Statistical mechanics and thermodynamics: A Maxwellian view

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his conception of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concept that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover.     

Der Eigenartige Einfluß Witelos auf die Entwicklung der Dioptrik

Summary Witelo's Perspectiva, which was printed three times in the sixteenth century, profoundly influenced the science of dioptrics until the Age of Newton. Above all, the optical authors were interested in the so-called Vitellian tables, which Witelo must have copied from the nearly forgotten optical Sermones of Claudius Ptolemy. Research work was often based on these tables. Thus Kepler relied on the Vitellian tables when he invented his law of refraction. Several later authors adopted Kepler's law, not always because they believed it to be true, but because they did not know of any better law. Also Harriot used the Vitellian tables until his own experiments convinced him that Witelo's angles were grossly inaccurate. Unfortunately Harriot kept his results and his sine law for himself and for a few friends. The sine law was not published until 1637, by Descartes, who gave an indirect proof of it. Although this proof consisted in the first correct calculation of both rainbows, accomplished by means of the sine law, the Jesuits Kircher (Ars Magna, 1646) and Schott (Magia Optica, 1656) did not mention the sine law. Marci (Thaumantias, 1648) did not know of it, and Fabri (Synopsis Opticæ, 1667) rejected it. It is true that the sine law was accepted by authors like Maignan (Perspectiva Horaria, 1648) and Grimaldi (Physico-Mathesis, 1665), but since they used the erroneous Vitellian angles for computing the refractive index, they discredited the sine law by inaccurate and even ludicrous results.That even experimental determinations might be unduly biased by the Vitellian angles is evident from the author's graphs of seventeenth century refractive angles. These graphs also show how difficult it was to measure such angles accurately, and how the Jesuit authors of the 1640's adapted their experimental angles to the traditional Vitellian ones. Witelo's famous angles, instead of furthering the progress of dioptrics, delayed it. Their disastrous influence may be traced for nearly thirty years after Descartes had published the correct law of refraction.

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Vorgelegt von C. Truesdell     

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior.Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.     

From centripetal forces to conic orbits: a path through the early sections of Newton’s Principia

In this study, we test the security of a crucial plank in the Principia’s mathematical foundation, namely Newton’s path leading to his solution of the famous Inverse Kepler Problem: a body attracted toward an immovable center by a centripetal force inversely proportional to the square of the distance from the center must move on a conic having a focus in that center. This path begins with his definitions of centripetal and motive force, moves through the second law of motion, then traverses Propositions I, II, and VI, before coming to an end with Propositions XI, XII, XIII and this trio’s first corollary. To test the security of this path, we answer the following questions. How far is Newton’s path from being truly rigorous? What would it take to clarify his ambiguous definitions and laws, supply missing details, and close logical gaps? In short, what would it take to make Newton’s route to the Inverse Kepler Problem completely convincing? The answer is very surprising: it takes far less than one might have expected, given that Newton carved this path in 1687.     

Newton's early computational method for dynamics

On December 13, 1679Newton sent a letter toHooke on orbital motion for central forces, which contains a drawing showing an orbit for a constant value of the force. This letter is of great importance, because it reveals the state ofNewton's development of dynamics at that time. Since the first publication of this letter in 1929,Newton's method of constructing this orbit has remained a puzzle particularly because he apparently made a considerable error in the angle between successive apogees of this orbit. In fact, it is shown here thatNewton's implicitcomputation of this orbit is quite good, and that the error in the angle is due mainly toan error of drawing in joining two segments of the oribit, whichNewton related by areflection symmetry. In addition, in the letterNewton describes quite correctly the geometrical nature of orbits under the action of central forces (accelerations) which increase with decreasing distance from the center. An iterative computational method to evaluate orbits for central forces is described, which is based onNewton's mathematical development of the concept of curvature started in 1664. This method accounts very well for the orbit obtained byNewton for a constant central force, and it gives convergent results even for forces which diverge at the center, which are discussed correctly inNewton's letterwithout usingKepler's law of areas.Newton found the relation of this law to general central forces only after his correspondence withHooke. The curvature method leads to an equation of motion whichNewton could have solvedanalytically to find that motion on a conic section with a radial force directed towards a focus implies an inverse square force, and that motion on a logarithmic spiral implies an inverse cube force.     

Preservation ofBordetella pertussis

Summary Bordetella pertussis has been shown to remain viable for a period of 13 years on freeze-drying. The revived cultures had unaltered antigenic composition and biological activity.Thanks are due to Dr M. Balasubrahmanyan for his guidance and Dr M.S. Zakharova, Gamaleya Institute of Microbiology and Epidemiology, Moscow, USSR for supplyingB. pertussis factor sera. We thank Mr Ram Jas for his technical assistance.     

La conservation de la vie par le froid

Summary It has been found that, by addition of a certain amount of glycerol, it is possible to store living animal tissues in the frozen state over very long periods of time. The cooling velocity, the temperature of storage and the rate of thawing are important factors. Under the optimal conditions, experiments done on the heart of the chick embryo have shown that complete recovery of the normal physiological activities can be achieved after freezing in liquid nitrogen.     

Erhöhung der Körpertemperatur vonPeriplaneta americana L. im Verlauf zweier Bakteriosen

Summary It is shown that two bacterial diseases ofPeriplaneta americana are accompanied by a significant increase of body temperature of the insect.     

电信空调冷却塔供冷系统节能应用

根据电信机楼的空调负荷特点，在冬季和部分过渡季节，选择使用冷却塔加板式换热器的间接式免费供冷空调系统为电信机楼提供冷量。介绍了冬季机房空调送风温度和冷却塔供冷温度的确定，分析了冷却塔供冷温度对冷却塔运行消耗的影响。通过预测计算确定冷却塔免费制冷的的运行时间及节能效果。并引入了冷负荷供需指数的概念，经过现场测试计算得出江苏电信第二枢纽工程中影响该指数的三个因素，最后总结了江苏电信免费制冷技术的节能情况和应用潜力。     

Thermische Denaturierung von Kaltblüter-Enzymproteinen

Summary The temperature, which leads to 50% reduction of catalytic activity by heat denaturation, has been determined for 8 different enzymes from cod muscle, as being in the range between 30 and 52°C. Therefore, there are no indications of a generally different heat resistance of enzymes from cold-blooded animals as compared with those from warm-blooded animals. The same conclusion is derived from calculations ofQ ₁₀-values, measured between +37 and – 37°C for cathepsin and glycylglycine dipeptidase.

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Die Untersuchungen wurden dankenswerterweise durch eine Beihilfe des Bundeswirtschaftsministeriums Bonn unterstützt. HerrnDegener, i. Fa. Hanseatische Hochseefischerei A.G., Bremerhaven-F., verdanken wir das Untersuchungsmaterial.     

Synthesis of a ubiquitously present new HSP60 family protein is enhanced by heat shock only in the Malpighian tubules ofDrosophila

A homologue of the chaperonin protein of the HSP60 family has not been shown so far inDrosophila. Using an antibody specific to HSP60 family protein in Western blotting and immunocytochemistry, we showed that a 64-kDa polypeptide, homologous to the HSP60, is constitutively present in all tissues ofDrosophila melanogaster throughout the life cycle from the freshly laid egg to all embryonic, larval and adult stages. A 64-kDa polypeptide reacting with the same antibody in Western blots is present in all species ofDrosophila examined. Using Western blotting in conjunction with³⁵S-methionine labeling of newly synthesized proteins and immuno-precipitation of the labeled proteins with HSP60-specific antibody, it was shown that synthesis of the 64-kDa homologue of HSP60 is appreciably increased by heat shock only in the Malpighian tubules, which are already known to lack the common HSPs.     

Variance to mean ratio and the spatial distribution of animals

Summary Biological and statistical aspects of the application of variance to mean ratio to describe spatial distribution of animals are discussed. It is shown that the parameterb inTaylor's power laws ²=a m ^b shows intra-specific variation depending on the distribution of the constituent units of the population.a andb are only parameters of a very empirical way of describing the relation between variance and mean, which itself is an indicator for spatial distribution. Hence,a andb depend on the distribution behaviour of the animals, and not vice versa.Acknowledgments: The work was developed whilst I was at the Department of Entomology, University of Nairobi. I am grateful to ProfessorT. R. Odhiambo for his interest. I thank the referee for comments.     

Essay review

This paper treats van Helmont's attack on Aristotle as an example of the difficulty of accounting for one author's attack on another by simply comparing the texts of the two authors. The Aristotle that van Helmont is attacking is the Aristotle represented in contemporary textbooks, and the attack on his authority is closely connected to the attack on the importance of verbal disputation in education. The importance of knowledge of Aristotle and of argumentative skills means van Helmont displays them to claim competence in them, while arguing they are worthless, and states many of his own doctrines as denials of Aristotelian doctrines. After a brief account of van Helmont's cosmology, three texts of his are examined: the conclusion of Causae et initia naturalium, where van Helmont demonstrates the worthlessness of Aristotelian method, by giving an example of his own method's greater success, the beginning of Physica Aristotelis et Galeni ignara, where he argues in Aristotelian terms against an Aristotelian definition of nature, and his general attack on Aristotelian method and on verbal disputation in Logica inutilis.     

The third law in Newton’s Waste book (or, the road less taken to the second law)

On the basis of evidence drawn from the Waste book, Westfall and Nicholas have argued that Newton arrived at his second law of motion by reflecting on the implications of the first law. I analyze another argument in the Waste book which reveals that Newton also arrived at the second law by another very different route. On this route, it is the consideration of the third law and the principle of conservation of motion—and not the first law—that prompts Newton to formulate the second law. The existence of these two routes is significant because each employs a distinct kind of reasoning about forces. Whereas the Nicholas-Westfall route via the principle of inertia bears the mark of Descartes’s influence, the alternative route proceeds from the action-reaction principle, which is widely regarded as an original Newtonian contribution to mechanics. In the course of exploring this alternate route to the second law, the origins and justification of the third law are examined.     

Naturally occurring pea diamine oxidase inhibitors obtained fromSorghum vulgare during germination

Summary During germination ofSorghum vulgare seeds, inhibitors of pea diamine oxidase appeared in the embryos. One was heat labile, dialysable and inhibited the enzyme in vitro, while another was heat stable and inhibited the enzyme synthesis when pea seeds were soaked and allowed to germinate in the extract containing the inhibitors.Acknowledgments. We thank Dr S.K. Srivastava for his helpful suggestions and access to his facilities.