• [1831] J. Marshall. An account of the population in each of six thousand of the towns and parishes in England and Wales... London.
• [1832] J. Marshall. Mortality of the metropolis. London. This is "a statistical view of the number of persons reported to have died, of each of more than 100 kinds of disease, and casualties within the Bills of Mortality, in each of the two hundred and four years, 1629-"-1831.
• [1833] J. Finlaison. Tables for providing relief in sickness and old age, for payments at death, and endowments for children. (8 pages) London: J.T. Pratt.
• [1835] J. Marshall. An Analysis and Compendium of all the returns made to Parliament ... relating to the increase of Population in Great Britain and Ireland.... London.
• [1838] Augustus de Morgan Essay on Probabilities, for the Cabinet Encyclopedia, pp. xviii, 306, XL.
• [1838] Augustus de Morgan "On a Question in the Theory of Probabilities," Trans. Camb. Phil. Soc., Vol. VI, pp. 423-430. He corrects an error made by Laplace (page 279) and by Poisson (page 209) of their works on the Theory of Probabilities.
• [1838] Augustus de Morgan A Treatise on the Theory of Probabilities (Encyclopedia Metropolitana) 
• [1839] Thomas Galloway. A Treatise on Probability. Edinburg: Adam and Charles Black. An article for the Encyclopedia Britannica, 7th Edition.
• [1843] John Tozer. "On the Measure of the Force of Testimony in Cases of Legal Evidence," Transactions of the Cambridge Philosophical Society 8, pp. 143-158.
  
• [1843] William Rowan Hamilton. "On some investigations connected with the Calculus of Probabilities," Report of the British Association for the Advancement of Science 13, 2nd part, pp. 3-4.
• [1843] William Rowan Hamilton. "Researches in the calculus of probabilities." Proc. Roy. Irish Acad., 2, 420-2.
• [1843] John Stuart Mill. Chap. XVII. Of chance and its elimination. Chap. XVIII Of the calculaiton of chances. Chap. XXIII. Of approximate generalizations, and probable evidence. A system of logic, ratiocinative and inductive,... Volume I and Volume II.
• [1843] Passy. "On the division of heritable property, and its influence on the distribution of wealth, translated by Sir John P. Boileau. J.R. Statist. Soc., 6, 185-67.
• [1844] E. Chadwick. "On the best mode of representing by returns the duration of life and causes of mortality." J. Roy. Statist. Soc., 7, 1-40.
  
• [1844]  William Fishburn Donkin. An Essay on the Theory of the Combination of Observations. The Ashmolean Society. See also "Sur la théorie de la combinaison des observations," Journal des Mathématiques Pures et Appliquées (1850), pp. 297-322. He seeks to establish a kind of Statics metaphysics. Merrimann remarks that his reasoning is not always clear or rigorous.
• [1844] Robert Leslie Ellis "On the Method of Least Squares," Transactions of the Cambridge Philosophical Society 8, pp. 204-219. Ellis provides a summary of the arguments in support of the method.
• [1844] D. Jones. "On the value of annuities and reversinary payments, with numberous tables. To which is appended: A treatise on probability, by Sir William Lubbock and J.E. Drinkwater Bethune." Library of Useful Knowledge. London. Volume I, Volume II.
• [1844] Francis Gustav Paulus Neison. "Method of conducting inquiries on comparative sanitary condition of various districts." J. R. Statist. Soc., 7, 40-68.
• [1844] J.R. Young. Elementary treatise on Algebra, theoretical and practical, with an appendix on probabilities and life annuities. 4th ed.
• [1844] J.R. Young. "On a Principle in the Theory of Probabilities," Report of the ... Meeting of the British Association 14 (2nd part), pp. 1-2.
• [1845] Francis Gustav Paulus Neison. "Contributions to vital statistics, etc." J.R. Statist. Soc., 8, 290-343; 9, 50-76. (Also published separately, London: 2nd ed. (1846). 3rd ed. (1857).)
• [1845] Robert Leslie Ellis "On a question in the theory of probabilities," Cambridge Mathematical Journal 4, pp. 127-133.
  
• [1845] S. Earnshaw. "On a certain Method of representing Diagrams the Result of Observations," London, Edinburgh, and Dublin Philosophical Magazine 27, pp. 127-129.
• [1846] Thomas Galloway. Probabilities. Encyclopaedia Britannica. 7th edition, Volume 18, pp. 591-639.
  
• [1846] Thomas Galloway. "On the application of the Method of Least Squares to the Determination of the most probable Errors in a Portion of the Ordnance Survey of England," Mem. Astron. Soc. Lond., Vol. XV, pp. 23-69. A discussion of triangulation.
• [1846-50] Augustus de Morgan "On the Structure of the Syllogism, and on the Application of the Theory of Probabilities to Questions of Argument and Authority," Transactions of the Cambridge Philosophical Society 8, pp. 379-408; "On the Symbols of Logic, the Theory of the Syllogism, and in particular of the Copula, and the Application of the Theory of Probabilities to some questions of Evidence," Transactions of the Cambridge Philosophical Society 9, pp. 79- 127.
• [1847] Augustus de Morgan "Theory of Probabilities," Encyclopedia of Pure Math. (Encycl. Metrop.) Pt. II, pp. 393-490. The author of this section is given as Alfred De Morgan, FRS. Much of this is a translation of Laplace 1812 with comments.
• [1847] Augustus de Morgan. Arithmetical books, from the invention of printing to the present time. London: Taylor & Walton.
• [1847] Augustus de Morgan. Formal logic; or the calculus of inference, necessary and probable. Lond: Taylor & Walton.
• [1847] Augustus de Morgan. "On the symbols of logic, the theory of the syllogism and in particular the copula, and the application of the theory of probabilities to some questions of evidence." Proc. Camb. Phil. Soc., I, 90-5. Also Trans. Camb. Phil. Soc., 9, 79-127.
  
• [1847] Thomas Galloway "Probabilities" Encycl. Britannica, seventh ed., Vol. XVIII, pp. 591-636. Eighth edition, Vol. XVIII, pp. 588-636. Also separately, Edinburgh, 1848. This contains Poisson's analysis (1824) and Gauss' proof of 1823.
• [1847] Thomas P. Kirkman. "On a problem in combinations." Camb. & Dublin Math. J., 2, 191-204.
• [1847] Protimalethes. Miracle versus nature: being an application of certain propositions in the theory of chances to the Christian miracles. Cambridge.
• [1847] Protimalethes. The independence of the testimony of St. Matthew and St. John tested and vindicated by the theory of chances. Cambridge, London. This is a sequel to the previous work Miracle versus nature.
  
• [1847] Henry Warburton. "On the partitions of numbers, on combinations and on permutations." Proc. Camb. Phil. Soc., 1, 43-53.
  
• [1849] A. D. Bache. "Comparison of the Results obtained in Geodesy by the Application of the Theory of Least Squares," Proc. Amer. Assoc. for Advancement of Science for 1849, pp. 102-105. Probable errors of measurements of angles in US Coastal Survey triangulations.
• [1849] Robert Leslie Ellis "On the Foundations of the Theory of Probabilities," (Read 1842)  Transactions of the Cambridge Philosophical Society 8, pp. 1- 6.
• [1849] J. Tozer. "On the measure of the force of testimony in cases of legal evidence." Trans. Camb. Phil. Soc., 8, (2), 143-58.
• [1850] A. Cayley. "On the triadic arrangements of seven and fifteen things." Phil. Mag. (3) 37, 50-3.
  
• [1850] Hugh Godfray. "Theorems on Factorials established by the Theory of Probabilities." The Mathematician 3, pp. 89 - 96.
  
• [1850] William A. Guy. "On the Relative Value of Averages derived from different Observations,"' Jour. Statis. Soc., Vol. VIII, pp. 30-45. The observations here are statistical facts.
• [1850] John Frederick William Herschel. "Lettres à S.A.R. le Duc règnant... (Letters addressed to H.R.H. the Grand Duke...)" A review of Quetelet's work. The Edinburgh Review, Vol. 92, pp. 1-56. See also Herschel's Essays (London, 1857), pp. 365-465. This contains another proof of the method of least squares. Ellis recast the proof into algebraic language. See also Adrain 1808, Bravais 1846, Boole 1857, Thompson and Tait 1867, Schlömilch and Glaisher 1872.
• [1850] Robert Leslie Ellis "Remarks on an alleged proof of the 'Method of Least Squares,' contained in a late Number of the Edinburgh Review," London, Edinburgh, and Dublin Philosophical Magazine 37, pp. 321-328, (Note on the former) 462. Herschel's proof is discussed and found wanting. See Glaisher 1872.
• [1850] James D. Forbes. "On the alleged evidence for a physical connexion between stars forming binary or multiple groups deduced from the doctrine of chances." Phil. Mag. (3) 37, 401-427.
• [1850] Hugh Godfray. "Theorems on factorials established by the theory of probabilities." Mathematician, 3, 89-96.
• [1850] Benjamin Gompertz. Hints on porisms, in a letter to T.S. Davies... London. This work is a sequel to the Two Tracts on Imaginary Quantities. Tract I (1817), Tract 2 (1818).
• [1850] Thomas P. Kirkman. "Query." Lady's and Gentleman's Diary, 48.
  
• [1850] Thomas P. Kirkman. "On the trials made with fifteen things." Phil. Mag., (3) 37, 169-71.
• [1850] Thomas P. Kirkman. "Note on an unanswered prize question." Camb. & Dublin Math. J., 5, 255-62. 
• [1850] J. Reid. "On the duration of pregnancy in the human female." Lancet, 2, 77-81.
• [1850] T. Weddle. "On annuities and assurances on successive lives." Phil. Mag. (3) 36, 8-13.

Publications in French

See also Augustin-Louis Cauchy, Irénée-Jules Bienaymé and  Eugene Catalan.

• [1831] C.F. Degen. "Recherches sur la parabole, déterminée par la méthode des moindres carrés et qui représenté le moins défectueusement, qu'il soit possible, un système quelconque de points donnés dans un plan," Mém. Acad. St.-Pétersbourg par divers savants 1, pp. 13-28.
• [1831] Louis Puissant "Application du calcul des probabilités à la mesure de la precision d'un grand nivellement trigonométrique," Mém. Acad. Paris 10, pp. 533-547. Connaissance des Temps for 1834, pp. 3-17. He gives a modification of Laplace's method described in his third supplement (1820).
• [1832] Louis Puissant "Deuxième mémoire sur l'application du calcul des probabilités aux mesures géodesiques," Mém. Acad. Paris 11, pp. 123-156. The adjustment of triangulations, determination of probable errors, etc.
  
• [1833] Jean Victor Poncelet."Application de la méthode des moyennes à la transformation, au calcul numérique et à la determination des limites du reste des séries,"  Journal für die reine und angewandte Mathematik 13, pp. 1-54.
• [1833] A.M. Guerry. Essai sur la statistique morale de la France. Crochard, Paris.
• [1834] Gauthier d'Hauteserve. Application de l'algèbra élémentaire au calcul des probabilités. Paris. No work with the given title can be located. The link here is to Traité sur les Probabilités. It appears to be identical the work immediately below but bears a shorter title. The preface to this work as the other advises that only elementary algebra is used.
  
• [1834] Gauthier d'Hauteserve. Traité élémentaire sur les probabilités. Paris.
• [1834] Franz Joseph Mone & Emile Tandel. Théorie de la statistique. Louvain.
  
• [1835] Jean Victor Poncelet. "Sur la value approchée linéaire et rationnelle des radicaux de la form sqrt(a²+b²), sqrt(a²-b²) etc. Journal für die Reine und Angewandte Mathematik, 13, 277-291.
• [1835] Bénard. "Note sur une question de probabilités," Journal de l'École Polytechnique 15. Issue 24. pp. 264-278.
• [1836] Antoine Meyer. "Recueil de quelques développements peu connu en analyse combinatoire." Mém. Bull. Acad. Roy. Sci. Lett., Beaux-Arts Belg, (1) 3, 322; 432. This merely reports the existence of a manuscript with the title.
  
• [1837] É. Mondésir."D'une question qui se présente dans le calcul des probabilités," Liouville Journal Math.. 2, pp. 3- 10.
• [1838] A. Bravais. "Sur les probabilités des erreurs de situations d'un point." C.R. Acad. Sci., Paris, 7, 77.
• [1838] Antoine Augustin Cournot. "Sur les applications du Calcul des Chances à la Statisique judiciaire," Journal de mathématiques pures et appliquées 3, pp. 257-334.
• [1838] A. Guibert. "Mémoire sur les probabilités des arrêts de deux sortes de cours d'appel," Comptes Rendus 7, pp. 650-652.
  
• [1838] A. Guibert. "Solution d'une question relative à la Probabilité des Jugements rendus à une majorité queconque," Journal de mathématiques pures et appliquées 3, pp. 25-30.
  
• [1838] Louis Puissant "Sur l'application du calcul des probabilités à la mesure de la precision d'un grand nivellement géodésique independant des distances respectives des stations," Comptes Rend. Acad. Paris 7, pp. 1132-1135. He deduces the mean errors of adjusted elevations.
• [1838] P.F. Verhulst. "Notice sur la loi que la population suit dans son accroissement." Corresp. Math. Phys. (Bruxelles), 10, 113-21.
• [1838-40] L. Brion. "Une application du Calcul des Probabilités," Mémoires Société de l'émulation d'Abbeville, pp. 251-256.
• [1839] Niels Henrik Abel. Oeuvres complètes. Christiania: Chr. Gröndahl. Tome Premier and Tome Second.
• [1839] I. Didion. "Expériences sur la justesse comparée du tir des balles sphériques, plates et longues." J. École polytn., Paris, 16, 51-74.
• [1840] P.A. Dufau. Traité de statistique. Paris.
• [1840] Jules Gaverret. Principes généraux de statistique médicale. Paris.
• [1842] Louis Puissant Traité de géodesie, ou exposition des méthodes trigonométriques et astronomiques, applicables à la mesure de la terre, et à la construction du canevas des cartes topographiques (Paris) Volume I, Volume II, Volume III. A valuable work on Geodesy. Results of previous papers are contained within it.
  
• [1842] L.M.P. Coste. "Question de Probabilité applicable aux décisions rendues par les jurés," Journal de Mathématiques pures et appliquées 7, pp. 169-183.
  
• [1842] Du Hays, "Du jeu de loto," Journal Mathématiques pures et appliquées 7, pp. 192-202.
  
• [1842] A. Lévy. "Question sur les Probabilités," Nouvelles Annales Mathématiques. 1 pp. 179-183.
  
• [1842] Ramus. "Sur une question de probabilité relative aux corrections des hauteurs barométriques," Crelle's Jour. Math. 24, pp. 80-84.
  
• [1842] Nicholai Lobatschevsky. "Probabilité des résultats moyens tirés d'observation répetées," Journal für die reine und angewandte Mathematik 24, pp. 164-170. Expressions for the probability of error are deduced.
  
• [1843] Antoine Augustin Cournot. Exposition de la théorie des chances et des probabilités (Paris) German trans., Braunschweig 1849. It contains chapters on the theory of means and the adjustment of observations. Merrimann remarks that his methods are awkward.
• [1843] J. Pétrequin. "Sur les diverses couleurs de l'iris et leurs proportions dans nos climats". Annales d'Oculistique, 10, 120-5.
  
• [1844] J.P.M. Binet. "Recherches sur une question de analyse des probabilités, relative à une série d'épreuves à chances variables, et qui exige la détermination du terme principal du dé veloppement d'une factorielle, formée d'un grand nombree de facteurs," Comptes Rendus 19, pp. 375-381.
• [1845] Léon L.C. Lalanne. Description et usage de l'Abaque, ou comteur universel qui donne à vue les résultats de tous les calculs d'arithmètique, de géometrie, etc. Paris. The last section is entitled "Abaque statistique."
  
• [1845] P.F. Verhulst. "Recherches mathématiques sur la loi d'accroissement de la population." Nouveaux Mém. Acad. Brux. 18, pp. 1-38.
  
• [1846] Auguste Bravais."Analyse Mathématique sur les probabilités des erreurs de situation d'un point," Mémoires présentés par divers savants 9, pp. 255-332. Observations are made on the coordinates of a point in the plane. See Herschel 1850.
  
• [1846] Olry Terquem. "Problème sur les probabilités," Nouvelle Annales Mathématiques 5, pp. 218 - 221, 260.
  
• [1846] Olry Terquem. "Sur les équations du premier degré en nombre plus grand que celui des inconnues; applications géométriques." Nouvelles annales de mathématiques 5, pp. 551- 556.
• [1847] C.H.D. Buijs Ballot. Les changements périodiques de température. Utrecht.
• [1847] Friedrich Georg Wilhelm Struve. Études d'Astronomie stellaire. Sur la voie lactée, et sur la distaance des étoiles fixes. St. Pétersbourg.
• [1847] P.F. Verhulst. "Deuxième mémoire sur la li d'accroissement de la population." Mém. Acad. Roy. Sci. Lett. Beaux-Arts Belg. 20, (separate pagination).
• [1848] Anton Meyer  "Resolution d'un problème du calcul des probabilités," Bulletin de L'Académie royale des Sciences Bruxelles Vol. XV, Pt. II, (No. 7). pp. 508-512.
• [1848] Anton Meyer "Memoire sur l'application du calcul des probabilités aux operations du nivellement topographique,"' Mem. Acad. Belgique, Vol. XXI, 2-23 pp. A practical paper.
• [1849] M.G. Lamé. "Note sur les chances du brelan, au jeu de la bouilotte." Comptes Rendus Paris 28, pp. 705-708.
  
• [1850] Houssard and Poudra. "Seconde Théorème de minimum pour un systeme de aroite dans l'espace," Nouv. Ann. Math., Vol. IX, pp. 241-242. On the center of gravity of a system of points.
  
  

• [1831] D. Brewster. "Ueber die mathematischen Ausdrücke für die mittlere Wärme der Luft und die magnetische Intensität; aus einem Schreiben des Hrn. Dr. Brewster an Hrn. Alex. von Humboldt."  Annalen der Physick und Chemie. 21 pp. 323-325.
• [1831]  Johann August Grunert "Berechnung der wahrscheinlichsten Resultate aus gegebenen Beobachtunge. Methode der kleinsten Quadrate," Klügel's Mathematisches Wörterbuch 5, Art. "Wahrscheinlichkeitsrechnung," pp. 983-1027. This is a presentation of the method of least squares according to the proof of Gauss 1809.
• [1831] P.A. Hansen. "Darlegung einer neuen Methode, bei Anwendung der Methode der kleinsten Quadrate bei Gewichte der unbekannten Grössen zu berechnen." Astr. Nachr., 8, 463-8.
• [1831] P.A. Hansen. "Über die Anwendung der Wahrscheinlichkeitsrechnung auf geodätische Vermessungen im allgemeinen, und über die Maupertuis'sche Gradmessung." Astr. Nachr., 9, 189-204, 205-220.
• [1831] Joseph Johann von Littrow "Bemerkungen zumpractischen Gebrauche der Wahrscheinlichkeitsrechnung," Zeitschrift für Physik und Mathematik 9, pp. 433-449.
• [1831] Gustav Theodor Fechner. Massbestimmungen über die galvanische Kette. Leipzig.
  
• [1831-36] Ludwig Oettinger."Von warscheinlichsten Ereignissen," Abhandlungen der Mathematisch-physikalischen classe 2 pp. 199-242, "Von dem Werthe der Erwartung," pp. 243-270.
• [1832] Joseph Johann von Littrow Über Lebensversicherungen und andere Versorgungsanstalten. Wien.
• [1832] Johann Franz Encke "Ueber die Begründung der Methode der kleinsten Quadrate," Abhadl. Akad. Berlin for 1831, pp. 73-78 of the mathematical part. He prefers the proof of Gauss (1809) for the method of least squares assuming the arithmetic mean gives the most probable result. 
• [1833] Joseph Johann von Littrow Die Wahrscheinlichkeitsrechnung und ihre Anwendung auf das wissenschaftliche und practische Leben. (Wien).
• [1834-1850] Johann Franz Encke "Über die Methode der kleinsten Quadrate," Berliner astronomisches jahrbuch-1834, pp. 249-312;  Berliner astronomisches jahrbuch-1835, pp. 253-320;  Berliner astronomisches jahrbuch-1836, pp. 253-308; a notice is "Hr. Encke las einen Beitrag zur Begründung der methode der kleinsten Quadrate,"  Bericht uber die zur Bekanntmachung geeigneten Verhandlungen (1850), pp. 211-213. Many textbooks have been written based on these papers. The first article was translated into English and reprint of the tables may be found in Taylor's Scientific Memoirs (1841), Vol. II, pp. 317-369. The second article provides Gauss' algorithm for the solution and methods of determining weights by both Gauss (1823) and Hansen (1830 and 1831). The third article discusses conditioned observations.
• [1836] Peter G. Lejeune Dirichlet. "Über die Frage, in wiefern die Methode der kleinsten Quadrate bei sehr zahlreichen Beobachtungen unter allen linearen Verbindungen der Bedingungsgleichen als das vorteilhafteste Mittel zur Bestimmung unbekannter Elemente zu betrachten sei," (extract). Abhandlungen der Akademie der Wissenchaften Berlin 33, 67-68. Werke, Vol. 1, "Ueber die methode der kleinsten quadrate," (1889) pp. 281-282 (extract); Vol 2, "Bemerkungen über die zweckmässigste art, beobachtungen zure bestimmung unbekannter elemente zu verbinden," (1897), pp. 347-351 (complete) See also G. Lejeune Dirichlet's Werke Vol. 1
• [1836] Moritz Wilhelm Drobisch. Neue Darstellung der Logik...logisch-mathematischen Anhange. Leipzig. 2nd edition (1851), 3rd (1863), 4th (1875), 5th (1887).
• [1837] Brune. "Neue Sterblichkeits-Tabellen für Witwen-Cassen." Crelle's J. reine angew. Math., 16. 58-64.
  
• [1837] Wilhelm Heinrich von Rouvroy. Ueber die Methode der kleinsten Quadrate, appendix to the Mechanik. Vol. 4 of Leitfaden zum Unterricht in der Mathematik.  (Dresden and Leipsig). 
• [1837] Ludwig Oettinger. Die Lehre von den Combinationen. Freiburg.
  
• [1837] Julius Weisbach. "Beurtheilung der Fehler beim Marscheiden mittelst der gewöhnlichen Instrumente," Zeitschrift für Physik und verwandte Wissenschaften 4, pp.24-54.
• [1837] Gotthilf Heinrich Ludwig Hagen. Grundzüge der Wahrscheinlichketis-Rechnung. (Berlin). Edition of 1867. This work presents his proof of the method of least squares. It is more elementary than the presentations of Laplace (1812) and Poisson (1830 and 1836). Merrimann considers it one of the best. It is repeated by many others.
  
• [1839] S. Stampfer. "Ueber das Verhältnis der Wiener Klafter zum Meter." Jahrbucher des K.K. Polytechnisches Institutes in Wien (Vienna) 20, pp. 145-176.
• [1839] Peter Andreas Hansen  "Auflösung einer allgemeinen Aufgabe aus der Wahrscheinlichkeitsrechnung." Astronomische Nachrichten 16, pp. 9- 16, 27 - 32. The determination of the values and weights of observed quantities subject to conditional equations.
  
• [1839] Gustav A. Jahn. Die Wahrscheinlichkeitsrechnung und ihre Anwendung auf das wissenschaftlich und praktische Leben. (Leipsig)
• [1839] Peter Gustav Lejeune Dirichlet. "Über eine neue Methode zur Bestimmung vielfacher Integrale," Kgl. Preuss. Akad. Wiss. pp. 61-79.
• [1839] Ludwig Moser. Die Gesetze der Lebensdauer. Berlin.
  
• [1840] Clemens. "Ueber die Methode der kleinsten Quadrate," Tilsit Gymnasium Programm for 1839-40, pp. ____; for 1848, pp. 1-12. Merrimann reports that the first part has not been seen. The second considers periodic observations.
• [1840] Magnus Georg von Paucker  "Über die Grenzen der Sicherheit in den Thatsachen dwer neuen Astronomie." Arbeiten der Kurländischen Gesellschaft für Literatur und Kunst. Mitau. 1 pp. 73-77.
• [1840] Christian Ludwig Gerling Pothenot'sche Aufgabe, in practischer Beziehung dargestellt. (Marburg) . The solution of 1822 Gauss. See also Schott 1866.
• [1840] Friedrich Wilhelm Spehr. Vollständiger Lehrbegriff der reinen Combinationslehre mit Anwendungen derselben auf Analysis und Wahrscheinlichkeitsrechnung. Braunschweig.
• [1840] Christoph Bernoulli. Populationistik oder Bevölkerungswissenschaft. Ulm.
• [1841] Christoph Bernoulli. Handbuch der Populationistik oder der Völker-und-Menschenkunde nach statistischen Ergbnissen. Ulm.
  
• [1841] Julius Ambrose Hülsse. Ueber die Berechnung von Beobachtungen durch die Methode der kleinsten Quadratssumme. (Leipsig)  p. 15.
• [1841] Peter Andreas Hansen  "Eine Aufgabe aus der practischen Geodäsie und deren Auflösung," Astron. Nachr. 18, col. 165-176.
• [1841] Ludwig Oettinger. "Beiträge zur Wahrscheinlichkeits-Rechnung," Archiv der Mathematik und Physik 1, pp. 113-136.
• [1842] Johann August Grunert   "Ueber Cauchy's Interpolationsmethode," Archiv. Math. u. Physik 2, pp. 41-60. See Cauchy 1835.
• [1842] Joseph Johann von Littrow "Theorie der kleinsten Quadrate," Gehler's Physicalisches Wörterbuch 10, Pt. 2, Art. "Wahrscheinlichkeitsrechnung," pp. 1200-1251. He describes the theory according to the method of Encke.
• [1842] A.R. Luchterhandt. "Ueber einen Lehrsatz aus der Wahrscheinlichkeitsrechnung,"  Archiv der Mathematik und Physik 2, pp. 65-67.
  
• [1842] Jakob Fries. Versuch einer Kritik der Principien der Wahrscheinlichkeitsrechnung. (Braunschweig)
• [1842] Gustav Adolf  Jahn. Aufgaben für Anfänger in der Buchstabenrechnung, Algebra und Wahrscheinlichkeitrechnung. Leipzig.
  
• [1842] Röber. "Experiment." Art. in Handwörterbuch Chemie u. Phys. (Berlin), pp. 773-790. See Archiv. Math. u. Phys., Vol. XI, p. 375.
• [1843] Christian Ludwig Gerling Die Ausgleichungs-Rechnungen des Practischen Geometrie, oder die Methode der Kleinsten Quadrate mit ihren Anwendungen für Geodätische Aufgaben (Hamburg and Gotha) According to Merrimann, this is the best systematic development of the application of the method of least squares to the treatment of geodetic measurements. Papers 1845, 1855, and 1862 are supplements.
  
• [1843] C.G. Reuschle. "Ueber die Deduction der Methode der kleinsten Quadrate aus Begriffen der Wahrscheinlichkeitsrechnung,"' Crelle's Jour. Math. 26, pp. 333-364; Crelle's Jour. Math 27, pp. 182-184. Critical examination of the deduction of the expression for the probability of an error between given limits. Encke's proof (1832) of the validity of the arithmetic mean is found imperfect.
  
• [1843] Berkhan. Ueber die Methode der kleinsten Quadrate. (Blankenburg)
• [1843] Christoph Bernoulli. Neuere Ergebnisse der Bevölkerungstatistik. Zuglich als Nachtrag zum Handbuch der Populationistik. Ulm.
• [1843] Johann-Ludwig Casper. Über die wahrscheinliche Lebensdauer des menschen. Berlin.
• [1843] Johannes Fallati. Einleitung in der Wissenschaft der Statistik. Tübingen.
• [1843] R.Hermann Lotze. Logik. Leipzig. 2nd ed. (1880). English translation by B. Bosaquet (1884): Oxford.
• [1843-52] Ludwig Oettinger."Untersuchungen über die Wahrscheinlichkeitsrechnung," Journal für die reine und angewandte Mathematik 26, (1843) pp. 217- 267 (sections 1-13); 311- 332 (sections 14-18). Journal für die reine und angewandte Mathematik  30, (1846) pp. 232- 268 (sections 19- 24), pp. 296-336 (sections 25- 28); Journal für die reine und angewandte Mathematik 34 (1847) pp. 153-192 (sections 29- 34); Journal für die reine und angewandte Mathematik 36 (1848) pp. 221- 267 (sections 35- 44), pp. 296-316 (sections 46-48); "Nachtrag" Journal für die reine und angewandte Mathematik  42 (1852) pp. 213-221 (section 49). (Also reproduced as Die Wahrscheinlichkeitslehre.)
• [1844] Johann Franz Encke "Bemerkungen zu der Abhandlung No. 22 Band 26. Heft 4. dieses Journals," Journal für die reine und angewandte Mathematik 28, pp. 213-222. This paper concerns a paper by Reuschle. See "Ueber die Deduction der Methode der kleinsten Quadrate aus Begriffen der Wahrscheinlichkeitsrechnung,"' Crelle's Jour. Math. 26, pp. 333-364; Crelle's Jour. Math 27, pp. 182-184.
  
• [1844] F.W.A. Argelander."Ueber die Anwendung der Methode der kleinsten Quadrate auf einen besondern Fall," Astronomische Nachrichten 21, pp. 163-168. Simplification of the normal equations.
• [1844] Johann August Grunert   "Einige Bemerkungen über fehlerzeigende Dreiecke." Archiv der Mathematik und Physik 4, pp. 348-355.
• [1845] Christian Ludwig Gerling "Nachträge zur Ausgleichungs-Rechnung," Archiv. Math. u. Phys., Vol. VI, pp. 141-146, 375-378. This contains three supplements to his book.
• [1845] August Friedrich Huberdt. Die Principien der Wahrscheinlichkeitsrechnung. Berlin.
  
• [1845] Carl Gustav Jacob Jacobi. "Ueber eine neue Auflösungsart der bei der Methode der kleinsten Quadrate vorkommenden lineären Gleichungen," Astronomische Nachrichten 22, pp. 297-306. An abridged method for the solution of certain forms of normal equations.
• [1846] Carl Gustav Jacob Jacobi. "Ueber eine leichtes Verfahren die in der Theorie der Säcularstörrungen vorkommenden Gleichungen numerisch aufzulösen." J. reine angew. Math., 30, 51-94.
  
• [1845] Philipp Fischer. Die Theorie der Beobachtungsfehler und ihre Ausgleichung durch die Methode der kleinsten Quadrate. Pt. I of his Lehrbuch der höheren Geodäsie (Darmstadt).
• [1846] Johann-Ludwig Casper. Denkwürdigkeiten zure medicinischen Statistik und Staatsarzneikunde. Für Criminalisten und Aerzte. Berlin.
  
• [1847] Oscar Schlömilch."Ueber eine in der Wahrscheinlichkeitsrechnung vorkommende analytische Aufgabe," Archiv der Mathematik und Physik 9, pp. 372-379.
• [1848] E. W. Grebe. "Erörterung einer Spielerei durch die Wahrscheinlichkeitsrechnung." Archiv der Mathematik und Physik 11, pp. 441- 443.
  
• [1848] W. Matzka. "Beweis des obersten Grundsatzes der Methode der kleinsten Quadrate," Archive der Mathematik und Physik 11-12, pp. 369-377. Derives the rule of the arithmetic mean.
  
• [1849] Johann Jacob Baeyer. Die Kastenvermessung und ihre Verbindung mit der Berliner Grundlinie. (Berlin) This is a valuable work for geodetic engineers.
  
• [1849] W.C. Götze. "Ueber die Bestimmung der Bedillgungsgleichungen bei der Aufsuchungen der wahrscheinlichsten Elemente eines Himmelskörpers aus einem vollständigen Systeme yon geocentrischen Beobachtungen," Astron. Nachr., Ergänzungs Heft, col. 159-234, 239-240.
  
• [1849] Theodor Wittstein. "Die Methode der kleinsten Quadrate," Appendix to Wittstein's Lehrbuch der Differential-und-Integralrechnung (Hannover, 1868-9, 3 volumes), Vol. II, pp. 343-442 contains the treatment of least squares. A clear exposition of Hagen (1837).
• [1849-51] Magnus Georg von Paucker "Der Ausgleichungsbau und der mittlere Fehler der Beobachtungen,"   Arbeiten der Kurländischen Gesellschaft für Literatur und Kunst. Mitau. 6, pp. 41- 83; "Einflus der Gewichte auf die Unsgleichung," Arbeiten der Kurländischen Gesellschaft für Literatur und Kunst. Mitau. 9 pp. 183-193.
• [1850-52] W. Denzler. "Uber den Fundamentalsaz der Methode der kleinsten Quadrate," Mittheilungen der Naturforschende Gessellschaft in Zürich 2, pp. 110-118.
  
• [1850] Johann Franz Encke "Ueber die Anwendung der Wahrscheinlichkeits-Rechnung auf Beobachtungen," Berlin Astron. Jahrb. for 1853, pp. 310-351. The object is to establish greater confidence in the use of the arithmetic mean and the assumption of the exponential law of error. Six of the ten problems from Lagrange's memoir (1774) are translated. Hagen's demonstration (1837) is given in full. 
• [1850] Johann Franz Encke. "Beitrag zur Begründung der Methode der kleinsten Quadrate." Bericht Bekanntmmachung Verhandlungen. K. Preuss. Akad. Wiss. Berlin, 1850, 211-14.
• [1850] Carl GustavAdolf Knies. Die Statistik als selbständige Wissenschaft. Kassell: Luckhardt.
• [1850] Magnus Georg von Paucker "Der mittlere Fehler zweiter Ordnung," Arbeiten der Kurländischen Gesellschaft für Literatur und Kunst 8 pp.104-112.
• [1850] Magnus Georg von Paucker "Zur Theorie der kleinsten Quadrate," Bulletin de la Classe Physico-Mathématique St-Pétersbourg 9, pp. 113-126; Bulletin de la Classe Physico-Mathématique St-Pétersbourg 10,  pp. 33-43, 233-237.
• [1850] Gideon Jan Verdam. Verhandeling over de methode der kleinste quadraten (Groningen) Vol. I, pp. xxi, 409. A very complete textbook on the use of the method of least squares. Volume I is practical. A volume II was promised on theory.
• [1851] Magnus Georg von Paucker "Der Grenzbau und die beiden Ditterfässe," Mitau Arb. Kurländ. Gs. 9 pp. 141-182.
• [1851] Magnus Georg von Paucker "Zur Theorie der kleinsten Quadrate," Bull. phys. math. Acad. St. Pétersbourg 9, col. 113-125; Vol. 10, col. 33-43, 233-238.  These issues are bound together in the link. Mélanges math. Acad. St. Pétersbourg 1 (1849-1853), pp. 188-204, 333-346, 433-439. Merrimann states these are of little value.
  

• [1832] Giovanni Tamassia. Ragionamento sulle Statistiche. Cremona.
• [1834] Melchiorre Giola. Tavole statistiche ossia norme per descrivere, classificare tutti gli oggetti de; amministrazione privata e pubblica. M.D. Lugano.
• [1836] G. Bellavitis. "Su alcuni principj fondamentali della teroria delle Probabilità," Il Poligrafo, 4 pp. 3-14.
• [1836] Placido Bonicelli. "Sopra un ghiaccio straordinario." Ann. Sci. Reg. Lomb.-Veneto, 6, 161-3.
• [1836] Francesco Pizzolato. Nozioni generali di statistica. Palerno
• [1836] Cesar della Valle. Elementi della scienza statistica. Napoli.
• [1835] F. Ferrara. Dubbi sulla statistica.
• [1839] L. de Samuele Cagnazzi. Sullo stato della statistica nel Reame di Napoli al cadere del sec. XVIII e comincaire del XIX. Napoli.
• [1839] Giuseppe Zurardelli. Preliminari alle teorie statistiche. Pavie.
• [1839] Giuseppe Zurardelli. Saggi di teorie statistiche e di un sistema di scienza legislativa.
  
• [1840] Guiseppe Bravi. Teorica e practica del probabile. (Bergamo) Volume 1 & Volume II.
• [1841] F. Ferrara. "Dell'unico modo in cui forse si potrebbe oggidi avviare abilmente la scienza della statistica." Giornale di Statistica. Sicilia, 6.
• [1841] Gabrio Piola. "Intorno l'applicazione del calcolo delle probabilità a quelle questioni nelle quali gli avvenimenti dipendono da cause morali." Giornale R. Ist. Lombardo, 2, 11ff.
  
• [1843] Placido Bonicelli. "Nuove formlole per valutare la prova testimoniale." Annali di fisica, chimica e matematiche, Vol. 12, pp. 167-177.
• [1844] A. Rosmini-Serbati. Saggio sulla statistica. Milan.
  
• [1845] Placido Bonicelli. "Calcoli sul publico Lotto," Annali di Fisica, chimica e Mathematiche 20, pp. 97-104.
• [1847] Francisco Maranesi. Introduzione allo studio della statistica. Bologna
  
• [1847] Antonio Toschi."Errore che può nascere dal diverso modo di desumere il medio aritmetico di molti dati numeri," Raccolta di Lettere 3, pp. 312-315.
  
  

• [1834] H. Strootman. Bevattelijk onderrigt in de Kansrekening, of de leer der Waarschijnlijkheden. (Breda). This is an adaption of Quetelet's Instructions Populaires sur le calcul des probabilités for the Dutch.
  
• [1835] Nikolai D. Brashmann. "Solution of a problem in the calculus of probabilities." Scientific Memoirs of the Imperial University of Moscow 10, pp. 523-525.  
• [1838] Lalos Bitnicz.  "A' Legkisebb Négyzetek' Elve," A'Magyar Tudós Társaság Évkönyvei 3, pp. 42-51. (Methodius minimorum quadratorum.)
• [1840] Pithanophilus (Patre). Probabilismus: methodo mathematica demonstratus. Typis Caesaris Giani. This is a work on Probabilism by Honoré Fabri.
  
• [1841] Carl Gustav Jacob Jacobi. "De formatione et proprietatibus Determinantium," Crelle's Jour. Math. 22, pp. 285-318. He discusses the application of determinants to the solution of equations and to finding weights in the method of least squares.
  
• [1842] Ludwig Merz. De theoria probabilitatis adhibita in physicam. (Monachii)
• [1843] D.B. de Haan. Dissertatio mathematica inauguralis de Lemniscata Bernouillana, etc. Amstelodami.