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.     

Die physikalische Kieme der Wasserinsekten

Summary The air stores carried by a number of aquatic insects have: a) a hydrostatic function (Brocher, Oortwijn-Botjes, Thorpe, andCrisp); b) the function of an oxygen store (Ege, de Ruiter et al.) and c) the function of a physical gill (Strauss-Durckheim, Ege, etc.). The fact that oxygen is taken up from water with the aid of an air bubble was demonstrated forNotonecta by comparing the life time of insects with and without physical gill (while replenishing the oxygen store from the air was prevented) byEge, and forCorixa byPopham, whileVlasblom determined the oxygen uptake from water with and without air bubble forNotonecta, Naucoris, Corixa, Sigara andNepa. Nepa andSigara can take up considerable quantities of oxygen by cutaneous respiration.During the summer, the gill function of the air store ofNotonecta andNaucoris is of importance only when a water current passes along the animal, caused by ventilation movements of the legs (de Ruiter et al.). At low temperatures, however, the metabolic rate is so low that in many instances the physical gill provides the oxygen required without ventilation movements.An apparatus for the simultaneous determination of oxygen uptake from air and water (Wolvekamp andVlasblom) gave results that provided a means of evaluating the importance of the physical gill function.In some cases, the air store, although in direct contact with the water, does not need to be replenished. InAphelocheirus andElmis, the negative pressure in the bubble, caused by oxygen consumption and the diffusing out of part of the nitrogen, is compensated for by the mechanical resistance of a feltwork of thin hairs and the surface tension of the boundary layer of the water (Thorpe andCrisp). In the African beetle,Potamodytes, the unprotected air bubble is permanent because the strong river currents produce a lowered pressure around the animal according toBernoulli's principle (Stride).     

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.     

Der Mathematiker Abraham de Moivre (1667–1754)

Summary Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them.The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular equations, the roots of which can be written in the form . He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos +i sin ) ⁿ =cos n +i sin n and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form.In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability.The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution.The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of Probability of life. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables.

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Abkürzungen a.a.O. am angegebenen Ort = Verweis auf das nach Verfassern alphabetisch geordnete Literaturverzeichnis. Eine vor a.a.O. in runden Klammern angegebene Zahl kennzeichnet die entsprechende Nummer der im Literaturverzeichnis aufgeführten Arbeiten eines Autors. - AC Ars conjectandi = Jakob Bernoulli (4) a.a.O. - AE Acta Eruditorum - a.S. alter Stil⁴⁷ - BM Bibliotheca Mathematica - DMV Deutsche Mathematiker-Vereinigung - JL Journal Literaire - MA Miscellanea Analytica, London 1730 - n.S. neuer Stil⁴⁷ - PT Philosophical Transactions of the Royal Society of London - r.F. rekurrente Folge - r.R. rekurrente Reihe - SMA Miscellaneis Analyticis Supplementum, London 1730 - v. veröffentlicht (nur im Briefverzeichnis verwendet) Prof. Dr. Kurt Vogel zum 80. Geburtstag Vorgelegt von J. E. Hofmann     

Démonstration du caractère géographique de la parthénogénèse deSaga pedo Pallas et de sa polyploïdie,par comparaison avec les espèces bisexuéesS. ephippigera Fisch. etS. gracilipes Uvar

Summary The males of two species of Palestine,Saga ephippigera Fisch. andS. gracilipes Uvar have respectively 33 and 31 chromosomes in the diploid state.S. pedo Pallas, a parthenogenetic thelytoc species largely distributed in Europe, has 68 chromosomes and probably represents a tetraploid. The cells of the three species have identical dimensions and the polyploidS. pedo is even the smallest in size.     

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)     

Curamycin. II. Structure of the hydrolysis products ‘curacin’ and ‘d-curamicose’

Zusammenfassung Curacin, die chlorhaltige Fraktion der milden Hydrolyse des Antibiotikums Curamycin, wurde durch ihre chemischen und physikalischen Eigenschaften als 4-O-Dichlor-iso-everninyl-2-deoxy-d-rhamnose aufgeklärt. Ausserl-Lyxose und 4-O-Methyl-d-fucose besitzt auch das Curamycin ein drittes Monosaccharid,d-Curamicose, welches als 2,6-Di-O-methyl-d-mannose identifiziert wurde.     

Synthesis and structure of Fungisporin

Zusammenfassung Die Struktur von Fungisporin, eines Zyklopeptides aus Sporen verschiedener Spezies vonPenicillium undAspergillus-Arten, wird durch Synthese und Vergleich mit dem Naturprodukt als die eines Zyklotetrapeptides, cyclo-(l-Phe-d-Val-l-Val-d-Phe-), bewiesen.     

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.     

Nachweis von Scilliglaucosidin in den Zwiebeln vonBowiea volubilis Harvey

Summary Hellebrigenin was converted to Scilliglaucosidin-19-ol and 3-Epi-Scilliglaucosidin-19-ol. This proves the correctness of the assumption ofStoll et al. ³ that the aldehydic group of Scilliglaucosidin is in position C-10.Comparison of a reduction product of Nabogenin, a substance isolated earlier from the bulbs ofBowiea volubilis Harvey, with Scilliglaucosidin-19-ol and 3-Epi-Scilliglaucosidin-19-ol showed its identity with the first named compound. This proves that the so called Nabogenin was a mixture consisting mainly of Scilliglaucosidin.

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8. Mitteilung über die Glykoside vonBowiea vocubilis Harvey und 162. Mitteilung über Glykoside und Aglykone.

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7. Mitt.:A. Katz, Helv. chim. Acta38, 1565 (1955).

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161. Mitt.:H. Kündig-Hegedüs undO. Schindler, Helv. chim. Acta39, 904 (1956).     

Stéréochimie d'acides grasα-hydroxylés isolés d'une souche deStreptomyces

Summary A strain ofStreptomyces contains a mixture (ca. 3:1) of 2d-hydroxy-12l-methyltetradecanoic and 2d-hydroxy-13-methyltetradecanoic acids; it has the same properties as a similar mixture prepared by synthesis.

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11e Communication sur la chimie des micro-organismes; 10e communication:C. Lacave, J. Asselineau etR. Toubiana, Europ. J. Biochem.2, 37 (1967).     

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     

“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.     

Interspecific protoplast fusion and complementation inaspergilli

Summary Protoplast fusion and nutritional complementation between auxotrophic mutants ofAspergillus nidulans andAspergillus fumigatus has been achieved. It is concluded that the nutritional complementation may be due to interspecific aneuploidy.The authors thank Mr.L. Manczinger and Mr.Gy. Oravecz for producing and characterizing the required mutants; Dr.D. Goldstein for providing the strainA. nidulans R. 21; Dr.D. Kerridge for the wild-type strainA. fumigatus 5085; and Mr.L. Nagy, MissÉva Sziráki and MissMária Pölös for skilful technical assistance.     

Synthesis of Seselin and its hydroderivatives

Zusammenfassung Die Synthese des Naturstoffes Tetrahydroseselin aus der FruchtSeseli indicum wird beschrieben.

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Part X of a seriesCoumarins and Related Compounds. Part IX, A. K.Das Gupta, R. M.Chatterje and K. R.Das, J. chem. Soc. (C), (1969), 2618.     

Einige Bemerkungen zur Form und zum Relief der Schädelausgüsse vonPithecanthropus und vonSinanthropus

Summary The general morphological and the fissural character ofDubois' andKoenigswalds Pithecanthropi andBlack's Sinanthropus (E) strongly suggest that thePithecanthropus brain had more anthropoid features than theSinanthropus brain.     

Catalytic properties of synthetic pentapeptides

Zusammenfassung Es wurde das Pentapeptidl-Thr-l-Ala-l-Abu-l-His-l-Asp synthetisiert, seine katalytische-hydrolytische Wirkung auf Essigsäure-p-nitrophenylester geprÜft und die katalytische Aktivität ca. 1/3 derjenigen seines isosterenl-Thr-l-Ala-l-Cys-l-His-l-Asp festgestellt.

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Work done on a leave of absence from the Research Council of Alberta, Canada.     

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.     

The isolation and amino acid sequences of new pyroglutamylpeptides from snake venoms

Zusammenfassung Die Strukturaufklärung von zwei neuen tryptophanhaltigen Peptiden im Schlangengift vonAgkistrodon halys blomhoffii ergeben:l-Pyroglutamyl-l-Glutaminyl-l-Tryptophan undl-Pyroglutamyl-l-Asparaginyl-l-Tryptophan. Diese Peptide sind in Schlangengiften der Viperidae- und Crotalidae-Arten verbreitet.

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Supported in part by a grant from the Ministry of Education (Japan).     

β-Pyrrolo-L-alanine,a new antimetabolite of phenylalanine and tyrosine inEscherichia coli

Zusammenfassung -Pyrrolo-l-alanin, dessen Synthese beschrieben ist, hemmt das Wachstum vonE. coli B auf synthetischen Nährböden. Die Hemmung wird vonl-Phenylalanin undl-Tyrosin vollständig, vonl-Tryptophan teilweise, nicht aber von Histidin aufgehoben. Stämme vonE. coli, die gegen-Pyrrolo-l-alanin bzw.p-Fluorophenyl-dl-alanin resistent sind, zeigen gekreuzte Resistenz.