On the Lowest Temperature Reached to Date1

H. Kamerlingh-Onnes.

Introduction. When we approach the question of producing cold by means of liquefied gases and of using it for laboratory investigations, then, in addition to the study of the properties of bodies at low temperatures and of methods for measuring these temperatures, two tasks come to the fore. The first of them concerns the construction of such apparatus as would permit experiments and measurements to be carried out within the limits of all temperatures hitherto attained by us, and the second—to descend to temperatures still inaccessible to us.

Without dwelling in detail on the first point, I consider it necessary to emphasize that the true characteristic of the Leiden laboratory is the composition of its service personnel and closest assistants, which could have been formed only through its prolonged functioning2. Thanks to continuous contact with exact investigations in various fields of experimental physics, and by gradually assimilating new improvements in the methods of carrying out these investigations at ever lower temperatures, this personnel has acquired traditions that make possible the application of all the experience gained and has become accustomed to solving new problems of the most varied kind. In this way the laboratory with its personnel carries out what is becoming more and more the aim of the efforts of international science. Modern

Ed.

science requires specialization in many of its fields. A researcher working in a certain field and wishing to carry out some experiments at low temperatures, for example, at temperatures attainable by using liquid hydrogen, will find substantial assistance for himself if he makes use of the services of personnel well acquainted with work in the field of low temperatures. He will be able to concentrate all his attention on the experiments that directly interest him, without being distracted by the apparatus for obtaining low temperatures, which are in themselves quite complex; thus, thanks to the help of this experienced personnel, handling liquid hydrogen becomes as simple as if it were not liquid hydrogen but, for example, water. The number of problems subject to development in this field is growing almost day by day.

When, about 40 years ago, I decided to begin working with low temperatures, I was, of course, convinced that such work must yield important results in the study of the properties of matter. But the breadth and the importance that work in this direction soon acquired far exceeded all my expectations. At the time when moderate quantities of liquid air became available for the investigations that occupied me then, the necessity soon arose of making measurements with liquid hydrogen. But before hydrogen was liquefied, helium had been discovered, and this substance subsequently proved capable of extending far the limit of the temperatures provided by hydrogen. And further, before helium was liquefied, Planck’s discovery of the quantum imparted an entirely new view to work at low temperatures. After the liquefaction of helium, the discovery of the superconductivity of bodies indicated an entirely new field for investigation. Thus new problems constantly arose here, their number continually increasing, and they could most likely find their solution in the Leiden laboratory. Although I shall welcome with great satisfaction the liquefaction of helium in newly established cryogenic laboratories, I nevertheless think that the international interest of the Leiden laboratory will continue to grow steadily in the future.

For today’s report, one important problem comes to the fore, to which I have already pointed: the problem of extending the limit of the lowest temperatures for our investigations.

Therefore I ask permission to give a preliminary survey of the experiments directed toward achieving the lowest temperature so far attained.

2. First experiments. As soon as the attempts to liquefy helium were crowned with success, attempts were of course also made to bring about its transition into the solid state. These attempts were even carried out on the very day when helium was first seen in the liquid state. The method consisted in evaporating liquid helium under reduced

pressure. Fig. 1 gives a diagram of the apparatus in which helium was first seen in the liquid state, and of the apparatus by means of which its liquefaction was achieved. After preliminary, proper cooling, the compressed helium passes through the coil of a refrigerator, in which it is cooled to the temperature of hydrogen evaporating under the reduced pressure of an air pump. Having been cooled to this extremely low temperature, it enters the coil of the actual refrigerator, the end of which is provided with an opening and a valve. Here it expands: part of it is liquefied by the Linde process, and the gas returns between the turns of the just-mentioned spiral refrigerator, while the vapors of the uncondensed helium are collected, by means of a pump, in a gas holder and are then again compressed by pumps. Liquid helium collects at the bottom of the glass vacuum vessel of the condenser, where its accumulation can easily be seen.

Fig. 1.

For this purpose the bottom of this vessel was left unsilvered; the vessel itself is surrounded by three other Dewar vessels, of which the first contains liquid hydrogen, the second liquid air, and in the third alcohol circulates at ordinary temperature; this last device serves to prevent the vessel with liquid air from becoming covered with hoarfrost from the deposition upon it of water vapor from the atmosphere. At the beginning of the experiment, in which the intention was to solidify helium by evaporating its liquid, the valve was closed and the air pumps were stopped. The helium vapor issuing from the liquid at the bottom of the vacuum vessel of the condenser passed, under atmospheric pressure, into the gas holder, and it was evident that the liquid helium was boiling quietly.

In order then to evaporate the helium under reduced pressure, it was sufficient to stop its communication with the gas holder, and

put into operation the compressors, which now had to act as vacuum pumps. The capacity of the pumps proved sufficiently great to remove the vapors so quickly that the temperature was considerably lowered; and when their action was strengthened by the addition of another powerful vacuum pump, the pressure fell to 1 cm, but the helium nevertheless remained liquid.

At that time it was impossible to proceed further in this direction, since only an improvised connection of the apparatus to a powerful vacuum pump could then be made. In 1909 the experiment was repeated after the proper preparations for this purpose had been made; the above-mentioned Burckhardt vacuum pump, with a capacity of 360 m³ per hour, could then develop its full power. But here too it turned out that, despite the lowering of the pressure to 2 mm, the helium still did not solidify. Although the liquid at this low temperature had lost its ability to stand at the walls of the glass with sharp boundaries like the blade of a knife, and now exhibited the usual property of capillarity, its astonishing mobility was nevertheless preserved. For obtaining solid helium such a result was discouraging. But, on the other hand, it indicated that the range of temperatures in which the properties of bodies could be investigated with the aid of liquid helium extended farther than could have been hoped by analogy with other gases possessing low critical temperatures; and in this sense the result was consoling, because it is very difficult to obtain constant and homogeneous temperatures by means of any substance below its melting point. With helium the difficulties would be so great that the temperature of its solidification would have to be regarded as the limiting one, below which it would be impossible to make use of it. Therefore, in the absence of an even more volatile substance, a limit to scientific investigation would here have been set. So long as, with further lowering of the vapor pressure, helium continued to remain liquid, this failure of the experiments to convert helium into the solid state turned out to be a gain: a new region of temperatures, especially important in view of its extreme position, thus became accessible to us.

§ 3. Improvements in the helium cryostat and cycle¹). Fortunately it was possible to obtain a considerably lower temperature than was mentioned above; but we soon reached a point at which the small density of the vapor sets a new limit for us, below which we cannot descend. I shall now dwell on the experiments by which, for liquid helium, a lowering to this limit was achieved.

¹) Here I must gratefully mention the considerable increase in the supply of helium which I received from the American Navy Department (Navy)—30 m³—and from Professor MacLennan—6 m³.

This progress, however, proceeded gradually, keeping pace with the proper development of the laboratory, and the last stages became possible only after considerable improvements in the devices for attaining these low helium temperatures. An important improvement was achieved when we succeeded in transferring the liquid helium from the apparatus in which it was liquefied into a cryostat, in which, like other liquefied gases, it could be used in the ordinary way as a bath for low temperatures. The cryostat \(C\) still remained closely connected with the liquefaction apparatus \(L\) (Fig. 2), but the space in the cryostat accessible for experiments was now no longer restricted above by a spiral refrigerator, as in the former apparatus. Various devices could be introduced into the cryostat from above through the cover (cf. Fig. \(5b\)), while the bath surrounding the apparatus in which the investigation was being carried out could be obtained by pouring helium by means of a siphon from the liquefaction vessel into the cryostat. Such cryostats were already used in many investigations of the properties of substances at very low temperatures, especially in the field of electricity and magnetism.

Fig. 2.

Fig. 3\(^1\) shows the apparatus together with the scheme of the improved circulation of helium; such a cryostat was introduced into this scheme. The helium that is liquefied, emerging through valve \(k\) from the spiral cooler, collects in the lower part of the vacuum vessel of the collector, as in the original apparatus. However, the bottom of this vessel is not sealed, but

\(^1\) Partly schematic, partly showing only the relative dimensions of the parts.

continues in the form of a siphon tube $s$ (Fig. 2) with double silvered walls, and the siphon ends with the valve $v$. When this valve is closed, the newly formed helium again collects in the reserve vacuum vessel. When the valve $v_0$ is opened (Figs. 2 and 5), liquid helium can enter the cryostat. The cryostat itself consists of an unsilvered vacuum vessel in which the liquid helium collects. This vessel is surrounded by another vacuum vessel. During its silvering two opposite strips were left uncovered, in order to see what is happening in the vessel with helium (cf. Fig. 5b). The second vacuum vessel is surrounded by a third, silvered in the same way and containing liquid air. Helium vapors, released from the cryostat and the reserve vessel, enter the pumps $P_1$ and $P$ (Fig. 3), whose purpose is as follows: when the circulation is operating, the vapors are driven into the reserve vessel and replenish there the supply of liquid helium. By means of such circulation the process of liquefying helium continues uninterruptedly the whole time that the experiments of interest are being carried out in the bath of liquid helium in the cryostat. As soon as the helium has evaporated to a considerable extent from the cryostat, a new portion of helium in the desired quantity is immediately admitted into it.

Fig. 3.

The improvement in working with helium, achieved by separating the cryostat from the reserve vessel, was also accompanied by improvement of the reserve vessel itself, which led to a more rapid preparation of liq-

...of helium and, at the same time, to a more economical consumption of liquid hydrogen. The chief part of the improvement consisted in a more complete utilization of the available cold. After it has been compressed to \(3\) atmospheres, the helium is divided between two spirals \(B\) and \(B'\) (Fig. 41), which again unite, conduct the helium through a tube containing charcoal cooled by liquid air, and then again divide into spirals \(C\) and \(C'\). The spirals \(B\) and \(C\) are cooled by cold hydrogen vapor coming from the liquid hydrogen in the refrigerator, while \(B'\) and \(C'\) are cooled by cold helium vapor coming from the liquefier. Both spirals are much longer than in the first liquefier; they join together and form the spiral \(D\), which is first cooled by hydrogen vapors surrounding \(D\), and then by liquid hydrogen surrounding \(E\), and passes into the refrigeration spiral \(F\), ending in the valve \(K\), as in the original liquefier.

Fig. 4.

Besides obtaining in this way a more perfect action of the liquefier, the circulation capacity itself was increased by the introduction of two large compressors \(Y\) and \(P_1\), which at the same time can operate as vacuum pumps.

Thus, in the new cryostat, for whole hours

one could have at one’s disposal a bath of liquid helium, evaporating at a pressure of 3 mm, with a capacity of about 500 cm³. Under these conditions it was possible to carry out, on a broad scale, experiments at temperatures whose attainment in earlier experiments with liquid helium could scarcely have been demonstrated. Such a cryostat with a bath of extraordinarily low temperature was used with great success in experiments on the further cooling of helium by its own evaporation. The apparatus for evaporation (Fig. 5), in which the helium was cooled to the lowest temperature that had ever been reached, consists of a vacuum vessel \(a\) with double walls (Fig. 5a) containing helium, when it is cooled as strongly as possible, and of a wide outlet tube \(b\) for the gas formed by evaporation. The evaporation vessel is immersed in the strongly cooled helium bath of the cryostat \(C\). The gas issuing through the tube \(b\) leaves the cryostat through the cover \(h\), which is connected with powerful vacuum pumps \(P\) (Fig. 6). It is clear that these pumps must not only produce a vacuum of a high degree, but at the same time must possess a very large capacity at this vacuum pressure, since the gas formed by evaporation will occupy a large volume at atmospheric temperature and at the low vapor pressure. It is likewise clear that the aim can be attained only if the cryostat allows these large volumes of gas to escape through wide outlet tubes, as is the case in our apparatus. If the tubes through which the gas moves are not very wide or are not at very low temperatures, then the motion of the gas at low pressures requires pressure differences of the same order as those at which the gas itself is pumped out. These differences may constitute a considerable part of the pressure at which evaporation of the helium takes place.

§ 4. Temporary stopping. These two considerations already show that great demands must be made on the apparatus for experiments of this kind, and especially with respect to the capacity of the vacuum pumps, if one has in mind attaining very low pressures. In 1910 the first experiment in this direction was made, based on the above-described principle, but with inadequate means. Although the cryostat had certain shortcomings, thanks to one fortunate accident a lower limit for the vapor pressure was reached than in 1909. Although this result could not be obtained again when the experiment was repeated with an apparatus arranged in the same way as in the first experiment, nevertheless there remained no doubt that the vapor pressure can be lowered very considerably below 2.2 mm without converting helium into the solid state, and that at a pressure of 0.2 mm it should in all probability remain liquid. This means that, in order to ensure further progress in this direction, much higher demands must be placed on the apparatus if we do not wish to be content with the minimum pressure of 2.2 mm. Several years passed before it was possible to think of lowering

of a limit lower than the 0.2 mm that had been reached by chance. This problem was set aside, and work began on the solution of other problems, more important at the time and more accessible to solution with the existing resources of the laboratory. Such, for example, was the question of “super-

Fig. 5.

conductivity, on the limiting magnitude of the magnetic field at which ordinary resistance arises in a superconductor. The lowest temperature obtained remained that which corresponds to a vapor pressure of \(0.2\) mm. I estimated this temperature at about \(1.15^\circ K\)1. Taking into account the unreliability of this estimate, it would be more cautious to say that in lowering the temperature we had approached \(1^\circ K\). As the work with helium advanced more and more, it became increasingly necessary to achieve a further lowering of the pressure limit below \(0.2\) mm, and also, in particular, to clarify the question of the possibility of lowering the temperature below \(1^\circ K\). At last it became possible to take up this problem again in 1919, when the difficulties connected with the war and the crisis had been overcome.

§ 5. A new attempt. Then, for the first time, in order to remove helium from the evaporating apparatus, a large Burckhardt vacuum pump \(V_b\) (Fig. 6), with a capacity of \(360\ \mathrm{m}^3\) per hour, was put into operation; it was connected in series with a pump \(V_{A_2}\) of \(18\ \mathrm{m}^3\) capacity and with a Siemens pump \(V_3\), of \(2\ \mathrm{m}^3\) capacity. The construction and operation of the large pump \(V_{B_1}\) were such that there was no possibility for gas from the lubricating oil to enter the vacuum. Moreover, the valves, which at first were kept closed by means of a spring until the gas, by its own excess pressure, raised them and flowed from the cylinder into the outlet pipe, were now opened and closed by a mechanical device at the proper moment for equalizing the pressure in both spaces. Subsequently, however, the valves on the pressure side were removed altogether, and this space was connected directly to the intake space of the auxiliary pump. With such an improvement in the action of the pumps, thanks to which it was possible to reduce the limiting intake pressure to \(0.04\) mm (in the best case to \(0.025\) mm), and with the evaporation vessel, which, although not as good as in the experiments that will be described below, nevertheless made it possible to pump out about \(2.7\) liters of gas per hour (at normal pressure and temperature), the intake pressure in the upper part of the cryostat was brought down to \(0.1\) mm; from this it was concluded that the evaporation pressure had again been lowered in comparison with that achieved in 1910; perhaps it may be estimated at \(0.15\) mm. When the pressure had fallen to this value, no further change was observed in the character of the evaporation, evidently owing to the establishment of equilibrium between the influx of heat and its removal by evaporation. Here too the helium did not solidify, and consequently the limit for the pressure had to be lowered still further, which in turn imposed increased requirements on subsequent experiments.

§ 6. BATTERY OF CONDENSATION VACUUM PUMPS.

Real progress could be achieved only with the execution of a long-desired plan, namely the construction of a whole series of vacuum pumps of large capacity, giving extreme degrees of rarefaction. It was intended to accomplish this goal by installing a larger number of Langmuir condensation pumps connected in parallel. In 1920 the first step was taken toward carrying out this plan, and since then the battery of such pumps has steadily increased. In the experiments described today, this battery had grown (Fig. 6) to twelve glass \(V_1\) and to six iron Langmuir pumps connected in parallel into a single whole. The Burckhardt pumps, still connected in series, served as auxiliary pumps. All this is shown in the schematic drawing, Fig. 6.

Fig. 6.

The battery of twelve glass pumps consists of three series of four pumps each, each series having, as it were, an auxiliary Langmuir pump (Fig. 6) before connection

to the present auxiliary pump, consisting of a set of Burckhardt pumps. In this battery the mercury of the condensation pumps is heated by gas. Since combustion is inadmissible in such a room as the department for experiments with helium, the battery of pumps is placed in a small separate room arranged in the same room. The room containing the battery is ventilated with outside air by means of a fan, which maintains a flow of air through openings in the walls into the helium department1. All connections in the glass pumps were made by soldering. The various series were connected to copper suction tubes, which joined in the main tube \(D_1\), 12 cm in diameter. Since the copper tubes were not soldered to one another, they were joined together by means of cement, exactly as the main tube was joined to the helmet of the evaporation apparatus. The only connection by rubber tubes was permitted in the connection of the tubes running from the auxiliary Langmuir pumps to the suction tube of the Burckhardt pump \(V_{\mathrm{b}}\). All the copper tubes were, moreover, varnished.

In general, iron pumps for the highest rarefactions are not as good as glass ones, but they are good enough to obtain those high degrees of vacuum with which we had to deal. They are heated electrically, and one must constantly keep in mind that none of the joints made with cement should become damaged. But I do not wish to dwell further either on these details or on the unexpected occurrences and failures with which, of necessity, one constantly had to contend in the work described.

With the battery of pumps with which I now work, at a pressure of 0.095 mm on the suction tube of the evaporation apparatus, a capacity of one liter (under normal conditions of temperature and pressure) of gas removed per hour was, in the end, attained; this corresponds to an amount of evaporated liquid helium equal to 1.25 cm³ at a temperature of \(2^\circ K\).

§ 7. Reduction to a minimum of the amount of heat communicated to the evaporating helium by thermal conduction. The large capacity of vacuum pumps can be utilized the better, the better the evaporating liquid helium is protected from the influx of heat and the more the frictional resistance is weakened on the path of helium vapor from the evaporating surface to the pumps. However, both these requirements are very difficult to fulfill simultaneously in the evaporation apparatus: a wider outlet tube will, of course, reduce friction, but at the same time it gives room for a stronger influx of heat to the helium through the glass walls and especially through thermal conduction in the column of the gaseous helium itself in the tube. Both requirements were [[unclear: continued on next page]]

possibilities are satisfied by the arrangement of the evaporation apparatus (Fig. 4), which was used in the last experiments in 1920 and 1921 (for clarification of certain details in the construction see also §§ 9 and 10). Besides the small vessel of the evaporator \(a\), with double walls and with an evacuated space between them, and the similar outlet tube \(b\), in which the space between the double walls can be evacuated through a stopcock, we also note the part \(g\) with a simple wall. The latter serves for introducing, by means of a special artificial procedure, liquid helium into the evaporator vessel \(a\).

For this purpose the liquid helium is introduced into the space connected with the pumps for producing the highest vacuum, i.e., into the evaporating apparatus, into the tube connecting it with the pumps, and into the pumps themselves, while they have been stopped. In this way the pressure in this space was allowed to rise above the vapor pressure in the cryostat bath, and then, inside the apparatus, the helium flowed down along the walls into its lower part. If the auxiliary pumps are put into operation again, evaporation under reduced pressure begins anew and continues until only the required amount of helium remains in the evaporator vessel; this helium is then further cooled owing to its complete protection from the influx of heat. In order to carry out still further cooling, the high-vacuum pumps are finally put into operation, and then the proposed experiment can already be begun. The pressure at the top of the evaporating apparatus, at which the suction was performed, was measured with a McLeod manometer (M—Fig. 6). Special efforts were made to eliminate the influx of heat to the helium in the evaporator through thermal conduction or through radiation. It is also necessary to draw attention to the radiation of heat by those parts of the apparatus which remained at ordinary temperature, for example, from the cap above the outlet tube through which the evaporating helium was removed. The order of magnitude of this radiation can be estimated by comparison with black-body radiation from a plane surface \((4.8 \cdot 10^{-9} T^{4}\ \mathrm{grcal.}\) in 1 hour and from \(1\ \mathrm{cm}^{2})\). Substituting into this expression the value of ordinary temperature, we obtain \(30\ \mathrm{grcal.}\), which, in view of the small heat of vaporization of helium—about \(6\ \mathrm{cal.}\)—is sufficient to evaporate an amount of liquid occupying a volume of \(30\) liters, at normal \(T\) and \(P\), in the gaseous state. However, the whole set of pumps is designed to remove, at the pressures under consideration, only an amount of gas corresponding to 1 liter at normal \(T\) and \(P\). It is therefore necessary that the radiation toward the evaporator vessel be intercepted as much as possible by opaque metal screens cooled to low temperatures, best of all to the temperature of the helium bath in the cryostat. The radiation from screens cooled to such a degree, owing to its dependence on the 4th power of the temperature, is so small that it may be neglected. Protection against radiation falling-

...toward the walls of the evaporating vessel can be carried out especially easily: the entire lower part of this vessel is surrounded by a metal hood, the upper part of which extends beyond the surface of the liquid air in the cryostat. Two slits were left open in the hood, in order to make the evaporating vessel visible through the unsilvered strips of the vacuum vessels. Usually the slits remain closed by two screens, which can rotate about the hood. They are moved aside only when it is necessary to observe the position of the liquid level; for illumination, small lamps with a metal filament are used, placed behind a solution of alum. To eliminate the transfer of heat from above by radiation into the evaporating vessel, a device was arranged, made by the chief glassblower of our department, Kesselring, and representing the height of the glassblower’s art. Above the evaporating vessel \(a\) a small glass hood with double walls is sealed into the glass, its intermediate space being connected to the vacuum tube. The helium in the cryostat flows into this intermediate space, the upper part of which is blackened and the lower part silvered. Radiation from above can penetrate only by reflection along the walls of this hood. Further, the transfer of heat from above was reduced to a minimum by narrowing the single-walled middle part as much as the strength of the apparatus and the quantity of flowing vapor permitted. Then the screens \(y\), cooled by the rising gas and by other means to be discussed below, were so placed in the outlet tube that they did not hinder the free discharge of the vapor. The inner walls of the outlet tube were blackened with a mixture of soot and a solution of celluloid, in order to diminish their reflecting power. Finally, the coil \(Sp\), which was introduced at the top of the tube and through which liquid hydrogen was passed, served the same purpose; by it part of the heat was removed which otherwise would have propagated downward along the walls. In still another respect the skill of our glassblower was used in constructing the evaporating apparatus. As we have seen, the outlet tube also has double walls in the upper part, which was silvered and evacuated between the double walls. The stresses arising in the glass, owing to the large temperature difference between the inner and outer walls, are removed by the metal box \(n\), soldered to the glass and acting as a spring. The heat carried from above by the walls through the constriction to the lower part of the test tube is taken up by the bath of the cryostat,\(^{1}\) since the level of the liquid in the cryostat is always maintained above the constriction \(g\). The purpose of this device was to ensure that the temperature of the helium gas above the evaporating vessel should not be appreciably higher than the temperature of the bath.

\(^{1}\) Heat thus diverted to the bath has no appreciable influence on the rate of evaporation, and consequently also on the time during which the experiment can continue.

The neck of the vessel in which evaporation takes place under very low pressure was made long and narrow: first, in order, as far as possible, to reduce the inflow of heat through the glass, the small radius making it possible to make the inner wall very thin; and second, in order to make the speed with which the vapor is removed sufficiently great, so as quickly to carry away the heat which otherwise would enter by thermal conduction along the column of helium gas. In all these arrangements the aim was always to reach the limit at which unfavorable frictional conditions might manifest themselves.

All the precautions just described were taken with the purpose of protecting, as far as possible, the helium in the evaporator vessel from the inflow of heat; thanks to them the evaporation, measured under normal conditions, was brought down to 0.9 liter. The suction pressure produced by the high-vacuum pumps in the helmet of the evaporating apparatus, according to the McLeod gauge, was about 0.0055 mm.

In the hope of reducing the quantity of glass which, in the end, had to be cooled by the evaporating helium, a special glass vacuum cup, $e$, with thin double walls was placed at the bottom of the evaporator vessel. It was assumed that, under continuous pumping, the liquid in the cup would continue to evaporate even after the liquid surrounding it had already evaporated, so that the conditions for cooling the helium would be more favorable, since less glass would have to be cooled and less heat would be transferred through the walls. It will now be seen that peculiarities in the course of evaporation caused the level of the liquid inside and outside the cup to fall at the same rate. As regards further progress in attaining lower temperatures, it turned out that this vessel did not justify our hopes.

§ 8. Reduction to a minimum of the frictional resistances on the path from the evaporating helium to the pumps. I now pass to the discussion of the question of reducing to a minimum the frictional resistances to the evaporating helium on its path from the surface of the liquid in the evaporating vessel to the high-vacuum pumps, and consequently of making the best use of the low suction pressure of these pumps. The width of the outlet tube could be increased only to the extent permitted by the dimensions of the upper part of the helmet of the cryostat $o$ (Fig. 5b). The opening in this part could not be enlarged without rebuilding the whole cryostat.¹

With the greatest width of the outlet tube at present accessible to us, the gas, owing to the considerable inflow of heat during its rise, acquires so great a velocity that it is too—

¹ Intensive work on the construction of a new cryostat with a wider opening in the upper part is under way.

...friction would have had to develop in our experiments, had special precautions not been taken. For this purpose a packing was placed in the upper end of the outlet tube, which could be strongly cooled by external means. The packing consisted of a copper coil \(Sp\), through which liquid hydrogen was passed. The coil was connected with a Dewar vessel filled with liquid hydrogen, and the liquid flowed through it under the action of a small excess pressure; the supply of liquid was regulated by means of a flow-velocity meter indicating the amount of hydrogen evaporating. This packing, being cooled in this way, not only considerably weakens the heating of the vapor as it exits through the outlet tube and helps to weaken the admission of radiation, by cooling the various screens, but it also takes up, as was said, part of the heat penetrating from above along the glass walls of the evaporating apparatus. By means of a small thermometer, constructed on the principle of electrical resistance and placed under the lower turn of the coil, one can always verify whether this device is operating properly. In the best experiments, the temperature under the coil fell to \(200^\circ\) C. Then the loss of pressure caused by frictional resistance, as we shall see, fell to \(0.01\) mm.

§ 9. Determination of pressure. In determining the pressure in the space immediately above the level of the evaporating helium, we used a manometer based on the principle of resistance. Pressures such as occur above the surface of evaporating helium are too small for them to be measured with a suitable mercury manometer; such a manometer would have to be given a very complicated construction, and then in the present case it would be very difficult to operate. From this point of view alone, a resistance manometer is more preferable. Moreover, the tube of the manometer can have very small dimensions, and the instrument can be calibrated very well within the pressure range from 5 to 20 bar. Whatever manometer is used, if the space of the manometer is at ordinary temperature and is connected with the space of lower temperature by a narrow tube, then the pressure in the manometer will not be equal to the measured one. At the low pressure at which the evaporation of helium occurs, the mean free path of the gas molecules is, in all probability, many times greater than the diameter of the tube, except in the case when our tube is kept at a very low temperature. Between the space at low temperature and the space at high temperatures there must exist a pressure difference equal to the thermal molecular pressure. Knudsen\(^{1}\) found that this diffi—

\(^{1}\) Leiden Comm. Supl. No. 34a.

measurement, characteristic of pressure measurements at low temperatures, could be eliminated by using a resistance manometer (i.e., here it was possible to keep the manometer tube itself at a low temperature), was, fortunately, confirmed by an experiment carried out by van Gulik. Thus the pressure in the evaporating vessel was determined by a resistance manometer, whose manometric tube was maintained at a temperature only slightly above the temperature of the evaporating helium, since it was immersed in a helium bath outside the evaporating vessel. In Figs. 5 b and c it is seen how the manometric tube is soldered to the lower part of the evaporating apparatus; in Fig. 6 the device \(W\) for measuring pressure is shown schematically. At first glance it seems doubtful whether the principle on which this manometer is based—i.e. the change in the resistance of its wire with temperature—can be applied at such low temperatures; for here not only must the resistance fall to a very small value, but it also no longer varies with temperature, as is indeed the case with a platinum wire cooled to the temperature of liquid helium. But it turns out that the residual resistance at this temperature is still sufficiently large (if a possibly small current flows through the wire) to heat the wire to such a point that the temperature rises enough for the resistance to begin to increase appreciably; then the effect of the pressure on the loss of heat from the wire becomes observable from the difference in the currents required to maintain one and the same resistance. Although the measuring instrument used in this way is rather an indicator than a pressure gauge, nevertheless, by means of calibration at known pressures, the desired aim can be attained. In this calibration the apparatus was filled with gaseous helium at rest, and its lower end was lowered in the same way as in the experiment into a bath of helium. The upper part, which passed upward through the cryostat, remained at ordinary temperature. Tube \(b\) is still not wide enough to make unnecessary a correction for the thermal molecular pressure between the upper and lower parts. The accuracy of the measured pressure values that will now be given will be increased in new experiments, when the uncertainty arising from the fact that the correction has so far only been calculated is eliminated. I shall not, however, dwell now on this correction, which barely reaches \(0.003\) mm. We shall also neglect the difference that may still exist between the pressure in the manometric tube and at the surface of the liquid helium.

§ 10. Device for stirring liquid helium. Finally, we must mention a small stirrer, \(r\), introduced into the evaporating vessel \(a\). In the evaporation apparatus shown in Fig. 4, it consists of a horizontal glass disk, attached

attached to a glass rod. It can move up and down by means of a wire fastened to the rod, which passes at the top through a glass tube; the tube is closed by means of a special stopper. ^1)

§ 11. Final experiments. For the success of experiments with so complex an apparatus as has now been described, and whose general appearance is given in Fig. 6, it is necessary that the numerous operations be carried out each at the time appointed for it and in the proper sequence, so that the success of every operation depends entirely on its careful preparation. A slight deposition of vapor on one of the glass walls through which the evaporator is to be observed is enough to make this observation impossible; on walls cooled by liquid hydrogen, a gas containing even mere traces of air gives its condensation. If one considers that, in order to keep the glass walls through which the observation was made transparent for whole hours after liquid helium had first been introduced into the cryostat, it will be clear that I owe a great deal to Flim (Flim), the head of the technical division, for his devotion to the work. Thanks to him, everything proceeded in complete order according to plan.

Early in the morning the preparation of 24 liters of liquid hydrogen began, since the entire preceding day had been spent, on the one hand, on evacuating the apparatus and bringing it into a condition ready for operation, and, on the other hand, on preparing a sufficient quantity of liquid air (more than 50 liters). At the same time the following preparations were carried out: the helium circulation was put in order; the pump was started in order to carry off the hydrogen from the helium liquefier under reduced pressure; then the space intended for the liquid air serving to cool the hydrogen was filled, and the space for the liquid hydrogen was likewise filled after it had been cooled with dry, cold hydrogen gas. At noon the liquid helium could be poured by siphon into the cryostat, after which we proceeded to further cooling of this bath by evaporation and by new filling with the aid of helium circulation. At 1 o’clock the condensation of helium in the evaporating vessel could be begun, and the lower part of the glass evaporator was filled somewhat above the cap with double walls, of which mention was made above. At 3 o’clock this helium had evaporated so much that it occupied only the lower part of the evaporator; at first the evaporation was carried out under the action of the auxiliary set of pumps, and subsequently under the combined action of the high-vacuum pumps with these auxiliary pumps, which—

^1) In the earlier experiments a spring was placed between the wire and the rod; a piece of diamond was suspended from the wire instead of the disk. If the solidified helium met resistance from the diamond, the spring would be stretched during the upward and downward motion.

and removes the helium from the evaporating apparatus. Evaporation was observed alternately, sometimes with the naked eye, sometimes with the cathetometer telescope, while the screens around the instrument were kept closed as far as possible. Neither by means of the stirrer, nor by observation with the naked eye or with the telescope, was anything observed that could indicate solidification of the helium; and even at the very lowest pressure that was attained, the liquid always retained complete mobility throughout its entire extent.

§ 12. Evaporation at different levels. It has already been noted that, contrary to our expectation, the liquid outside the small drawn-out cup would evaporate first, and only afterward the liquid inside it; in fact, both liquid levels fell at the same rate, so that they remained all the time in the same horizontal plane. If (see Fig. 7), with the aid of the stirrer \(c\) (Fig. 4), the liquid is poured from the inside outward, then the outer level falls rapidly while the inner one rises, until they again become level in one plane. If the screens are removed, allowing radiation from the lamp to fall on the evaporating vessel, then the outer layer evaporates; after the screens are closed again this layer forms anew at the expense of the liquid inside the cup, and it increases until both layers become equal again, and then they once more fall at the same rate. The rate of equalization in this distillation was astonishing. A proper judgment about this phenomenon will be possible only when the determinations which we have in mind have been made concerning the thermal conductivity of glass, vapor, and liquid helium; it is also desirable that measurements be made of the latent heat of evaporation and the specific heat of liquid helium and of glass, as well as of the viscosity of helium gas.

Fig. 7.

The property of maximum density exhibited by helium in the liquid state undoubtedly had a great influence on the observed phenomenon. The observations of 1911 first revealed the existence of this property, but at that time it had not yet been sufficiently established whether the density approaches a definite value or whether it decreases at still lower temperatures. That the former phenomenon takes place has been established by a repetition of the experiments undertaken together with Bock after the completion of the experiments in which we are now engaged. This assertion will be correct only insofar as no special feature is found in the expansion of glass. When the surface of helium is cooled

below \(2.2^\circ K\) it turns out that the coldest layers of the liquid remain at the top. Whereas in other cases, in work with a bath under low pressures, the liquid was subjected to vigorous stirring, here this stirring was omitted for lack of free space at the top of the cryostat. The presence of a stirrer in the outer bath would in all probability have made the transfer of heat to the evaporator still weaker than it actually was. One could hope that the means employed reduce the transfer of heat by half, if it is assumed that there is no special change here in the heat of evaporation of helium.

§ 13. The lowest limit of vapor pressure. Be that as it may, when the level of the liquid helium in the evaporator fell to the bottom of its narrowed part and to half the height in the small beaker, it turned out that the smallest vapor pressure that could be obtained in this apparatus had been reached. Neglecting the small corrections mentioned above, the pressure at the surface was \(0.012—0.014\) mm, on the average \(0.013\) mm. In the upper part the pressure was on the average about \(0.005\) mm, so that the pressure difference, caused by the friction of the rapidly removed vapors of low density, reached on the average \(0.008\) mm. This value agrees fairly well with the results of a special determination of the frictional pressure experienced by helium moving in the same apparatus and at the same speed. In this control experiment the evaporator was replaced by a tube through which helium flowed, cooled to the temperature of liquid hydrogen, with the same density and at the same speed as before. This control experiment gave for the frictional pressure the value \(0.009\) mm. The same value was obtained on the basis of calculations proceeding from the probable distribution of temperature along the ascending column of helium gas. In round numbers, and taking into account the existing shortcomings, we may say that the limit for the vapor pressure has been brought below \(1/50\) mm, and that we have advanced 10 times farther than in the experiments of 1910, on whose observations we based the estimate of the temperature then regarded as the lowest attained. The corresponding difference in temperatures, estimated in degrees of the Kelvin scale, will be, as we shall see in § 14, only of very small magnitude. Returning to the question of the solidification of helium, we arrive at the following conclusion. Since it is apparently beyond doubt that helium has a maximum density (see § 12), and since it was not converted into the solid state even at a temperature lying halfway below the temperature of minimum density, we cannot avoid the question whether helium will perhaps remain liquid even at the temperature of absolute zero.

§ 14. Determination of the temperature. It remains for us to consider the question of what temperature corresponds to the pressure found

evaporation. For the latter pressure we obtained a definite, as we shall now see, precisely established value, if one disregards the small corrections requiring further study; but we cannot say the same with respect to the temperature. In determining extremely low temperatures, where even a helium gas thermometer can no longer be used, we enter a region whose study has only just begun. Therefore we have to turn again to the law of corresponding temperatures of Van der Waals, in order, guided by it, to extrapolate the law connecting vapor pressure with temperature to lower temperatures than those for which it was established experimentally. This was done for temperatures down to which a helium gas thermometer could still be used. In this case the construction of the thermometer must be adapted to the pressure, which introduces a complication.

Fig. 8.

In reality the pressure must be very small, if the simple gas laws are to be applicable here. When the pressure becomes small, a correction must be introduced for the thermal molecular pressure (i.e., the difference of pressures between the reservoir of the thermometer at low temperature and the space of the manometer at ordinary temperature). But despite these difficulties we nevertheless succeeded in measuring the vapor pressure of helium down to \(1.5\,K\) in 1911 and 1913 with a thermometer equipped with a mercury micromanometer, and in 1917 with two thermometers equipped with wire manometers. The results are marked on the accompanying drawing (Fig. 8)

...in which the abscissas are the reciprocals of the reduced temperatures, and the ordinates are the logarithms of the reduced pressures.

The whole question is how to extrapolate the lines that pass through the observed points. For this purpose the vapor-pressure curves of ether, argon, neon, and hydrogen are drawn on the same graph, each ending at the triple point of the substance. The curve for mercury has an even lower reduced temperature than that reached with helium. All the curves have the common property that their curvature is very small; the greatest curvature of the helium curve is observed at higher temperatures. They differ from one another in that their slopes are different for different substances. In applying the law of corresponding states to normal substances, one must take into account such systematic changes of the parameters expressing the laws for liquids: for a substance with a low critical point, the slope of the line on the graph decreases as the critical temperature is lowered. In view of this, as is seen from the figure, helium satisfies this law in its generalized form; in particular, the slope of its curve agrees with the slope of \(Ar\), \(Ne\), and \(N\), and the slight curvature at higher reduced temperatures also falls on the extrapolation line that may be regarded as the most probable, and amounts to taking the tangent to the curve at the point where it ends as the continuation of the curve. This is what has been adopted in the figure. Hence, for the pressure limit attained by us in 1910, we obtain the value \(1.15\,K\), and for the present limit, giving the lowest temperature reached, the value \(0.082\,K\).

Taking into account the unreliability of extrapolation, it will be better to say that the lowest temperature so far obtained is several hundredths of a degree below \(0.09\,K\).

§ 15. Conclusion. The question posed above—whether we can descend below the temperature \(1^\circ K\)—thus receives an affirmative answer. In round numbers we have advanced by \(1/3\) of a degree, and one may say that, if we could advance by another \(1/6^\circ\), we would reach the limit obtainable with helium by the ordinary method. A clearer conception of the progress achieved than by means of these small numbers can be obtained if we express the lowering of temperature by the ratio in which we have lowered the absolute temperature. Whereas the transition from ordinary temperature to the temperature of helium evaporating at \(0.2^\circ\) mm signifies a lowering in the ratio \(250\) to \(1\), and from the melting point of hydrogen to the helium temperature just mentioned a lowering in the ratio \(13\) to \(1\), the present lowering is only from \(1.4\) to \(1\), and a further lowering from \(1.2\) to \(1\) will already be the limit that can be obtained with liquid helium. If we assume that our knowledge of dark structure makes it improbable that there has been found or obtained any...

or by some other substance more volatile than helium, then the limit indicated by us, from which we are so slightly removed, must prove to be the absolute limit set for us in the attainment of low temperatures.

However, we cannot regard this limit as anything but temporary. Already there are definite problems that require their solution beyond the region that seems to be an impenetrable barrier. As a simple example one may point to the question whether such a metal as gold can be made superconducting if it is cooled still more than we have been able to do up to now. This series of problems is drawing us away from the problem of liquefying the permanent gases. They resisted the efforts of the great experimenter whose glorious name is associated with our Society.¹ Half a century later, the liquefaction of hydrogen, the most stubborn gas with which Faraday had dealt, was the brilliant completion of the work of the last of his successors at the Royal Institution, Sir James Dewar.

We may feel confident that the difficulties that have now arisen on our path will also be overcome, and that the most important thing in this matter is the long and patient investigation of the properties of matter at the very lowest temperatures we can attain.

Translated by A. I. Sokolov.

¹ A lecture read at the Faraday Society.

1. If necessary, all gas burners can be extinguished at once. ↩↩↩↩

2. A detailed description of the Leiden Laboratory was given by Kamerlingh-Onnes, for example, in the Nobel lecture available in Russian translation (Voprosy Fiziki, 1914, p. 219). It should be remembered that in Kamerlingh-Onnes’s Laboratory the cascade method is used. A liquid gas obtained by means of the preceding cycle itself serves for cooling the next one. To obtain liquid helium, for example, cycles are passed through with the following substances: methyl chloride ($1 — 96^\circ$), ethylene ($-145^\circ$), oxygen ($183^\circ$), air ($-190^\circ$), hydrogen ($-255^\circ$). ↩