The development of the Laplace Transform, 1737–1937 II. Poincaré to Doetsch, 1880–1937

An earlier paper, to which this is a sequel, traced the history of the Laplace Transform up to 1880. In that year Poincaré reinvented the transform, but did so in a more powerful context, that of properly conceived complex analysis. Rapid developments followed, culminating in Doetsch' work in which the transform took its modern shape.     

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.     

The lunar and Paschal tables of De ratione paschali attributed to Anatolius of Laodicea

Summary of conclusions The seven MS lunar and Paschal tables of De ratione paschali fall into two distinct groups which we have classified as Sirmond-type and Padua-type respectively, and from these we have restored the tables of their archetype. The Sirmond-type tables preserve a unique lunar year, which we term the Anatolian lunar year, and they first emerge in the context of a larger computus which was assembled in southern Ireland c. 658, a copy of which Wilfrid had evidently obtained by the time of the Synod of Whitby. The weight of circumstantial evidence supports the hypothesis that it was he who then instigated the corruption of both the tables and the patristic authorities of De ratione paschali, a copy of which subsequently passed to Bede and thence to the Sirmond group of MSS. The Padua-type tables on the other hand are represented only by the Padua MS, and they appear to have originated from within Insular circles on the Continent. These too were crudely corrupted, first by changing their lunar year from Anatolian to Roman and moving their ferial data from January to December and changing some Paschal data, and then secondly by collation with Sirmond-type tables. In the case of both types the objective was clearly to weaken the relationship between the lunar and Paschal tables and to try and obscure the Paschal principles that they preserve and thereby undermine the position of those followers of the Insular latercus who relied on the authority of De ratione paschali for their Pasch. These conclusions naturally give a rather different colour to the events of Whitby from that given by Bede, who places them completely in a theological context. However in material terms what was really at stake at Whitby was the transfer of the patronage of the entire kingdom of Northumbria from the Celtic to the Roman church. Here then was sufficient motivation to justify the most ruthless of expedients.     

Evaluations of the beta probability integral by bayes and price

Summary The contribution of Bayes to statistical inference has been much discussed, whereas his evaluations of the beta probability integral have received little attention, and Price's improvements of these results have never been analysed in detail. It is the purpose of the present paper to redress this state of affairs and to show that the Bayes-Price approximation to the two-sided beta probability integral is considerably better than the normal approximation, which became popular under the influence of Laplace, although it had been stated by Price.The Bayes-Price results are obtained by approximating the skew beta density by a symmetric beta density times a factor tending to unity for n , the two functions having the same maximum and the same points of inflection. Since the symmetric beta density converges to the normal density, all the results of Laplace based on the normal distribution can be obtained as simple limits of the results of Bayes and Price. This fact was not observed either by Laplace or by Todhunter.     

The ascendancy of the Laplace transform and how it came about

The modern Laplace transform is relatively recent. It was first used by Bateman in 1910, explored and codified by Doetsch in the 1920s and was first the subject of a textbook as late as 1937. In the 1920s and 1930s it was seen as a topic of front-line research; the applications that call upon it today were then treated by an older technique — the Heaviside operational calculus. This, however, was rapidly displaced by the Laplace transform and by 1950 the exchange was virtually complete. No other recent development in mathematics has achieved such ready popularisation and acceptance among the users of mathematics and the designers of undergraduate curricula. Communicated by C. Truesdell     

Über das Auftreten von multiplen Adenomen in der Leber von cholinarm ernährten Ratten

Summary Hepatoma-like neoplasmas were found in the liver of rats that had been on a choline-deficient diet for 3 to 4 months. Thus, the work ofCopeland andSalmon is confirmed. In our experiments, however, the lesions were observed earlier.     

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     

Antibody against purified viper neurotoxin

Résumé L'anticorps contre la neurotoxine du venin deVipera palestinae est obtenu chez des lapins par immunisation de la neurotoxine purifiée liée à la cellulose carbométhylique.

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This work is part of a thesis submitted byN. Shaham to the

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This work is part of a thesis submitted byN. Shaham to the

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This work is part of a thesis submitted byN. Shaham to the

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This work is part of a thesis submitted byN. Shaham to the

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This work is part of a thesis submitted byN. Shaham to the     

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).     

Boltzmann's ergodic hypothesis

Summary Boltzmann's ergodic hypothesis is usually understood as the assumption that the trajectory of an isolated mechanical system runs through all states compatible with the total energy of the system. This understanding of Boltzmann stems from the Ehrenfests' review of the foundations of statistical mechanics in 1911. If Boltzmann's work is read with any attention, it becomes impossible to ascribe to him the claim that one single trajectory would fill the whole of state space. He admitted a continuous number of different possible mechanical trajectories. Ergodicity was formulated as the condition that only one integral of motion, the total energy, is preserved in time. The two reasons for this are external disturbing forces and collisions within the system. Boltzmann found it difficult to ascribe ergodic behavior to a single system where the theoretical dependence on initial conditions, though never observed, has to be admitted as possible. To circumvent the dependence, he invented the concept of a microcanonical ensemble.     

Der qualitative und quantitative Nachweis der «fixen Luft» (1756), ein Wendepunkt in der Geschichte der Chemie und Biologie

Summary Reference is made to a treatise published in 1756 byJoseph Black (1728–1799), which was the first work to contain conclusive evidence of a gas bound to solid bodies; and in this connection the historical significance of the earliest studies on carbon dioxide is emphasised. Attention is drawn in particular to a subject about which little has hitherto been known,i.e., the use whichBlack and his contemporaries (notablyDavid Macbride) made of this discovery by applying it to animal and human physiology.

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Eine ausführlichere Würdigung dieses geschichtlichen Sachverhalts erscheint in Gesnerus (Schweiz)1956, Heft 3/4.     

Antiviral substances in starfish

Zusammenfassung Eine Gruppe von teilweise chemisch charakterisierten Verbindungen, welche die Vermehrung des Influenza-Virus in Huhnembryo-Test verhindern, wurde aus den SeesternenAsterias forbesi, Asterias pectinifera undAcanthaster planci isoliert.

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This research was supported by the N.S.F. Sea-Grant Program. The author thanks Dr.H. W. Younken Jr. and Dr.L. R. Worthen for their encouragement and suggestions throughout this work. Thanks are also due to Dr.Hashimoto, Tokyo University, and Dr.Yasumoto, Tohoku University, for the specimen ofAsterina pectinifera, and Dr.B. M. Branham, University of Hawaii, forAcanthaster planci sample. The antiviral test was carried out by Dr.O. Liu, Northeast Shellfish Sanitation Research Center, D. H. E. W., Narragansett, Rhode Island, to whome the author expresses his sincere gratitude.     

Untersuchungen über die Wirkung von Kinetin auf Kallus und Tumoren bei Organkulturen vonNicotiana glauca,N. langsdorffii und deren amphidiploiden Bastard

Summary In leaf cultures ofNicotiana glauca, N. langsdorffii, and their amphidiploid hybrid, callus growth or tumor formation is enhanced by kinetin, depending on its concentration. Of the 2 species and their hybrid, maximum response was found in the hybrid, less inN. glauca, the slightest response being found inN. langsdorffii. These facts confirm the earlier finding of a connection between callus-forming potency inN. glauca and tumor formation in its hybrid.

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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.     

Solacasine,a new steroidal alkaloid fromSolanum pseudocapsicum possessing antimicrobial activity

Summary Systematic fractionation of alcohol extracts ofSolanum pseudocapsicum. showed that solacasine is the main antibacterial constituent. Based on physiochemical studies, a structure is proposed.The authors are grateful to Dr.R. Foltz, Battelle's Columbus Laboratories, and Mr.E. Fairchild of our laboratories for the mass spectral data, to Mr.Ruey-Ping Leu for the microbiological data, and to the NIH for grant No. AI-09846 in partial support of this work.     

“... 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     

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))     

The deamino derivatives of [4-threonine]-oxytocin and [4-threonine]-mesotocin; Analogs possessing a surprising spectrum of diminished pharmacological activities

Zusammenfassung Synthese (Merrifield-Methode) und pharmakologische Eigenschaften der Desamino-Derivate von (4-Threonin)-Oxytocin und (4-Threonin)-Mesoxytocin werden beschrieben.

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This work was supported in part by the Medical College of Ohio, a Contract (No. 69-2193) from the Center for Population Research of the National Institute of Child Health and Human Development, Research Grants from the National Science Foundation (No. GB-4932), the National Institute of Arthritis and Metabolic Diseases (No. AM-01940) and a General Research Support Grant to Columbia University from the National Institutes of Health. The authors wish to thank Mrs.Sara Crumm for performing the amino acid analyses and Mrs.Margot Acosta for performing the bioassays. An abstract of part of this work was presented at the 2nd American Peptide Symposium, Cleveland, Ohio, August 1970;M. Manning andW. H. Sawyer,Peptides (Ed.Saul Lande, Gordon and Breach, New York 1971), in press.     

Effect of butyl alcohol inDatura innoxia Mill

Zusammenfassung Die Behandlung der Samen vonDatura innoxia Mill. mitn-Butylalkohol und Temperaturschock ergibt in der nächsten Generation Pflanzen, deren Samen einen höheren Alkaloidgehalt aufweisen. Das Hauptalkaloid ist Scopolamin (Hyoscin) mit einem Anteil von 50–70% am Gesamtalkaloidgehalt.

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The author is grateful to Dr. K.Ganapathi, Director, and Dr. C. K.Atal, Scientist of this Laboratory, for their interest in the work.Shri Het Singh, Dr. K. L.Dhar and MissSubash Kumari helped by analyzing the seeds which is duly acknowledged.     

5-methyl-3-butyl-octahydroindolizine,a novel type of pheromone attractive to Pharaoh's ants (Monomorium pharaonis (L.)

Zusammenfassung Aus Arbeiterinnen der AmeiseMonomorium pharaonis (L.) wurde 5-Methyl-3-butyl-octahydroindolizin isoliert. Dieses Pheromon übt eine starke Lockstoffwirkung auf die Arbeiterinnen dieser Ameisenart aus. Die Struktur wurde durch Spektral-analyse und Synthese aufgeklärt. Unseres Wissens ist dies das erste Pheromon aus Insekten mit dem Indolizingerüst.

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Acknowledgment. This work was supported by the Ministry of Health and Environmental Hygiene of the Netherlands. Pharaoh's ants were supplied by Dr.A. Buschinger, Bonn, and Mr.W. R. C. M. van der Loo, Rotterdam. The spectroscopical work was done by a team includingR. Deen, P. J. F. Nooijen andS. J. Spijk andJ. M. Timmner assisted in the synthesis.