix 
 was approximately determined by throwing on the magnetic field for a 
 moment. The tube was then moved by steps of 2 to 5 mm. along the 
 helix, and readings of the temperature at each position were taken after 
 sufficient time had elapsed for the cobalt to take up the temperature of 
 its surroundings. As there is usually comparatively little lag in the 
 readings of a thermocouple, the fact that sometimes as many as twelve 
 or fifteen minutes were required before its readings became constant 
 indicated that the thermocouple was registering the actual temperature 
 of the cobalt. Usually it was possible to adjust the heating currents 
 so that a change of a centimeter in the position of the cobalt produced 
 a change of only 2° or in the readings of the thermocouple. At the 
 lower temperatures it was possible to do much better than this. Under 
 tiller circumstances, the assumption that the temperature of the ellipsoid 
 was uniform to at least l° C. seemed justifiable. 
 
 The ellipsoid was placed in the position indicated as that at the highest 
 temperature, and the tube was marked so that it was possible to replace 
 it exactly in this position. When the ellipsoid had reached thermal 
 equilibrium, the reading of the thermocouple was taken, the magnetic 
 luld was thrown on, and the dellection of the galvanometer when the 
 ellipsoid was jerked out of I he helix was noted. The magnetic field wa« 
 then thrown off and the ellipsoid was replaced in position and allowed 
 t<> o .1111 its former temperature. As a rule, three readings were taken 
 al • ,i< h held strength and the mean of the deflections w.ls used in calculate 
 
No. 4.] 
 
 MAGNETIZATION OF COBALT. 
 
 278 
 
 ing / and a. At the lower temperatures these readings usually agreed to 
 half a scale division in two hundred or more. At the higher temperatures 
 they were not so great and the agreement was not quite so good. However 
 the readings as a whole were very consistent even under these circum- 
 stances, usually agreeing with each other to within I per cent, or at most 
 2 per cent, up to 900 C. The reading of the thermocouple was taken 
 each time just before the ellipsoid was withdrawn, and — as a rule — these 
 readings were not allowed to differ by more than 15 microvolts, corre- 
 sponding to 1. 5 C, during a set of readings. At the very high tempera- 
 tures where the cobalt was especially sensitive to changes of temperature, 
 the variation was made even less. The mean of the thermo-couple read- 
 ings was used in calculating the temperature. 
 
 After nearly every set of readings, the galvanometer was calibrated 
 by means of the standard helix. The current, I', for this purpose was 
 read by a Siemens and Halske milliammeter which had been calibrated 
 with a standard ohm coil and potentiometer. For temperatures up to 
 1000 C, the values of I' Id' remained practically constant and the mean 
 value was used in calculating a. 
 
 The magnetic fields used ranged from 1,600 gausses to 6,900 gausses 
 for the lower temperatures, giving fields of from 800 gausses to 5,000 
 gausses inside the ellipsoids. As these were insufficient to produce 
 saturation below 350 C, the saturation values were determined by an 
 extrapolation similar to that of Weiss mentioned above. As neither 
 a and i/H nor a and 1/H 2 gave a straight line, both were plotted and the 
 mean of the values was used. The results at these lower temperatures 
 were not used in the theoretical deductions so that extreme accuracy in 
 the extrapolated results is not important. Above 350 C. saturation 
 could be reached with the fields used, and at the higher temperatures 
 fields as low as 3,500 gausses produced saturation. The values of the 
 magnetic field were corrected for the magnetic effect of the heating 
 coils whenever this effect was appreciable. 
 
 In the interval between 1050 C. and 1100 C. it was very difficult 
 to obtain consistent readings, as a very slight change in temperature 
 produced a marked change in a. At these higher temperatures also 
 thermoelectromotive effects in the galvanometer caused some difficulty, 
 rendering the zero of the galvanometer somewhat uncertain at times and 
 often causing it to drift steadily in one direction. These difficulties 
 were remedied in large measure by keeping the junctions of the platinum 
 leads from the helix and the copper connecting wires at o° C. 
 
H". TV. STIFLER. 
 
 [Vol. XXXIII. 
 
 Data. 
 
 The data obtained for ellipsoids C and E are summarized in the fol- 
 lowing tables. Tables II. and III. give the values of H and <r as observed 
 at various temperatures, and the values of ex K . Table IV. gives a sum- 
 mary of this. Fig. 6 shows the method of determining <r x below 400 C. 
 by extrapolation. The extrapolated values are probably accurate to 1 
 per cent. Curve A in Fig. 7 shows <x as a function of the temperature. 
 The close agreement between the results for ellipsoids C and E argues 
 for the accuracy of the data. 
 
 From the data we can also calculate B and draw magnetization curves 
 for high fields at various temperatures. Several of these curves are 
 shown in Fig. 8. 
 
 Theoretical Considerations. 
 In his article upon the magnetic properties of bodies at high tempera- 
 tures to which reference was made above, Curie called attention to the 
 
 Table II. 
 
 Ellipsoid C. 
 
 
 C. 
 
 130° C. 
 
 335° C. * 
 
 307 
 
 c. 
 
 4M° C. 
 
 H 
 
 a 
 
 If 
 
 a 
 
 H 
 
 1 " 
 
 H 
 
 
 II 
 
 a 
 
 725 
 
 102.4 
 
 713 
 
 103.0 
 
 625 
 
 108.4 
 
 500 
 
 115.9 
 
 460 
 
 119.2 
 
 1,955 
 
 139.6 
 
 2.154 
 
 114.2 
 
 1,984 
 
 149.2 
 
 1,980 
 
 149.6 
 
 2,055 
 
 145.8 
 
 2,985 
 
 149.1 
 
 3,031 
 
 151.5 
 
 3,026 
 
 151.8 
 
 3,060 
 
 149.9 
 
 3,135 
 
 146.3 
 
 3,450 
 
 153.2 
 
 3,774 
 
 153.5 
 
 3,816 
 
 152.5 
 
 3,825 
 
 150.4 
 
 3,930 
 
 146.4 
 
 3,955 
 
 154.6 
 
 4,200 
 
 153.3 
 
 4,386 
 
 152.8 
 
 4,425 
 
 150.4 
 
 4,515 
 
 146.4 
 
 4,270 
 
 155.2 
 
 
 
 
 
 
 
 
 
 
 = 161.0 
 
 
 = 158.5 
 
 
 = 154.0 
 
 
 = 151.0 
 
 
 = 146.4 
 
 54,0 c. 
 
 6 9 8 
 
 °c. 
 
 874 
 
 °c. 
 
 991° C. 
 
 K'43 
 
 °c. 
 
 H 
 
 a 
 
 H 
 
 a 
 
 H 
 
 
 H 
 
 a 
 
 II 
 
 a 
 
 445 
 
 120.2 
 
 140 
 
 87.5 
 
 215 
 
 83.4 
 
 370 
 
 72.3 
 
 770 
 
 46.4 
 
 2,160 
 
 139.9 
 
 855 
 
 124.1 
 
 1,300 
 
 97.9 
 
 1,680 
 
 72.1 
 
 2,070 
 
 47.5 
 
 3,250 
 
 139.6 
 
 1,620 
 
 124.3 
 
 2,015 
 
 97.9 
 
 2,385 
 
 73.1 
 
 2,780 
 
 49.1 
 
 4,015 
 
 140.2 
 
 2,115 
 
 125.2 
 
 2,510 
 
 98.7 
 
 2,880 
 
 73.3 
 
 3,290 
 
 48.9 
 
 4,610 
 
 140.0 
 
 2,400 
 
 124.9 
 
 3,915 
 
 97.9 
 
 3,335 
 
 71.9 
 
 3,680 
 
 49.5 
 
 *• 
 
 140.2 
 
 
 -125.2 
 
 
 = 9.X.7 
 
 =73.3 
 
 =49.5 
 
 10650 C. 
 
 108a C. 
 
 1104 
 
 C. 
 
 
 °c. 
 
 
 
 H 
 
 » 
 
 H 
 
 » 
 
 II 
 
 9 
 
 II 
 
 a 
 
 
 
 1,165 
 
 21.4 
 
 3,250 
 
 6.0 
 
 1,400 
 
 1.3 
 
 1,370 
 
 ? 
 
 
 
 2.4(H) 
 
 26.8 
 
 
 
 2,100 
 
 1.9 
 
 2,380 
 
 ? 
 
 
 
 (.(H,0 
 
 (ii (i 
 
 
 
 3,050 
 
 2.6 
 
 3,090 
 
 ? 
 
 
 
 3,570 
 
 29.7 
 
 
 
 
 
 (. W) 
 
 ? 
 
 
 
 4.(110 
 
 29.4 
 
 
 
 
 
 
 
 
 
 a , 
 
 30.0 
 
 -6.0 
 
 
 2.6(?) 
 
 *• 
 
 -? 
 
 
 
 ira|>-il.it inn from curve*. 
 
No. 4I 
 
 MAGNETIZATION OF COBALT. 
 
 Table III. 
 
 Ellipsoid E. 
 
 22° . 
 
 127° c. 
 
 232 c. 
 
 300 c. 
 
 415 
 
 3 c. 
 
 59° 
 
 C. 
 
 H 
 
 a 
 
 H 
 
 XT 
 
 H 
 
 a 
 
 H 
 
 a 
 
 H 
 
 
 H 
 
 
 490 
 
 66.6 
 
 876 
 
 94.3 
 
 720 
 
 103.9 
 
 540 
 
 114.6 
 
 650 
 
 108.9 
 
 690 
 
 106.8 
 
 1,285 
 
 104.6 
 
 2,190 
 
 138.6 
 
 2,050 
 
 147.0 
 
 2,175 
 
 145.6 
 
 2,160 
 
 142.2 
 
 2,305 
 
 132.7 
 
 2,575 
 
 134.2 
 
 3,135 
 
 147.1 
 
 3,115 
 
 148.3 
 
 3,140 
 
 146.8 
 
 3,240 
 
 141.6 
 
 3,385 
 
 133.0 
 
 3,260 
 
 142.6 
 
 3,905 
 
 148.9 
 
 3,930 
 
 149.6 
 
 3,970 
 
 146.8 
 
 3,990 
 
 142.6 
 
 4,155 
 
 133.4 
 
 4,065 
 
 148.3 
 
 4,225 
 
 149.5 
 
 4,930 
 
 149.0 
 
 4,505 
 
 147.3 
 
 4,625 
 
 141.2 
 
 4,760 
 
 132.9 
 
 4,445 
 
 149.6 
 
 
 
 
 
 
 
 
 
 
 
 a x x - 
 
 161.0 
 
 ir^i = 
 
 154.0 
 
 «V = 
 
 150.5 
 
 
 148.0 
 
 <r = 142.3 
 
 "ao = 
 
 133.1 
 
 687° C. 
 
 867°C. 
 
 I02g 
 
 °c. 
 
 1057° c. 
 
 1113 c. 
 
 1144 c. 
 
 165 
 
 81.2 
 
 200 
 
 78.7 
 
 710 
 
 53.0 
 
 850 
 
 34.7 
 
 3,800 
 
 3.5 
 
 1,420 
 
 ? 
 
 830 
 
 121.4 
 
 1,210 
 
 97.3 
 
 1,850 
 
 57.8 
 
 2,750 
 
 38.4 
 
 
 
 2,440 
 
 ? 
 
 1,515 
 
 121.9 
 
 1,950 
 
 96.3 
 
 1,590 
 
 56.8 
 
 3,185 
 
 38.4 
 
 
 
 3,360 
 
 ? 
 
 2,055 
 
 122.0 
 
 2,450 
 
 96.3 
 
 3,160 
 
 53.1 
 
 
 
 
 
 
 
 2,450 
 
 122.5 
 
 2,850 
 
 97.5 
 
 3,570 
 
 53.5 
 
 
 
 
 
 
 
 "=0 = 
 
 122.5 
 
 °"oO = 
 
 97.5 
 
 °"» = 
 
 57.0 
 
 
 38.4 
 
 <r=3.5 
 
 a 
 
 = ? 
 
 Table IV. 
 
 Saturation value of & as a function of the temperature. 
 
 Ellipsoid C. 
 
 Ellipsoid E. 
 
 Ellipsoid C. 
 
 Ellipsoid / . 
 
 Temp. 
 
 0*8) 
 
 Temp. 
 
 
 Temp. 
 
 
 Temp. 
 
 
 22° 
 
 161.0 
 
 22° 
 
 161.0 
 
 874° 
 
 98.7 
 
 867° 
 
 97.5 
 
 120° 
 
 158.5 
 
 127° 
 
 154.0 
 
 991° 
 
 73.3 
 
 1,029° 
 
 57.0 
 
 235° 
 
 154.0 
 
 232° 
 
 150.5 
 
 1,043° 
 
 49.5 
 
 1,057° 
 
 38.4 
 
 307° 
 
 151.0 
 
 300° 
 
 148.0 
 
 1,065° 
 
 30.0 
 
 1,113° 
 
 3.5 
 
 414° 
 
 146.4 
 
 415° 
 
 142.3 
 
 1,082° 
 
 6.0 
 
 1,144° 
 
 ? 
 
 542° 
 
 140.2 
 
 590° 
 
 133.1 
 
 1,104° 
 
 2.2 
 
 
 
 698° 
 
 125.2 
 
 687° 
 
 122.5 
 
 1,152° 
 
 ? 
 
 
 
 similarity between the curves showing / as a function of the temperature 
 for iron and nickel on the one hand, and the curves showing the relation 
 between the density of a vapor and the temperature on the other hand. 
 Langevin 2 a little later worked out on the electron theory a mathematical 
 theory of paramagnetism based upon the assumption that the molecules 
 of a paramagnetic substance obey the gas law. Weiss 3 extended this 
 theory to explain the phenomena of ferromagnetism by the aid of the 
 analogy pointed out by Curie. The sudden increase of density when a 
 vapor liquefies is due to the fact that an enormous internal pressure is 
 
 1 By extrapolation from curves. 
 
 4 Ann. de Chim. et de Phys., Ser. 5, 8, pp. 70-127, 1905. 
 'Journal de Physique, 36, pp. 661-690, 1907. 
 
2Sl 
 
 W. W. STIFLER. 
 
 [Vol. XXXIII. 
 
 Fig. 6. 
 
 160 
 
 e 
 
 e 
 
 o 
 
 
 
 
 1 
 
 • 
 
 > 
 
 
 
 
 
 AW 
 
 
 
 
 
 
 IU 
 
 
 
 
 
 
 no 
 
 
 
 
 
 
 to 
 
 
 if t' Of 
 
 dentil 
 
 £ HILL. 
 
 
 
 
 • tun 
 
 • Kiu 
 
 - Thl.rrf 
 
 It! «ua L 
 H|» (1 
 
 LA 1 Cur M 
 
 imdi c. 
 
 Ittrt I 
 
 «- 
 
 
 
 tb — a 
 
 1 
 fc> 
 
 • fi£ 
 
 UltU *M« 
 
 m 
 
 f; ">('«»!• 
 
 I taU 
 
 
 
 £ 
 
 ■ * 
 
 f„,l C«"» 
 • * 
 
 • 
 
 ' t 
 
 • /J 
 
 If 
 
 
 1 i K 7. 
 
No. 4.] 
 
 MAGNETIZATION OF COBALT. 
 
 282 
 
 suddenly brought into play in addition to the external pressure. Simi- 
 larly Weiss explained the fact that the ferromagnetic properties suddenly 
 appear when the temperature is lowered below a certain critical tempera- 
 ture by assuming that a strong molecular field is suddenly made operative. 
 This field is due to the action of the molecules upon each other and is 
 called by Weiss the "intrinsic molecular field." Of course the analogy 
 is not perfect for if it were we should expect the pressure-density curves 
 at constant temperature to 
 show the phenomenon of 
 hysteresis. Weiss has calcu- 
 lated the value of this intrinsic 
 field for iron, nickel, and mag- 
 netite. Kunz 1 has extended 
 this work by calculating the 
 moments of the elementary 
 magnets. 
 
 Before outlining the theory 
 as developed by these investi- 
 gators, the terms diamagnetic, 
 paramagnetic, and ferromag- 
 netic as used in this article 
 will be defined. 
 
 Diamagnetic substances are 
 those in which the induced 
 polarity opposes that of the 
 inducing field. 
 
 Paramagnetic substances 
 are magnetized feebly in the 
 direction of the magnetizing field. The susceptibility is independent 
 of the field strength and is inversely proportional to the absolute tem- 
 perature according to Curie. 
 
 Ferromagnetic substances are very strongly magnetized in the direction 
 of the magnetizing field. The susceptibility is a very complicated func- 
 tion of the field strength and the temperature. The phenomena of 
 hysteresis are characteristic of ferromagnetic substances. 
 
 The phenomena of diamagnetism are accounted for by assuming that 
 each atom contains at least one electron revolving in an orbit which lies 
 wholly within the atom. The orbits of the electrons are so arranged that 
 their external moment is zero. Since temperature affects the molecule 
 rather than the atom, the purely diamagnetic properties should be in- 
 
 1 Phys. Rev., 30, pp. 359-370, 1910. 
 
W. W. STIFLER. 
 
 [Vol. XXXIII. 
 
 dependent of the temperature. It is probable that even the paramagnetic 
 and ferromagnetic bodies also contain electronic orbits which give them 
 diamagnetic properties, but the effect is masked by the stronger opposing 
 
 phenomena. 
 
 In the paramagnetic and ferromagnetic bodies, the revolving electrons 
 are so arranged that there is no resulting external moment. Curie 1 showed 
 experimentally for a number of paramagnetic bodies that the paramag- 
 netic susceptibility, k = I H, is inversely proportional to the absolute 
 temperature. This is known as Curie's Law. Langevin, in his article 
 to which reference has already been made, has given a theoretical deduc- 
 tion of this law. Though some very recent experimental results 2 seem 
 to contradict Curie's Law, still on the whole it agrees with the experi- 
 mental facts in a large number of cases. 
 
 The present theory as developed by Langevin, Weiss, and Kunz may 
 be outlined as follows. In a gas at uniform temperature, not subject 
 to the action of gravity, the density is uniform throughout. If gravity 
 is suddenly allowed to act upon the gas, a rearrangement of the molecules 
 occurs; the lower layers of the gas become more dense, and the tempera- 
 ture of the gas rises, due to the fact that a certain amount of potential 
 energy has been converted into kinetic energy — i. e., into heat. The 
 change of pressure with height after equilibrium is established is now 
 given by the familiar exponential law 
 
 p = />oe- por,Po , 
 
 where po and po are the pressure and density respectively at the lowest 
 layer, and x is the height. This law has been generalized by Boltzmann 3 
 in the form 
 
 P = Poe tt, '* T , 
 
 where W is the change in the potential energy per unit distance and T 
 and R are respectively the absolute temperature and the universal gas 
 constant. 
 
 The arrangement of the molecules in a paramagnetic substance when 
 not under the influence of an external magnetic field is exactly analogous 
 to that of the gas molecules when not under the influence of gravity, 
 and the rearrangement caused by the action of a uniform magnetic field 
 will follow an exactly similar law. The number of molecules, (in, the 
 
 1 Ann. dc Chlm. ct de Phys.. Ser. 7, 3, pp. 289-405. 189s; CEuvrcs. pp. 332-334. 
 •du Boll and Honda. Koninlt. Akad. Wetensch.. Amsterdam, I'roc. S3, pp. 596-602, 
 March. 1910. 
 
 • Vorlctungen flber Ga»-Theorle, I Tell, p. 136. 
 
No. 4.] 
 
 MAGNETIZATION OF COBALT. 
 
 284 
 
 directions of whose axes are included in an elementary solid angle, dw, 
 will therefore be given by 
 
 dn = Ke"' lliT do>, (1) 
 
 where K is a constant. The potential energy of an elementary magnet 
 of moment M whose axis makes an angle 3> with a uniform magnetic field 
 His 
 
 W = HM cos <£. 
 
 But 
 
 do> — 27r • sin $> • d$. 
 Substituting this value and integrating from o to tt we have 
 
 n = sinh a, (2) 
 
 a 
 
 where 
 
 _ HM 
 a ~ RT 
 
 This result assumes that the resulting intensity of magnetization is in 
 the same direction as H. In general this will not be the case. If $ is 
 the angle between H and / we have 
 
 dl = M cos * dn 
 
 and 
 
 I = § a M cos $ dn. 
 
 Substituting the value of dn from (1) and integrating, and then sub- 
 stituting the value of K from (2) we have 
 
 cosh a 
 
 T %* I COSh 11 1 \ 
 
 I = nM I ~r~r — - ) , 
 \ sinh a a I 
 
 where n is the number of molecules in unit volume. Since it is the 
 thermal agitation of the molecules which opposes the action of H, if 
 there were no thermal agitation — i. e., if the substance were at absolute 
 zero — the intensity of magnetization would be a maximum and we would 
 have 
 
 I m = nM. 
 
 Hence 
 
 / cosh a 1 \ 
 
 I = I m \ —r-r I , (3) 
 
 \ sinh a at 
 
 Since 
 
 MH 
 a ~ RT ' 
 
28 S 
 
 W. W. STIFLER. 
 
 [Vol. XXXIII. 
 
 this eives 
 
 For paramagnetic substances, a is very small — much less than unity. 
 
 cosh a I 
 
 For values of a' 1 less than tt, — — - can be developed into a con- 
 
 smh a a 
 
 vergent series as follows: 
 
 cosh ail 2 4 
 
 — — = a — — a 3 + a 6 • ■ ■ 
 
 sinh a a 3 90 4542 
 
 For values of a less than 0.7, the terms of this series involving higher 
 powers of a than the first are negligible, and we have 
 
 a 
 
 'V- 
 
 _ HPnH 
 ~ 3~RT ' 
 = kH. 
 
 where k is constant for constant temperature, k is the paramagnetic 
 susceptibility and is seen to be inversely proportional to T, as found 
 by Curie experimentally. 
 
 In the case of ferromagnetic substances we have, in addition to the 
 external field, an internal or molecular field, II m . If this field acted 
 alone, the intensity of magnetization would be proportional to it and we 
 would have 
 
 Hm = NI, 
 
 and 
 
 Whence 
 
 Mil 
 a - RT , 
 
 MN£ 
 RT - 
 
 (iRT 
 
 1 " MX • (4) 
 
 where N is the factor of proportionality. Equation (4) shows that .at 
 any given temix-rature / is proportional to a. 
 
 For any temperature below that at which the spontaneous ferromagnc- 
 ti-in disappears, tin- value of / must satisfy both equations (3) and (4). 
 I Molt inn equation (3) we have the curve OCA of Fig. 9, while equation (4) 
 Kives the straight line OA. Obviously the values of / corresponding to 
 
No. 4-1 
 
 MAGNETIZATION OF COBALT. 
 
 286 
 
 the origin and to the point A satisfy (3) and (4) simultaneously. The 
 value for the origin is for 1 = 0. Hence the value of / which we wish 
 is that for the point A. 
 
 The line OA corresponds to some particular temperature T, and as T 
 varies, OA rotates about the point o. If denotes the temperature at 
 which the spontaneous ferromagnetism disappears, the tangent to the 
 curve at the origin corresponds to T = 9. 
 
 Fig. 9. 
 
 From a knowledge of the properties of a body in the neighborhood of 6 
 it is possible to calculate H m , the intrinsic molecular field, and M, the 
 moment of the elementary magnet. These calculations have been made 
 for iron, nickel and magnetite. The results are given in Table V., which 
 is taken from Kunz's 1 article. 
 
 Table V. 
 
 Substance. 
 
 / at 20 C. 
 
 
 
 
 N 
 
 NI=H m 
 
 MX 102° 
 
 Fe 
 
 1,860 
 
 2,120 
 
 756° C. 
 
 3,850 
 
 6,560,000 
 
 5.15 
 
 Fe 3 4 
 
 430 
 
 490 
 
 536° C? 
 
 33,200 
 
 14,300,000 
 
 2.02 
 
 Ni 
 
 500 
 
 570 
 
 376° C. 
 
 12,700 
 
 6,350,000 
 
 3.65 
 
 In order to make similar deductions for cobalt from the experimental 
 data, the method of calculating these quantities will be indicated. In 
 the neighborhood of the point at which spontaneous ferromagnetism 
 disappears, we have both the external field, H e , and the internal molecular 
 
 1 Phys. Rev., 30, pp. 359-370, 1910. 
 
287 W.W.STIFLER. [Vol. XXXIII. 
 
 field, H m , acting. That is 
 
 _ Mff = M(H. + 77 m ) 
 a RT RT 
 _ M(H„ + NT) 
 RT 
 
 or 
 
 _ M(H t + NI) 
 aR 
 
 While the body is ferromagnetic we have 
 
 (5) 
 
 RT RT * 
 
 For values of a less than 0.7, the curve for 
 
 7 cosh a I 
 7 m sinh a a 
 
 is a straight line, and we may take 
 
 MH MNI 
 
 and 
 
 7 _ a 
 
 Im m 3 
 
 7 = ; 7 m . (7) 
 
 This condition will certainly hold for T = 0. Hence, putting 7" = 9 in 
 (6) we have 
 
 MNI 
 Re ' 
 
 a = 
 
 Hence 
 
 Dividing (5) by (8) we have 
 
 T = 3/7. 3 7 
 6 aNI m ^al m ' 
 3H. 
 
 or 
 
 r - e ^ 
 e "at 
 
 _ M iV/ m a 
 
No. 4-1 
 
 MAGNETIZATION OF COBALT. 
 
 288 
 
 by (7). Hence 
 
 (r - e) J = § e. (9) 
 
 Equation (9) represents an hyperbola. The curves giving / as a function 
 of T for iron show this between 756 C. and 920 C. 
 
 To calculate H m , the value of N is necessary. This may be determined 
 from (9) by taking corresponding values of I and H, at some temperature 
 above 9. Solving (9) for N we have 
 
 N 9 
 
 I T-Q' 
 
 I 9 
 k T - 9 " 
 
 (10) 
 
 N may also be calculated from a knowledge of Curie's constant, C. By 
 Curie 's Law we have 
 
 k 
 
 C = X T = ^T, 
 
 where x is the specific susceptibility, and d is the density. But 
 
 »-£- 1 
 
 H H e + NI' 
 
 At T = 9, H e is negligible in comparison with N. Hence for this tem- 
 perature 
 
 K N' 
 
 or 
 
 or 
 
 C ~ N-d Q ' 
 
 d-C 
 
 N = —. (11) 
 
 Having iV we can calculate H m , taking / = I m , giving 
 
 H m = NI m . 
 
 From (8) we may obtain M, the moment of the elementary magnet, viz., 
 
 M = NT - = -jr-. (12) 
 
 Furthermore we may calculate 'the number of atoms which make up an 
 elementary magnet. Let N' be the number of molecular magnets per 
 
2S9 
 
 W. W. ST1FLER. 
 
 [Vol. XXXIII. 
 
 cubic centimeter. Then 
 or 
 
 N'M = In 
 
 IP = ^ (.3) 
 
 If there are « atoms per elementary magnet and each atom has a mass of m 
 grams, then 
 
 nN'm = mass per unit volume = d. 
 
 But 
 
 m = Anin, 
 
 where A is the atomic weight of the substance and m u is the mass of the 
 hydrogen atom. Hence we have 
 
 d d 
 
 " ~ N'm ~ AN'm n (h) 
 
 Application of Theory to Experimental Results. 
 
 Curve A of Fig. 7, showing a as a function of the temperature, indi- 
 cates that the Curie point is in the neighborhood of 1075 C. or 1348 Abs. 
 From this value a theoretical curve giving a as a function of T can be 
 calculated as follows. The curve OA in Fig. 9 gives us the relation 
 between I/Im, equal to <r/o- m , and the parameter a, and Table VI gives 
 the values of a\a m , calculated from equation (3) for various values of a. 
 Hence if we can determine the value of T corresponding to a given value 
 of a, we can at once determine the corresponding value of a/<r m either 
 from Table VI or graphically from the curve of Fig. 9. Knowing <r m 
 we can then calculate the value of a for the given value of T. 
 
 This relation between T and a comes from equation (4) which may be 
 written in the form 
 
 l a R 
 
 I m o m MNI m aT ' 
 
 From equation (8) we have 
 
 Hence 
 
 and 
 
 n MNI m 
 = u . 
 
 ° 1 T 
 
 Om 3/9 
 
 T = 
 
 a a m 
 
 This Kivcs us the required equation, and the values of a 'a m are niven in 
 Table VI. 
 
No. 4.] 
 
 MAGNETIZATION OF COBALT. 
 
 29O 
 
 Table VI. 
 
 
 cosh a 
 sinh a 
 
 I 
 
 a 
 
 a cosh a 1 
 (r m sinh « a 
 
 U.Ui 
 
 1 no nnnn 
 
 1UU.UUUU 
 
 1 no nnnn 
 
 u.uuuu 
 
 ft 1 
 
 1 n H900 
 
 1 u.uzyy 
 
 1 n nnnn 
 
 n H9QO 
 
 0.2 
 
 5.0676 
 
 5.0000 
 
 0.0676 
 
 0.3 
 
 3.4328 
 
 3.3333 
 
 0.0995 
 
 U.-i 
 
 O fx 1 1 7 
 
 z.oUUU 
 
 ft 1 "21 7 
 U. 10 1 / 
 
 U.o 
 
 9 1 A 2G 
 
 Z.UUUU 
 
 u. iooy 
 
 u.o 
 
 1 QA1 O 
 
 l.ooiy 
 
 1.000/ 
 
 n 1 
 u.iyoz 
 
 0.7 
 
 1.6546 
 
 1.4286 
 
 0.2260 
 
 0.8 
 
 1.5059 
 
 1.2500 
 
 0.2559 
 
 u.y 
 
 1 2QA1 
 
 1 1111 
 
 X. 1 1 1 1 
 
 ft 1Q ^ft 
 
 1 n 
 
 l.U 
 
 1 2 1 2 1 
 1.0 10 1 
 
 1 ftftftft 
 
 1 .uuuu 
 
 ft 21 21 
 
 1 9 
 
 1 1 GGS 
 
 1 . iyyo 
 
 ft Q 222 
 
 ft 2AA? 
 
 1.4 
 
 1.1295 
 
 0.7143 
 
 0.4152 
 
 1.6 
 
 1.0849 
 
 0.6250 
 
 0.4599 
 
 1 8 
 
 1 ai 
 
 I.UjOI 
 
 u. 00 00 
 
 ft ^nn^ 
 
 z.u 
 
 1 7 2 
 
 u.ouuu 
 
 ft ^27 2 
 
 O.U 
 
 1 ftftAQ 
 
 1 .uu^y 
 
 U.Oooo 
 
 ft fxl 1 A 
 
 u.o/ 10 
 
 4.0 
 
 1.0007 
 
 0.2500 
 
 0.7507 
 
 5.0 
 
 1.0000 
 
 0.2000 
 
 0.8000 
 
 6.0 
 
 1.0000 
 
 0.1667 
 
 0.8333 
 
 7.0 
 
 1.0000 
 
 0.1429 
 
 0.8571 
 
 8.0 
 
 1.0000 
 
 0.1250 
 
 0.8750 
 
 9.0 
 
 1.0000 
 
 0.1111 
 
 0.8889 
 
 10.0 
 
 1.0000 
 
 0.1000 
 
 0.9000 
 
 12.5 
 
 1.0000 
 
 0.0800 
 
 0.9200 
 
 As noted above, the work of Weiss and Onnes shows that the value of 
 a at the temperature of liquid hydrogen is less than 163.6. Assuming 
 this value for <r m , the values of a and T corresponding to various values 
 of the parameter a can be calculated. Thus, for a = 0.5 
 
 — = 0.1639, 
 
 Cm 
 
 from Table VI. Hence 
 
 a = 0.1639 X 163.6 = 26.8 
 
 and 
 
 3 X (1,0 7 5 + 273) 
 T = — X 0.1639 = 1326 Abs. = 1053 C. 
 
 Carrying out similar calculations for other values of a the results given 
 in Table VII. are obtained. In this table, t is the centigrade temperature 
 corresponding to the absolute temperature T. 
 
29I W.W. STIFLER. [Vol. XXXIII. 
 
 Table VII. 
 
 a 
 
 
 T 
 
 <r 
 
 t 
 
 0.5 
 
 0.1639 
 
 1326° 
 
 26.8 
 
 1053° 
 
 0.7 
 
 0.2260 
 
 1306° 
 
 37.0 
 
 1033° 
 
 1.0 
 
 0.3131 
 
 1266° 
 
 51.2 
 
 993° 
 
 2.0 
 
 0.5373 
 
 1086° 
 
 87.9 
 
 813° 
 
 3.0 
 
 0.6716 
 
 905° 
 
 109.9 
 
 632° 
 
 4.0 
 
 0.7507 
 
 759° 
 
 122.8 
 
 486° 
 
 5.0 
 
 0.8000 
 
 647° 
 
 130.9 
 
 374° 
 
 6.0 
 
 0.8333 
 
 562° 
 
 136.3 
 
 289° 
 
 7.0 
 
 0.8571 
 
 495° 
 
 140.2 
 
 222° 
 
 8.0 
 
 0.8750 
 
 442° 
 
 143.2 
 
 169° 
 
 9.0 
 
 0.8889 
 
 399° 
 
 145.4 
 
 126° 
 
 10.0 
 
 0.9000 
 
 364° 
 
 147.2 
 
 91° 
 
 12.5 
 
 0.9200 
 
 298° 
 
 150.5 
 
 25° 
 
 The values of a and / from Table VII. are plotted in curve B of Fig. 7. 
 This curve is of the same general shape as the experimental curve, A, 
 but it lies entirely below A. The difference between the two curves is 
 about 10 at o° C. and increases gradually to 20 at 6oo° C. From this 
 point on up to 1050 C. the difference between the two curves at any tem- 
 perature is practically constant, lying between 20 and 21. Hence if 
 the theoretical curve is shifted up 20 divisions it will coincide with the 
 experimental curve in the interval 500 C. to 1050 C. This is shown by 
 the double circles in Fig. 7. 
 
 In the interval above 1070 C. the experimental curve has the general 
 form of the hyperbola. This agrees with the requirements of equation (9) . 
 
 From the data at 1104 C. we can calculate the molecular field and 
 the moment of the elementary magnet. For this temperature we have 
 
 T = 1104 + 273 = 1377 Abs. 
 7 m = 163.6 X 8.77 = 1,435. 
 
 
 / 
 
 ////, 
 
 1 .400 
 
 11.1 
 
 0.00793 
 
 2,400 
 
 16.6 
 
 0.00692 
 
 3,050 
 
 23.3 
 
 0.00764 
 
 Mean value of ////, -* -0.00753. 
 
 Substituting these values in equation (10) we have 
 
 N . ' X ' MS „ - 6,,80. 
 0.00753 1,377 - 1.348 
 
No. 4.) MAGNETIZATION OF COBALT. 
 
 Hence 
 
 H m = NI m = 6,180 X 1,435 = 8,870,000. 
 From equation (12) we have 
 
 292 
 
 M = 
 
 3RQ 
 NI m 
 
 The value of R to be used is that corresponding to one molecule, viz., 
 R = 1.36 X io-" 5 . Hence 
 
 3 X 1.36 X IO- 16 X 1,348 ^- v in— 20 
 
 M = z. — - — — = 6.21 X to 20 . 
 
 6,180 X i,435 
 
 The number of elementary magnets per cubic centimeter from equation 
 (13) is 
 
 N' = 
 
 Ira 1,435 
 
 M 6.36 X 10 
 
 - = 2.31 X 10- 
 
 The number of atoms making up an elementary magnet is given by 
 equation (14), viz., 
 
 d d 
 H ~ N'm ~ N'Am H ' 
 
 The values to be substituted are: 
 
 d = 8.77, N' = 2.31 X io 22 , 
 A = 59.00, m H = 1. 61 X io -24 , 
 
 giving 
 
 59.00 X 2.31 X io 22 X 1.61 X 10- 
 
 u = 4-oi. 
 
 Hence four atoms of cobalt make up the elementary magnet. The value 
 4.01 is far more nearly an exact integer than the accuracy of the data 
 would lead us to expect, and this is strong evidence of the accuracy of the 
 value of 9. 
 
 It is interesting to compare these results with those given in Table V. 
 The results are summarized in Table VIII. 
 
 Table VIII. 
 
 
 /at 2o C. 
 
 
 
 
 N 
 
 N/ m = H m 
 
 MX io 20 
 
 n 
 
 N> 
 
 Fe 
 
 1,860 
 
 2,120 
 
 756° C. 
 
 3,850 
 
 6,560,000 
 
 5.15 
 
 2 
 
 4.12 X 10 22 
 
 Ni 
 
 500 
 
 570 
 
 376° C. 
 
 12,700 
 
 6,350,000 
 
 3.65 
 
 6 
 
 1.56 X 10 22 
 
 Co 
 
 1,421 
 
 1,435 
 
 1,075° C. 
 
 6,180 
 
 8,870,000 
 
 6.21 
 
 4 
 
 2.31 X 10 22 
 
 As was to be expected, the values of / and I m for cobalt lie between the 
 corresponding values for iron and nickel. The same is true of N and N'. 
 
293 
 
 W. W. STIFLER. 
 
 [Vol. XXXIII. 
 
 G how ever is much higher, while the intrinsic molecular field is one third 
 larger than that of iron or nickel, and the moment of the elementary 
 magnet is one fifth larger than that of iron and two thirds larger than 
 that of nickel. 
 
 It is very interesting to note that the elementary magnet of cobalt 
 consists of four atoms while the elementary magnet of iron, as indicated 
 by the work of Kunz, consists of two atoms and that of nickel of six 
 atoms. 
 
 Using the laws of electrolysis, another important physical constant 
 can be calculated, namely the elementary charge, e. This is done as 
 follows. The number of atoms per cubic centimeter of cobalt is 
 
 N* = nN'. 
 
 Hence the number of atoms per gram is 
 
 N = N'/d = nN'/d 
 
 and the number of atoms per gram atom is 
 
 AN = nN'Ajd. 
 
 Hence the quantity of electricity required to deposit one gram atom is 
 
 nN'A 
 
 Q = -d— v - e > 
 
 where v is the valency. But from the laws of electrolysis 
 
 Q = v- 96,540 coulombs 
 
 = r-9-65 X io 3 c.g.s. electromagnetic units. 
 
 Hence 
 
 or 
 
 nN ' A r ^ 3 
 
 — - — ve = t"9.65 X io 3 
 
 d 
 
 = 9.65 X io 3 X d 
 C nN'A 
 
 Substituting the values obtained above this gives 
 
 9.65 x 1 o 3 x s.77 
 6 4 X 2.31 X 10** X 59 
 = 1-55 X I o -20 c.g.s. electromagnetic units, 
 = 4.65 X io -10 c.g.s. electrostatic units. 
 
 Until the recent work of Millikan 1 the accepted value for e was 4.(>5 X 
 1 Piivs. Rev., j*. pp. 349-397. 19" • 
 
No. 4-1 
 
 MAGNETIZATION OF COBALT. 
 
 294 
 
 io -10 c.g.s. electrostatic units. This exact agreement is certainly far 
 better than would reasonably be expected, and is further evidence of 
 the reliability of the results at high temperatures. 
 
 The recent work of Weiss mentioned above gives values for x f° r 
 the interval from 1156 C. to 1302 C. Calculations of N, M, H m , and 
 n based upon his results are in fair agreement with the results deduced 
 above. 
 
 The chief results of this investigation are the following: 
 
 1. The saturation value of the intensity of magnetization of cobalt 
 has been determined at intervals of one hundred to one hundred and 
 fifty degrees throughout the interval from 22 C. to 1150 C. 
 
 2. The "Curie Point," or point of magnetic transformation from the 
 ferromagnetic to the paramagnetic state, has been established at 1075 C. 
 
 3. The curve giving cr as a function of the temperature has been shown 
 to be of the same general character as that demanded by theory, though 
 differing from the theoretical curve by a constant amount throughout 
 most of its length 
 
 4. The values of the intrinsic molecular field, H m , the moment of the 
 elementary magnet, M, the number of atoms in an elementary magnet, 
 n, and the elementary charge, e, have been calculated and found to have 
 the following values: 
 
 The author takes pleasure in acknowledging his indebtedness to 
 
 Professor A. P. Carman for the facilities for this investigation, and to 
 
 Professor Jakob Kunz both for his general supervision of the work and for 
 
 many valuable suggestions. 
 
 Laboratory of Physics, 
 University of Illinois, 
 May 8, 1911. 
 
 Summary. 
 
 H m = 8,870,000, 
 M = 6.21 X io- 20 , 
 
 n 
 
 n = 4, 
 e = 4.65 X io- 10 E.S. 
 
VITA 
 
 William Warren Stifler was born in Davenport, Iowa, December 22, 
 1883. His early education was received in the public schools of Detroit, 
 Michigan, Sioux Falls, South Dakota, and Upper Alton, Illinois, and in 
 the Preparatory Department of Shurtleff College. He was graduated 
 from Shurtleff College, Upper Alton, Illinois, in June 1902 with first 
 honors in scholarship, receiving the degree of A.B. During the years 
 1902-1906 he was professor of Chemistry and Physics in Ewing College, 
 Ewing, Illinois. 
 
 His graduate work was done at the University of Illinois. In 1906- 
 1907 he was fellow in Physics; in 1907-1909, assistant in Physics; in 
 1909-1910, instructor in Physics; in 1910-1911, fellow in Physics. He 
 also taught in the summer sessions of 1907, 1908, and 1909. He received 
 the degree of A.M. in June 1908. His major work has been in experi- 
 mental physics, with mathematics and mathematical physics as minors. 
 
 He is an associate member of the American Physical Society (1907), 
 and is also a member of the Illinois Chapter of Sigma Xi (1909) and of 
 the Illinois Chapter of the Gamma Alpha Graduate Scientific Fraternity 
 (1909). 
 
 Publications: 
 
 The Resistance of Certain Electrolytes in a Magnetic Field. 
 
 Physical Review, 28, pp. 382-385 (1909). 
 Tests on Certain Electrical Insulators at High Temperatures. 
 
 Physical Review. 32, pp. 429-432 (1911).