THE DISCOVERY OFSUPERFLUIDITY

Two of the greatest physicsdiscoveries in the first

half of the 20th century weresuperconductivity and super-fluidity.1 Superconductivityinvolves the frictionless con-duction of electricity in wires,and superfluidity the friction-less flow of superfluid liquidhelium through channels.Both discoveries led to the ar-cane phenomenon of macro-scopic quantization: the manifestation of the laws of quan-tum mechanics not just on atomic dimensions but also onthe scale of common laboratory apparatus. Both discov-eries required the liquefaction of helium, which was firstdone in 1908.

Superconductivity was discovered almost immediatelyafter liquid helium became available—by 1911—and itsimportance in the construction of magnets was quicklyrecognized.2 Although there were hints as early as 1911that something was peculiar about liquid helium near 2 K,it was not until 1938 that superfluidity was discoveredand named. (Figure 1 is a remarkable photograph of asuperfluid-helium fountain, one of the hallmarks of super-fluidity.) Analogies between the two phenomena playedan important part in the discovery. Why was it that theseclosely related discoveries occurred more than a quarterof a century apart? No technical barrier stood in the wayof the discovery of superfluidity, and as we shall see,suggestions of a new phenomenon were definitely present.

Liquid heliumHelium was not discovered on Earth. It was found in thespectrum of light from the Sun during a total solar eclipsevisible in India in 1868.3 The French astronomer JulesJanssen, equipped with a spectroscope, observed a yellowline in the spectrum of light from the Sun, which hecorrectly attributed to the radiation from a chemical ele-ment not heretofore observed on Earth. Janssen's discov-ery was confirmed by Joseph Norman Lockyer, who pro-posed the name "helium," from the Greek helios, the Sun.Helium was finally discovered on Earth in 1895 by WilliamRamsay, as a remnant of the radioactive decay of uraniumin the mineral Norwegian clevite. Helium was soon foundto be present in substantial quantities in gas wells in theUnited States.

A race began to liquefy helium at various laboratories,and in 1908 Heike Kamerlingh Onnes won that race atthe University of Leiden, the Netherlands, observing that

RUSSELL DONNELLY teaches physics at the University ofOregon, in Eugene.

Superfluidity and superconductivity havestrong analogies to each other. Why then

did over a quarter of a century passbetween the discoveries of these two

phenomena?

Russell J. Donnelly

the normal boiling pointwas near 4 K. Onnes'steam immediately tried tosolidify the liquid by theusual cooling method of re-ducing the vapor pressure,and hence the temperatureof the liquid, by pumping.By 1910 it was clear thatthe liquid would not freezeeven at 1 K. We know to-day that helium at ambient

pressure will remain liquid even to absolute zero, becauseof its large zero-point energy. The small mass of the 4Heatom results in this large zero-point energy, which keeps thefluid's density small even though interatomic forces arestrong enough to form a liquid phase at low temperatures.

In the late fall of 1910 Onnes began a series ofmeasurements with Cornelius Dorsman and Gilles Hoistthat revealed, among other things, that liquid heliumreaches a maximum density near 2.2 K. (See figure 2a.)This result puzzled Onnes, who found it strange that sucha simple liquid should exhibit a density maximum at aseemingly uninteresting temperature. We know now thatthey were observing a further fundamental phenomenon,the lambda transition, that would not be recognized formany years.

The main thrust of research of the Onnes group,however, was to measure the electrical resistance of met-als. They reported to the Royal Academy of Amsterdamon 21 April 1911 that they observed resistance of a threadof mercury vanishing very rapidly as the temperaturedropped. Indeed, within a few months, the disappearanceof resistance in mercury had been established. By March1913 Onnes was referring in print to "the superconduc-tivity of mercury," thus naming the phenomenon. On 10December 1913 he received the Nobel Prize "for his in-vestigations on the properties of substances at low tem-perature, which investigations, among other things, haveled to the liquefaction of helium." Not long thereafter theoutbreak of World War I put a temporary end to experi-ments with liquid helium.3

The next developments occurred in 1922 and 1923when Onnes and Johan D. A. Boks remeasured the den-sity maximum first observed in 1910, and Leo Dana andOnnes measured the latent heat and specific heat of liquidhelium. Dana and Onnes remarked about the latent-heatcurve at 2.2 K that "near the maximum density somethinghappens to the helium which within a small temperaturerange is perhaps even discontinuous." This appears to bethe first time that what is now called the lambda transi-tion was identified as a discontinuity.4 (See my article onDana in PHYSICS TODAY, April 1987, page 38.) The lambdatransition is so named because the shape of the specific-heat

30 JULY 1995 PHYSICS TODAY ' 1995 American Institute of Physics

HELIUM FOUNTAINphotographed in the 1970sby Jack Allen at theUniversity of St. Andrews,in Scotland. Allen, one ofthe discoverers ofsuperfluidity, was the firstto observe this spectacularphenomenon. FIGURE 1

JULY 1995 PHYSICS TODAY 31

0.15

0.14 -

0.13 -

0.12

b 120

1 2 3 4

TEMPERATURE (kelvin)

y

u

TEMPERATURE (kelvin)

curve resembles the Greek letter A (see figure 2b); itstemperature is usually denoted by Tx.

Two phasesAn important step in the sequence of discovery was takenin 1927. In a paper entitled "Two Different Liquid Statesof Helium," Willem Keesom and Mieczyslaw Wolfke con-cluded that above the lambda transition a phase theynamed liquid helium I exists, and below the transitionthere exists a stable phase called liquid helium II, exhib-iting different physical properties.3

A dramatic example of the different properties occursduring cooldown. When liquid helium is put in a cryostatand the cryostat is evacuated with a vacuum pump, theliquid begins to evaporate and cools the remaining liquid.In this way the temperature can be lowered to about 1 K.During this "pump down" the liquid boils vigorously untilthe lambda transition, at which it suddenly becomesabsolutely quiet and bubble-free. This happens becauseof helium II's enormous effective thermal conductivity,owing to its two-fluid nature (which I shall discuss below).This dramatic behavior was not even mentioned in print

DENSITY AND SPECIFIC HEAT of liquid helium as afunction of temperature, a: The peculiar density maximumwas first seen in 1910 and suggested that something importantoccurs near 2.2 K. b: Specific heat shows its characteristic"lambda" behavior. (Adapted from ref. 3.) FIGURE 2

for some 25 years after the first liquefaction. Indeed, oneof the discoverers of superfluidity, John F. (Jack) Allen,recently remarked: "In my PhD work in Toronto onsuperconductivity I had often seen the sudden cessationof boiling at the lambda temperature Tk, but had paid itno particular attention. It never occurred to me that itwas of fundamental significance."5

The slowly evolving discovery of superfluidity can bemore readily appreciated if we describe how we think ofhelium II today.6 At low velocities of flow helium II actsas if it is a mixture of two fluids. One, called thesuperfluid, has no viscosity or entropy and can flowthrough extremely narrow channels without dissipation.The other, called the normal fluid, does have a finiteviscosity 17 and carries all the entropy. We picture theliquid to be all normal fluid at the lambda transition andall superfluid at absolute zero. The proportions of eachfluid can be measured, for example, by measuring thefraction of liquid that clings to an oscillating disk by virtueof its viscosity. The density of normal fluid is denoted pn;the density of superfluid, ps. The total density p is given

by Pn + Ps-The superfluid is pictured as a "background fluid"

that is, in effect, at absolute zero. The normal fluid isthe sum of elementary excitations, or quasiparticles, con-sisting of phonons and rotons, which are excited from thesuperfluid in increasing numbers as the temperature isincreased from absolute zero. Phonons are quantizedsound waves and occur in solids as well as in liquid helium.Rotons are higher-energy excitations than phonons, andtheir properties are still under study. These elementaryexcitations are often investigated by inelastic neutronscattering, where a neutron excites a phonon or roton inthe process of interacting with the fluid.

The two-fluid model of helium II is now highly devel-oped, and equations of motion have been advanced thatare able to describe many phenomena observed in heliumII, including hydrodynamic instability and turbulence.

Physicists consider the most fundamental aspect of asuperfluid to be the condensate.1 At absolute zero someof the atoms (about 10%) are in a state of zero energyand momentum. The condensate is described by a quan-tum mechanical wavefunction that extends over not justindividual atoms but the entire container. This macro-scopic quantization of the condensate has very importantramifications. For example, if the container is rotatedslowly, the normal fluid will move with the container, butthe superfluid will remain at rest. Above some criticalvelocity of rotation,7 one quantized vortex line will appearin the center of the container, and every atom in thecontainer will have an angular momentum h. This resultsin a lockstep motion of the superfluid.1

In superconductivity, a dramatic demonstration offrictionless flow is the perpetual flow of electricity rounda superconducting ring. One can establish a persistentcurrent in the ring by applying a magnetic field throughthe loop above the transition temperature, cooling throughthe transition temperature and removing the applied field.The superfluid fraction of helium II also can be made toflow in a loop, usually a tube packed with fine emery

32 JULY 1995 PHYSICS TODAY

powder to prevent the normal component from moving.One starts the flow by rotating the loop above the lambdatransition, then cooling it through the lambda transitionand stopping the rotation. The presence of the supercur-rent can be detected by the fact that the superfluid flowin the loop acts like a fluid gyroscope and has a gyroscopicreaction when the axis of rotation is disturbed.

A famous lecture demonstrationAt the end of the 1920s the story of the discovery ofsuperfluidity switches from Holland to Canada. Allen wasborn in 1908 in Winnipeg, Manitoba, Canada, and studiedphysics at the University of Manitoba, where his fatherwas the first professor of physics. In 1929 Allen went tothe University of Toronto and began to work under thesupervision of Sir John McLennan, who had built a copyof Onnes's helium liquefier in 1923. Much of Allen's thesisresearch concerned superconductivity, and early in 1932he designed and built a cryostat to study persistent cur-rents in superconducting rings.

This cryostat was the source of a famous event inlow-temperature physics.2 McLennan was asked to givean evening discourse on superconductivity at the RoyalInstitution in London in 1932. Deciding that a demon-stration would enliven the lecture, McLennan took Allen'scryostat to England. Because the closest source of liquidhelium was in Leiden, across the North Sea, McLennanasked his friend William Francis-Sempill, Lord McMasterof Sempill (a Scottish estate) to fly the cryostat to Leidento be filled, to start the superconducting current in thelead ring and to return to London. Sempill was a promi-nent and colorful aviator and a vigorous promoter ofaeronautical affairs generally.

The cryostat was filled in Leiden at about 3 pm theday the demonstration was to take place, and Keesom andGerrit Jan Flim, Leiden's chief technician, drove toSchiphol airport near Amsterdam to meet Sempill, whohad arrived in a single-engine airplane. Flim boarded theairplane and carried the cryostat in his hands during theflight. The trip was rough and a good deal of the liquidevaporated. They landed at Lympne airfield in England,passed their strange load through customs and proceededto Hanworth airfield near London. A fast taxi ride gotthem to the Royal Institution by 8:30 pm, and the cryostatwas deposited before McLennan and his audience. Themagnetic field produced by some 200 amperes circulatingin the superconducting ring was demonstrated by meansof a compass fitted with a mirror to reflect light on a screen.After the lecture the cryostat was emptied and the audienceshown that it contained only a lead ring. Today this cryostatis in a museum at the Royal Institution.

Misener and KapitsaIn 1935 Donald Misener, another graduate student at theUniversity of Toronto, performed a novel experiment todetermine the viscosity of helium II. Writing to me in1988, Misener explained that he embarked on this venturebecause had to do some research as a requirement for theMA degree in science: "It was evident that the physicalproperties of this liquid had never been measured even

Torsion fiber

Mirror

Support rod

VISCOSITYMEASUREMENTSCHEME used byDonald Misener in1935. An oscillatingpendulum immersedin liquid heliummeasures the liquid'sviscosity. Thesuspended cylinder is2.5 cm in diameterand 9 cm long; theentire apparatus isabout 1 meter inheight. Thecylinder's conicalends keep impuritiesfrom entering it anddeflect the bubblesthat occur in helium I.(Adapted from ref. 8.)FIGURE 3

Oscillatingcylinder

though it showed some peculiar behavior patterns (littlebuckets of it emptied themselves by the liquid climbingup the sides and dropping off the outside—and if a flaskof the stuff was jarred the liquid kept sloshing with verylittle damping)."

Misener constructed a pendulum consisting of a cyl-inder suspended in liquid helium by a torsion fiber andset in rotary oscillations. (See figure 3.) The unusuallylong decay time for these oscillations showed that theviscosity was small indeed—an order of magnitude lessthan that of air—and that it all but disappeared at thelambda transition.8 We know today that the viscosity ofhelium II does not disappear at the lambda transition,but that Misener's oscillating apparatus was measuringdamping depending on -qpn and not the viscosity rj alone,which varies slowly as the temperature is lowered. Thedensity pn of normal fluid, however, drops very rapidly asthe temperature is reduced below the lambda transition.

Another central figure in the discovery of superfluiditywas the Russian physicist Peter Leonidovich Kapitsa, whowas born in Kronstadt in 1894, the son of a general in theCzar's engineer corps. He was educated at the PolytechnicInstitute of nearby Saint Petersburg as an electrical engineer,graduating in 1918. He remained there as a lecturer until1921, during which time he came to know Abram Ioffe, anoutstanding Russian physicist and a student of WilhelmRontgen, the discoverer of x rays. Just as Kapitsa wasbecoming interested in physics, an influenza epidemic carriedoff his wife and two children. This tragedy, and the unstablesituation following the revolution, convinced Kapitsa to makehis way eventually to Cambridge, England where he becamea student of Ernest Rutherford's in the Cavendish Labora-tory. Initially he studied radioactivity, but his engineeringbackground soon took his interests to the generation oflarge magnetic fields. In 1925 he was elected a fellow ofTrinity College.

JULY 1995 PHYSICS TODAY 33

By 1928 Kapitsa was heading a department of magneticresearch and had begun to realize that he should be exam-ining materials at veiy high magnetic fields and very lowtemperatures. A liquid hydrogen plant was constructed tomake this possible. Rutherford, as president of the RoyalSociety of London, appointed Kapitsa Messel Professor ofthe Royal Society in 1930 and established a new laboratoryfor research at high fields and low temperatures called theRoyal Society Mond Laboratory. In 1929 Kapitsa was electeda fellow of the Royal Society and a corresponding memberof the Academy of Sciences of the USSR. Indeed, Kapitsamaintained his citizenship, and beginning in 1926 paid visitsto Moscow almost every year.

Seeing the need for temperatures even lower thanthose attainable with liquid hydrogen, Kapitsa again usedhis superb skills as an engineer and by 1934 had success-fully constructed a helium liquefier of his own uniquedesign at the Mond Laboratory. This liquefier was theforerunner of the modem machines in use today, and aversion of it built at Yale University by Cecil T. Lane justafter World War II was in the laboratory at Yale when Icame as a graduate student in 1952.

Allen (pictured on the right in figure 4) arrived inCambridge in the autumn of 1935 hoping to work underKapitsa, but Kapitsa was being detained by Stalin inRussia, having gone back as usual in the early summerexpecting to return to Cambridge in the autumn. Thereasons for Kapitsa's detention will perhaps never be

completely clear, but the historian Lawrence Badash hassuggested that one reason may have been the Sovietgovernment's hope that Kapitsa could be instrumental inthe electrification of the nation.9 Production of energywas to be a first step in the restructuring of the Sovieteconomy after the revolution. When it became clear thatKapitsa could not return, Cambridge allowed the SovietUnion to buy the entire equipment and contents of theMond except for the helium liquefier. Kapitsa soon hada liquefier built in Moscow and quickly established himselfat home as a major figure in physics.

Viscosity measurementsThe 8 January 1938 issue of Nature carried two letterson a different type of viscosity measurement in helium II:flow through a channel or tube. "Viscosity of LiquidHelium Below the A Point" was by Kapitsa in Moscow,10

and "Flow of Liquid Helium II" was by Allen and hisgraduate student Misener in Cambridge.11 The two pa-pers exploited essentially the same idea—to determine theviscosity by flow through channels instead of by oscillatingcylinders. In both experiments pressure differences weremeasured by means of liquid levels, which, owing to thelow density of liquid helium, correspond to small pressuredifferences. Kapitsa used the apparatus shown schemati-cally in figure 5. When the tube filled with liquid heliumII was raised, the liquid quickly flowed out, at a rate thatsuggested a maximum viscosity of 10~9 poise—indeed so

ALLEN and some associates on the roof of the Mond Laboratory, in Cambridge, England, in 1936-37. Left to right: a visitornamed Hirschlaff, graduate students Teddy Shire and Zaka Uddin, theorist Rudolf Peierls, a graduate student named Curtis andAllen. Allen, Peierls and Uddin showed in 1937 that the heat conductivity of helium II becomes essentially infinite in very finetubes. FIGURE 4

34 JULY 1995 PHYSICS TODAY

small that Kaptisa guessed by analogy to superconductorsthat it might be zero and "that the helium below theA-point enters a special state that might be called a'superfluid.'"10

Allen and Misener measured the flow through narrowtubes of radii 10~5-10~2 cm. They found that in thenarrowest tubes the flow is almost independent of pressureand observed that "consequently any known formula can-not, from our data, give a value of viscosity which wouldhave any meaning."11

These two letters to the editor mark the discovery ofsuperfluidity—or, more precisely, the realization that he-lium II exhibits superfluidity. Much more, however, re-mained to be done, for the oscillating cylinder and flowthrough channels turned out not to be measuring the samething. In the two-fluid picture, the oscillating cylinder isdamped by the normal fluid, whereas it is the superfluidthat passes through the narrowest tubes without friction.Kapitsa mentioned the Toronto viscosity measurements8

and concluded (erroneously) that the reported finite vis-cosity must be due to turbulent flow.

Fountain effectShortly afterward, Allen and Harry Jones discovered thethermomechanical effect in helium II, popularly known asthe "fountain effect."12 This was an accidental discoverymade in the process of investigating thermal conductionin fine tubes. Allen, in a recent account5 and in lettersto me, wrote that in the experiments the conductivity ofheat appeared to increase as the size of the capillary borecarrying the heat became smaller. For the smallest tubesand lowest temperatures, the rise in liquid level shownin figure 6 was observed for the first time. Allen recalls:

In addition, in the same dewar, was a small tubewith an open bulb at the bottom containingemery powder, since we thought we would ex-amine the flow through powder to compare itwith the flow through a smooth tube. To makesure that the right piece of apparatus appearedin the clear strip I had a small pocket torch[flashlight]. As the emery powder tube cameinto view in the light of the torch helium spurtedout of the top of the tube. It continued to spurtas long as the torch light shone on the powderand ceased when a card cut off the light, andtherefore the radiant heat, to the bulb. Thefountain had appeared. Admittedly it was onlyone or two millimeters high, but it was there.Great excitement, everybody in the lab wasbrought in to see it, and a camera rigged to takea picture.

By the next week we had a properly designedtube to produce a real fountain about 15 cm highwhen irradiated by a 60 watt desk lamp bulb.Figure 6 depicts the improved fountain apparatus,

and figure 1 is a modern photograph of a beautiful heliumfountain. The black horizontal line in the photo is theelectrical heater connection; the heater is a spiral insidethe glass apparatus.

The two-fluid picture described earlier was first putinto mathematical form by Laszlo Tisza around 1938-40.13

These equations showed that sound in helium II consistsof ordinary (first) sound, which is fluctuations in totaldensity, and second sound, which is fluctuations in thedensities of the normal and superfluid components.6 Sec-ond sound makes itself known as temperature fluctuationsand can be generated by heaters and detected by ther-mometers. The entry of Lev Landau into the field in 1941brought a more rigorous treatment of the two-fluid equa-tions; this effort was helped by the existence of new

'Thread

Glass disks

- Glass tube

Helium bath

CHANNEL-FLOW SCHEME hy Peter Kapitsa in Moscow tomeasure the viscosity of helium II. Kapitsa raised theoptically flat glass disks and glass tube from the helium bathby means of the thread. The viscosity was measured by thepressure drop when the liquid flowed through the narrow gapbetween the disks. The pressure difference was given by theheight of the liquid column in the glass tube. Above thelambda transition temperature 7\ a level difference could beobserved for several minutes. Below TA the differencedisappeared in seconds, leading Kapitsa to conclude that theviscosity of helium II was at least 1500 times less than that ofhelium I. FIGURE 5

experiments and by the development of the quasiparticlepicture of the normal component mentioned above.

Reasons for slow discoveryPerhaps now we can speculate as to why superconductivitywas discovered in 1911, only three years after the firstliquefaction of helium, and superfluidity in 1938, 30 yearsafter the liquefaction.

First, there was already much experimental and theo-retical interest in the fall with temperature of electricalresistance in wires. This decrease was already seen withliquid air and liquid hydrogen. But no past experienceeven remotely resembling superfluidity was available be-fore the liquefaction of helium.

Second, once superconductivity was discovered it wasimmediately obvious to Onnes and others that there wereimportant applications, such as persistent-current mag-nets, to be developed. Superconductivity was soon foundin other materials, thus widening the accessibility of andinterest in the phenomenon.

Third, the subtle transformation from helium I to helium

JULY 1995 PHYSICS TODAY 35

SETUP USED BY ALLEN in the discovery of thefountain effect. The powder, called a superleak, formsmany fine channels for superfluid flow. Whenradiation warms the powder, quasiparticles (rotonsand photons) are excited from the superfluid andexpand. The expansion pushes up on the free surfaceof the liquid, drawing superfluid from the baththrough the superleak. The pressure becomes so highthat fluid exits the top of the tube continuously aslong as the powder is warmed. FIGURE 6

Cotton wool

Emery powde

II near 2.2 K wasnot recognized until1927. Until the im-portance of the lamb-da transition was es-tablished there wasno real motivation tolook for other exoticphenomena.

Fourth, the earlyviscosity measure-ments in Torontoshowed a substantialdrop in the dampingof the oscillating cyl-inder below thelambda transitionbut not the disap-pearance of friction.The disappearanceof friction had towait for the 1938 ex-periments, whichshowed the analogybetween supercon-

ductivity and superfluidity: Electrons flow through asuperconducting wire with no voltage difference, and asuperfluid flows through narrow channels with no pres-sure difference. The possibility of turbulent flow leadingto false conclusions about the viscosity was fully appreci-ated by all investigators.

Finally, there was no great scientific leader active inunderstanding liquid helium in the early days. WhenKapitsa and the great theoretical physicist Landau, fol-lowed by physicists such as Fritz London, Lars Onsager,Richard Feynman and other greats, came on board, therewas a tremendous surge of excitement, which lasted formany years and helped bring the subject to its presentstate of understanding.

As we have noted, the forced retention of Kapitsa byStalin in 1934 resulted in the founding of a new low-temperature laboratory in Moscow. By 1941 the workthere had established one of the most important chaptersin the history of Russian (and indeed all) physics. Kapitsanot only began experimental work in Moscow, but he wasin close contact with Landau and his graduate students.Landau, with his colleague Evgenii Lifshitz, wrote themagnificent Course of Theoretical Physics, a ten-volumeseries that has had a major impact on all of modern

physics. The nature of superfluidity was rapidly estab-lished in Moscow and elsewhere and was eventually rec-ognized by the award of Nobel Prizes to both Kapitsa andLandau. It is somewhat surprising that the Mond Labo-ratory, which produced many distinguished low-tempera-ture investigators over the years, seems to have receivedless credit than it truly deserves.

The importance of superfluidity lies mainly in whatit tells us about the condensed state of matter. In par-ticular, the quantum mechanical consequences of the ex-istence of a condensate lie at the very foundation of ourunderstanding of the behavior of matter at low tempera-tures. The lambda transition in helium has proved to bea major testing ground for models of phase transitions,which are of far broader significance than the lambdatransition by itself. The two-fluid model has proved to bea major testing ground for understanding a new systemof hydrodynamic equations. Superfluidity is becomingconceptually well understood and offers an entirely newfrontier in fluid mechanics for the study of inviscid flows,stability, turbulence and shock waves.

The tendency for helium II to become turbulent veryeasily because of its low viscosity was understood by thepioneers in this subject. This tendency may itself evolveinto a tool for the generation of the highest-Reynolds-num-ber flows ever achieved under laboratory conditions. Suchwork is now a major thrust of low-temperature physics.

References1. D. R. Tilley, J. Tilley, Superfluidity and Superconductivity,

3rd ed., Adam Hilger, Bristol, UK (1990).2. P. F. Dahl, Superconductivity, AIP Books, New York (1992).3. W. H. Keesom, Helium, Elsevier, Amsterdam (1942).4. R. J. Donnelly, A. W. Francis, eds., Cryogenic Science and

Technology: Contributions by Leo I. Dana, Union CarbideCorp. (1985).

5. J. Allen, Physics World, November 1988, p. 29.6. R. J. Donnelly, Experimental Superfluidity, U. Chicago P.,

Chicago (1967).7. R. J. Donnelly, Quantized Vortices in Helium II, Cambridge

U. P., Cambridge, UK (1991).8. J. O. Wilhelm, A. D. Misener, A. R. Clark, Proc. R. Soc Lon-

don, Ser. A 151, 342 (1935).9. L. Badash, Kapitsa, Rutherford and the Kremlin, Yale U. P.,

New Haven, Conn. (1985).10. P. Kapitsa, Nature 141, 74 (1938).11. J. F. Allen, A. D. Misener, Nature 141, 75 (1938).12. J. F. Allen, H. Jones, Nature 141, 243 (1938).13. L. Tisza.J. Phys. Radium, Ser. VIII1, 164, 350 (1940) •

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