Miscellaneous Investigations 1801-1830

This period is marked by the publication of Laplace's Théorie Analytique des Probabilités in 1812 and followed shortly thereafter with the Essai Philosophique sur les probabilités in 1814.

A paper is placed under the subject heading of Least Squares if it is among the entries of the Catalog of Scientific Papers, Merriman or Harter. Dates given are those of publication and not of writing. If an author has not been set in boldface, I have not been able to locate the work online.

General

[1803] Daniel Encontre. "Mémoire sur la théorie des probabilités". Receuils Bulletin de Montpelier. Vol. 1. Encontre takes exception to the solutions presented by Cousin in his calculus text. He solves Mairan's problem of even and odd and the division of stakes.
[1805] Daniel Encontre. "On différens Problèmes relatifs à la théorie des combinaisons". Recueil Bulletins Montpelier Vol. 2 pp. 68-76. This paper is in the form of a letter to an unknown Professor of Mathematics regarding the probability that the partners in the game of Sizette are seated contiguously. A description of the game may be found in the game section of the Encyclopédie Methodique attached to volume 3. This game is played by 6 people sitting in a circle.
[1807] Thomas Young (signed Hydrophilus) "Example of a Calculation in the Doctrine of Chances; a Tide Table; and Remarks on the breaking of Wavers. In a Letter from a Correspondent," Journal of Natural Philosophy, Chemistry and the Arts. (Nicholson's) Vol. 18, pp. 116- 121.
[1808] Opsimath. "Doubts respecting some of the received Doctrines of Chance. In a Letter from a Correspondent. Journal of Natural Philosophy, Chemistry and the Arts (Nicholson's) Vol. 21. pages 66-68.

This is followed by a response "Some further Remarks on the Doctrine of Chance, in a Letter from a Correspondent. (B.H.) Journal of Natural Philosophy, Chemistry and the Arts (Nicholson's) Vol. 21 pages 121-124.

The exchange continues with "Remarks on the Doctrine of Chance, in Answer to Opsimath, in a Letter from W. Saint, Esq." Journal of Natural Philosophy, Chemistry and the Arts (Nicholson's) Vol. 21 pages 204-210.

The matter is finally laid to rest by the editor with "Further Remarks on the Doctrine of Chance" by Opsimath. Journal of Natural Philosophy, Chemistry and the Arts (Nicholson's) Vol. 21 pages 210-214. Included here are the comments by the editor.
[1811] Giovanni Angelo de Cesaris. "Sul limite degli errori probabili nelle osservazioni astronomiche." Milano, Effemeridi Astronomiche, pp. 102-111.
[1812] François Corbaux. Essais métaphysiques et mathématiques sur le Hasard, Volume I The topic is the game of Twenty-one. The author promised to complete his work in a second volume but I have seen no evidence of it.
[1814-16] Charles Julien Brianchon. "Recherches sur un jeu des combinaisons" Correspondance sur École Royale Polytechnique 3 (Jan. 1814-Jan 1816), pp. 387-392. We have here a combinatorial magic trick.
[1820] C. F. de Nieuport. "Mémoire sur un cas de la théorie des probabilités au jeu". Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles. Vol. 1 (1789-1820) pages 89-102.
[1822] Giuseppe Bianchi. "Riflessioni Critiche sopra il Saggio Filosofico intorno alle probabilità del Signor Marchese LAPLACE fatte dal Dott. Paolo RUFFINI." Memorie di Religione, di Morale, e di Letteratura 1, pp. 57- 83, 181-209.
[1822] Paolo Ruffini. Riflessioni Critiche sopra il Saggio Filosofico intorno alle probabilità del Sig. C. Laplace fatte dal Dott. Paollo Ruffini Professore di Clinica Medica, di Medicina pratica, e di Mathematica applicata nella R. Università di Modena, Rettore della medesima, ec. Modena (1821) Nuovo Giornale de'Letterati 1, pp. 201-212. The topic is Laplace's Philosophical Essai.
[1823] Charles Babbage. "An examination of some questions connected with games of chance". Transactions of the Royal Society of Edinburgh, Vol. IX. Pages 153-177. The paper concerns the betting system known as the martingale. It was read March 21, 1820.
[1827] Thomas Young (a Correspondent) "Practical Application of the Doctrine of Chances, as it regards the Subdivision of Risks," Quarterly Journal of Science, Literature and the Arts 22, pp. 84-94.
[1828] Gustav Adolf Greisinger. "Berechnung der Vortheile des Banquiers im Pharaospiele." [Computation of the advantages to the Banker in the Game of Pharaon] Zeitschrift für Physik und Mathematik 4, pages 210-227.
[1829] A.A. Cournot."Solution d'un problème d'analyse combinatoire," Bulletin des sciences mathématiques, physiques et chimiques. 11, pp. 93-97.
[1830] John William Lubbock and John Elliot Drinkwater-Bethune. On Probability. This work appeared as part of the Library of Useful Knowledge. It contains a discussion of inverse probability.

Problems

[1811-12] Giovanni Plana. "Mémoire sur divers problèmes de probabilité," Mém. Acad. Turin pp. 355-408.
[1818] Giovanni Plana. "Soluzione generale di un problema di probabilità," Memorie di mathematica e di fisica della Società italiana delle Scienze Modena 18,1. pp. 31-45.
[1820] Luigi Rangoni. "Nuove considerazioni intorno ad un problema di probabilità," Memorie della Società Italiana della scienze Moderna, 18, Part 2, pp. 518-554.
[1822] Pietro Abbati Marescotti. "Sopra un Problema dei Signori Daniele Bernoulli, e de la Grange," Memorie della Società Italiana delle Scienze Modena 19 (fasic 2 matematica). pp. 385-480.
[1826] C. F. de Nieuport. "Mémoire sur une question relative au calcul des probabilités." Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles. Vol. 3, pages 141-152.
[1830] J.W. Lubbock. ``On the calculation of annuities, and on some questions in the theory of chances." Read May 26, 1828. Transactions of the Cambridge Philosophical Society, Vol. 3, Part 1. Pages 141- 154 with several pages of life tables following.

Least Squares Method

[1805] Louis Puissant. Traité de Géodesie, ou Exposition des Méthodes Astronomiques et Trigonométriques, Vol. 1 (Paris), Vol. 2, 1819.
[1805] Svanberg, Jons Exposition des opérations faites en Lapponie, pour la détermination d'un arc du méridien en 1801, 1802, et 1803,... (Stockholm)
[1805] Franz Xavier von Zach. "Versuch einer auf Erfahrung gegrundeten Bestimmung terrestrischer Refractionen," Monatliche Corresponenz 11, pp 389-415, 485-504.
[1806-10] J.B. Delambre (ed.) Base du Systême Métrique Décimal, ou Mesure de l'Arc du Méridien Compris entre les Parallèlles de Dunkerque et Barcelone, Executée in 1792 et Années Suivantes, par MM. Méchain et Delambre. Vol. 1, 1806; Vol. 2, 1807; Vol. 3, 1810.
[1806] Kammer-Roth von Lindenau. "Über den Gebrauch der Gradmessungen zur Bestimmung der Gestalt der Erde. Monatliche Corresponenz 14, pp. 113-158.
[1813] J.B. Delambre. Abrégé d'Astronomie, ou Leçons Élémentaire d'Astronomie Théorique et Pratique. (Paris)
[1813-14] Claude Louis Mathieu."Sur les expériences du pendule, faites par les navigateurs espagnols, en différens points du globe," Connaissance des Tems pur 1816, pp. 314-332.
1813 Giovanni Plana. "Mémoire sur divers problèmes de probabilité". Mémoires de l'Académie Impériale des Sciences Turin, for the years 1811-1812, Pages 355-408. Plana concerned himself with the approximation of functions developed by Laplace in "Mémoire sur les approximations des formules qui sont fonctions de très-grands nombres," Mém. Acad. R. Sci. Paris, 1782 (1785), p. 1-88.
[1816] J.F. van Beeck-Calkoen. "Over de theorie den gemiddelde waardij uit ken zeker aantal grootheden of afzonderlwke waarnemingen,"
Verhandelingen der Eerste Klasse, Vol. 2. pp. 1- 19.
[1818] Giovanni. Plana. "Allgemeine Formeln, um nach der Methode der kleinsten Quadrate die Verbesserungen von 6 Elementen zu berechnen, und zugleich das jeder derselben zukommende Gewicht zu bestimmen. Zeitschrift für Astronomie und verwandte Wissenschaften 6, pp. 249-270.
[1818] Robert Adrain "Investigation of the Figure of the Earth and of the Gravity in different Latitudes," Trans. Amer. Phil. Soc., Vol. 1, pp. 119-135.
[1818] Robert Adrain "Research concerning the mean diameter of the Earth," Trans. Amer. Phil. Soc., Vol. 1, pp. 353-336.
[1818] Littrow. "Ueber die gerade Aufsteigung der vornehmsten Fixsterne," Zeitschrift für Astronomie, Vol. VI, pp. 1-26.
[1818] Lindenau "Versuch einer Bestimmung der wahrscheinlichsten Bahn des Cometen von 1680, mit Rücksicht auf die planetarischen Störungen während der Dauer seiner Sichtbarkeit," Zeitschrift für Astronomie, Vol. VI, pp. 27-120, 129-208.
[1819] Paucker. Ueber die Anwendung der Methode der kleinsten Quadratsumme auf physikalischen Beobachtungen. (Mitau) pp.32. See also Muncke (1825).
[1819] Henr. Joh. Walbeck. Dissertatio de forma et rnagnitudine telluris, ex dimensis arcubus meridiani definiendis. Abo, 8vo.
[1819] Thomas Young. "Remarks on the probabilities of error in physical observations, and on the density of the earth, considered, especially with regard to the reduction of experiments on the pendulum.' Phil. Trans. for 1819, pp. 70-95.
[1821] Jöns Svanberg, "Om Roterande Systemers Principal-Axlar och Sannolikaste Medel-Resultatet af gifna Oservationer" Kongliga Vetenskaps Academiens Handlingar pp. 388-408.
[1821-1822] Subscriber. "Probabilités. dissertation sur la recherche du milieu le plus probable, entre les résultats de plusieurs observations ou experiences". Annales de Mathématiques pures et appliquées, T. 12, pages 181-204. As the title indicates, this concerns the most probable mean.
[1822] George Harvey. "On the Method of Minimum Squares, employed in the reduction of experiments, being a translation of the Appendix to an Essay of Legendre's entitled: 'Nouvelles Methodes pour la Determination des Orbites des Cometes,' with remarks." The Edinburgh Philosophical Journal 7, pp. 292- 301.
[1822] J.F. Encke. Die Entfernung der Sonne von der Erde aus dem Venusdurchgange von 1761, (Gotha) pp. 179. Part II entitled Der Venusdurchgang von 1769 .... (Gotha, 1824) pp. 112.
[1824] Christianus G. Berlin Explanatio methodi quadratorum minimorum. Lundæ, 4to.
[1824] Puissant "Application de la methode la plus avantageuse à la determination de l'aplatissement du sphéroïde osculateur en France, par Ie comparaison d'un arc de méridien avec un arc de paralléle," Ferussac's Bull. Sci. Math., Vol. I, pp. 271-274. "Supplément à la détermination des longitudes terrestres les observations azimutales," Connaissance des Tems for 1827, pp. 230-232
[1825] G.W. Muncke. "Beobachtung," Physikalisches Wörterbuch, 2nd ed. (Leipzig) Vol. 1, pp. 884-912 concerning the Barometer.
[1825] James Ivory. "On the Method of Least Squares," Tilloch's Philosophical Magazine, 65, pp. 1-10, 81-88, 161-168. See also the 13 Proofs.
[1826] James Ivory. "On the Method of Least Squares," Tilloch's Philosophical Magazine, 68, pp. 1-10, 81-88, 161-168.
[1827] Rosenberger "Ueber die, auf Veraustaltung der französischen Academie, während der Jahre 1736 und 1737 im Schweden vorgenommene Gradmessung," Astron. Nachr., Vol. VI, col. 1-32. See Hansen (1831) and Abhandlungen von Bessel, Vol. III, pp. 16-19.
[1827] Rosenberger Ueber die Theorie der Zuverlässigkeit der Beobachtungen und Versuche und der von derselben abhängigen Bestimmungen des Mittels aus gegebenen Zahlen. (Berlin)
[1827] Nürnberger. "Betrachtungen über die Methode der kleinsten Quadrate," Abhandlungen der Naturforschenden Gesellschaft zu Görlitz 1, pp. 22-31.
[1830] P. A. Hansen Commentatio de gradus precisionis computatione. (Gotha) See "Darlegung einer neuen Methode, bei Anwendung der Methode der kleinsten Quadrate, die Gewichte der unbekannten Grössen zu berechnen," Astron. Nachr. 8, col. 463-468, and Encke in Berlin Astron. Jahrbuch for 1835, p. 297.
[1830] C. F. Hauber. "Ueber die Bestimmung der Genauigkeit der Beobachtungen," Baumgartner's Zeitschrift für Physik und Mathematik 7, pp. 286-314.
[1830] C. F. Hauber. "Verallgemeinerung der Poisson'schen Untersuchungen über die Wahrscheinlichkeit der mittlern resultate der Beobachtungen in den Additions à la Connaiss. des tems de 1827," Zeitschrift für Physik und Mathematik 7, pp. 406-429.
1830-1832 C. Fr. Hauber "Theorie der mittleren Werth," Zeitschrift für Physik und Mathematik 8, pages 25-56 (sections 1-16), 147-178 (sections 17-27), 295-315 (sections 28 - 31), 443-455 (sections 32 - 34); Zeitschrift für Physik und Mathematik 9, pages 302- 322 (sections 35 - 37); Zeitschrift für Physik und Mathematik 10, pages 425 - 457 (sections 38 - 44).
[1830] C. von Riese. '[Eine Recension.]' Jahrbücher für Wissenschaftliche Kritik, 1 (1), col. 269-284.

Popular Texts

1801 L'art de conjecturer à la loterie by Sébastien Antointe Parisot. This is based on the Genoise lotto and the Lottery of Paris.
1801 Refutation of the errors of d'Alembert by Josef Niklas Windisch-Graetz. D'Alembert wrote extensively on what he thought were problems with the foundations of the theory. See also Niklaus Bernoulli and Daniel Bernoulli.
1802 Considerations sur la théorie mathématique du jeu by Andre-Marie Ampere. In this work, Ampere argues for the certainty of gambler's ultimate ruin. For English see Considerations of the mathematical theory of the game.
1806 Versuch einer Theorie der Wahrscheinlichkeit, Vol. 1 by Hans Ernst von Globig. This is a work on law.The first volume develops the theory. The second apparently suggests application toward correcting evidence.
1814 The Doctrine of Chances or the Theory of Gaming by William Rouse. This is a very elementary text that presents a short history of gambling instruments and of solves various problems concerning the games of Whist, dice, an interesting dice game called "The Game of Points", Lotteries, horse racing. It terminates with several miscellaneous problems and tables to assist the gambler.
1816 Traité élémentaire du calcul des probabilités by Sylvestre Lacroix. This work follows the desire of Condorcet to introduce the applications of the theory to the social sciences in the schools. It includes Bernoulli's Theorem, development of inverse probability, treatment of annuities, and the analysis of testimony and decisions by electorate.
1818 Un peu de tout, ou Amusemens d'un sexagénaire, depuis 1807 jusqu'en 1816 by C.F. de Nieuport. On pages 67 - 147 are 7 conversations on the probabilities in the games of chance. With the exception of conversation 6 on annuities, the others concern essentially heads and tails.
1819 Philosophischer Versuch über die Wahrscheinlichkeit by Friedrich Wilhelm Tönnies and with a forward by Karl Christian von Langsdorf. This is a translation the 3^rd edition of Laplace's Essai Philosophique sur les probabilités.
1821 Riflessioni Critiche sopra Il Saggio Filosofico intorno alle probabilità del Sig. Conte Laplace by Dottor Paolo Ruffini. (Modena)