Miscellaneous Investigations between 1780 and 1800

[1780-81] Pierre Prévost. From him we have two memoirs criticizing the theory of probability.
[1781] Jean-Charles de Borda. Although having nothing to do with probability, Todhunter mentions his paper on voting due to its connection to Condorcet.
[1781] Antoine Deparcieux. Traité des annuités, accompagné de plusieurs table très utiles. Paris.
[1781] W. Black. Observations medical and political on the small-pox and inoculation and on the decrease of mankind at every age. London. 2nd edition greatly enlarged (1781).
[1782] Giovanni Francesco Malfatti. Malfatti wrote a memoir "Esame Critico di un Problema di probabilità del Sig. Daniele Bernoulli, e soluzione d'un altro Problema analogo al Bernulliano," which criticizes Daniel Bernoulli's solution of the urn problem.
[1782-4]. J.A.C. Michelsen. Anleitung zur juristischen, politischen und ökonomishchen Rechenkunst. Erster Theil and Zwenter Theil.
[1783] F. Maseres. The principles of the doctrine of life-annuities; explained in a familiar manner...with a variety of new tables, of the values of such annuities, etc. London.

[1783] C. F. de Bicqueley: Du calcul des probabilités. A second edition published in 1805. The extract made from the introduction cited by Todhunter is presented here:

"The theory of Probabilities drafted by some celebrated Geometers has seemed to me susceptible of being examined thoroughly, and being made part of elementary instruction: I have thought that a treatise would not at all be unworthy of being offered to the public, which would be able to enrich with new truths this interesting matter, and put it in the range of the greatest number of readers."

[1784 & 1786] Jean d'Aniers. The two memoirs written by him are not mathematical but rather serves to classify games into two classes: those which are ruinous and those which are not.
[1784] Jacques Necker. De l'administration des finances. Tome I, Tome II, and Tome III.
[1785] Encyclopédie Méthodique. Volume I (1784), Volume II (1785) and Volume III (1789). The encyclopedia reprints some articles from the Encyclopedia of Diderot. In particular, there are the following articles: Absent, Probabilité and Substitutions each by Condorcet and the article Milieu by John Bernoulli III. As Todhunter mentions, there is an addition to Volume III appearing as Dictionnaire des Jeux (1792).
[1785] August Friedrich Wilhelm Crome. Statistisch-geographische Beschreibung der sämtlichen oestreichischen Niederlande, oder des burgundischen Kreises... Mit einer neuen Karte. Dessau & Leipzig.
[1785] August Friedrich Wilhelm Crome. Über die Grösse und Bevölkerung der sämtlichen europäischen Staaten, etc. Leipzig.
[1785-6] J.N.Tetens. Einleitung zur Berechnung der Leibrenten und Anwartschaften die vom Leben und Tode einer oder mehrerer Personen abhangen, mit Tabellen. 2 vol. Erster Theil and Zweyter Theil. Leipzig.
[1787] Fridericus Augustus Schmelzer. De probabilitate vitae ejusque usu forensi, commentatio...qua maxima theoriam expectationis vitae antiquitati vindicat. Göttigen.
[1787] G. Toaldo et alii. Tavoli di vitalità. Padova.
[1788] P.N. Huyn. La Theorie des Jeux de Hasard, or, Analyse du Krabs, du Passe-dix, de la Roulette, du Trente & Quarante, du Pharaon, du Biribi & du Lotto. The title says it all.
[1788] W. Black. A Comparative View of the Mortality of the Human Species at all ages, and of diseases and casualties with charts and tables.
[1789] Fontana & Toaldo. Saggi di statistica politica e di publica economia. Turin.
[1789] W. Black. An Arithmetical and Medical Analysis of the Diseases and Mortality of the Human Species. London. Analyse arithmétique et médicale des maladies et de la mortalité de l'espèce humaine. Paris (1789).
[1789] Louis Brion de la Tour. Tableau de la population de la France, avec les citations des auteurs...Paris.
[1790] Thomas Brook Clark. A statistical view of Germany, in respect to the imperial and territorial constitutions...and ecclesiastical state; ... the state of their trade and commerce etc. London: C. Dilly.
[1790] Thomas Brook Clark. A statistical view of Europe. London: Dilly.
[1791] P.F. Weddigen. Statistische Übersicht von Westphalen. Berlin.
[1791] J. Sinclair. Specimen of the Statistical Account of Scotland, drawn up from the communications of the ministers of the different parishes. Edinburgh.
[1791-9] J. Sinclair. The statistical account of Scotland; drawn up from the communications of the Ministers of the different Parishes. 21 Volumes. Edinburgh. Volume First; Volume Second; Volume Third; Volume Fourth; Volume Fifth; ... Volume Eleventh; ... Volume Twenty-first.
[1791-4] W. Morgan. On the method of determining, from the real probabilities of life, the values of contingent reversions in which three lives are involved in the survivorship. Phil. Trans., 81, 246-77; 84, 223-61.
[1791-1807] Francis Maseres. Scriptores Logarithmici; or, a collection of several curious tracts on the nature and construction of logarithms...together with some tracts on the Binomial Theorem, etc. 6 volumes: Volume I, Volume II, Volume III, Volume IV, Volume V, and Volume VI. London.

[1792] Edward Waring. His An Essay on Principles of Human Knowledge contains a treatment of probability on pages 35-47 and on the first two pages of the Addenda he discusses derangements. In his Meditationes Algebraicae, 3rd edition (1782) he gives in Problem IX a rule for detecting the existence of complex roots of equations by examination of signs on which he says (page 69).

Haec methodus in quadraticis aequationibus verum praebet numerum impossiblium radicum: in cubicis autem eius probabilitas inveniendi impossibiles radices non videtur maiorem habere rationem ad probabilitatem fallendi quam 2:1. In aequationibus autem multo superiorum dimensionum haec methodus verum impossibilium radicum numerum perraro deteget.

This method in quadratic equations provides the true number of impossible roots: but in cubics the probability of it discovering the impossible roots is not seen to have a ratio to the probability of being mistaken greater than 2:1. But in equations of much higher dimension this method will detect the true number of impossible roots very rarely.

How the ratio is determined is not clear. Later (page 73) he says

Haec methodus semper impossibiles radices deteget, quando praecedens regula in Ex. 1 data eas inveniet; & saepe impossibiles radices inveniet, quando praedicta fallit. e.g. In cubicis aequationibus impossibiles, si modo ullae sint, radices semper deteget; in aequationibus n dimensionum, quarum (n vel n-1) radices sint impossibliles, probabilitas verum impossibilium radicum numerum e praecedente regula detegendi videtur esse ad probabilitatem verum impossibilium radicum numerum ex hac regula detegendi prope in ratione 2^n-2: 3^n-2

This method will always detect impossible roots, when one will find them by the preceding rule given in Ex. 1; & often will find impossible roots, when the previous rule fails. E.g., in a cubic equations, it will always detect impossible roots, if there are any; in equations of n dimensions, of which (n or n-1) roots are impossible, the probability that the preceding rule will detect the true number of impossible roots, is seen to be to the probability of detecting the true number of impossible roots in this rule nearly in ratio 2^n-2:3^n-2.

The Meditationes Algebraicae has been translated into English by Dennis Weeks (1991) AMS.

Finally, we note the curious work entitled On the principles of translating algebraic quantities into probable relations and annuities, &c. (1792). This is a short pamphlet of 60 pages of which only the first 26 are of interest. His idea is to convert general algebraic expressions into probabilities by appropriate substitutions.

[1793] Michael Curtis Curtius. Geschichte und Statistik von Hessen. Marburg.
[1794-5] Louis Frédéric Ancillon. His memoir belongs to the Class de Philosophie Speculative. Enough said.
[1795-6] François Jacques Durand. Statistique élémentaire, ou Essai sur l'état géographique, physique et politique de la Suisse. 4 volumens. Lausanne. Tome 2, Tome 3, Tome 4.
[1795-1802] H.M.G. Grellmann. Statistische Aufklärungen über wichtige Theile und Gegenstände der österreichischen Monarchie. 3 Bd. Göttingen. Erster Band, Zweyter Band, Dritter Band.
[1796] Cornelis Breevilt. "Verhandeling over de Kans-rekening," [Essay concerning chance reckoning] dating from 3 September 1788, but published much later. Pages 81 - 125. Mengelwerk van Uitgeleezene en andere Wis-en Natuurkundige Verhandelingen 1.
[1796] A.L. Lavoisier, J.L. Lagrange & A. Diannyere. Collection de divers ouvrages d'arithemetique politique par Lavoisier... Delagrange et autres. Paris.
[1796] J. Scott & L. Dunbar. Statistical Accounts of the Town and Parish of Perth [by J. Scott] and Parish of Kinnoul [by L. Dunbar] in 1794 and 1795. Perth.
[1796-97] Prévost & Lhulier. The pair contribute four memoirs. The first examines an urn problem without replacement, the others are printed in the Class de Philosophie Speculative. The second and third concern the principle of Laplace they name the Etiological Principle. The fourth examines the assessment of testimony.
[1798] Matthew Young. "On the force of Testimony in establishing Facts contrary to Analogy," found in Vol. VII of the Transactions of the Royal Irish Academy (1800) occupying pages 79-118.
[1798] Rev. George Miller. "On the Nature and Limits of Certainty and Probability," Transactions of the Royal Irish Academy, vol. V. Pages 199-226.
[1798] J. Gard. Odds and chances of cocking, and other games, algebraically and arithmetically investigated.
[1798] Chr. Kramp. Analyse des réfractions astronomiques et terrestres. This work contains a table of the integral of exp(-t² ) on the interval [t,∞) for t= 0 to t = 3 in steps of 0.01. It also contains a corresponding table of the logarithms of these integrals. pp. 195-206.
[1798] Martin von Schwartner. Statistik des Königreichs Ungarn. Ein Versuch. Pest. Part 1 (1809), Part 2 (1810) and Part 3 (1811).
[1853] Bishop Terrot. Although later than 1800, Todhunter notes that his paper "Summation of a compound Series and its Application to a Problem in probabilities" is related to the first one by Prévost & L'hulier.