Einstein,Nordström and the early demise of scalar,Lorentz-covariant theories of gravitation

Conclusion The advent of the general theory of relativity was so entirely the work of just one person — Albert Einstein — that we cannot but wonder how long it would have taken without him for the connection between gravitation and spacetime curvature to be discovered. What would have happened if there were no Einstein? Few doubt that a theory much like special relativity would have emerged one way or another from the researchers of Lorentz, Poincaré and others. But where would the problem of relativizing gravitation have led? The saga told here shows how even the most conservative approach to relativizing gravitation theory still did lead out of Minkowski spacetime to connect gravitation to a curved spacetime. Unfortunately we still cannot know if this conclusion would have been drawn rapidly without Einstein's contribution. For what led Nordström to the gravitational field dependence of lengths and times was a very Einsteinian insistence on just the right version of the equality of inertial and gravitational mass. Unceasingly in Nordström's ear was the persistent and uncompromising voice of Einstein himself demanding that Nordström see the most distant consequences of his own theory.     

Hensen's node — The ’Organizer’ of the amniote embryo

Conclusion If the hundred years of study on theHensen's node — i.e. on gastrulation and early determination of the embryos of amniote vertebrates — teach anything, they teach in the first place how limited and fragmentary our knowledge is about one of the most central problems of the whole developmental biology. We know that the events in early amniote development — or early avian development, on which our data and ideas are nearly all based — in many ways resemble those in early Amphibian development, which is only slightly better understood, but we also know that direct extrapolations from anamniotes to amniotes cannot be made without proper reservations and without studying the amniote embryos themselves. And we have practically no idea of what is really going on in the cells of the blastoderm when they move, invaginate, induce or are induced, interact, become determined and begin their differentiation. We know that at the stages of gastrulation, the node, and indeed the whole blastoderm, is in a very labile state and can be regulated in many ways to produce a harmonious whole — or a monster — although we only understand very poorly the modes of this regulation. The progress made during the decades, and particularly in recent years, shows, however, that useful information is accumulating to produce a coherent picture, and there is no reason to be pessimistic.Dedicated to ProfessorEtienne Wolff on the occasion of his retirement.     

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.     

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.     

Untersuchungen über die Tumorbildung beim amphidiploiden Bastard vonNicotiana langsdorffii undNicotiana glauca

Summary The occurrence of tumours of the amphidiploid hybrid ofNicotiana glauca andN. langsdorfii can — as was found in organculture — be connected with the specific formation of callus ofN. glauca. Those factors ofN. glauca which hinder callus growth, are obviously disturbed by the hybridization withN. langsdorffii, so thatN. glauca's potency in forming callus can manifest itself uninhibitedly and thus produce tumours.

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Den Herren Prof. Dr.G. de Lattin (Zoologisches Institut der Universität des Saarlandes) und Prof. Dr.F. Anders (Genetisches Institut der Justus Liebig-Universität, Giessen) bin ich für die Förderung dieser Arbeit zu grösstem Dank verpflichtet.     

Essais de solubilisation et de détoxification de la Tyrothricine

Summary As Tyrothricin —Dubos's discovery of the antibiotic agent extracted from cultures ofB. brevis — does not give true aqueous solutions and retains, in the colloïdal state of the usually employed solutions, toxic properties for polymorphonuclear blood cells, we have attempted to effect the solubilization and detoxification of this compound. Treatment with formalin in given proportions results in making it water-soluble. The action of the formalin-treated compound on blood cells suspended in Ringer's solution seems to show a loss of toxicity. Subcutaneous and intramuscular injections in mice do not give visible general toxic effects, and the experiments incite to further investigations in this direction.     

Prelude to dimension theory: The geometrical investigations of Bernard Bolzano

This paper treats Bernard Bolzano's (1781–1848) investigations into a fundamental problem of geometry: the problem of adequately defining the concepts of line (or curve), surface, solid, and continuum. Bolzano's interest in this problem spanned most of his creative lifetime. In this paper a full discussion is given of the philosophical and mathematical motivation of Bolzano's problem as well as his two solutions to the problem. Bolzano's work on this part of geometry is relevant to the history of modern mathematics, because it forms a prelude to the more recent development of topological dimension theory.     

Neue Gesichtspunkte zum 5. Buch Euklids

Summary The author's purpose is to read the main work of Euclid with modern eyes and to find out what knowledge a mathematician of today, familiar with the works of V. D. Waerden and Bourbaki, can gain by studying Euclid's theory of magnitudes, and what new insight into Greek mathematics occupation with this subject can provide.The task is to analyse and to axiomatize by modern means (i) in a narrower sense Book V. of the Elements, i.e. the theory of proportion of Eudoxus, (ii) in a wider sense the whole sphere of magnitudes which Euclid applies in his Elements. This procedure furnishes a clear picture of the inherent structure of his work, thereby making visible specific characteristics of Greek mathematics.After a clarification of the preconditions and a short survey of the historical development of the theory of proportions (Part I of this work), an exact analysis of the definitions and propositions of Book V. of the Elements is carried out in Part II. This is done word by word. The author applies his own system of axioms, set up in close accordance with Euclid, which permits one to deduce all definitions and propositions of Euclid's theory of magnitudes (especially those of Books V. and VI.).In this way gaps and tacit assumptions in the work become clearly visible; above all, the logical structure of the system of magnitudes given by Euclid becomes evident: not ratio — like something sui generis — is the governing concept of Book V., but magnitudes and their relation of having a ratio form the base of the theory of proportions. These magnitudes represent a well defined structure, a so-called Eudoxic Semigroup with the numbers as operators; it can easily be imbedded in a general theory of magnitudes equally applicable to geometry and physics.The transition to ratios — a step not executed by Euclid — is examined in Part III; it turns out to be particularly unwieldy. An elegant way opens up by interpreting proportion as a mapping of totally ordered semigroups. When closely examined, this mapping proves to be an isomorphism, thus suggesting the application of the modern theory of homomorphism. This theory permits a treatment of the theory of proportions as developed by Eudoxus and Euclid which is hardly surpassable in brevity and elegance in spite of its close affinity to Euclid. The generalization to a classically founded theory of magnitudes is now self-evident.

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Vorgelegt von J. E. Hofmann     

“... in Christophorum Clavium de Contactu Linearum Apologia” Considerazioni attorno alla polemica fra Peletier e Clavio circa l'angolo di contatto (1579–1589)

Summary In this work 1 focus my attention upon the question of the angle of tangency in the XVI^th Century, especially in the polemic between J. Peletier and Chr. Clavius (1579–1589). The interest in the question favored deliberation about the theory of proportions, the principle of Eudoxus-Archimedes and the set of angles of tangency (this is a non-Archimedian set); there were problems about logical proofs and geometrical proofs.

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Memoria presentata da H. Freudenthal     

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     

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))     

Aus der Chemie der Naturstoffe

Summary This lecture was held in Zürich to commemorate the 70^th birthday of Prof.Paul Karrer; it briefly outlines his life-work as a scientist and then reviews, in greater detail, some of his important work in various fields: vegetable dyestuffs (carotenoids), vitamins (particularly vitamins A, E and K) and curare alkaloids.As is the purpose of this lecture, a review is also given of the author's own work: ergot alkaloids and their derivatives; cardiac glycosides of squill, digitalis etc.; and finally, the most recent results of research on chlorophyll — the crystallization of natural chlorophylla andb after many years of endeavour.

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ErstePaul-Karrer-Vorlesung, gehalten im Rahmen der öffentlichen Feier zum 70. Geburtstag von Prof.Paul Karrer, am 25. April 1959 in der Aula der Universität Zürich.     

“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.     

Rapporto fra “metodo” e “contenuti matematici” in P. Gesualdo Melacrinò da Reggio Calabria

Summary Father Gesualdo Melacrinò (1725–1803), from Reggio Calabria (Italy), is an unknown Capuchin philosopher and theologian, who produced several works at the time he was teaching (only five years, from 1748–53); these works contained an original approach to the foundations and philosophy of mathematics. His main purpose was to reconciliate the classical traditions with the reality of his time. For him, this included a critical examination of the scholastic curriculum and a new orientation towards the methodological relevance of mathematics for all other sciences, especially for philosophy. Concerning mathematics, he emphasized the necessity of a basic revision and logical reconstruction of its foundations. This paper provides a comparative examination of Melacrinò's work with reference to its cultural and historical environment.     

Antibacterial activity ofPenicillium divergens bainier

Zusammenfassung Aus den Kulturfiltraten des SchimmelpilzesP. divergens Bainier wurden drei antibiotische Stoffe — Patulin, Gentisinalkohol und Gentisinsäure — isoliert.     

Fluorescence of blood cells of the tunicatesPhallusia mamillata andCiona intestinalis

Zusammenfassung Von den Blutzellen derPhallusia mamillata Cuvier zeigen nur die stark vakuolisierten (compartment cells) im UV-Licht eine stabile blaue Fluoreszenz ( _max =5200 und 4600 Å). Sie ist in den Zellgranula lokalisiert. Bei den Blutzellen vonCiona intestinalis L. tritt dagegen eine gelbe Fluoreszenz ( _max = 5900, 5200 und 4600 Å) auf, die nur von den Vanadocyten ausgeht. Diese Fluoreszenz, welche auch von den Testazellen der Oocyten gegeben wird, geht innerhalb einiger Minuten in die blaue Fluoreszenz über.

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This work has been carried out in the Stazione Zoologica, Napoli (director Dr.P. Dohrn) and in the Istituto di Biologia Generale e Genetica della Università di Napoli (director Prof. Dr.B. de Lerma). —M. de Vincentiis wishes to thank Dr,P. Dohrn for placing at his disposal a working place of the Consiglio Nazionale delle Ricerche, Roma. —W. Rüdiger thanks sincerely the Deutsche Forschungsgemeinschaft, Bad Godesberg, for providing grants, and Prof. Dr.H.-J. Bielig for his interest.     

The nature of carbonate contents in tooth mineral

Zusammenfassung Der Aufbau der Zahnhartsubstanz ist im Verlaufe ihrer Bildung durch mehrere Faktoren — u.a. Begleitionen, Texturvorlage (Proteinmatrix) — bestimmt. Der Einfluss des Carbonatgehalts wurde in diesem Zusammenhang besonders im Hinblick auf dessen kristallchemische Funktion bei der Zahnmineralisation (parakristalline Struktur des teilweise isomorph substituierten Apatitis) untersucht.

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See preceding communication:H. Newesely andE. Hayek, Exper.19, 459 (1963).     

A history of the axiomatic formulation of probability from Borel to Kolmogorov: Part I

This paper, the first of two, traces the origins of the modern axiomatic formulation of Probability Theory, which was first given in definitive form by Kolmogorov in 1933. Even before that time, however, a sequence of developments, initiated by a landmark paper of E. Borel, were giving rise to problems, theorems, and reformulations that increasingly related probability to measure theory and, in particular, clarified the key role of countable additivity in Probability Theory.This paper describes the developments from Borel's work through F. Hausdorff's. The major accomplishments of the period were Borel's Zero-One Law (also known as the Borel-Cantelli Lemmas), his Strong Law of Large Numbers, and his Continued Fraction Theorem. What is new is a detailed analysis of Borel's original proofs, from which we try to account for the roots (psychological as well as mathematical) of the many flaws and inadequacies in Borel's reasoning. We also document the increasing realization of the link between the theories of measure and of probability in the period from G. Faber to F. Hausdorff. We indicate the misleading emphasis given to independence as a basic concept by Borel and his equally unfortunate association of a Heine-Borel lemma with countable additivity. Also original is the (possible) genesis we propose for each of the two examples chosen by Borel to exhibit his new theory; in each case we cite a now neglected precursor of Borel, one of them surely known to Borel, the other, probably so. The brief sketch of instances of the Cantelli lemma before Cantelli's publication is also original.We describe the interesting polemic between F. Bernstein and Borel concerning the Continued Fraction Theorem, which serves as a rare instance of a contemporary criticism of Borel's reasoning. We also discuss Hausdorff's proof of Borel's Strong Law (which seems to be the first valid proof of the theorem along the lines sketched by Borel).In retrospect, one may ask why problems of geometric (or continuous) probability did not give rise to the (Kolmogorov) view of probability as a form of measure, rather than the study of repeated independent trials, which was Borel's approach. This paper shows that questions of geometric probability were always the essential guide to the early development of the theory, despite the contrary viewpoint exhibited by Borel's preferred interpretation of his own results.     

Zur Pathogenese des Urämiesyndroms1. Über den Einfluss von Tyramin auf die Acetoinsynthese aus Brenztraubensäure in Rattenleberhomogenat2

Summary Tyramine enhanced the production of acetoin from pyruvate in rat liver homogenates. A stimulation of acetoin synthesis was only observed, when tyramine was oxidized during the incubation. Tyrosol (p-hydroxyphenylethanol) stimulated acetoin synthesis whereasp-hydroxyphenylacetic acid and ammonia were ineffective.

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Mit Unterstützung des »Schweizerischen Nationalfonds» und der Firma F. Hoffmann-La Roche & Co. AG, Basel.

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8. Mitteilung. 1. Mitt.:H. Thölen, F. Bigler undH. Staub, Path. Microbiol. (Basel)24, 262 (1961). — 2. Mitt.:F. Bigler, H. Thölen undH. Staub, Helv. physiol. Acta19, C 11 (1961). — 3. Mitt.:H. Thölen, F. Bigler undH. Staub, Exper.17, 359 (1961). — 4. Mitt.:F. Bigler, H. Thölen undH. Staub, Schweiz. med. Wschr.91, 1259 (1961). — 5. Mitt.:H. Thölen, F. Bigler, A. Heusler, W. Stauffacher undH. Staub, Exper.18, 454 (1962). — 6. Mitt.:F. Bigler, H. Thölen undH. Staub, Schweiz. med. Wschr.92, 746 (1962). — 7. Mitt.:F. Bigler, H. Thölen undH. Staub, in Vorbereitung.     

Geometrical constructions equivalent to non-linear algebraic transformations of the plane in Newton's early papers

Summary The theory of constructive formation of plane algebraic curves in Newton's writings is discussed in § 1: the apparatus by which Newton forms the curves, Newton's theorems on forming unicursal curves, his theory of conics, and his theory of (m, n) correspondence. Special Cremona plane and space transformations obtained by Newton's organic method are dealt with in § 2. The article ends with § 3, which shows two different directions in the theory of the constructive formation of plane algebraic curves in the XVIII-XIXth centuries. A synopsis is appended.Abbreviations MPN The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside, Vols. 1–3, Cambridge, 1967–1969 - Hudson H. Hudson, Cremona Transformations in Plane and Space, Cambridge, 1927 - PT (abridged) Philosophical Transactions of the Royal Society 1665–1800 (abridged), London, 1809 - Andreev ₁ K. A. Andreev, On geometrical correspondences ... (in Russian), Moscow, 1879 - Andreev ₂ K. A. Andreev, On the Geometrical Formation of Plane Curves (in Russian), Kharkov, 1875