P.S. Laplace's work on probability

Taken together with my previous articles [77], [80] devoted to the history of finite random sums and to Laplace's theory of errors, this paper sheds sufficient light on the whole work of Laplace in probability. Laplace's theory of probability is subdivided into theory of probability proper, limit theorems and mathematical statistics (not yet distinguished as a separate entity). I maintain that in its very design Laplace's theory of probability is a discipline pertaining to natural science rather than to mathematics. I maintain also the idea that the so-called Laplacian determinism was no hindrance to applications of his theory of probability to natural science and that one of his utterances in this connection could have well been made by Maxwell's contemporaries.Two possible reasons why the theory of probability stagnated after Laplace's work are singled out: the absence of new fields of application and, also, the insufficient level of mathematical abstraction used by Laplace. For all his achievements, I reach the general conclusion that he did not originate the theory of probability as it is now known. Dedicated to the memory of my Father, Boris A. Sheynin (1898–1975), the first generation of the Russian revolution Cette inégalité [Lunaire] quoique indiquée par les observations, était négligée par le plus grand nombre des astronomes, parce qu'elle ne paraissait pas résulter de la théorie de la pesanteur universelle. Mais, ayant soumis son existence au Calcul des Probabilités, elle me parut indiqués avec une probabilité si forte, que je crus devoir en rechercher la cause.(P. S. Laplace (Théor. anal. prob., p. 361))     

Kepler,Tycho, and the ‘Optical Part of Astronomy’: the genesis of Kepler's theory of pinhole images

In the last half of the 16^th century, the method of casting a solar image through an aperture onto a screen for the purposes of observing the sun and its eclipses came into increasing use among professional astronomers. In particular, Tycho Brahe adapted most of his instruments to solar observations, both of positions and of apparent diameters, by fitting the upper pinnule of his diopters with an aperture and allowing the lower pinnule with an engraved centering circle to serve as a screen. In conjunction with these innovations a method of calculating apparent solar diameters on the basis of the measured size of the image was developed, but the method was almost entirely empirically based and developed without the assistance of an adequate theory of the formation of images behind small apertures. Thus resulted the unsuccessful extension of the method by Tycho to the quantitative observation of apparent lunar diameters during solar eclipses. Kepler's attention to the eclipse of July 1600, prompted by Tycho's anomalous results, gave him occasion to consider the relevant theory of measurement. The result was a fully articulated account of pinhole images. Dedicated to the memory of Ronald Cameron Riddell (29.1.1938–11.1.1981)     

The conceptual import of Carnot's theorem to the discovery of the entropy

Summary Among many other things, Carnot stated a principle and proved a theorem. In 1850, Clausius corrected Carnot's theory, modifying it according to Joule's principle. He might have considered a corollary of the theorem as the mathematical formulation of Carnot's principle. We challenge the corollary: it is based on hidden assumptions, nor is it true for all cycles. Clausius realized the corollary's lack of generality, but on different grounds. In 1854, he generalized the theorem, and gave an (other) expression to Carnot's principle. We analyze Clapeyron's account of Carnot's theory, Thomson's account of 1849 and some of Clausius belated comments on his 1850 paper, as well Clausius' paper of 1854. We hope that they shed light on the corollary's tacit hypotheses and on the meaning of Carnot's principle. It is our contention: Clausius took seriously a contemporary meaning of the principle, and looked for a condition of integrability that could express recovery of the initial conditions of the reservoirs. Furthermore, he seems to have had some prior knowledge of the form the expression of the principle should take. Actually, this was the theory's natural candidate.     

Die Entwicklung der Valenzlehre und Alfred Werner

Summary Surveying the various concepts of valency which have been put forward sinceDalton for the classification of chemical phenomena, it is found that the principles have been either dualistic (Berzelius, Blomstrand, Arrhenius, Kossel) or unitarian (Gerhard, Couper, Kekulé). The phenomena of inorganic chemistry can be classified only by using dualistic concepts, whereas unitarian systems proved to be superior for the phenomena of organic chemistry. In the conceptions of G. N.Lewis and N.Sidgwick, a combination of dualistic and unitarian concepts in one theory was achieved by distinguishing two types of bonds (mobile-immobile, polar-non-polar, ioniccovalent). With the octet rule, ions as well as molecules (uncharged and charged) may be derived and it is readily understood that bonds may vary from extreme polarity to non-polar links.The coordination theory ofWerner neither fits into the dualistic nor the unitarian class of valency principles.Werner derives the compounds by using principal and auxiliary valencies (Haupt- und Nebenvalenzen) and distinguishes addition and insertion compounds (Anlagerungs- und Einlagerungsverbindungen). However, he avoids making any statement concerning the nature of the bonds, which makes his system very adaptable but difficult to grasp. Today it is readily understood thatWerner's principal valency characterizes the stoichiometry and his coordination number characterizes the structure of the compound in question without making any statement about the nature of the bonds involved. Because of thatWerner's concepts have survived and are indispensable even today, in spite of the rise of atomic physics which has changed our views on the nature of the chemical bonds so drastically.

---

---

Paul-Karrer-Vorlesung, gehalten am 22. Juni 1966 zum Anlass der hundertsten Wiederkehr des Geburtstages vonAlfred Werner, dem Vorgänger von Professor Karrer auf dem Lehrstuhl für Allgemeine Chemie der Universität Zürich.     

Newton and the classical theory of probability

Summary Probabilistic ideas and methods from Newton's writings are discussed in § 1: Newton's ideas pertaining to the definition of probability, his probabilistic method in chronology, his probabilistic ideas and method in the theory of errors and his probabilistic reasonings on the system of the world. Newton's predecessors and his influence upon subsequent scholars are dealt with in §2: beginning with his predecessors the discussion continues with his contemporaries Arbuthnot and De Moiver, then Bentley. The section ends with Laplace, whose determinism is seen as a development of the Newtonian determinism.An addendum is devoted to Lambert's reasoning on randomness and to the influence of Darwin on statistics. A synopsis is attached at the end of the article.Abbreviations PT abridged Philosophical Transactions of the Royal Society 1665–1800 abridged. London, 1809 - Todhunter I. Todhunter, History of the mathematical theory of probability, Cambridge, 1865 To the memory of my mother, Sophia Sheynin (1900–1970)     

“Will someone say exactly what the H-theorem proves?” A study of Burbury's Condition A and Maxwell's Proposition II

Summary Many historians of science recognize that the outcome of the celebrated debate on Boltzmann's H-Theorem, which took place in the weekly scientific journal Nature, beginning at the end of 1894 and continuing throughout most of 1895, was the recognition of the statistical hypothesis in the proof of the theorem. This hypothesis is the Stosszahlansatz or hypothesis about the number of collisions. During the debate, the Stosszahlansatz was identified with another statistical hypothesis, which appeared in Proposition II of Maxwell's 1860 paper; Burbury called it Condition A. Later in the debate, Bryan gave a clear formulation of the Stosszahlansatz. However, the two hypotheses are prima facie different. Burbury interchanged them without justification or even warning his readers. This point deserves clarification, since it touches upon subtle questions related to the foundation of the theory of heat. A careful reading of the arguments presented by Burbury and Bryan in their various invocations of both hypotheses can clarify this technical point. The Stosszahlansatz can be understood in terms of geometrical invariances of the problem of a collision between two spheres. A byproduct of my analysis is a clarification of the debate itself, which is apparently obscure.     

The problem of the invariance of dimension in the growth of modern topology,part II

Summary This work examines the historical origins of topological dimension theory with special reference to the problem of the invariance of dimension. Part I, comprising chapters 1–4, concerns problems and ideas about dimension from ancient times to about 1900. Chapter 1 deals with ancient Greek ideas about dimension and the origins of theories of hyperspaces and higher-dimensional geometries relating to the subsequent development of dimension theory. Chapter 2 treatsCantor's surprising discovery that continua of different dimension numbers can be put into one-one correspondence and his discussion withDedekind concerning the discovery. The problem of the invariance of dimension originates with this discovery. Chapter 3 deals with the early efforts of 1878–1879 to prove the invariance of dimension. Chapter 4 sketches the rise of point set topology with reference to the problem of proving dimensional invariance and the development of dimension theory. Part II, comprising chapters 5–8, concerns the development of dimension theory during the early part of the twentieth century. Chapter 5 deals with new approaches to the concept of dimension and the problem of dimensional invariance. Chapter 6 analyses the origins ofBrouwer's interest in topology and his breakthrough to the first general proof of the invariance of dimension. Chapter 7 treatsLebesgue's ideas about dimension and the invariance problem and the dispute that arose betweenBrouwer andLebesgue which led toBrouwer's further work on topology and dimension. Chapter 8 offers glimpses of the development of dimension theory afterBrouwer, especially the development of the dimension theory ofUrysohn andMenger during the twenties. Chapter 8 ends with some concluding remarks about the entire history covered. Dedicated to Hans Freudenthal     

Interactions between mechanics and differential geometry in the 19th century

Conclusion 79. This study of the interaction between mechanics and differential geometry does not pretend to be exhaustive. In particular, there is probably more to be said about the mathematical side of the history from Darboux to Ricci and Levi Civita and beyond. Statistical mechanics may also be of interest and there is definitely more to be said about Hertz (I plan to continue in this direction) and about Poincaré's geometric and topological reasonings for example about the three body problem [Poincaré 1890] (cf. also [Poincaré 1993], [Andersson 1994] and [Barrow-Green 1994]). Moreover, it would be interesting to find out how the 19^th century ideas discussed here influenced the developments in the 20^th century. Einstein himself is a hotly debated case.Yet, despite these shortcommings, I hope that this paper has shown that the interactions between mechanics and differential geometry is not a 20^th century invention. Klein's view (see my Introduction) that Riemannian geometry grew out of mechanics, more specifically the principle of least action, cannot be maintained. On the other hand, when Riemannian geometry became known around 1870 it was immediately used in mechanics by Lipschitz. He began a continued tradition in this field, which had several elements in common with the new view of mechanics conceived by the physicists and explicitly carried out by Hertz.Before 1870 we found only scattered interactions between differential geometry and mechanics and only direct ones for systems of two or three degrees of freedom. For more degrees of freedom the geometrical ideas were in some interesting cases taken over by analogy, but these analogies did not lead to formal introduction of geometries of more than three dimensions.     

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.

---

---

Vorgelegt von C. Truesdell     

Reconstruction of a Greek table of chords

Summary R. R. Newton has shown that Ptolemy's table of solar declinations (Almagest I, 15) was not computed from Ptolemy's own table of chords. Newton explains this by assuming that Ptolemy copied his table of declinations from an earlier source, and that originally the table has been computed by means of a less accurate table of chords.In the present paper I shall venture a tentative reconstruction of the method of computation of this ancient table of chords. The clue to this reconstruction is a recursion formula which allows a rapid calculation of the chords belonging to arcs of 1°, 2°, ... in a circle. This recursion formula, which was suggested to me by a verse in the ryabhtya of ryabhata, can be deduced from a theorem of Archimedes concerning a certain sum of chords in a circle. I suppose that this recursion formula was used by Apollonius of Perga in order to obtain a table of chords, and that this table of chords was used by a Greek author (possibly Apollonios himself or Hipparchos) to calculate the table of solar declinations used by Ptolemy. If this hypothesis is adopted, the errors in Ptolemy's table can be explained.     

Isaac Newton and the problem of the earth's shape

In this article I discuss the theory of the earth's shape presented by Isaac Newton in Book III of his Principia. I show that the theory struck even the most reputable continental mathematicians of the day as incomprehensible. I examine the many obstacles to understanding the theory which the reader faced — the gaps, the underived equations, the unproven assertions, the dependence upon corollaries to practically incomprehensible theorems in Book I of the Principia and the ambiguities of these corollaries, the conjectures without explanations of their bases, the inconsistencies, and so forth. I explain why these apparent drawbacks are, historically considered, strengths of Newton's theory of the earth's shape, not weaknesses.     

Cystinurie undl -cystinsteinbildung beim hund

Summary Cystinuria andl-Cystine lithiasis, is a rather rare hereditary metabolic disease in human beings. Due to the high purity ofl-Cystine stones formed in the urinary tract, they can serve as ideal models for studies on the chemical dissolution of kidney stones in general. By systematic examinations, it is possible to find for these purposes, dogs in which a cystinuria is present.

---

---

Herrn Prof.Forenbacher, Vet. Med. Fakultät der Universität Zagreb, danken wir für die Übersendung von Steinen, und FrauM. Stoffers für die technische Mitarbeit.     

Some surprising facts about (the problem of) surprising facts: (from the Dusseldorf Conference,February 2011)

A common intuition about evidence is that if data x have been used to construct a hypothesis H, then x should not be used again in support of H. It is no surprise that x fits H, if H was deliberately constructed to accord with x. The question of when and why we should avoid such “double-counting” continues to be debated in philosophy and statistics. It arises as a prohibition against data mining, hunting for significance, tuning on the signal, and ad hoc hypotheses, and as a preference for predesignated hypotheses and “surprising” predictions. I have argued that it is the severity or probativeness of the test—or lack of it—that should determine whether a double-use of data is admissible. I examine a number of surprising ambiguities and unexpected facts that continue to bedevil this debate.     

Identification of teleost gonadotrope cells using methallibure (I.C.I. 33, 828) and thiourea

Zusammenfassung Die versuchsweise Identifizierung gonadotroper Zellen der Teleostier-Hypophyse (Plectoplites ambiguus) gelang nach Behandlung mit Methallibure (I.C.I. 33, 828) und Thiourea.

---

---

The work was supported by a University of Sydney Research Grant. I thank Mr.J. Collard, of the Veterinary Division of I.C.I.A.N.Z. Ltd., for supplies of Methallibure and Mrs.M. Weinstock for her technical assistance.     

Über die Konstitution des Visamminols

Summary The structure of Visamminol (I), a compound isolated fromAmmi visnaga bySmith, Pucci, andBywater, has been elucidated by degradation and by a comparison of the UV.-spectra of I and its derivatives with those of other chromones.     

Pseudomonas aeruginosa cause epidemic disease in the milkweed bug,Oncopeltus fasciatus dallas (Insecta,Heteroptera)

Summary Pseudomonas aeruginosa was recognized as the causative organism of an epidemic disease occurring in a laboratory breed ofOncopeltus fasciatus. The infection probably occurs peroral and is favoured by high temperature and humidity.Pseudomonas aeruginosa destroys the fat body of the bug.For her interest and discussion I thank Dr.G. Hausner, Miss I. vonGraevenitz and Miss.H. Schilling gave techincal support.     

Der Briefwechsel von E. S. von Fedorow und A. Schoenflies, 1889–1908

Ohne Zusammenfassung Vorgelegt von B. L. van der Waerden Herrn Professor I. I. Schafranovsky, Berginstitut Leningrad, in Dankbarkeit gewidmet     

Metabolically regulated cyclical contractures in microinjectedSpirostomum: A pharmacological study

Summary Spirostomum was treated extracellularly and intracellularly with a range of metabolites to investigate the intracellular regulation of cyclic calcium movements. The results indicate, close links between calcium movements and mitochondrial metabolism.We are grateful to Dr.A. Gaudemar, Institut de Chimie des Substances Naturelle, Gif-sur-Yvette, France for a gift of bongkrekic acid, to Dr.D. C. Aldridge, Biochemistry Dept., I. C. I. Ltd., Macclesfield, U. K. for a gift of avenceolide and toE. M. Ettienne for many hours of discussion. Dr.R. B. Hawkes is a Visiting Research Fellow at the Hebrew University of Jerusalem.     

J. Zaragosa's centrum minimum,an early version of barycentric geometry

Summary Using the properties of the Centre of Gravity to obtain geometrical results goes back to Archimedes, but the idea of associating weights to points in calculating ratios was introduced by Giovanni Ceva in De lineis rectis se invicem secantibus: statica constructio (Milan, 1678). Four years prior to the publication of Ceva's work, however, another publication, entitled Geometria Magna in Minimis (Toledo, 1674), 2 appeared stating a method similar to Ceva's, but using isomorphic procedures of a geometric nature. The author was a Spanish Jesuit by the name of Joseph Zaragoza.Endeavouring to demonstrate an Apollonius' geometrical locus, Zaragoza conceived his idea of centrum minimum — a point strictly defined in traditional geometrical terms — the properties of which are characteristic of the Centre of Gravity. From this new concept, Zaragoza developed a theory that can be considered an early draft of the barycentric theory that F. Mobius was to establish 150 years later in Der barycentrische Calcul (Leipzig, 1827).Now then, whereas Ceva's work was rediscovered and due credit was given him, to this day Zaragoza's work has remained virtually unnoticed.     

Bazzanenol,a new sesquiterpene alcohol having a skeleton of Bicyclo[5.3.1] undecane system from hepaticae,Bazzania pompeana (Lac.) Mitt

Zusammenfassung Isolierung und Strukturaufklärung eines neuen Sesquiterpenalkohols ausBazzania pompeana (Lac.) Mitt.

---

---

Studies on chemical constituents from Hepaticae, Part III: S.Hayashi, A.Matsuo and T.Matsuura, Tetrahedron Letters,1969, 1599 and ref.² are regarded as Part I and II.