CURRENT STATE OF THE PROBLEM OF MAGNETIC SPECTRA.

V. K. Arkadiev, Moscow.

Three years ago a brief outline¹) was given of the theory and the basic facts of magnetic spectroscopy, a new scientific field that is the result of transferring the theoretical and experimental methodology of spectral analysis to the domain of magnetism. Magnetic properties can be studied by observing the absorption, reflection, or refraction of electromagnetic waves incident on ferromagnetic bodies. The name magnetic spectrum is given to the curve showing the dependence on wavelength of the refractive index, reflection coefficient, or absorption, as determined by the magnetic properties of the given magnetic substance. In studying the magnetic properties of iron or steel in rapidly varying magnetic fields, we likewise obtain magnetic spectra; they have the form of curves expressing the dependence of permeability and other magnetic characteristics on the number of field alternations or on the wavelength.

In explaining the fact of the absorption of electromagnetic waves by magnetic substances, we had to ascribe to the latter a special property, analogous to that electrical conductivity $\sigma$ which we ascribe to insulators when an electromagnetic wave of a definite period undergoes absorption in them. By analogy, I called this property magnetic

¹) V. K. Arkadiev. Uspekhi fizicheskikh nauk, 4, 263, 1924. See also New Ideas in Physics, No. 11, 1925.

conductivity. The latter, as well as the coefficient \(\rho\) characterizing it, were first introduced by me into the theory in the analysis of magnetization processes occurring in iron over a very short time, of the order of a billionth of a second; since, however, in ferromagnetic substances absorption of the energy of the magnetic field also takes place in slow processes, the coefficient of magnetic conductivity \(\rho\) has also found application in the description of slowly occurring electromagnetic phenomena that take place in alternating-current electrical engineering at ordinary frequencies.

As a consequence, the expression for the density of the magnetic current in Maxwell’s equations has for us, for sinusoidal processes of different periods, the same form as that which the density of the electric current has:

\[ j_m=\rho H+\frac{\mu}{4\pi}\frac{dH}{dt}, \]

\[ j_e=\sigma E+\frac{\varepsilon}{4\pi}\frac{dE}{dt}. \]

Here the first terms of the sums represent conduction currents, and the second terms displacement currents; \(\mu\) denotes the magnetic permeability, \(\varepsilon\) the dielectric constant, and \(E\) and \(H\) the electric and magnetic fields.

Maxwell’s equations themselves acquire the following form:

\[ \operatorname{rot} H=\frac{4\pi\sigma}{c}\,E+\frac{\varepsilon}{c}\frac{dE}{dt} \]

\[ \operatorname{rot} E=-\frac{4\pi\rho}{c}\,H-\frac{\mu}{c}\frac{dH}{dt}. \]

In slowly occurring processes and in fields that are not weak, as is usually the case in practice, the magnetic conductivity can be determined from the hysteresis heat \(Q\):

\[ \rho=\frac{2Q}{T H_0^{2}}, \tag{1} \]

where \(H_0\) is the amplitude of the magnetic field, and \(T\) is the period. In calculations, however, one most often has to deal not with \(\rho\),

and with the product \(2\rho T\), which I call the “magnetic leakage” and denote by \(\rho'\), so that

\[ \rho' = 2\rho T = \frac{4Q}{H_0^2}. \]

This quantity constantly figures in our equations alongside the magnetic permeability \(\mu\), and often enters with it into various combinations \((\mu_k\) and \(\mu_n)\).

The coefficient \(\rho\) in our theory of the electromagnetic field in magnetic metals is just as necessary for a complete characterization of a substance from the magnetic side as, in the old Maxwellian theory, for a complete characterization of a substance from the electrical side, in addition to \(\varepsilon\), \(\sigma\) is also necessary.

Therefore, at the present time, in order to estimate the magnetic properties of one material or another, one should indicate not only its magnetic permeability \(\mu\) for magnetic fields of different strengths, but also its magnetic conductivity \(\rho\). High values of the first indicate the easy magnetizability of the given specimen; high values of the second indicate a large retentive force and a large hysteresis heat. For the manufacture of permanent magnets we shall require from the factory a material with large magnetic leakage, while for dynamo and transformer steel—specimens with high permeability and small magnetic leakage.

Work on magnetic spectra and the studies that followed from it have led to the following principal results:

1. A new form was given to Maxwell’s equations, convenient for taking account of hysteresis heat and magnetic friction.

2. A theory was developed of a new type of dispersion and absorption of electromagnetic waves, namely one caused by oscillations of magnetic centers embedded in the substance.

3. New experimental data were obtained concerning the behavior of magnetic substances in alternating magnetic fields, i.e. magnetic spectra were obtained and studied.

In the present survey we shall consider what new results have been achieved along these three lines in the 3 years that have passed since the appearance in Uspekhi of the first article on magnetic spectroscopy.

1. Further Use of the Supplemented Maxwell Equations

In calculating the resistance of iron wires to alternating current, in taking account of the heat of Foucault currents, in investigating the magnetic properties of metals at high frequency, and in a number of other cases, formulas were formerly used that had been obtained without taking magnetic losses into account, i.e., without introducing magnetic conductivity. At the present time, when our work has established the possibility of introducing this factor into the equations of Maxwell’s electromagnetic field, it has become necessary to review and reformulate the old formulas of Stefan, Rayleigh, and Zenneck. This work was carried out abroad by Gans, Ullrich, Truksa, and Tonks; in our country, by Vvedensky and Shiller, it was brought to completion. The latter obtained formulas and curves that make it possible to calculate the effective resistance and permeability of cylindrical wires in an alternating field with any hysteresis losses. These formulas assume, however, that the permeability $\mu$ and the magnetic conductivity $\rho$ do not depend on the field strength. Meanwhile $\mu$, $\rho$, and $\rho'$ are not constant. For the first time, values of $\rho'$ for fields of different strength, in parallel with values of $\mu$, were calculated for iron of various specimens in my 1925 article in the Transactions of GEEI. In 1926 and 1927,

Fig. 1. Curves of magnetic permeability and magnetic conductivity in constant fields.

such dual characteristics of magnetic materials subjected to practical testing were obtained by us, by A. A. Ermolaev in Moscow1, and abroad by Mittelstrass in Jena (Fig. 1).

The diploma work of one and the doctoral dissertation of the other essentially concerned one and the same question: their aim was to determine the magnitude of the error that we make in calculations when assuming that \(\mu\) and \(\rho'\) are constant. Ermolaev did this by measuring the resistance of iron wires for alternating current and comparing the values obtained with those calculated from the formulae of Vvedensky and Schiller, while Mittelstrass measured the depth to which an electric alternating current penetrates into a wire, and then calculated this depth using our magnetic conductivity \(\rho\).

Remarkable methods proved possible to employ in Jena: for studying the depth of penetration of an electromagnetic wave into an iron cylinder, all the resources available in Jena thanks to the proximity of the firm Zeiss were used. In order to embed special probes in the iron cylinder for tracing the penetration of the current, the cylinder was cut into two parts and the halves were polished in such a way that parallel interference fringes appeared on the applied flat glass plate; after the wires had been inserted, the two halves were compressed, whereby perfect magnetic contact was achieved.

Both works, carried out simultaneously and independently of one another, showed that the introduction of the coefficient of magnetic conductivity \(\rho\), calculated by our formula (1), gives good values for the resistance of wires and for the attenuation coefficient of waves penetrating into the depth of the wire. From further work one should expect the elimination of the small discrepancy still remaining between the experimental and theoretical values.

2. New Confirmation of the Theory of Magnetic Dispersion and Absorption.

In 1908–1911 I investigated, by two methods, the magnetic properties of iron, steel, and nickel in the magnetic fields of rapid electric oscillations. One method¹ consisted in measuring the absorption of the energy of waves propagating along parallel wires made of the metal under investigation. By measuring the absorption coefficient, one can calculate the apparent permeability \(\mu_k\). It turned out that this quantity decreases for short waves and, at a wavelength of about \(1\ \mathrm{cm}\), is close to unity, as is seen from the following table:

The curve of the dependence of the absorption coefficient on the wavelength has a form similar to the curves \(f=\frac{\mu_k}{\lambda}\) in Fig. 2; it reveals a maximum of absorption for waves of a definite period. The maximum \(f\), the decrease of the magnetic properties with \(\lambda\), and also other features of the dependence on wavelength of the functions \(f\) and \(\mu_k\), which are magnetic spectra, are well explained by our theory of magnetic dispersion and absorption, based on the hypothesis of the elastoviscous motion of elementary magnets.

Special rules for analyzing the curve \(f=\frac{\mu_k}{\lambda}\) make it possible easily to find the three fundamental parameters characterizing the particles of the substance in which dispersion occurs; namely, the natural wavelength of the elementary magnets \(\lambda_0\), the measure of damping

¹ Ж. Р. Ф. О. 44, 165, 1912, Ann. d. Phys. 58, 105, 1919.

of the natural oscillations of magnets \(\theta\) and the share of the participation of magnets with natural wave \(\lambda_0\) in the total polarization of the substance by a constant field, characterized by the “partial coefficient of polarization” \(k\infty\). With the aid of these three coefficients \(\lambda_0\), \(\theta\), and \(k\infty\), one can compute the values \(\mu\) and \(\rho'\) that follow from the theory of oscillations of elementary magnets:

\[ \mu = 1 + \frac{m(1-v^2)}{\theta^2 v^2 + (1-v^2)^2} \tag{2} \]

and

\[ \rho' = \frac{m\theta v}{\theta^2 v^2 + (1-v^2)^2}, \tag{3} \]

where \(v=\lambda_0/\lambda\) and \(m=4\pi k\infty\).

From these quantities \(\mu\) and \(\rho'\) there can be determined \(\mu_k=\sqrt{\mu^2+\rho'^2}+\rho'\) and \(f=\mu_k/\lambda\); the quantities thus obtained in the form of curves were compared with the experimental ones, and a satisfactory agreement between the two was found. These curves were also presented in my first article in Uspekhi.

During the past three years I have succeeded in processing experiments carried out by the second method1, which consisted in comparing the coefficient of reflection of waves from sparse Hertzian gratings made of magnetic wires with that for nonmagnetic wires.

The measurements showed that in this case the magnetic properties manifest themselves much more weakly, and that they disappear at a longer wavelength than in the case of absorption of waves in wires. A detailed theoretical analysis of the reflection of waves from Hertz gratings enabled me, in 1924–1925, to ascertain the cause of such a sharp difference in the manifestation of magnetic properties. It turns out that, in reflection from sparse gratings, the magnetic properties are due to another kind of apparent permeability, namely \(\mu_n\); the theory of gratings enabled me to compute its values from experiment. These quantities are presented in the same table.

Visible labels in Fig. 2: \(Fe\), \(Ni\), \(R. b.\), \(f\), \(\mu\), \(\rho\cdot 10^{-10}\), \(\rho\cdot 10^{-9}\), \(K\), \(\varepsilon\), \(\lg \lambda\).

Fig. 2. Absorption bands and dispersion of Hertzian waves in iron and nickel (magnetic spectra) and of light waves—in the dye “Rose Bengal” (electric spectra).

The distinction between \(\mu_k\) and \(\mu_n\) according to our theory of the electromagnetic field consists in the following:

\[ \mu_k=\sqrt{\mu^2+\rho^2}+\rho' \tag{4} \]

\[ \mu_n=\sqrt{\mu^2+\rho^2}-\rho' \tag{5} \]

These formulas first of all explain why the permeability found from reflection from wires is smaller than that obtained from the absorption of waves in wires. From (4) and (5) it is easy to find that:

\[ \mu=\sqrt{\mu_k\mu_n}\quad \text{and}\quad \rho=\frac{\mu_k-\mu_n}{4T}. \]

The calculations which I carried out in 1926, using the values of \(\mu_n\) obtained from experiments with gratings and the old values of \(\mu_k\), give experimental values of \(\mu\) and \(\rho\) which, as is evident from Fig. 2, agree well with the theoretical ones, represented in the form of curves. The points representing the experimental values of \(\rho\), in the case of iron and in the case of nickel, lie near the curves and clearly trace out the maximum of \(\rho\). The curves of \(\mu\), owing to the small number of experimental points, are not revealed in all their details; the points, however, follow well the bends of the theoretical curves.

In the field of optics, where the theory of dispersion was born and developed, where it has full rights of citizenship and where the experimental technique is considerably simpler and more perfect, even there comparison of theoretical and experimental numbers still does not lead to complete agreement. As an example I cite one curve from the best investigation in this field, belonging to Fander Platts.

Curve \(K\) in Fig. 2 represents the coefficient of absorption of light in a 10% solution of the dye Bengal rose. On the basis of an analysis of this curve the parameters characterizing this substance, \(\lambda_0\), \(\theta\), and \(k\infty\), were obtained; with the aid of a formula analogous to (2), the values of \(\varepsilon\) were obtained. The theoretical curve \(\varepsilon\) deviates noticeably from the experimental points. However, both in the case of magnetic and in the case of electric dispersion the points lie close to the curves,

thereby revealing satisfactory agreement of experiment with the predictions of the theory. In the optical region the agreement is still better for weaker dye solutions. In the region of magnetic phenomena, the noticeable discrepancy is due above all to the insufficient accuracy of calculating \(\mu_n\) from observations of the reflection of waves from wires; moreover, the influence of other absorption bands, especially those lying near \(\lambda = 100\) cm, has not been taken into account here. Nevertheless, in all cases the experimental points follow the bends of the theoretical curves. This may be regarded as evidence of the closeness to reality of the assumption underlying the theory of dispersion concerning the resonance of the structural elements of matter, in particular concerning the resonance of elementary magnets.

3. New Experimental Data in the Field of the Investigation of Magnetic Spectra.

Magnetic spectra in the region of the shortest Hertzian waves, from 20 to 1 cm in length, were investigated in 1911; to this day this work remains the only one, which is explained by the difficulty of obtaining short waves. For the investigation of magnetic spectra in the region of still shorter, ultrahertzian waves adjacent to thermal waves, a recently discovered mass radiator, emitting a continuous spectrum of waves down to tenths of a millimeter, will be useful. In 1921 Gans and Loyarte succeeded in tracing the spectrum of nickel from waves of 100 cm down to 20 cm in length; at about 24 cm they found a maximum similar to that obtained by us in 1911. In its interpretation they follow our theory entirely and calculate from it, by our formulas, the parameters \(\theta\), \(\lambda_0\), and \(k\infty\) introduced by us. During the last 3 years a number of works have appeared abroad in this field: Israel, Gutton and Mioll, Uyeita, Bush and Sokolov; two investigations, by Mityaev and Malov, were carried out in our country.

The German works—those of Israel and of Bush and Sokolov—are distinguished by the greatest thoroughness. In Israel’s work the spectrum of nickel wires of 0.6 and 1.16 mm diameter was investigated. With the aid of a Mie vibrator there were obtained

electric waves from 30 to 200 cm in length. The spectrum \(\mu_k\) was determined from the resistance of the wires, calculated from the decrement of damping of a wire rectangle resonating with a vibrator\(^1\). Onto the parallel wires of the rectangle, stretched at a distance of 10 mm from one another, there could be moved a coil magnetizing them, 120 cm long, which gave a field of up to 600 gauss.

Fig. 3. Magnetic spectra of nickel wires according to Gans and Israil (from 20 to 175 cm).

In Fig. 3 are presented the spectra of a nickel wire 0.6 mm in diameter; the lower curve pertains to an unmagnetized wire, the upper—to one retaining residual magnetization; the black points refer to repeated observations after returning the wire to its initial state after magnetization or demagnetization. The curves of Israil and Gans in general indicate a decrease of \(\mu\) from waves of 30 cm to waves

\(^1\) On the methods of magnetic spectroscopy see Vol. XVII, Part II, of the supplementary volume of the physics course by O. D. Khvolson.

at 204 cm. The Gans curve, owing to an insufficient number of points, does not give those details which are visible on the Israel curves. Israel as a whole accepts our theory and the very fact of the existence of magnetic spectra1. He confirms many of the Moscow observations, such as, for example, that magnetic spectra depend on the diameter of the wire, and that thick wires give more complex spectra than thin ones.

At the Fifth Congress of Physicists, held in Moscow in December 1926, G. Busch (Jena) gave a report, “Magnetic spectroscopy of high resolving power.” Busch says2: “If we ask ourselves in what direction the investigation of this field should first of all develop, then,

Fig. 3a. Spectrum of soft iron at low frequencies and weak fields.

I believe my opinion coincides with that of Prof. V. K. Arkadiev, that the nearest, most necessary, and most important task consists in a fundamental study of this new field in all directions, i.e. it is necessary to investigate the dependence of magnetic spectra on all the circumstances affecting them: on the chemical state, crystalline structure, physical factors (for example, temperature, tension, degree of magnetization), geometrical form—the diameter of wires, etc.

“To these tasks work has already in part been begun in V. K. Arkadiev’s laboratory. Here what is required of the methods of measurement is not so much accuracy as speed of determination, in view of which the methods developed by Arkadiev and his pupils, as well as by Gans and Loyarte, prove very convenient here; the sufficient accuracy of these methods, at least for establishing the phenomenon in its main features, is demonstrated by the good agreement of results obtained by completely different methods.

“The next important task after this seems to me to be increasing the accuracy of the measurements, in order to investigate the finer structure of magnetic spectra. We observe quite the same distribution of work in optical spectroscopy: part of its tasks, namely the finding of spectral lines, requires a spectrograph or spectroscope with an insignificant degree of accuracy (a prism or a small grating), with which one can work quickly and conveniently.

“On the contrary, for the study of the fine structure of spectral lines, complex methods of interference spectroscopy are needed: the Michelson echelon grating, the Lummer–Gehrcke plate, the Fabry and Perot plates, possessing great resolving power, i.e. great accuracy1.

Having imagined how large a part of the successes of modern spectroscopy arose from the second of the above-named fields of work, we arrive at the conclusion that in magnetic spectroscopy, too, one should expect a deeper study of the phenomena as a result of increasing the resolving power of the apparatus.

The first step in this direction may be considered my experiments and the work of my student Vukkel, directed toward refining Arkad’ev’s method—the measurement of waves in wires.

After this Bush sets forth the method of measuring the resistance of wires to high-frequency current, developed by Vukkel and improved by another of his students, L. Sokolov; the latter applied it to the study of the spectrum of iron wire. Sokolov’s work was later published in Annalen der Physik. In Fig. 4 the curves obtained by him are presented. Bush says the following about them:

Fig. 4. Magnetic spectra of iron wires according to Bush and Sokolov (from 3 to 11 m) and according to Kartschagin.

“The measured values of \(k\) and \(\mu_k\), presented in Fig. 4, which depicts the results of measurements carried out by Sokolov on wires of pure electrolytic iron (from Heraeus, Hanau), of diameter \(0.50\ \mathrm{mm}\), over the range of wavelengths from \(3.21\) to \(10.9\ \mathrm{m}\); \(k\) is the measured absorption coefficient, \(\mu_k\) the magnetic permeability determined from it in the usual way, and \(\mu_n\) the corresponding permeability from self-induction, which, according to Arkad’ev, is found from the difference of wavelengths in iron and copper wires. In agreement with Arkad’ev’s theory, \(\mu_n\) is always smaller than \(\mu_k\), except for the point \(\lambda = 4.71\ \mathrm{m}\), \(\mu_n = 82\), to which, however, owing to the small accuracy of the measurement of \(\mu_n\), no significance should be attached.”

“For comparison, a curve for \(\mu_k\), obtained by Karchagin in the same region of waves, has been drawn. As is evident, it deviates considerably from the curve found by Sokolov. The difference could be explained by the difference in the material of the wires: electrolytic unannealed iron in Sokolov’s case, Swedish forged annealed iron in Karchagin’s. I attach much greater significance to the fact that the maxima of \(\mu_k\) observed by Karchagin also appear in our case, though weakly, yet nevertheless undoubtedly; this means that at the positions of the bands observed by Karchagin there is an anomaly even in the purest iron.

“How these bands are situated separately and how, in particular, they depend on the chemical composition of the wire, its previous heat treatment, crystalline structure, etc., can be clarified only by further measurements.

“The fact that the method described has already yielded results is still very little; for the most part, its ‘magnetic spectroscopy of increased resolving power’ still remains a program. But this is understandable, since the existing technique, as is clear from the preceding, is extraordinarily difficult and takes much time.

“We have every reason to hope that further work will proceed more rapidly. In this respect electrical spectroscopy can serve us as an example.

“If we recall how extremely troublesome and laborious the first methods of interference spectroscopy were, what enormous labor and time even such a brilliant experimenter as Michelson expended in order to investigate the structure of only one spectral line of cadmium, and if we compare this with the speed of the modern elegant methods of interference spectroscopy, then we may hope that sooner or later exact methods of magnetic spectroscopy will also appear, by using which we shall be able to measure not only accurately, but also quickly.”

Gutton looks at magnetic spectra differently. The history of these investigations is as follows.

In 1924 his student Laville published an extensive work in which, with the help of undamped oscillations, he tests the theory of absorption of electric waves in wires. From the theoretical side his work is very valuable; as for his calculations, however, they give rise to a number of doubts. For the coefficient $\beta$ of absorption of waves in wires made of aluminum bronze, he gives the following values of $\beta \cdot 10^5$, obtained from experiment and calculated theoretically:

It is seen from the table that the numbers calculated by him agree with the experimental ones to fractions of a percent. If, however, one checks his calculations, it turns out that Laville’s formulas give values larger by 1–3%; moreover, his formulas themselves are inaccurate: in calculating the resistance of wires to alternating current he takes a simplified expression (whereas, according to Zenneck, a certain term 0.277 should also be added). If this is done, the numbers obtained are those given in the last row of the table, 3.4–6.8% larger than the observed ones. Thus Laville’s verification of the theory of propagation of waves in wires in fact gives a systematic deviation exceeding 5%. Laville also investigated wires made of magnetic material. The latter all gave an exceptionally constant value of the permeability of iron at different waves from 3 to 87 m: 74, 73.5, 73.6, 73.5, 75, and 74. The error made by Laville in testing the theory placed this result in great doubt. Moreover, the errors of measurement of $\beta$ in his work sometimes amounted, as he himself says, to 4%, which could not ensure agreement of the permeability values to better than within 8%. All this compelled me to write to Gutton and send him offprints of our works. It turned out that our investigations were not known to him; the constancy

\(\mu_k\) in Laville’s work Gotton explains by the fact that Laville did not fall within the dispersion band. After this Gotton undertook, together with Miol, an investigation of the magnetic properties of iron, which gave the results presented as points in Fig. 5\(^1\).

As we see, they obtained an insufficient number of points for all the maxima\(^1\) of Nikitin’s curves to be outlined; however, the points lying in the region of the curve of Bush and Sokolov reproduce fairly well two of their maxima and minima. Gotton and Miol themselves, not knowing of the observations of Bush and Sokolov, explained the oscillations of their quantities by errors of measurement. When Sokolov’s article appeared in Annalen der Physik, I informed Gotton of it and sent him the drawing of Fig. 5. They repeated their measurements again and, as he writes to me in a letter of 28 October 1927, in the region they investigated they could not acknowledge as real the existence of a large number of bands of magnetic

Fig. 5. Magnetic spectra of iron wires according to Gotton and Miol, according to Bush and Sokolov, according to Karchagin, and according to Nikitin.

\(^1\) The curve through Gotton’s points was drawn by me so as to show that his data do not contradict Nikitin’s data.

absorption. A small number of bands, consequently, is allowed by them. Looking at Fig. 5, it is nevertheless difficult to imagine that both maxima at wavelengths of 8.8 and 10.6 m for both authors are accidental. Also characteristic is the descent of the curves in the region from 11 to 12.5 m, which is observed on all six curves of all three works. It is hardly the result of observational errors.

It remains now to speak of work in the region of hundred-meter waves. All investigations carried out in Moscow give more or less concordant results, presented in Fig. 6. The drawing indicates the names of the authors, the years in which the investigations were performed, the strength of the alternating magnetic field, and the diameter of the iron wires: 0.1, 0.5, and 1.4 mm. Some of the spectra were obtained in wires magnetized by a constant magnetic field reaching 600 gauss in Mityaev’s work and 8,000 gauss in Malov’s. In this case only a lowering of the curve was observed, without any noticeable displacement of the maxima and minima. The latter is in complete agreement with the theoretical investigation of Akulov, who studied the question of the influence of an additional constant field on the position of the bands of magnetic dispersion.

Because the peculiar behavior of magnetic permeability in this region of waves, discovered as early as 1921 in the Moscow Magnetic Laboratory, is very unexpected and paradoxical, special attention was paid to the influence of observational errors on the calculation of the reduced curves. Consequently, Malov measured the magnitude of the permeability of nonmagnetic materials, i.e. substances with permeability equal to 1 and certainly constant. Such materials for him were wires of nickel silver, phosphor bronze, and manganin. Their permeability, as the wavelength changed, proved constant within 1–4%, whereas for iron it changed by 20–50%.

In America, these phenomena were reproduced by Wight, who, in evaluating his results, came to the conclusion that there was no anomaly of permeability near the wavelength of 100 m; his curve, representing the apparent permeability \(\mu\)

Fig. 6. Bands in the magnetic spectrum of iron near the wavelength of 100 meters according to Vvedensky, Mityaev, and Malov.

iron wires, determined from the increase in the self-induction of the coil into which they are inserted, is given in Fig. 7.

Uyeita’s work was carried out in the Department of Terrestrial Magnetism of the Carnegie Institution in Washington. This investigation raises even more perplexities than the work of Laville and the conclusions of Hutton.

First of all, one cannot fail to express surprise at a number of inaccuracies and errors in the references to the work of Vvedensky and Teodorchik, which is the subject of criticism in Uyeita’s article.

Fig. 7. The Vvedensky and Teodorchik band in Uyeita’s interpretation.

The permeability curves of Vvedensky and Teodorchik, presented in Fig. 4 of their article in Annalen der Physik, are reproduced here in Fig. 8. The differently marked points were obtained with the aid of different coils A, B, C, and D, introduced into the oscillatory circuit. It is clearly seen that the points corresponding to the different coils, alternating with one another, lie on a common smooth curve and that, consequently, changing the coils in the apparatus does not change the result of the measurements.

After the accuracy of the method had been carefully checked, wires of other thicknesses were investigated as well; for them it was sufficient to obtain points only at the most characteristic places of the curves; the smallest number of points fell on the wires of 82 and 97 microns; it is the latter curve that Uyeita chooses as the object of his objections.

1. Wait explains the maximum obtained by Vvedensky and Teodorchik by the fact that, after the wave of \(90\ \text{m}\) (see Wait’s diagram, Fig. 7), the latter switch to another coil. We have seen that Vvedensky and Teodorchik, on a number of curves, showed that a change of coil does not affect the result.

Figure text: legend — Coil A; Coil B; Coil C; Coil D. Vertical label: \(\mu\). Horizontal label: \(\lambda\) (meter). Panel labels: 0.043; 0.097; 0.082; 0.052.

Fig. 8. Band near \(100\ \text{m}\) for different wirings according to Vvedensky and Teodorchik.

1. Wait cites as an example his own curve, which supposedly “cuts” the maximum of Vvedensky and Teodorchik. It is sufficient, however, to note that it is artificially raised above the abscissa axis and represents, moreover, an entirely different quantity, namely the apparent permeability \(\mu\),

not corrected for Foucault currents. In a properly made drawing it should lie considerably below the curve of Vedensky and Teodorchik.

1. In Fig. 9 the same Weiss curve is presented, only corrected by me for Foucault currents. We see that in reality Weiss’s permeability systematically falls toward long waves: when changing from 84 to 114 m, \(\mu\) falls from 32.5 to 12.9, and moreover not along a smooth curve, but forming a noticeable step. A 60% fall in permeability cannot be regarded as the absence of an anomaly; it is more likely, however, that here the shortcomings of Weiss’s apparatus are making themselves felt—shortcomings inadmissible, of course, in work that must be carried out exemplary, since it is being set up for the purpose of checking other work. The anomaly found by Vedensky and Teodorchik has an entirely different character and manifests itself sharply only in very weak fields, of the order of hundredths and tenths of a gauss (see Fig. 6); in Weiss’s experiments, however, the field was “always less than 20 gauss.” It is interesting, however, that in Weiss’s other experiments, where the field was 0.05–0.6 gauss in the case of the investigation of powders, and, in the case of the investigation of thin iron wires (about \(20\mu\) in diameter), still 0.6 gauss, changes in permeability were observed; however, Weiss attributed them to peculiarities of the apparatus and in subsequent experiments suppressed them (incipient spectra?) by some improvement of the instruments (perhaps by strengthening the field?). Weiss, however, gives no detailed description or results of these experiments in his article.

Fig. 9. Spectrum actually obtained by Weiss.

1. Weiss gives the curve of Vedensky and Teodorchik with the indication that it relates to a bundle of 20 wires, Fig. 7. In reality, as follows from Table IV of the article

Vvedensky and Teodorchik, their curve refers to 4 wires stretched over a glass tube. This, like other oversights, points to insufficient attention by Uyeit to the work he criticizes1.

1. Uyeit says that maxima and minima were also observed on their spectral curves, but that they depended on the manner in which the instruments were connected and passed into one another when the length of the wires connecting the individual capacitance condensers of the oscillatory system was changed. In Moscow this was checked by Malov, who came to a negative conclusion regarding the influence on the spectrum of the connecting wires in his instruments.

2. Uyeit does not touch upon the fact that Vvedensky and Teodorchik checked the anomaly they had found at about 100 m by three other methods as well, and in all cases found concordant results.

3. Uyeit also does not explain the circumstance that, in the experiments of Vvedensky and Teodorchik, steel gives its own spectrum, different from the spectra of iron and nickel.

The experiments carried out in 1921 by Vvedensky and Teodorchik, and in 1927 by Malov, indicate the great influence of the strength of the high-frequency field on the sharpness of the spectral bands in this region: the greater the strength of the magnetic field, the more blurred the bands; at a field strength of 10 gauss Vvedensky and Teodorchik observed only a weak sign of a band (see their Fig. 7 in Annalen d. Physik).

It is possible that, with a field strength up to 20 gauss, which Uyeit had, and with the particular grade of iron with which he was dealing, only that faint trace should remain of the spectral bands which we find on his corrected curve presented in Fig. 9.

Undoubtedly, the chemical composition, treatment, and temperature of iron cannot remain without influence on the spectra obtained; experiments carried out by Akulov show that the tension of an iron wire affects its resistance to alternating current. Owing to the laboriousness of the methods for obtaining magnetic spectra, the influence of these factors has not yet been investigated.

It should be noted that electrical spectra in Hertzian waves also lend themselves to investigation only with great difficulty. This field has existed for 30 years, but a rational method for obtaining spectra in Hertzian waves is only now beginning to become clear, thanks to the work of the school of Prof. Mie in Freiburg. One of his students, Frankenberger, begins his 1927 dissertation as follows: “The works of Colley, Rukop, and Weichmann, which up to now have been carried out on the question of the absorption and dispersion of decimeter electric waves in water, have given results that differ greatly from one another. The present work aims to bring final clarity to a small part of the spectrum of water, namely between waves of 52 to 58 cm in length, where Weichmann found a sharp band of anomalous dispersion.”

Indeed, in 1921 Weichmann was the first to obtain in water the characteristic bands of electrical dispersion and absorption lying between waves of 29 to 56 cm. Six years passed, and Frankenberger in the same laboratory of Mie found that in perfectly pure water there is no band at 55 cm, but that when millionths of sodium silicate are added to distilled water the band appears again; this meant that in Weichmann’s case it had been caused by a substance of the glass vessel dissolved in the water in which the experiment was performed. Precise measurements showed that this band consists of three elementary bands caused by centers with the following proper wavelengths \(\lambda_0\): 54.49, 55.55, and 53.29 cm. From this point of view it is easy to explain why, in the investigation of wire made of chemically pure iron, Sokolov did not obtain the sharp bands that Karchagin had observed: in the iron of Sokolov and Gutton, perhaps, there were not those constituent parts that—

...were in Karchagin’s wire. How sharply the spectrum of a mixture of alcohol with water changes with the slightest change in concentration was shown already in 1907 by Colley; his pupil Ivanov in 1915 discovered a sharp dependence of the spectrum of water on temperature: when it is raised to 50°, a number of bands lying between wavelengths from 60 to 124 cm completely disappear.

The electrical spectrum of liquids depends so strongly on different conditions. Yet liquids are bodies that are the most definite in a physical sense; it is not without reason that a column of mercury of known length is taken as the unit of resistance, water serves as the measure of specific gravity and heat capacity, benzene as that of the dielectric constant. Solids are not used as a measure of one or another physical property because their properties, even in the crystalline state, are very inconstant. They are difficult to subject to chemical purification and always, depending on the treatment, may have one density or another, electrical conductivity, dielectric constant, refractive index, etc. As for ferromagnetic substances, the latter are especially sensitive to all variations of thermal and mechanical treatment, to the previous magnetic history of the given specimen, to its mechanical vibrations and tensions, not to mention dependence on chemical composition. By changing the latter, we can obtain a material with permeability in a constant field from tens of thousands to hundreds of units, and with coercive force from hundredths of a gauss to hundreds of gauss, etc. It is therefore not difficult to understand that magnetic spectra obtained in solid iron, steel, or nickel cannot but differ from one another; as Moscow and German works show, in certain regions of waves they change greatly even depending on the diameter of the wire. All this should explain those apparent contradictions that are observed in the results of works by different authors.

Conclusion.

Summing up what has been said, we come to the conclusion that magnetic spectra throughout the enormous range of the scale of electromagnetic waves have still been insufficiently studied. By the very

In essence, they must depend on a multitude of parameters, and now we are faced with the task of establishing the normal form of magnetic spectra, together with a detailed clarification of the influence upon them of all those conditions in which a solid body may find itself. So far very little has been done in this direction; the Moscow investigations are the first, while abroad these problems are only just being approached, and all work in this field has more of a reconnaissance character. In an effort to encompass the behavior of ferromagnetic substances over as broad a wavelength interval as possible, iron began to be studied over such a wide extent of the scale that, in old electrical spectroscopy, not a single substance had yet been investigated over it.

At times one hears the opinion that the observations of Miehl and White disproved the existence of bands in magnetic spectra and the results of the related works on electromagnetism in general. On this point the following may be said:

1. The reduction of Maxwell’s equations to symmetric form by introducing magnetic conductivity, justified by the requirements of real experiment, in no way depends on the existence of bands in magnetic spectra. Therefore the Moscow works of Vvedensky, Shiller, and Ermolaev, which are based on Maxwell’s augmented equations, as well as the German investigations of Truksa and Uller and the dissertation of Mittelstrass, cannot in any measure be annulled.

2. The development of the general theory of magnetic spectra and of the general theory of magnetic dispersion and absorption, based on the hypothesis of the elastically bound motion of magnetic centers, carried out in Moscow, cannot be deprived of its fundamental significance; it has so general a character that it does not depend on in which parts of the electromagnetic wave scale there are bands of magnetic dispersion and where there are none.

3. We have seen that the existence of bands in magnetic spectra has been established quite firmly in periods of about a minute and hundredths of a second (Fig. 3a) and about billionths

fractions of a second (Fig. 2). They cannot fail to exist also in the region of transition from Hertzian to thermal waves, where the magnetic properties surely disappear.

Therefore the theory of the new dispersion and absorption cannot be without not only fundamental, but also practical, significance.

LITERATURE

(Continuation; for the beginning see vol. IV, p. 263, 1924.)

1. V. Arkadiev. On the calculation of iron conductors for alternating current. Transactions of the GEI. No. 15, p. 70, 1926.

2. K. A. Mittelstrass. Untersuchungen über die Hautwirkung in Eisenleitern. Arch. f. Elektrot. 18, 595, No. 6, 1927.

3. B. Vvedensky. Calculation of the surface effect in ferromagnetic cylinders with magnetic permeability. Transactions of the GEI. No. 6, p. 39, 1925; No. 15, p. 14, 1926.

4. B. Vvedensky and B. Shillerov. Tables and curves for the calculation of the surface effect in ferromagnetic cylinders with magnetic permeability. Transactions of the GEI. No. 15, p. 23, 1926. Zh. R. F. O. 58, 241, 1926. Zs. f. Phys. 34, 309, 1925.

5. V. Arkadiev. On Hertz gratings. Transactions of the GEI. No. 15, 1926. Ann. d. Phys. 75, 426, 1924.

6. V. Arkadiev. Reflection of electromagnetic waves from a magnetic medium. Zh. R. F. O. 58, 148, 1926. ZS. f. Phys. 33, 903, 1926.

7. V. Arkadiev. Reflection of electric waves from ferromagnetic Hertz gratings. Zh. R. F. O. 58, 159, 1926. Ann. d. Phys. 81, 649, 1926.

8. V. Arkadiev. Oscillations and resonance of elementary magnets. Reports of the Academy of Sciences, A. 1927, p. 12; C. R. d. S. d. l’Ac. d. S. 183, 777, 1926.

9. Bergn. J. Vander Plaats. Ann. d. Phys., 47, 421, 1915.

10. V. Arkadiev. Electromagnetic spectroscopy of metals, Chapter XVII of the supplementary volume to O. D. Chwolson’s course of physics, 1926.

11. V. Arkadiev. On magnetic dispersion and absorption. Zh. R. F. O. 56, 194, 1924.

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13. V. Arkadiev. Magnetic spectra of iron and nickel wires in the region of centimeter Hertzian waves. Zh. R. F. O. 57, 24, 1925; ZS. f. Phys., 28, 11, 1924.

14. V. Arkadiev. Problems of general spectroscopy. (Speech at the opening of the Fourth Congress of Physicists in Leningrad). Zh. R. F. O. 57, 57, 1925.

15. H. Israël. Magnetospektroskopische Untersuchungen an Nickeldrähten mit kurzen Hertzschen Wellen. ZS. f. Phys., 39, 841, 1926.

1. H. Busch. Magnetic spectroscopy of increased resolving power. Zh. R. F. O. 60, No. 1, 1928.

2. Leo Sokolow. Eine Präzisionsmethode zur Messung der magnetischen Permeabilität bei sehr schnellen Schwingungen. Ann. d. Phys. 83, 1136, 1927.

3. C. Gutton et J. Mihul. Sur la perméabilité du fer aux fréquences élevées. C. R. 184, 1234, 1927.

4. G. Laville. Recherches expérimentales sur la propagation des ondes électromagnétiques le long des fils. Annales d. Physique. 2, 328, 1924.

5. G. R. Wait. Magnetic permeability of iron and magnetite in high frequency alternating fields. Phys. Rev. 29, 566, 1927. See also Phys. Rev. 31, 330, 1928.

6. V. K. Mitkevich. The influence of a constant magnetic field on magnetic spectra. Zh. R. F. O. 58, 181, 1926. ZS. f. Phys. 38, 716, 1926.

7. N. S. Akulov. On magnetic permeability in the case of pulsating magnetic fields. Zh. R. F. O. 58, 577, 1926. Proc. GAEI. No. 15, 1926.

8. N. N. Malov. The influence of strong magnetic fields on magnetic spectra. Fifth Congress of Russian Physicists. P. 62. 1926.

9. Ernst Frankenberger. Die anomale Dispersion einer Silikatlösung zwischen 50 und 60 cm Wellenlänge. Ann. d. Phys. 82, 394, 1927.

10. K. Ivanov. Investigation of dispersion in the electrical spectrum of water. Izv. Warsaw University 1915. Ann. d. Phys., 65, 481, 1921.

1. Recently in Physical Review there appeared a second abstract on the work of Uyeit et al., again not free of misunderstandings; the wire of 0.5 mm sent by me to the director of the Institute of Terrestrial Magnetism, Dr. Bauer, is ascribed by them to Vvedensky and Teodorchik, being called “a specimen of Vvedensky and Teodorchik,” whereas the latter described an investigation of wires from 0.043 to 0.097 mm in diameter. ↩↩↩↩↩

2. I quote from the translation from the manuscript made by N. A. Nikitin and to be printed in Zh. R. F. O., vol. 60, issue I. ↩