- The liquefaction of helium was a spectacular manifestation of the molecular hypothesis, and the law of corresponding states first proposed by Van der Waals in 1880, and exploited to its utmost by Kamerlingh Onnes, especially after his proof of a theorem in 1881 concerning this law. For an analytical presentation of these theorems, see Gavroglu K. Goudaroulis Y. Heike Kamerling Onnes' Researches at Leiden and their Methodological Implications Studies in the History and Philosophy of Science in press
- The first hint of the fact that liquid helium undergoes a drastic modification at a temperature of 2·19 K was found by H. Kamerlingh Onnes in 1911 during measurements of the density of the liquid. The decisive experimental evidence for the two modifications of liquid helium was provided largely by W. H. Keesom and his collaborators, and was furnished by measurements on such physical properties as, for example, the dielectric constant and the heat of vaporization, which showed anomalies at the temperature of 2·19 K. Keesom concluded that two states of liquid helium exist which pass one into the other at the temperature mentioned. He designated the liquid at temperatures between 2·19 K and the boiling point (4·2 K), helium I; and the modification below 2·19 K, helium II. Keesom's measurement of the specific heat of liquid helium showed most convincingly the profound nature of the change. Indeed it was on account of the shape of the specific heat-temperature curve that Ehrenfest referred to the transition temperature as the λ-point. Subsequent work showed the heat conduction to be quite anomalous and, finally, serious attention was focused on what was by 1936 an entirely perplexing situation. The experiments that led to the discoveries of most of the truly peculiar properties of the fluid were all conducted in 1938; see Keesom W.H. Helium Amsterdam 1942 For a detailed treatment of the historical and methodological aspects of the developments related to the properties of superfluid helium between 1908 and 1939, see K. Gavroglu and Y. Goudaroulis, ‘From Physica to Nature: The Tale of a Most Peculiar Phenomenon’, Janus (in the press).
- This kind of situation where the use of a particular concept to comprehend the behaviour of a particular object under different conditions leads to two irreconcilable overall ‘pictures’ is not unique to superfluidity, and it has been noticed both in superconductivity and in elementary particle physics. See Gavroglu K. Goudaroulis Y. Some Methodological and Historical Considerations in Low Temperatures Physics: The Case of Superconductivity 1911–1957 Annals of Science 1984 41 135 149 and K. Gavroglu, ‘Popper's Tetradic Schema, Progressive Research Programs and the Case of Parity Violation in Elementary Particle Physics 1953–1958’, Zeitschrift für allgemeine Wissenschafts theorie, 16, (1985), 261–286
- London , F. July 1946 . “ The Present State of the Theory of Liquid Helium ” . In International Conference on Fundamental Particles and Low Temperatures , July , Cambridge : Cavendish Laboratory . 22–27 published by the Physical Society (1947), II, 1–18 (p. 1). For a detailed treatment of the methodological problems associated with the development of theories of macroscopic quantum phenomena in low temperature physics, see K. Gavroglu and Y. Goudaroulis, Methodological Aspects of the Developments in Low Temperature Physics 1881–1956 (Dordrecht, 1988)
- London . July 1946 . “ The Present State of the Theory of Liquid Helium ” . In International Conference on Fundamental Particles and Low Temperatures , July , 3 – 3 . Cambridge : Cavendish Laboratory . 22–27
- See Gavroglu K. Goudaroulis Y. Some Methodological and Historical Consideration in Low Temperature Physics, II: The Case of Superfluidity Annals of Science 1986 42 137 146 See also Y. Goudaroulis, ‘Many-particle Physics: Calculational Complications that Become a Blessing for Methodology’, International Conference, Criticism and the Growth of Knowledge: 20 Years After (Thessaloniki, 1986).
- See Gavroglu Goudaroulis From Physica to Nature: The Tale of a Most Peculiar Phenomenon Janus in press
- Tisza , L. 1949 . The Present State of the Helium Problem . Proceedings of the International Conference on the Physics of Very Low Temperatures . Sept. 6–10 1949 , Cambridge, Massachusetts. pp. 1 – 3 . (p. 2)
- London , F. 1938 . The λ-phenomenon of liquid helium and the Bose-Einstein degeneracy . Nature , 141 : 643 – 644 . ‘On the Bose-Einstein condensation’, Physical Review, series 2, 54 (1938), 947–54; ‘The State of Liquid Helium Near Absolute Zero’, Journal of Physical Chemistry, 43 (1939), 49–69.
- London , F. July 1946 . “ The Present State of the Theory of Liquid Helium ” . In International Conference on Fundamental Particles and Low Temperatures , July , 8 – 8 . Cambridge : Cavendish Laboratory . 22–27
- London , F. July 1946 . “ The Present State of the Theory of Liquid Helium ” . In International Conference on Fundamental Particles and Low Temperatures , July , 8 – 8 . Cambridge : Cavendish Laboratory . 22–27
- Tisza , L. 1938 . Transport Phenomena in Helium II . Nature , 141 : 913 – 913 .
- Tisza , L. 1938 . Sur la supraconductibilite thermique de l'helium II liquide et le statistique de Bose-Einstein . Comptes Rendus hebdomadaires des Seances de l'Academie des Sciences, Paris , 207 : 1035 – 1037 .
- London , H. 1939 . Thermodynamics of the Thermomechanical Effect of Liquid He II . Proceedings of the Royal Society A , 171 : 484 – 496 .
- Kapitza , P.L. 1941 . The Study of Heat Transfer in Helium II . Journal of Physics (USSR) , 4 : 181 – 181 . reprinted in Collected Papers of P. L Kapitza, edited by D. Ter Haar II (London, 1965), 581–624
- Kapitza , P.L. 1941 . Heat Transfer and Superfluidity of Helium II . Journal of Physics (USSR) , 5 : 59 – 59 . reprinted in, ibid., 625–39
- Gavroglu and Goudaroulis . 1986 . Some Methodological and Historical Consideration in Low Temperature Physics, II: The Case of Superfluidity . Annals of Science , 42 : 138 – 138 .
- Kapitza . 1941 . The Study of Heat Transfer in Helium II . Journal of Physics (USSR) , 4 : 581 – 581 .
- See Keeson W.H. Keesom A.P. On the Heat Conductivity of Liquid Helium Physica 1936 3 359 360
- Kapitza , P.L. 1941 . ‘Problems of Liquid Helium’, . Sovetskaya Nauka , 1 : 33 – 33 . A report at the General Assembly of the USSR Academy of Sciences, 28 December 1940, translated from in P. L. Kapitza, Experiment, Theory, Practice: Articles and Addresses (Boston, 1980), pp. 12–34 (p. 24)
- Kapitza . 1941 . ‘Problems of Liquid Helium’, . Sovetskaya Nauka , 1 : 24 – 24 . A report at the General Assembly of the USSR Academy of Sciences, 28 December 1940, translated from
- Kapitza . 1941 . The Study of Heat Transfer in Helium II . Journal of Physics (USSR) , 4 : 638 – 638 .
- Landau , L.D. 1941 . The Theory of Superfluidity on Helium II . Journal of Physics (USSR) , 5 : 71 – 90 . Reprinted in Z. Galasiewitz, Helium 4 (Oxford, 1971), pp. 191–233.
- Landau himself claimed that Tisza's viewpoint ‘cannot be considered as satisfactory … the explanation advanced by Tisza not only has no foundation in his suggestions but is in direct contradiction to them’; Ginzburg stated that ‘the condensation of a Bose gas has nothing to do with the properties of helium. The latter have been explained by Landau's theory only’, and Peshkov rejected the London-Tisza theory as ‘very artificial and unconvincing’. F. London and Tisza responded by pointing out that ‘the B–E gas, at any rate, has provided an idealized model for nearly all the unique properties of liquid helium, which model has furthermore led to predictions of new effects … Landau's theory appeared too late to make all these inferences in form of predictions', and that ‘one has to give the preference to the B–E theory over … [Landau's] quantum hydrodynamic approach’. See Landau L. The Theory of Superfluidity on Helium II Journal of Physics (USSR) 1941 5 192 192 V. L. Ginzburg, ‘Scattering of Light in Helium II’, Journal of Physics (USSR), 7 (1943), 305–6 (p. 305); V. Peshkov, ‘Determination of the Velocity of Propagation of the Second Sound in Helium II’, Journal of Physics (USSR), 10 (1946), 389–98, reprinted in Z. Galasiewitz (footnote 25), 166–87, (p. 167); F. London (footnote 4), p. 13; Tisza (footnote 8), p. 2.
- See Frohlich H. The Theory of Superconductive State Reports on Progress in Physics 1961 24 1 23 (especially p. 21)
- An excellent historical account from this point of view is Brush S.G. Statistical Physics and the Atomic Theory of Matter Princeton 1983 172 203 It has to be noted here that even the two theoretical discussions, of F. London and of Tisza, of the effect of the Bose-Einstein degeneracy on the transport properties, differ considerably in detail. (See K. Gavroglu and Y. Goudaroulis, ‘The Two-Fluid Model in View of the London-Tisza Correspondence’, to be published.)
- Frenkel , J. 1946 . The Kinetic Theory of Liquids 308 – 308 . Oxford especially
- For a review of these developments, see Dingle R.B. Theories of Liquid Helium Advances in Physics 1952 1 111 168
- Landau , F. 1949 . On the Theory of Superfluidity . Physical Review , 75 : 884 – 885 . series 2 Reprinted in Collected Papers of L. D. Landau, edited by D. Ter Haar (London 1965), pp. 474–7 (p. 474) (emphasis added).
- Landau . 1941 . The Theory of Superfluidity on Helium II . Journal of Physics (USSR) , 5 : 209 – 209 . (emphasis added)
- In his ‘quantized hydrodynamics’ the macroscopic density and velocity of the fluid would be replaced by noncommuting quantum-mechanical operators. Rather than attempt to derive hydrodynamics from the Schrodinger equation, Landau was following one of the paths by which the Schrodinger equation itself could have been derived in an axiomatic treatment of quantum mechanics. ‘Such a theory called for an experimental test in the classic hypothetico deductive tradition even though (here as in other cases) scientists do not let theories stand or fall on the basis of experiment alone.’ Brush S.G. Statistical Physics and the Atomic Theory of Matter Princeton 1983 182 182
- ‘This name was suggested by I. E. Tamm’, Landau The Theory of Superfluidity on Helium II Journal of Physics (USSR) 1941 5 200 200 note on
- The statement in Keesom's book Helium Amsterdam 1942 that in Landau's theory ‘phonons and rotons act the part of superfluid and normal fluid respectively’ is erroneous.
- Andronikashvilli , E. 1946 . A Direct Observation of Two Kinds of Motion in Helium II . Journal of Physics (USSR) , 10 : 201 – 206 .
- Landau was at this time unaware of Tisza's prediction of temperature waves. In his paper cited in footnote 31, p. 474, we read ‘Tisza's detailed paper J. Phys. rad. 1940 1 165 165 350 was not available in USSR until 1943 owing to war conditions, and I regret having missed seeing his previous short letter [Comptes Rendus, 207, 1035, 1186 (1938)]’.
- According to Peshkov Determination of the Velocity of Propagation of the second Sound in Helium II Journal of Physics (USSR) 1946 10 167 167 ‘An attempt to detect the second sound by the beats in standing waves radiated by oscillating piezoquartz was undertaken in the Institute for Physical Problems by Shalnikov and Sokolov before the war, but without success’.
- Brush . 1983 . Statistical Physics and the Atomic Theory of Matter 184 – 184 . Princeton
- Lifshitz , E. 1944 . Radiation of Sound in Helium II . Journal of Physics (USSR) , 8 : 110 – 110 . Reprinted in Galasiewicz (footnote 25), 234–42, (p. 241).
- Peshov , V. 1944 . Second Sound in Helium II . Journal of Physics (USSR) , 8 : 381 – 381 . It is interesting to note that in 1940, Ganz sent a heat pulse down a long capillary of He II and estimated its velocity to be of the order of 100 m/s. ‘Although it was not then recognized as such, this must be considered to be the first observation of a traveling temperature wave in helium II.’ J. F. Allen, ‘Liquid Helium’, in F. Simon, Low Temperature Physics, Four Lectures (New York, 1952), pp. 66–94 (p. 90).
- Peshkov . 1946 . Determination of the Velocity of Propagation of the second Sound in Helium II . Journal of Physics (USSR) , 10 : 185 – 185 . At this point it would seem that the second-sound data favoured Tisza's theory over Landau's, but as Peshkov said ‘Only after experiments at lower temperatures will be carried out will it be possible to determine whether … the microscopic theory of helium II should be modified in some manner’ (ibid., p. 186). Landau himself stated that ‘The experimental data which are available at present are yet insufficient to disprove Tisza's assertion, because of the comparatively small role of the phonons in the temperature region explored. But I have no doubt whatever that at temperatures 1·0–1·1°K the second-sound velocity will have a minimum and will increase with the further decrease in temperature. This follows from the values of the thermodynamic quantities of helium II calculated by me’. (Landau, footnote 31, p. 476.) Tisza accepted the challenge and maintained that his own formula for second-sound velocity should be more accurate at lower temperatures. (See L. Tisza, ‘On the Theory of Superfluidity’, Physical Review, series 2, 75 (1940), 885–6.) Peshkov, by extending the range of his experiments to 1·03°K, was able to show a slight increase in the velocity at the lowest temperature. The question was, however, definitely settled by Pellam and Scott who studied second-sound pulses in magnetically cooled helium. They found that by cooling they could raise the velocity of second sound to 34m/s. This spectacular increase left little doubt, that, as regards the propagation of second sound, the prediction of Landau appeared to be the more probable one. (V. Peshkov, ‘Skorost'vtorogo zvuka ot 1·3 do 1.pe°K’, Zhurnal eksperimentalnoi i teoretichesko fiziki, 18 (1948), 951–2; J. P. Pellam, R. B. Scott, ‘Second Sound Velocity in Paramagnetically Cooled Liquid Helium II’, Physical Review, series 2, 76 (1949), 869–70.) However, for finite temperatures there was a discrepancy between theory and experiment. (See footnote 41.)
- ‘Although this discrepancy is not very large, it is too large to be attributed to the inaccuracy of the experimental data on the thermodynamic quantities of helium II’. Landau L. On the Theory of Superfluidity of Helium II Journal of Physics (USSR) 1947 11 91 92 Reprinted in Galasiewicz (footnote 25), 243–6, (p. 243).
- Landau , L. 1947 . On the Theory of Superfluidity of Helium II . Journal of Physics (USSR) , 11 : 245 – 245 .
- Landau , L. 1947 . On the Theory of Superfluidity of Helium II . Journal of Physics (USSR) , 11 : 91 – 92 .
- Tisza , L. 1947 . The theory of Liquid Helium . Physical Review , 72 : 838 – 854 . series 2
- Bogoliubov , N. 1947 . On the Theory of Superfluidity . Journal of Physics (USSR) , 11 : 23 – 32 . Reprinted in Galasiewicz (footnote 25), 247–67 (p. 260).
- As Tisza said in his paper The Present State of the Helium Problem Proceedings of the International Conference on the Physics of Very Low Temperatures Proceedings of the International Conference on the Physics of Very Low Temperatures Cambridge Massachusetts Proceedings of the International Conference on the Physics of Very Low Temperatures Cambridge Massachusetts Sept. 6–10 1949 2 3 ‘Recent experiments … indicating an increase in second sound velocity if the temperature drops below 1°K, provide strong support to the view of Landau. Again there seems to be no difficulty in incorporating this aspect into the B-E theory.’ (Emphasis added).
- Allen . Second Sound in Helium II . Journal of Physics (USSR) , 8 92 – 92 .
- London , F. 1949 . The Rare Isotope of Helium, He3; A Key to the Strange Properties of Ordinary Liquid Helium, He4 . Nature , 163 : 694 – 696 . (p. 696)
- London , F. 1949 . The Rare Isotope of Helium, He3; A Key to the Strange Properties of Ordinary Liquid Helium, He4 . Nature , 163 : 694 – 696 . The enormous success of nuclear physics in the 1940s made it possible to obtain He3 in quantities sufficient for experimentation. In 1948 at Los Alamos it was shown that He3 liquefies at 3·2K, and a new quantum liquid was made available to physicists. (S. Sydoriak, E. Grilly and E. Hammel, ‘Condensation of pure He3 and its Vapor Pressures Between 1·2° and its Critical Point’, Physical Review, series 2, 75 (1949), 303–5. The fact that He3 could be obtained as a liquid at atmospheric pressure might itself be considered a point against the London-Tisza view, since London himself stated that owing to its high zero-point energy it is ‘almost certain that pure He3 cannot exist in a liquid phase at any temperature …’ and this view was shared by Tisza. (See F. London and O. Rice, ‘On Solutions of He3 in He4’, Physical Review, series 2, 73 (1948), 1188–93 (p. 1193); L. Tisza, ‘Helium, the Unruly Liquid’, Physics Today, August 1948, 4–8, 26, (p. 26).) In 1956, Landau developed a separate theory for Fermi liquids. (L. Landau, ‘The Theory of a Fermi Liquid’, Zhurnal eksperimentalnoi i teoreticheskoi fiziki, 30 (1956), 1058; ‘Oscillation in a Fermi Liquid’, ibid., 32 (1957) 59). When superfluidity was finally discovered in He3 in late 1971, Landau's theory was found best suited to describe it. (See D. Osheroff, R. Richardson and D. Lee, ‘Evidence for a New Phase of Solid 3He’, Physical Review Letters, 28 (1972), 885; T. Alvesalo, Y. Anufriyev, H. Collan, O. Lounasmaa and P. Wennerstrom, ‘Evidence for Superfluidity in the Newly Formed Phases of 3He’, ibid., 30 (1973), 962.) For a clear description of the superfluid phases of 3He including both experimental observations and the essential ideas behind the theory, see N. David Mermin and David M. Lee. ‘Superfluid Helium 3’. Scientific American. 325 (6) (1976), 56.
- Bogoliubov . 1947 . On the Theory of Superfluidity of Helium II . Journal of PHysics (USSR) , 11 : 247 – 247 .
- London , F. 1947 . On the Theory of Superfluidity of Helium II . Journal of Physics (USSR) , 11 : 248 – 248 . It should be emphasized that a quasi-particle is a purely theoretical construct, which does not involve an individual helium atom, but motion of the liquid as a whole. Nevertheless, the behaviour of a quasi-particle gas is remarkably similar to that of a real gas, with two important differences. The first of these concerns the relation between the energy and momentum of a quasi-particle. This relation reflects the properties of the modes of motions of the whole liquid and is quite unlike the corresponding relation for a real particle. The second difference concerns the number of particles in a given sample of materials. In a real gas the number is fixed. In helium II it depends on the temperature. At absolute zero there are no quasi-particles, and their number increases as the temperature, and hence energy of the fluid, is raised.
- Brush . 1983 . Statistical Physics and the Atomic Theory of Matter 189 – 189 . Princeton
- Bogoliubov . 1947 . On the Theory of Superfluidity . Journal of Physics (USSR) , 11 : 248 – 248 .
- In such a kinetic theory of a quantum liquid the states of angular momentum l=2,4, … give no contribution at very low temperatures. The radial distribution function then obtained is very different from that of a normal liquid. It is supposed that the transition is located at that temperature for which the last non-vanishing state of angular momentum begins to disappear. In a sense this explanation of the existence of He II is similar to that suggested by Landau. According to him the curious properties of He II are to be correlated with the insufficiency of quantized vortex (rotational) states, whilst according to Green they are to be correlated with the insufficiency of quantized states with non-zero relative angular momenta. It is a feature of the theory that the classical conceptions of temperature and pressure are no longer applicable. This first law of thermodynamics takes different forms depending on whether the liquid is in steady motion or undergoing periodic displacements. The latter case leads to the possibility of the excitation of thermal waves which transfer heat energy and liquid bulk in opposite directions; to these are ascribed the transport phenomena of the He II. Born M. Green H.S. A General Kinetic Theory of Liquids. Quantum Mechanics of Fluids Proceedings of the Royal Society 1947 A191 168 181
- It shows roughly how a λ-type of specific heat anomaly may arise in He4, but not be found in He3, and leads to a negative expansion coefficient below the λ-point. Prigogine I. Philippot J. Theorie Moléculaire du Point λ de l'Helium Liquide Physica 1952 18 729 748
- He cites in evidence Taconis' assumption that He3 dissolves only in the normal part of He II. Taconis made this suggestion in 1949 in an attempt to explain his experimental result that the effect on the vapour pressure of He II caused by the addition of He3 is much greater than that predicted by Raoult's law. It may be noted that according to others Raoult's law is obeyed in this case. Temperley H.N.V. On the Relationship Between the Landau and London-Tisza Models of Liquid Helium II Proceedings of the Physical Society (London) 1952 A65 490 511 O. K. Rice, ‘Statistical Mechanics of Helium II near 1°K’, Physical Review, 96 (1954), 1460–3.
- Daunt and Mendelssohn have drawn attention to the analogous behaviour of He II and superconductors, and extended the two-fluid conception to both phenomena. They suggested that both are due to a new state of aggregation, composed of ‘z-particles’, in which frictionless transport is closely associated with zero entropy without order in coordinate space. (See Mendelssohn K. The Frictionless State of Aggregation Proceedings of the Physical Society 1945 57 323 371 389 5 In 1946, Macleod and Yeabsley put forward the theory that He II is a mixture of ordinary He I and the intermediate form of a fluid indicated by Van der Waals' equation, and Benedicks has suggested that the properties of He II may be explained in terms of an allotropic transformation at the lambda-point arising from the ionization of the helium atoms by frictional electricity at the walls of the vessel. (See R. H. Dingle, footnote 30.)
- London , F. 1951 . Limitations of the Two-fluid Theory . Proceedings of the International Conference on Low Temperature Physics . August 22–28 1951 , Oxford. Edited by: Bowers , R. pp. 206 – 206 . (pp. 2–3)
- Feynaman , R. 1955 . “ Application of Quantum Mechanics to Liquid Helium ” . In Progress in Low Temperature Physics Edited by: Gorter , J. Vol. I , 17 – 53 . chapter 2 (p. 25) (emphasis added)
- Feynman , R. 1953 . The λ-transition in liquid helium . Physical Review , 90 : 1116 – 1117 . series 2 (p. 1116). See also his ‘Atomic Theory of the λ-Transition in Helium’, ibid., 91 (1953), 1291–301 (p. 1291).
- Feynman , R. 1953 . Atomic Theory of Liquid Helium near Absolute Zero . Physical Review , 90 : 1301 – 1308 . series 2
- Feynman , R. 1954 . Atomic Theory of the Two-fluid Model of Liquid Helium . Physical Review , 94 : 262 – 270 . series 2
- Feynman , R. and Cohen , M. 1956 . Energy Spectrum of the Excitations in Liquid Helium . Physical Review , 102 : 1189 – 1204 . series 2
- Osanger , L. 1949 . Remark at a Low Temperature Physics Conference at Shelter Island in 1948 . Nuovo cimento , 6 : 249 – 249 . in supplement
- Feynman . 1955 . “ Application of Quantum Mechanics to Liquid Helium ” . In Progress in Low Temperature Physics Edited by: Gorter , J. Vol. I , 45 – 45 . in chapter 2
- It has to be noted here that the considerations following from the Landau spectrum gave a critical velocity νc ≈ 8000–24 000 cm/s. An experimental evidence of the existence of vortex lines was given first by Hall and Vinen in 1956, and in 1958 Vinen at the Royal Society Mond Laboratory in Cambridge observed the quantized vortex lines predicted by Onsager and Feynman. (See Vinen W. Detection of Single Quanta of Circulation in Rotating Helium II Nature 1958 181 1524 1525 ‘The Detection of single Quanta of Circulation in Liquid Helium II’, Proceedings of the Royal Society of London, A 260 (1961), 218–36. See also G. Rayfield and F. Reif, ‘Evidence for the Creation and Motion of Quantized Vortex Rings in Superfluid Helium’, Physical Review Letters, 11 (1963), 305–8).
- Feynman . 1955 . “ Application of Quantum Mechanics to Liquid Helium ” . In Progress in Low Temperature Physics Edited by: Gorter , J. Vol. I , 17 – 17 . in chapter 2
- Reif , F. Superfluidity: the Paradox of Atomic Simplicity and Remarkable Behaviour . Proceedings of the Batsheva Seminar . 1968 , Haifa. Quantum Fluids , Edited by: Wiser , N. and Amit , D.J. pp. 1 – 14 . New York in (p. 4). See also his ‘Superfluidity and “Quasi-particles”’, Scientific American, 203 (5) (1960), 139–50.
- Frohlich , H. 1966 . “ Superconductivity and the Many Body Problem ” . In Perspectives in Modern Physics (Essays in Honour of Hans Bethe) Edited by: Marshak , R.E. 539 – 552 . New York in (p. 550)
- London , F. 1961 . Superfluid , second edition Vol. I , 2 – 3 . New York
Annals of Science
Volume 45, 1988 - Issue 4