On the Superconductivity of Metals1

K. A. Kromelin.

In 1913 Professor Kamerlingh-Onnes in Leiden (Holland), in his cryogenic laboratory, discovered that there exist metals whose electrical resistance at the temperature of liquid helium becomes zero. This new state, into which a metal can be brought, was called the state of superconductivity. Before turning to a description of the experiments that led to this remarkable discovery, we shall give a brief outline of the earlier investigations of metallic resistance at low temperatures.

There is nothing surprising in the fact that, from the time when gases began to be liquefied in various laboratories, the question of measuring at low temperatures so important a quantity, in both theoretical and practical respects, as electrical resistance became a subject of investigation. As early as 1885 there appeared a fairly detailed work by Cailletet and Bouty [1], who, however, did not go below \(-123^\circ\text{C}\), a temperature obtainable without particular difficulty with the aid of liquid ethylene. Only when liquid oxygen and liquid air had been obtained was it possible to continue the investigation. Holborn, partly in work carried out jointly with W. Wien [2], studied the dependence of the resistance of a pure platinum wire on temperature in the range from \(0\) to \(-190^\circ\), the temperature being carefully determined by a hydrogen thermometer. The aim of the investigation was to establish the possibility of accurately determining low temperatures by measuring resistances. This problem was excellently solved by Holborn and later investigators, so that at the present time a thermometer with platinum resistance should be regarded as the most suitable secondary thermometer for low temperatures. Although investigations in the same direction had already earlier been carried out by Wroblewski [3] and Olszewski [4], they did not succeed in achieving significant success, precisely because their tempe—

a temperature bath was insufficiently constant, and the temperature measurements were inaccurate. The thermometer with platinum resistance became a precision instrument of great importance only after the above-mentioned measurements of Holborn and Wien, and later of Travers and Gwyer [5], and especially after the investigations of Kamerlingh-Onnes and his collaborators Meijling [6], Clay [7], and Holst [8], carried out in the Leiden cryogenic laboratory, and the work of Henning [9] and Holborn, performed at the State Physical-Technical Bureau in Charlottenburg.

However, in these investigations not only practical aims were pursued. Much could also be expected from their results for the electron theory of metals. It had been repeatedly observed that the change of resistance with temperature proceeded quite differently at low temperatures than at high ones. Often (for example, for platinum) the temperature coefficient of resistance decreases strongly with temperature. Sometimes an inflection point is found on the curve representing resistance as a function of temperature. The question naturally arises as to how the resistance behaves in the immediate vicinity of absolute zero. Lord Kelvin [10], as early as 1902, came to the conclusion that, from the standpoint of the classical electron theory of metals, the resistance at absolute zero should become infinitely large; the free electrons, insofar as they still remain such, must completely lose their mobility. Kamerlingh-Onnes spoke of the condensation or freezing of electrons. Meanwhile, it had not yet been possible to confirm this theory experimentally. The minimum that might have been expected on the resistance curve did not appear even at the temperature of liquid hydrogen (boiling point temperature — 253°, triple point — 259°).

On July 10, 1908, Kamerlingh-Onnes succeeded in obtaining liquid helium,—and thus an entirely new region of temperatures, lying in the immediate vicinity of absolute zero, was opened up for investigation.

Helium boils at atmospheric pressure at \(4^\circ,22 K\), and at a pressure of \(1/50\) mm of mercury temperatures from \(0^\circ,8\) to \(0^\circ,9 K\) can be reached\(^1\). Among the numerous measurements that had been carried out in this interval since 1910 in the Leiden laboratory, measurements of the resistance of metals occupy an important place. The first measurements concerned a wire of pure platinum, \(0.1\) mm thick, whose resistance had already been measured in the region of “hydrogen” temperatures and which it was now desirable to investigate further at temperatures attainable with the aid of helium.

\(^1\) In what follows, the temperature of helium is given on the absolute scale (\(K\)—Kelvin scale).

The results of these first determinations were most striking. Namely, it was found that the resistance in the helium region remains quite constant (see Fig. 1); no trace whatever was discovered of the minimum that should have been expected according to Kelvin. To explain this entirely unexpected result, K.-Onnes proposed that drawn metallic wires are never entirely pure, and that the observed residual resistance might be a consequence of the presence of exceedingly small amounts of some impurities. A perfectly pure metal should have, at helium temperature, a resistance equal to zero, as indicated by the dotted curve in Fig. 1.

Fig. 1.

Although the experiments were only preliminary in character, they nevertheless made it entirely clear that it was necessary to abandon Kelvin’s theory, which for a number of years had been the leading theory in this field. No trace was found of the expected minimum. Of course, it was not yet possible to create a new theory of metallic conductivity on the basis of these experiments; the experimental data were wholly insufficient for that. Nevertheless, already in this work, devoted to describing the first experiments, K.-Onnes published a preliminary formula by means of which he succeeded in expressing the results of his experiments with the aid of Planck’s theory of quanta. We shall return to this theoretical assumption later. Further investigations showed that the hypothesis of the resistance going to zero is confirmed experimentally for quite pure metals. Mercury represents

a material which, by repeated distillation in a vacuum, can be obtained in an incomparably purer form than any drawn metal wire. However, the manufacture of suitable mercury resistors presented considerable difficulties. Mercury enclosed in a zigzag capillary with a cross-section of \(0.005\ \mathrm{mm}^2\), upon freezing, would inevitably have ruptured it (for mercury contracts on solidifying), had special measures not been taken. These measures consisted in soldering a small reservoir with mercury to the upper part of the zigzag-bent capillary (see Fig. 2). With slow and careful cooling of the mercury column from the lower end, the material was replenished from the reservoir, and in this way it was finally possible to make a resistance of suitable magnitude (for example, 172 ohms at \(0^\circ\mathrm{C}\)). It is scarcely necessary to add that this success was preceded by many vain efforts.

Fig. 2.

In Fig. 3 one can see how this mercury resistance, having a cylindrical form, is mounted in a helium cryostat. \(Hg_1\) denotes the resistance; \(Hg_2\)—tubes filled with mercury and serving to lead in the current (in order to avoid thermoelectric forces); \(Eah_3\)—an evacuated double-walled tube through which liquid helium flows from the condensation apparatus; this tube at \(Eak_2\) is closed with a small, conically cut cork stopper. Two evacuated vessels which surround the tube with helium are filled with liquid hydrogen and liquid air.

The efforts expended on preparing these resistors were richly rewarded. It was found that at helium temperature the resistance of mercury is indeed equal to zero, or at least becomes immeasurably small. But the most remarkable point proved to be that at \(4^\circ.2\ \mathrm{K}\) the resistance drops abruptly from a measurable value to zero. The temperature at which this discontinuity occurs was called by K.-Onnes the transition temperature; and the state in which the resistance is equal to zero—the state of superconductivity.

Mercury was thus the first substance for which a superconducting state was discovered. Later, K. Onnes found (partly in joint work with Dr. Tuyn) that tin, lead (and its isotope RaG), thallium, and indium also exhibit the state of superconductivity. The transition temperatures for them differ considerably from one another, as the following table shows:

Cf. also Fig. 4. No significance should be attached to the extraordinarily large residual resistance of indium. It is possible that the indium wire was not pure and that pure indium will show a more normal value of the residual resistance. These investigations are not yet completed.

It is of the highest interest to know whether superconductivity should be regarded as a general property of matter, or whether it appears only as an exception. To answer this question, a large number of metals were investigated for superconductivity; it turned out that the phenomenon should, to a certain extent, be regarded as an exception. Zinc, gadolinium, germanium, aluminum, platinum, gold, copper, iron, silver, bismuth, potassium, sodium, and lithium all exhibit constant resistance, exactly as is the case for platinum (see above). For cadmium the situation has not yet been clarified; some wires show constant resistance, others superconductivity; but it may be considered probable that pure cadmium is not a superconductor. Theoretical investigations also led to regularities which clearly show—

Fig. 3.

show that superconductivity is not a general property of matter. We shall return to this later.

The next important question is whether other physical quantities, besides resistance, experience a discontinuity at the temperature jump point. To answer this question, preliminary experiments have been carried out on measurements of the coefficient of elasticity of tin, the specific heat and thermal conductivity of mercury, and the crystalline structure of lead. It is remarkable that none of these quantities exhibits a discontinuity at the jump temperature.

The jump temperature is not such a sharply defined constant as one might have concluded from Fig. 4, where the scale is small. On one tin wire it proved possible to make measurements in the region of the discontinuity, as Fig. 5 shows. On a large scale it is seen that this region is represented by a real curve with a point of inflection; it should only be noted that the difference of temperatures between the region of measurable resistances and resistances equal to zero is extremely small, only slightly more than \(1^\circ,04\).

Fig. 4.

The superconducting state of a metal can be destroyed in various ways. It is known that a magnetic field, at ordinary temperature, affects the resistance, the resistance becoming greater if the metal is placed in a magnetic field. In the superconducting state something similar occurs; in this case the transition from the superconducting to the ordinarily conducting state, as the magnetic field increases, takes place discontinuously. The “resistance—magnetic field” curves reveal, qualitatively, exactly the same character as the “resistance—temperature” curves (see Fig. 6, which depicts the longitudinal and transverse effect on a lead wire). With this effect, consequently, one may speak of a threshold value (Schwellenwert) of the magnetic field, i.e. a value that cannot be exceeded without destroying the superconducting state. This threshold value is a function of temperature; at a lower temperature a stronger magnetic field is required in order to destroy the superconducting—

On the Superconductivity of Metals

...ing state than at a high temperature; but at a constant temperature this value, just like the temperature of the jump, is not a sharply delineated constant; in exactly the same way, the strength of the current passed through the conductor has some, albeit small, influence on the limiting value. The superconducting state can also be destroyed discontinuously, by means of a sufficiently large current passed through the conductor. If the resistance were in fact exactly equal to zero (which is not yet known with certainty), then the Joule heat would likewise be zero, and it would be possible to apply an arbitrarily strong current without causing heating of the wire leading to the establishment of ordinary resistance. But in reality this does not occur. Although under favorable circumstances one can apply very strong currents with impunity (for example, 1200 amperes per mm², in mercury), nevertheless in this respect as well there is a limiting value of the current strength which cannot be exceeded. One might be inclined to think that the wire is, after all, heated owing to the presence of an immeasurably small residual resistance, and to regard the existence of this residual resistance as thus proven. However, there is nothing impossible in the fact that the magnetic field arising owing to the presence of the current is the cause of the increase in resistance and of the destruction of the superconducting state. This is precisely the hypothesis of Silsbee [¹¹] (1916), which may be formulated as follows: the limiting value of the current strength is equal to the value at which the magnetic field arising under the action of the current reaches the magnetic limiting value.

Fig. 5.

From the observations of K. Onnes and Tuyn one can obtain sufficient data for a more or less accurate test of this hypothesis; on the basis of these data it may apparently be considered established that the indicated hypothesis is correct, although it cannot be regarded as strictly proven. I should like to mention here one beautiful experiment. If the hypothesis is correct, then one can

hope to restore the superconductivity of a metal, destroyed by an excessively strong current, by means of an external magnetic field; for this it is only necessary to give the external magnetic field a direction directly opposite to the field produced by the current. This was in fact accomplished. A hollow tin cylinder was cooled to the superconducting state and was then again brought into the state of ordinary conductivity by passing a current exceeding the limiting value. Then, along a copper wire stretched along the axis of the cylinder, a current was passed in the opposite direction, whose magnetic field therefore weakened the magnetic field of the current in the cylinder.

Fig. 6.

In this way it proved possible again to restore the superconducting state of tin, without thereby reducing the current in the tin cylinder. This experiment should be regarded as an important confirmation of Silsbee’s hypothesis.

Another remarkable phenomenon consists in the fact that, for a wire stretched by means of a small screw, the temperature jump corresponds to a higher value of the temperature than for an unstretched wire. Stretching is, therefore, the cause under the action of which the wire more readily becomes superconducting. The opposite phenomenon was also observed: namely, a wire under a pressure of 200 atm. exhibits a lower temperature jump than a wire under ordinary pressure. Below we shall return once more to the theoretical interpretation of this phenomenon.

We now turn to the description of a series of extremely important experiments by K. Onnes, by means of which he demonstrated the stability of the current in a superconductor and which were later used in order to try to answer the question whether a superconductor possesses resistance at all or not. Although these experiments do not reveal any new phenomena, nevertheless they are to such a degree

ON THE SUPERCONDUCTIVITY OF METALS

are so striking that before the discovery of superconductors one could not even dream of the possibility of such experiments. Let us place a small closed coil, wound on itself, of tin or lead wire in a cryostat at room temperature in a magnetic field, i.e., between the poles of an electromagnet (the planes of the turns perpendicular to the magnetic lines of force); then cool the coil to a temperature below the transition point and quickly switch off the magnetic field; a current is thereby induced, and this induced current will circulate continuously through the coil, since it encounters no resistance whatsoever. This experiment was first performed by K.-Onnes in 1914, and by analogy with the conception of Ampère’s theory of magnetism, these circular currents, circulating without any external electric or electromagnetic force, were called Ampère currents.

At the beginning of the last century Ampère, on the basis of the discoveries of Oersted and of his own, put forward the hypothesis that the field near a magnetized body originates from a large number of small circular currents which flow around molecules without resistance, and therefore without damping; magnetization consists, consequently, in the turning of these molecular currents parallel to one another.

This hypothesis makes it possible to reduce the properties of paramagnetic and ferromagnetic bodies to the action of electric currents. But already in Ampère’s time doubts arose as to the correctness of such a conception, since not a single example of a non-decaying circular current was known. It seems all the more remarkable that the hypothesis of molecular currents can now be illustrated on an ordinary metallic wire.

Fig. 7.

The electromagnetic field of an Ampère current was at first observed with the aid of a magnetic needle placed outside the cryostat, and already in the first experiments it could be established that the strength of the current decreases in any case by less than 1% per hour. But since the degree of constancy of the current strength is of essential importance for answering the question whether a superconductor has any resistance at all or not, in recent years an ingenious apparatus has been constructed which makes it possible to measure this degree of constancy very accurately (see Fig. 8). In the cryostat there are two lead rings, of which the outer one, \(B\), is fixed immovably, while the inner one, \(A\), can rotate about a vertical axis. The rotation of \(A\) can be estimated with the aid of

head \(K\), divided into degrees. Between the ring and the head there is placed a torsion spring of phosphor bronze. The twisting is observed through the window \(H\) with the aid of the mirror \(G\), a tube, and a scale. Having cooled the lead rings in liquid helium and thereby brought them into the superconducting state, currents of the same direction are induced in both rings, exactly as was described above. (Only in these experiments, instead of a large electromagnet, wire coils were used, with which it is much more convenient to work, and whose magnetic field is quite sufficient for these experiments.) The rings then attract one another. If the head had been twisted so that the rings formed an angle of \(30^\circ\) with one another, then, in the presence of currents, it is necessary to turn the head somewhat farther, and this additional rotation is the measure of the mutual attraction of the rings. When the stationary state is reached, the mirror \(G\) and both control mirrors \(H\) and \(I\) are observed, in order to investigate how constant the attraction between the rings remains and, consequently, the current strength. In general and on the whole, as the result of a long series of measurements it turned out that Ampère’s current changes probably by less than \(1/80000\) per hour, i.e. it proves to be far more constant than had earlier been inferred from preliminary measurements with a magnetic needle.

Fig. 8.

I consider it necessary to mention briefly that an entirely similar phenomenon was discovered in experiments with an open coil (the initial and final ends of whose wire were not connected to one another) or with a lead ring cut at one place. Even the magnitude of the magnetic moment was approximately the same as for a closed ring. However, these exceedingly striking experiments are still too new and too few in number, and, since as yet there is no satisfactory theoretical explanation of them, I shall not dwell on them further.

Some further remarkable experiments will be mentioned below in connection with the exposition of theoretical considerations.

Until now we have limited ourselves to considering the experimental material. We must now give a brief survey of some theoretical views concerning the superconducting state, namely the theoretical assumptions recently expressed by K. Onnes himself. It must be admitted that, in general, matters have not gone beyond assumptions, although many investigators have taken up this question. And this is understandable—for the ordinary electron theory of metals is still struggling with very great difficulties; how, then, could one expect that a completed theory of so complex a phenomenon, characterized by discontinuity, as superconductivity proves to be, would already have been created?

Since it was clear in advance that the classical electron theory of metals (Drude [12], Rikke [13], Lorentz [14]) was not capable of giving even a qualitative account of the phenomenon, many investigators attempted to develop ideas and establish formulas resting on the foundations of the quantum theory. K. Onnes published one such formula immediately after his discovery; at approximately the same time and independently of him Nernst did the same.

I shall pass over these works, as well as the earlier works of Lindemann [16], Keesom [17], W. Wien [18], Haber [19], Stark [20], Benedicks [21], and Bridgman [22], and shall dwell in more detail on the theory of J. J. Thomson, which still rests on classical foundations, since the later ideas of Kamerlingh-Onnes are closely connected with this theory and since it is the only theory that gives an account of the temperature jump. Thomson proceeds from conceptions quite different from those of the founders of the old electron theory of metals. He admits the existence of electric dipoles in the atom. If no electric force acts, the axes of these dipoles are oriented in space arbitrarily in all directions. But if an external electric force acts in a definite direction, then the axes must tend to set themselves along the direction of the field, while other influences, for example thermal motion, are superposed upon the first and tend to destroy the orientation that is being established, thus making it incomplete. In order to fix the idea, we may suppose that part of the axes is fully oriented, while the rest are not oriented at all. This state must be equivalent to the actually existing universal but incomplete orientation. We further imagine that the oriented dipoles line up in rows and form chains. According to Thomson, the transport of electrons under the action of an external electric force takes place along these chains. Developing this conception, it can be shown that for all temperatures that are not very low Ohm’s law holds and, moreover, that the resistance depends linearly on the temperature, as is in fact approximately the case for pure metals. This theory was applied by Thomson to the superconducting state, and he suc—

...managed to show that for certain metals there must exist a quite definite critical temperature, below which the metal will be a superconductor, while above it it will exhibit no special phenomena. The considerations by means of which he arrives at this remarkable result are not excessively complicated, but nevertheless it would be difficult to set them out here in full. I shall therefore confine myself merely to referring to the original work.

It should be noted, however, that however simple this theory may seem, it nevertheless contains difficulties that are not easy to resolve; and therefore this theory can in no case be regarded as entirely satisfactory.

K.-Onnes observes that, however one may picture the electrical conductivity of metals, it must be admitted that superconductors force us to abandon the idea of a rectilinear free path of the electron. Indeed, if these free paths are calculated for the superconducting state, one obtains utterly impossible values, exceeding, for example, by 10,000 times the diameter of the wire used. K.-Onnes puts forward the following hypothesis: in metals there exist long atomic chains (as in Thomson’s theory), and electrons can slide along these chains over the surface of the atoms, without consuming or giving up electrical energy, i.e., in an “adiabatic” manner. In that case one must imagine that in the superconducting state these chains freeze in their places and assume an almost immobile position within the metal. The concept of the “mean free path” under this conception must be interpreted as the “path traversed in an adiabatic manner.”

With respect to this theoretical view, the following experiments are of particular importance and interest. In order to be able to set them out precisely at this point, I deliberately avoided describing them in the experimental part of the review.

First of all, the idea of atomic chains gives reason to think that the contact point between two superconductors will not allow current to pass without resistance from one metal to another. Such, too, was Einstein’s opinion \[24\] when he wrote his article in the jubilee volume dedicated to K.-Onnes. However, it turned out that the contact point was entirely superconducting. A ring soldered from 24 alternating sectors of tin and lead exhibited exactly the same phenomena as a simple lead ring. Likewise, a cut ring of tin and lead gave the same phenomenon and the same magnetic moment. The second experiment was as follows. In an apparatus with two lead rings, the inner rotating ring was replaced by a thin spherical lead shell. When currents are induced in the fixed ring and in the rotating sphere in the usual way, a distribution of current arises in the sphere,

On the Superconductivity of Metals

the calculation of which was carried out by Lorentz \[25\]. In the case of an ordinary conductor, when the sphere was rotated, no attractive force acting on the stationary lead ring would have been found. On the contrary, in the superconducting state exactly the same effect was found as in the case of two lead rings, which proves that the paths of the currents inside the sphere are firmly fixed in the metal; this experiment may be regarded as a splendid confirmation of the hypothesis of rigid atomic chains.

In 1924 K. Onnes attempted to connect the phenomena of superconductivity with Bohr’s atomic theory and to derive from it certain regularities. First of all, let us consider the question, already touched upon in the experimental part, namely whether superconductivity is a general property of matter, or whether it should be regarded as a phenomenon exceptional to a certain degree. In all probability, the latter is the case, as follows also from the experimental results. But if one considers the positions of the superconductors in Mendeleev’s periodic system, it turns out that the superconductors form a closed group.

Five superconductors (underlined in the table) form a close group, and even metals located in immediate proximity to this group (such as, for example, Bi and Cd) do not exhibit any traces of superconductivity.

Considering the known curves of atomic volumes as functions of the atomic number, we find in both places where superconductors are located small waves on the ascending curves. The same is seen in the curves representing the quantities reciprocal to the melting and compression temperatures.

In trying to apply Bohr’s theory, as K.-Onnes did together with Dr. Kramers of Copenhagen, we obtain a further, extremely interesting regularity. First of all, from Bohr and Coster’s table it follows that, in order to reach the superconductors, one must approach elements with completely filled shells of 18 electrons, with principal quantum numbers 4 and 5, and possessing two, three, or four valence electrons; one valence electron (Au, Ag) is insufficient, five (Sb, Bi) is too many.

Fig. 9.

Fig. 10.

Kramers drew up diagrams for a series of metals, intended to convey quantitatively the relation between the distance of the nuclei in the crystal, on the one hand, and the distance of the outer electron orbits from the nucleus, on the other—with the accuracy permitted by our present knowledge of the structure of atoms. Some of these diagrams are reproduced here (Figs. 9, 10, and 11). In these diagrams the solid circles denote completely filled shells (18 electrons), and the dotted circles denote shells with valence electrons. Although one might perhaps have expected that small mutual distances of the outer electron orbits would favor the onset of superconductivity, the diagrams show that precisely the opposite is the case. With the exception of a few less convincing examples

(Bi and Ga, on the one hand, Sn on the other), it is clearly seen that the superconductors correspond to larger, and the non-superconductors to smaller, mutual distances of the outer electron orbits; on the basis of these drawings one may predict with fairly great confidence that cadmium, doubtful to a certain degree, will not prove to be a superconductor.

However, the interpretation of these drawings is not easy and in any case is entirely hypothetical. One might observe that with large distances of the electron orbits the probability increases for the electron to find a longer stationary path, or that the remaining thermal motion may be stronger and still not destroy the atomic chains, etc.; but at present it is quite impossible to say anything more definite about this.

Fig. 11.

In conclusion, in connection with these interpretations, I should like once again to point to the already mentioned experiment, from which it follows that a stretched wire more readily (i.e. at a higher temperature) becomes superconducting than an unstretched one, and that in wires under pressure just the opposite is observed. These results are in full agreement with the theoretical considerations developed above.

LITERATURE.

The bibliographical references, except for those relating to superconductivity, make no claim to completeness.

Comm.—Communications from the physical Laboratory of the University of Leiden.

Suppl.—Supplements to the preceding.

1. Measurement of resistances at low temperatures (excluding helium temperatures).

1) L. Cailletet and E. Bouty. Journ. de physique (2) 6 (1885) p. 29.
2) L. Holborn und Wien. Wied. Ann. 59 (1896) p. 211.
2) L. Holborn. Ann. d. Phys. 6 (1901) p. 242.
3) S. von Wroblewski. Wied. Ann. 26 (1885) p. 27.
4) K. Olszewski. Akad. Wiss. Krakau, Juni 1895.
5) M. W. Travers and A. G. C. Gwyer. Proc. Roy. Soc. 4 (1905) p. 74.
6) B. Meilink. Comm. Nos. 77, 93. Diss. Amsterdam 1904.

7) H. Kamerlingh-Onnes und J. Clay. Comm. Nos. 95d, 99c, 107c, 197 Suppl. No. 17.
8) H. Kamerlingh-Onnes und G. Holst. Comm. No. 141a, 142a.
9) F. Henning. Die Grundlagen, Methoden und Ergebnisse der Temperaturmessung, Braunschweig. 1915 (contains extensive bibliographic references).
10) Lord Kelvin. Phil. Mag. (6) 3 (1902) p. 257.

II. Measurement of resistances at helium temperatures.

It was impossible to cite all these works in definite places in the article, and for this reason they have not been numbered. All their most important results, however, have been used.

H. Kamerlingh-Onnes. Comm. Nos. 119, 120b, 122b, 124c, 133a, b, c, 133d, 139f, 140b, c, 141b; Suppl. Nos. 29, 34b, 35 (Nobel lecture); 4th Conseil de Physique Solvay 1924 — Suppl. No. 50a.

H. Kamerlingh-Onnes und G. Holst. Comm. No. 142a.
H. Kamerlingh-Onnes und W. Tuyn. Comm. Nos. 160, 167a.
W. Tuyn. Doktordissertation Leiden. 1924.

Reviews.

C. A. Crommelin. Le Génie civil 64 (1914) p. 245. Chemisch Weekblad 16 (1919) p. 640, Phys. Zeitschrift 21 (1920) p. 274, 300, 331; Revue gén. d. Sc. 15 Jan. 1923, Chemisch Weekblad 18 (1921); Jahrb. d. Rad. u. El. 19 (1922) p. 38.

III. Further, chiefly theoretical, literature.

11) F. B. Silsbee. Journ. Wash. Ac. of Sc. 6 (1916) p. 597; Sc. pap. of Bur. of Stand. 14 (1917) No. 307.
12) P. Drude. Ann. de Phys. (4) 1 (1900) p. 566; 3 (1900) p. 369.
13) E. Riecke. Wied. Ann. 66 (1898) p. 353, 545, 1199.
14) H. A. Lorentz. Versl. Kon. Ak. Amsterdam, Dez. 1904, Jan. 1905.
15) W. Nernst. Sitz. Ber. Berlin 1911 p. 311.
16) F. A. Lindeman. Sitz. Ber. Berlin 1911 p. 316.
17) W. H. Keesom. Versl. Kon. Akad. Amsterdam, Mai 1913, Suppl. No. 306; Phys. Zeitschr. 14 (1913) p. 670.
18) W. Wien. Sitz. Ber. Berlin 1913 p. 184.
19) E. Haber. Sitz. Ber. Berlin 1919 p. 506.
20) J. Stark. Jahrb. Rad. und El. 9 (1912) p. 188.
21) C. Benedicks. Jahrb. Rad. und El. 13 (1916) p. 351; 14 (1917) p. 471.
22) P. W. Bridgman. Proc. Nat. Ac. Am. 3 (1917) p. 10.
23) J. J. Thomson. Phil. Mag. (6) 30 (1915) p. 192.
24) A. Einstein. Het Natuurk. Lab. Leiden. Jubelband. H. K. Onnes. Leiden 1922, p. 429.
25) H. B. Lorentz. Suppl. 50b.
26) N. Bohr und D. Coster. Zeitschr. f. Physik. 12 (1923) p. 342.

1. Translated from the author’s German manuscript. ↩