introduced the method of measuring hysteresis by means of an electro-dynamometer used ballistically. The fixed and suspended coils of the dynamometer are respectively connected in series with the magnetizing solenoid and with a secondary wound upon the specimen. When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre. For specimens of large sectional area it is necessary to apply corrections in respect of the energy dissipated by eddy currents and in heating the secondary circuit. The method has been employed by the authors themselves in studying the effects of tension, torsion and circular magnetization, while R. L. Wills[1] has made successful use of it in a research on the effects of temperature, a matter of great industrial importance.
C. P. Steinmetz (Electrician, 1891, 26, p. 261; 1892, 28, pp. 384, 408, 425) has called attention to a simple relation which appears to exist between the amount of energy dissipated in carrying a piece of iron or steel through a magnetic cycle and the limiting value of the induction reached in the cycle. Denoting by W the work in ergs done upon a cubic centimetre of the metal (= 14π ∫ HdB or ∫ HdI), he finds W = ηB1.6 approximately, where η is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction. The value of the constant η ranges in different metals from about 0.001 to 0.04; in soft iron and steel it is said to be generally not far from 0.002. Steinmetz’s formula may be tested by taking a series of hysteresis curves between different limits of B, measuring their areas by a planimeter, and plotting the logarithms of these divided by 4π as ordinates against logarithms of the corresponding maximum values of B as abscissae. The curve thus constructed should be a straight line inclined to the horizontal axis at an angle θ, the tangent of which is 1.6. Ewing and H. G. Klaassen (Phil. Trans., 1893, 184, 1017) have in this manner examined how nearly and within what range a formula of the type W = ηBε may be taken to represent the facts. The results of an example which they quote in detail may be briefly summarized as follows:—
| Limits of B. | Hysteretic Constant. η | Index. ε (= tan θ) | Degrees. θ |
| 200 to 500 | . . . | 1.9 | 62.25 |
| 500 to 1,000 | . . . | 1.68 | 59.25 |
| 1,000 to 2,000 | . . . | 1.55 | 57.25 |
| 2,000 to 8,000 | 0.01 | 1.475 | 55.75 |
| 8,000 to 14,000 | 0.00134 | 1.70 | 59.50 |
It is remarked by the experimenters that the value of the index ε is by no means constant, but changes in correspondence with the successive well-marked stages in the process of magnetization. But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index ε = 1.6, and assigning a suitable value to η, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small. Alexander Siemens (Journ. Inst. Eng., 1894, 23, 229) states that in the hundreds of comparisons of test pieces which have been made at the works of his firm, Steinmetz’s law has been found to be practically correct.[2] An interesting collection of W-B curves embodying the results of actual experiments by Ewing and Klaassen on different specimens of metal is given in fig. 16. It has been shown by Kennelly (Electrician, 1892, 28, 666) that Steinmetz’s formula gives approximately correct results in the case of nickel. Working with two different specimens, he found that the hysteresis loss in ergs per cubic centimetre (W) was fairly represented by 0.00125B1.6 and 0.00101B1.6 respectively, the maximum induction ranging from about 300 to 3000. The applicability of the law to cobalt has been investigated by Fleming (Phil. Mag., 1899, 48, 271), who used a ring of cast cobalt containing about 96% of the pure metal. The logarithmic curves which accompany his paper demonstrate that within wide ranges of maximum induction W = 0.01B1.6 = 0.527I1.62 very nearly. Fleming rightly regards it as not a little curious that for materials differing so much as this cast cobalt and soft annealed iron the hysteretic exponent should in both cases be so near to 1.6. After pointing out that, since the magnetization of the metal is the quantity really concerned, W is more appropriately expressed in terms of I, the magnetic moment per unit of volume, than of B, he suggests an experiment to determine whether the mechanical work required to effect the complete magnetic reversal of a crowd of small compass needles (representative of magnetic molecules) is proportional to the 1.6th power of the aggregate maximum magnetic moment before or after completion of the cycle.
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| Fig. 16. |
| a, Fine steel wire 0.257 mm. diam. |
The experiments of K. Honda and S. Shimizu[3] indicate that Steinmetz’s formula holds for nickel and annealed cobalt up to B = 3000, for cast cobalt and tungsten steel up to B = 8000, and for Swedish iron up to B = 18,000, the range being in all cases extended at the temperature of liquid air.
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| Fig. 17. |
The diagram, fig. 17, contains examples of ascending induction curves characteristic of wrought iron, cast iron, cobalt and nickel. These are to be regarded merely as typical specimens, for the details of a curve depend largely upon the physical condition and purity of the material; but they show at a glance how far the several metals differ from and resemble one another as regards their magnetic properties. Curves of magnetization (which express the relation of I to H) have a close resemblance to those of induction; and, indeed, since B = H + 4πI, and 4πI (except in extreme fields) greatly exceeds H in numerical value, we may generally, without serious error, put I = B/4π, and transform curves of induction into curves of magnetization by merely altering the scale to which the ordinates are referred. A scale for the approximate transformation for the curves in fig. 12 is given
