Experimental Studies in Strong Magnetic Fields*

P. L. Kapitza, Cambridge

Introduction

It is well known that the intensity of a magnetic field obtained by means of electromagnets is limited by the saturation of the cores of the latter. At the present time the highest magnetization at saturation is possessed by the alloy “ferrocobalt,” discovered by Prof. Weiss; but even with the aid of this alloy the maximum value of the field that can be created in a volume sufficient for experimental investigations does not reach even 100 gauss. Until alloys with a higher magnetization at saturation are discovered, an increase of the magnetic field can proceed only at the cost of increasing the dimensions of the electromagnet. However, with an increase in dimensions (volume) the magnetic field grows in proportion to the logarithm of the volume.

It is doubtful whether one could go far in this direction after the giant electromagnet of Prof. Cotton was built in France. It is also well known that strong magnetic fields can be obtained in a coil if it is cooled sufficiently well—for example, by a strong jet of water. By this method fields of about 60–70 kilogauss can be obtained. This is probably a practical limit, since there exists a po—

* Report read at the Solvay Congress in Brussels in October 1930.

visible limit for the amount of cooling substance that can be brought into contact with the unit surface of the coil. This method has not found practical application, is more complicated than the electromagnet method, and does not open up great possibilities. A considerable increase of the magnetic field can be achieved if the time of its existence is reduced to small fractions of a second. This sacrifice in time of course presents certain difficulties in carrying out investigations on magnetism, but since it is evidently the only hope at present of obtaining strong magnetic fields, we have followed this path.

Undoubtedly some phenomena requiring a certain time for their establishment, such as, for example, the growth of crystals, cannot be studied in this way. There remain, however, very many phenomena, probably the most interesting ones, that can be studied by this method. We are chiefly interested in atomic phenomena, and since a strong magnetic field is the only most fruitful means for distorting the motion of electrons in atoms, molecules, and crystals, experiments in this field are of great interest for modern physics. The main difficulty encountered in implementing this method is as follows: first, the actual obtaining of the field in a short interval of time; second, the method of measuring the phenomenon. In this article I wish to dwell in detail on the second part of the question, since the first part was described in detail earlier.*

Description of the method for obtaining magnetic fields in short intervals of time

It is obvious that the most important point in obtaining strong magnetic fields in short intervals of time consists in protecting the coil from overheating and in arranging the experiment in such a way that all the heat liberated—

* Proceedings of the Roy. Soc. A. 105, 691, 1924; see also Ya. G. Dorfman, “Strong magnetic fields and the work of Kapitsa,” Uspekhi fizich. nauk, vol. X.

was absorbed by the coil itself as a consequence of its heat capacity. If the magnetic field is produced in a coil of radius \(a\) and a winding made of a material with specific resistance \(\rho\) (taking into account also the volume occupied by the insulation of the winding), and the applied power is equal to \(W\) kW, then the field strength will have the value

\[ H = k \sqrt{\frac{w}{a\rho}} . \]

In this formula, which was given in such a convenient form by Fabry,* \(k\) is a coefficient depending on the shape of the coil, and in ordinary coils cannot exceed 0.179. From this formula it is clearly seen, for example, that in order to obtain a field of 1 million gauss in a coil with a cross-sectional diameter of 1 cm, it is necessary to apply 40 thousand kW, and in practice even considerably more. At such a power, a coil of ordinary dimensions would have to heat up by more than \(10\,000^\circ\) per second. If, however, the time is reduced to 0.01 sec., we shall have a temperature increase of only \(100^\circ\), and this is already permissible. From this point of view, the advantage of obtaining the field in short intervals of time is obvious. In carrying out this method, considerable difficulties are encountered. The first is the production of large powers. Obviously, the use of a station of several thousand kilowatts for 0.01 sec. is not only extremely disadvantageous, but practically impossible for a physics laboratory, and it is clearly necessary to develop a special source of energy. The solution of this problem suggests itself. For this purpose any electrical installation is suitable that can accumulate energy and then, within fractions of a second, deliver the energy stored in it. We may imagine four basic types of installations, depending on the method by which energy is accumulated in them.

The first method is electrostatic, the second magnetic, the third chemical, and the fourth mechanical.

The first method is carried out by means of a large capacitor battery, which is slowly discharged through the coil. This

* Journ. de Phys., ser. 4, IX, 129, 1910.

the solution is entirely possible, but has major practical shortcomings. It must be remembered that not only is great power required, but also a certain amount of energy must have been accumulated, sufficient to produce the field and to maintain it for a period of time not too short for carrying out the experiment. In practice, the most convenient time proved to be between 0.02 and 0.01 sec. It can be shown that a capacitor bank capable of supplying the required energy has practically inconveniently large dimensions and makes it necessary to charge it to very high potentials, which greatly complicates the question of insulating the coil. Experiments along these lines were carried out by Dr. Wall,* whose results confirm our general considerations.

The second method of accumulating energy is magnetic energy, usually accumulated in the iron core of an induction coil. Indeed, at first we conducted experiments with a specially constructed induction coil, the secondary winding of which consisted of a very small number of turns and was connected to the coil. Theoretically this method should be more acceptable and more practical than the capacitor-bank method, but here we encounter great difficulties in practical implementation. The chief difficulty is that in the secondary winding, which has almost no capacitance and is connected to a circuit with large self-induction (a solenoid), colossal overvoltages arise when the primary current is interrupted and, roughly speaking, it may happen that the energy, instead of going into the coil, is dissipated in the switch. Calculations showed that switching off the primary current is a very difficult and practically impossible task, and therefore this method was abandoned.

The first method that made it possible to accumulate energy satisfactorily was the chemical one.** For this purpose

* Wall, Journal of the Institution of Electric Engineers, XIV, 745, 1926.
** A detailed description of this method may be found in Proc. Roy. Soc., loc. cit., 1924.

A special storage battery was built, having a very small capacity, determined by the thinness of the active layer. The accumulators were made very strong and were placed close to one another, in the form of a voltaic pile. These accumulators could be charged in the course of several seconds and ordinarily were completely discharged in fractions of a second. With this storage battery it was possible to obtain a power of about 1,000 and 2,000 kW, and the first experiments in briefly acting magnetic fields were carried out in short intervals of time. In this way experiments on the Zeeman effect were performed with fields of approximately up to 125,000 gauss, and these same fields were used to obtain deflections of the paths of $\alpha$-rays in a Wilson chamber.* These experiments made it possible to determine the change in the velocity of helium particles when they passed through such gases as air or hydrogen.

A certain increase in the magnitude of the magnetic field can be obtained by increasing the dimensions of the storage battery, which causes considerable difficulties. After 1–2 years the cells gradually increased their capacity and thereby reduced the power delivered; they deteriorated.

However, the difficulty lies in switching off a direct current of several thousand amperes in a sufficiently short time in comparison with 0.01 sec. This leads, in the end, to the last possibility of accumulating energy, namely by mechanical means, applying the flywheel principle.*** This can be accomplished by using an alternating-current generator—a type of turbogenerator—which has a massive rotor making a large number of revolutions and therefore possessing a large kinetic energy. From engineering practice it is well known that, in the event of a short circuit, large powers can be obtained from such a generator at the moment of switching on.

Alternating-current generators, which are built for un-

* Kapitza and Skinner, Proc. Roy. Soc. 109, 224, 1925.
* Kapitza, Proc. Roy. Soc. 106, 602, 1924.
* Proc. Roy. Soc. 115*, 658, 1927.

of continuous use, are calculated in such a way that the short-circuit current cannot give a large power, since this increases the danger of operation. In the design of our generator we proceeded from the opposite principle, and indeed, the machine built by us could deliver, under short circuit, about 200,000 kW (70 thousand amperes and 3 thousand volts), whereas its dimensions corresponded to a machine for continuous operation at 1500 kW. This change in design leads to a very interesting study of mechanical stresses in an electrical machine. In ordinary machines this is not of essential importance, but in our case the mechanical stresses play such an essential role that the question of them is the most important one in the design, and many special features, unlike ordinary practice, have to be introduced in order to make the machine strong. The use of an alternating-current machine is also of great advantage because it greatly facilitates the problem of interrupting the current. Since only half-waves are used, it was necessary to design such a synchronous device that could interrupt the current at the moment when the value of the current becomes equal to zero.

In such a case the problem of interrupting the current is reduced to the problem of designing a fast-acting synchronous switch. We refer the reader to a more detailed description of the switching device, which is an interesting mechanical problem and operates on the principle of a camshaft.

At first glance it seems that the use of alternating current creates a difficulty in obtaining a constant magnetic field for even 0.01 sec., but by corresponding changes in the excitation of the field one can create a wave having a flat top. In Fig. 1 we have an oscillogram of an ordinary wave, and in Fig. 2 a wave with a flat top. The machine itself is shown in Fig. 3. The principal difficulty in this method of obtaining a magnetic field, which sets the limit to the strength of the field obtained, lies in the coil itself. The large current density, reaching 100 thousand amp.

per \(1\ \mathrm{cm}^2\) in a strong magnetic field, inevitably produces large stresses in the body of the coil itself. These stresses

Fig. 1.

Fig. 2.

flatten the coil along the axis and reduce its diameter. An ordinary coil, made of copper, was destroyed with a great crash when a field of intensity

Fig. 3.

of 200,000 gauss was produced in it. This question required a careful study of the forces arising in the coil, and after the development of methods for calculating these stresses by Dr. Cock-

...by P. Kapitza* it proved possible to ascertain that, if the coil is compressed by a massive steel bandage, then the reaction forces from the bandage, together with the electromechanical forces tending to tear the coil apart, create conditions analogous to all-round hydrostatic pressure. The coil was made of a special alloy of cadmium with copper, which possessed greater strength than copper and good conductivity. By means of a coil with a bore diameter of 1 cm, 320 kilogauss was obtained inside it, and one may hope that, in the end, with further improvement of the coil design, it will be possible to obtain, in a volume of 1–2 cm³, a field of about half a million gauss; but if no special alloy is invented with good electrical conductivity and a strength approaching that of steel, then the question of obtaining fields above 1 million gauss is very doubtful. The hydrostatic pressure in the coil in our case reaches several thousand kilograms per 1 cm², and it is very surprising that up to the present time we have not had cases of insulation failure. But in this case nature helps us, namely: the arc formed after breakdown even of thin insulation is extinguished by the magnetic field, and the current continues to circulate in the usual way. We have had several cases in which the insulation was clearly unsuitable, but nevertheless no arc was formed. When a coil is destroyed as a result of stress, there is a very large explosion and fragments of the coil fly apart. Before we learned to build coils capable of withstanding forces of this kind, 4 or 5 coils were blown apart.

Further progress in increasing the field strength may be achieved only very cautiously and gradually.

Experimental methods

The following basic idea guides the methods of measurement in strong magnetic fields. We are compelled to carry out the experiment during 0.01 sec., which is a very small interval for experimental technique, but sufficient

* Cockroft, Phil. Trans. A. 227, 317–343, 1928.

given in order that the phenomenon which we are studying could already become established. In fact, since the magnetic field, by virtue of its strength, considerably exceeds the ordinary one, the phenomena in it are so greatly intensified that they can be studied even in such a short time.

What is lost in time is gained in magnitude

In most cases the method of briefly acting fields cannot cover the region below 30 kilogauss, and it becomes necessary to carry out supplementary work with ordinary electromagnets, if this is of interest.

The first question that we shall consider is the measurement of the field itself. It reduces only to measuring the current in the coil with the aid of an oscillograph. The oscillograph which we used has a very small natural period and low sensitivity, but since the current in the coil can reach 20 thousand amperes, we can always take 1–2 amperes in order to pass them through the oscillograph, and during the short time of the experiment itself the oscillograph will not have time to heat up. In order to determine the magnitude of the magnetic field of the current, it is necessary to know the constant of the coil. This is done by a somewhat modified ballistic method.

A small coil was placed at the center of another, large coil. This small coil was short-circuited until the current in the main coil (solenoid) reached its maximum value; then the coil was automatically switched off and connected to a ballistic galvanometer, by whose deflection the field strength could be determined in the usual way. We found that the field in the main coil (solenoid) is proportional to the current, and that a field of the order of 4 thousand gauss, produced by the steel bandage of the coil, gave no noticeable deviation from proportionality. The various manipulations that are necessary for carrying out the experiment in 0.01 of a second made it necessary to perform a whole series of switchings entirely synchronously. At present the whole experiment is carried out by pressing a button, and everything is done auto-

automatically for the duration of 0.01 sec., during which the experiment lasts.

Change in the Resistance of Metals in Strong Magnetic Fields

It is obvious that, for every phenomenon that is to be investigated in these strong fields over such a short time, it is necessary to develop a special method of investigation. A priori there are no fundamental difficulties in devising such methods for all kinds of investigations that are carried out in ordinary fields. The first question that we studied was the question of how the magnetic field obtained from the dynamo changes the resistance of metals.*

The basic idea of the experimental arrangement reduces to the following. A sample of the metal under investigation, preferably taken in the form of a wire, was wound bifilarly into a small coil and had 2 potential leads and 2 current leads, which were placed at the ends of the winding in the usual way. The leads were also connected bifilarly to the measuring instrument. The potential ends were connected to a sensitive oscillograph, and if the current passing through the current leads is constant, then the deflections of the oscillograph should be proportional to the resistance of the wire under investigation.

In our case we had the great advantage, in the sense that we could send through the wire currents considerably larger than usual, for there is no need to fear heating during 0.01 sec. Only one difficulty arises—the determination of the electromotive force of induction arising owing to the change of field in the solenoid. But this latter can be eliminated by sending the current through the wire in separate pulses, as shown by curve 1 in Fig. 1. The duration of the pulse was 3–4 times less than the duration of the current in the solenoid (curve $H$), and evidently the current in the oscillograph measuring the difference of potentials (curve $P$), caused by the change of magnetic

* Proc. Roy. Soc. A. 119, 358–443, 1928; 123, 292–372, 1929.

fields will be the same, but the current caused by the difference of potentials and depending on the resistance of the wire will reach its maximum, and the amplitude at each switching on or application of current in the wire will be proportional to the resistance of the wire.

In this way 35 different metals were investigated, some of them at low temperatures, since in this case the changes in resistance are more considerable than at room temperature. It was found that, with the exception of ferromagnetic metals, the change of resistance in most metals follows a quadratic law in weak fields, as had long ago been established by Patterson* and others, but in strong fields this law passes over into a linear one. As an example, Fig. 4 gives curves for three copper wires. The second interesting phenomenon which we found consists in the fact that the physical properties of the wire exert a substantial influence on the form of the curve. Thus, for the purest and best-annealed wire, the quadratic part is the shortest and the linear part begins earliest (Fig. 4). This was found in all specimens without exception. This led the author to the assumption of an analogy between the increase of resistance under the influence of chemical and physical impurities of the substance and the increase of resistance under the influence of the perturbing action of the magnetic field. Assuming that the internal perturbations produce the same action as a certain hypothetical field \(H_k\), oriented opposite

Field (kilogauss)
Fig. 4.

* Patterson, Phil. Mag. 3, 642, 1902.

in all directions, and that the true change in resistance is proportional to the resultant vector of the internal magnetic field, one can readily obtain the formula for the change in resistance; namely, the relative increase of the resistance

\[ \frac{\Delta R}{R}=\beta \frac{H^{2}}{H_k} \qquad H < H_k \]

\[ \frac{\Delta R}{R}=\beta\left(H-H_k+\frac{H_k^{2}}{34}\right) \qquad H > H_k \]

where \(\beta\) is a constant for the given material.

It follows from this hypothesis that in an ideal, perfect crystal the scattering factor may be very small and the linear law should hold almost from the very beginning and may be observed in ordinary magnetic fields. Crystals of cadmium, zinc, and tin were studied by K. D. Sinelnikov and by me personally, and it was indeed found that, when a sufficiently perfect crystal was prepared, the linear law began at fields below 2 thousand gauss, instead of 30 thousand and 60 thousand gauss in the case of wire. In fact, however, it is by no means simple to obtain a good crystal. It actually turned out, for example, that one cannot take a crystal in one’s hands, since the negligible pressure thereby exerted completely spoils the crystal. It was possible to obtain a perfect crystal which gave the linear law at the very lowest fields; for this purpose the crystalline rod under investigation was grown together with offshoots to it, which were made of the same metal, and was introduced into the magnetic field without the slightest deformation. The method of growing crystals is analogous to that described by the author for bismuth crystals:* the metal was simply grown freely on a quartz plate, so that it was not necessary to break a glass tube when removing the crystal. Each such crystal, after being cooled by liquid air for several hours, increased its re-

* Kapitza, Proc. Roy. Soc. A. 119, 363, 1928.

resistance, and the linear law began at higher fields than before cooling.

Such crystals also had a lower resistance in liquid air than crystals of the same metals studied earlier (imperfect crystals). For example, in the case of the best Cd crystal the ratio of its resistance at room temperature to its resistance at the temperature of liquid air was 0.75, instead of 0.25 obtained for a crystal of the same metal by Meissner.* But after repeated coolings the crystal gradually acquires a higher resistance, 0.21. X-ray analysis showed no difference between the spoiled crystal and the perfect one; this indicates that the distortions produced by heating and cooling the crystal are very small, but nevertheless sufficient for a noticeable change in the conducting properties. These studies yielded many interesting results which support the hypothesis we have put forward and are at present being prepared for publication.

The second point following from our hypothesis is that the resistance due to the disturbing factor can easily be obtained from the curve of the change of resistance in strong magnetic fields, if a tangent to the curve is drawn. It can be proved that the segment from the origin of coordinates to the point where this tangent intersects the abscissa axis is equal to the additional resistance due to disturbances. It is natural to suppose that this additional resistance should not depend on temperature and should be equal to the residual resistance at absolute zero.

This makes it possible to test our hypothesis, and for this purpose we measured the residual resistance of the specimens on which we experimented. This still cannot give a final answer; for this a temperature below that of liquid hydrogen would be required, which at present is not attainable in our laboratory. The results

* Meissner, Z. Physik 26, 708, 1926.

these investigations showed that, within an accuracy of 30–40%, the residual resistance measured at liquid-hydrogen temperatures and the additional resistance measured in a magnetic field coincide. Some numerical results of the investigations are given in the table below.

Table 1

It can be seen that in all metals with a cubic lattice the agreement occurs with an accuracy not exceeding the limits of error and of the approximate nature of the theoretical assumption, and this, I think, is undoubtedly not accidental. In the case of a non-cubic lattice of the metals cadmium, zinc, and gallium, it is hopeless to look for any agreement. This may easily be explained by the insufficiency of the basic assumption that the additional resistance is independent of temperature. In non-cubic crystals this is hardly the case, as is easy to verify by looking at the data for the cadmium single crystal grown by Sineľnikov and ourselves.

At the temperature of liquid air its resistance was 0.175 of the resistance at room temperature, whereas the same ratio for Meissner’s crystal was equal to 0.254. We may thus expect that the residual resistance of Meissner’s crystal will not be

exceed \(0.254—0.175=0.079\). Measurements at the temperature of liquid helium showed that the residual resistance of Meissner’s crystal is equal to \(0.00047\), or more than 100 times smaller.

This means that the additional resistance must depend on the temperature. It is possible that, in the case where we had an aggregate of small crystallites not of the cubic system, the thermal expansion was different along the different axes of the crystal, and, upon cooling or heating such a rod, stresses were formed. The action of these stresses was the cause of the change in the additional resistance. Owing to the ease with which a pure crystal can be deformed, one cannot expect, even in the case of a pure substance, very good agreement between the various residual resistances unless special experimental precautions are taken; and this is probably the reason for the incomplete agreement of the residual and additional resistances of gold crystals, as observed by Meissner and Scheffers.* At present, investigations of the change in the resistance of metals in strong magnetic fields open up new possibilities for finding the ideal resistance of metals and probably indicate that the course of the change of resistance with temperature, especially at low temperatures, must be somewhat more rapid than was previously thought. For a final clarification of this question it is necessary to carry out many more experimental investigations and to take greater precautions with regard to the perfection and purity of the specimens studied.

Magnetic Susceptibility

The nearest directions in which investigations with strong magnetic fields will proceed will include magnetic susceptibility and magnetostriction. Again, as in the preceding case, the magnetic-field strength makes it possible

* Meissner und Scheffers, Z. Physik 30, 827–836, 1929.
Kapitza, Proc. Roy. Soc. (A) 126, 683, 1930.

to carry out these investigations only over a small fraction of a second, and the scale of the phenomenon increases greatly. For example, if one takes a gram of some weakly magnetic substance, with magnetic susceptibility \(\chi\) of order \(10^{-6}\), and places it in a field of 300 thousand gauss with an inhomogeneity of 10% per 1 cm, we shall have

\[ \frac{dH}{dx}=30 \text{ thousand}. \]

The force experienced by the substance

\[ F=\chi H \frac{dH}{dx} \text{ per gram}. \]

as is not difficult to see, will be of the order of 10 per gram.

The question comes down to the construction of a balance with aperiodic damping and a natural frequency of about 100 oscillations per second and with a sensitivity sufficient to detect a force of 10 g. It can easily be shown that suitable balances with a natural frequency of 1000 oscillations/sec, having a mass of 1–2 g, will be displaced under the influence of a force of 10 g by only \(10^{-5}\)—\(10^{-4}\) cm; therefore, to observe such a displacement we must be able to magnify it approximately \(10^{5}\) times. After a whole series of attempts, the following hydraulic method of magnification was invented, which proved very successful. A schematic drawing is given in Fig. 5. The instrument consists of a flexible diaphragm 1, to which the specimen under investigation is suspended. The diaphragm is closed by a small chamber 3 with a small aperture 4. The entire space above the chamber and the diaphragm was filled with oil, and provision was made so that no air would enter there. When the diaphragm was displaced under the influence of the force acting on the specimen, the oil passed through aperture 4 with a velocity greater than the velocity of displacement of the diaphragm. In this way, we obtained a 50-fold magnification. To record the motion of the oil through the aperture, a small mirror with an area of 0.5 cm² was freely suspended in front of the latter. The moving oil deflected the mirror, which produced a deflection of the spot from the light beam 6 on a moving photographic plate. This optical lever gave a further 2000-fold magnification, which thus brought—

reached 100 thousand. By a suitable choice of the thickness of the diaphragm and the viscosity of the oil, the balance can be set to the required sensitivity and at the same time made to have aperiodic damping. It was found that, during the short time of the experiment, the small mirror exactly followed the motion of the oil without any lag, while the slow motions of the oil, caused by thermal expansion of the apparatus, etc., produced no displacement of the mirror, which was held at rest by its own weight. With the aid of this balance, which has only recently been set up, we have studied the magnetic susceptibility of amorphous bismuth at ordinary temperatures, but no deviation from the linear law of magnetization was found up to fields of 300 thousand gauss. It may be hoped that this balance will allow us to study, at low temperatures, the saturation of paramagnetic bodies and thus determine the value of the elementary magnetic moment.

Fig. 5.

It should be noted that our method of measuring magnetic susceptibility differs from that ordinarily used in a constant field. In our case we are dealing not with isothermal magnetization, but with adiabatic magnetization, since during the short experiment the specimen does not have time to come into (thermal) equilibrium with the surrounding medium. This change in the temperature of the specimen upon magnetization, first calculated by Langevin,* may be noticeable down to the very lowest temperatures. In substances such as bismuth, whose diamagnetism increases with decreasing temperature, still lower temperatures can be obtained by magnetization.

* Langevin, Ann. de Phys., VIII, 5, 123. 1905.

P. L. KAPITSA

Magnetostriction

If a substance is placed in a magnetic field, its shape may change under the influence of many causes. One of the first effects, which we may call classical magnetostriction, is due to the stresses produced by magnetic forces with which the two poles of a magnetized body act upon one another. This effect for diamagnetic bodies, such as, for example, bismuth, in fields of 300 kilogauss is very small in magnitude, reaches the order of \(10^{-6}\), and is not of special interest for the study of the magnetic properties of a body, since it can be calculated from the elastic and magnetic constants of the given body.

On the other hand, we may expect that other phenomena must also occur, caused by distortion of the electrodynamic structure of the atoms of the metal, which may manifest themselves in changes of the body’s shape. Since the magnitude of this phenomenon has not yet been calculated theoretically, we could only devise a method for measuring magnetostriction and see whether it might not accidentally prove larger than classical magnetostriction.

Fig. 6.

The apparatus used for magnetostriction is very similar to that with which we studied magnetic susceptibility and which was described above. The arrangement is shown schematically in Fig. 6. The balance \(1\) is fixed on a very massive base \(2\), and the rod \(3\) of the substance under investigation is attached to a piston \(4\) of considerable mass, which can move in a small clearance in the cylinder \(5\), firmly fixed to the base \(2\). The space below and above the piston \(4\) is filled with oil. A solenoid surrounds the rod. It is obvious that if the rod changes its length in the course of \(0.01\) sec, the piston will not be able during this time to move, owing to its large inertia and the viscosity of the oil, and

all the motion is transmitted to the plate, and the balance will increase the change in length by 100,000 times. On the other hand, any slow changes in the length of the rod or of the parts connected with it, occurring under the influence of temperature, will be transmitted to the piston, and in this way it is possible to eliminate all distortions due to temperature, which in ordinary methods of measurement cause numerous inconveniences. If the magnification given by the balance is \(10^{-5}\) and the length of the specimen is several centimeters, then on this apparatus one can detect a change in length \(\Delta l\) of the order of \(10^{-7}\). The first substance that we investigated was a drawn bismuth rod, which showed a small contraction, somewhat greater than that expected from classical magnetostriction. When the bismuth rod was grown in the form of a crystal, a more considerable effect was observed, which could be explained only by magnetostriction caused by the influence of the magnetic field on the bonds in the lattice.

A more detailed investigation showed that if the trigonal axis is parallel to the field, the rod elongates; when this axis is perpendicular to the field, the rod contracts. The contraction and elongation in one and the same field proved to be practically the same, so that in the finely crystalline rod one compensated the other, which explains the absence of the effect in it. The experiments showed that the change in length in a bismuth crystal is proportional to the square of the magnetic field and increases considerably as the temperature is lowered. At the temperature of liquid nitrogen, the magnetostriction is many times greater than at room temperature, and the relative change in length \(\frac{\Delta l}{l}\) in a field of 300 thousand gauss reaches the value \(5 \cdot 10^{-5}\), which exceeds the values previously found for some ferromagnetic bodies. These results also explain why earlier attempts to detect magnetostriction in bismuth were unsuccessful.* In those experiments the maximum field reached only

* E. van Aubel, Phys. Rev. 16, 60, 1903.

3 thousand gauss, so that even in a bismuth single crystal the magnetostriction could amount only to \(5 \cdot 10^{-9}\), and since in fact the experiment was carried out on a polycrystalline rod, the effect could have been of the order of \(10^{-10}\), which is too small to measure.

We also have the possibility of detecting magnetostriction in other crystals of the non-cubic system, such as tin, cadmium, and graphite, but here the effect is considerably smaller and is still being investigated.

The general picture of the phenomenon appears approximately as follows. The elementary cell of a bismuth crystal is very similar to a cube slightly elongated along one of its diagonals, which coincides in direction with the trigonal axis. In a magnetic field, evidently, such a cube becomes still more elongated in the same direction.

From the general theory of magnetostriction we must expect that such a deformation of the lattice, if it can be caused by external stresses, should lead to an increase in the diamagnetic susceptibility in the direction perpendicular to the crystal axis and to a decrease along it. We also made several investigations of the magnetostriction of Ni and found that in Ni, after the application of a field of several thousand gauss, no further change in length is observed up to fields of 100 thousand gauss. From the study of all these phenomena it is evident that the chief interest in research on the magnetic properties of the solid state is represented by crystals, and that it is extremely important to have as perfect a crystal as possible. Three principal factors distort the lattice of a crystal: the first is impurities, the second is the stress factor, and the third is temperature. And the principal future of magnetic investigations probably lies in the study of very pure and well-grown crystals at very low temperatures. Strong magnetic fields most productively eliminate the effects of distortions in the crystal in the most proper way and make it possible to find the magnetic properties under these simple conditions.

There are also other areas for investigation, such as the action

…the action of a magnetic field on the absorption, emission, and scattering of light (the Zeeman effect, the Faraday effect, etc.). Our work has already shown that this too can be done in short-duration fields, since, for example, the splitting in the Zeeman effect alone is so large that an apparatus of high light-gathering power can be used; and the use of a strong light source makes it possible to reduce the exposure time to 0.01 sec. Another area of magnetic research, such as the deflection of $\alpha$- and $\beta$-rays, is also of considerable interest, and it is noteworthy that this method can be applied to a whole range of physical investigations much more easily than might at first appear.