Miscellaneous 1866

Miscellaneous Investigations 1866-1875

This period is noted for the beginnings of investigations by Francis Galton. As before, the literature is dominated by studies of least squares and the theory of errors.

Publications are sorted by language and then year of publication.

Published in English

[1866] T.R. Edmonds. "On the law of human mortality expressed by a new formula." Phil. Mag., (4) 31, 1-21.
[1866] W.S. Jevons. "Brief account of a general mathematical theory of political economy." J.R. Statist. Soc., 29, 282-6.
[1866] John Venn. The Logic of Chance. London: Macmillan. 2nd ed. 1876; 3rd ed. 1888.
[1866] William Allen Whitworth. "Permutations and combinations." Oxford, Cambridge & Dublin Mess. Math., 3, 193-200.
[1866] J.M. Wilson. "On some Problems in Chances," Ph. Mg. 31, pp. 170-172.
[1867] William Chauvenet. A Treatise on the Method of Least Squares. (Philadelphia)
[1867] J.M. Duncan. "On the laws of the fertility of women." Trans. Roy. Soc. Edin., 24, 287-314.
[1867] William Matthew Makeham. "On the law of mortality." London Assurance Magazine, 13, 325-58.
[1867] Charles S. Peirce. "On an improvement in Boole's calculus of logic." Proc. Amer. Acad. Arts Sci., 7, 250-61.
[1867] J. Power. "On the problem of the fifteen schoolgirls." Quart. J. Pure Appl. Math., 8, 236-51.
[1867] J.J. Sylvester. "Thoughts on inverse orthogonal matrices." Phil. Mag., (4) 34, 461-75.
[1867] P.G. Tait. "On a question of arrangement and probabilities," Edinb. R. S. P. 8, pp. 37-44.
[1867] Thompson and Tait. "Experience," Chapter 3 of Treatise on Natural Philosophy, Vol. 1, pp. 305-320. Herschell's proof (1850) is given. See Schlömilch 1872.
[1867] W.A. Whitworth. Choice and chance, an elementary treatise on permutations, combinations and probability, with 300 exercises. 2nd ed. (1870). 3rd ed. (1878), 4th ed. (1886): Cambridge.
[1868] M.W. Crofton."On the theory of local probability, applied to straight lines drawn at random in a plane; the methods used being also extended to the proof of certain new Theorems in the Integral Calculus," Phil. Trans. 158, pp. 181-199.
[1868] H.G Day. "Problem in Chances," Quarterly Jour. Math. 9, pp. 354-355.
[1868] James Jerwood "On the Application of the Calculus of Probabilities to Legal and Judicial Subjects." Reports and Transactions of the Devonshire Association. T. 2 Pt. 2, pp. 578-598.
[1868] E.J. Stone. "On the rejection of discordant observations," Month. Not. Astron. Soc. Lond. 28, pp. 165-168. Peirce's (1852) and Chauvenet's (1864) criteria are rejected. His own is proposed. See Glaisher and Stone 1873.
[1868] W.A. Whitworth."Problems supplementary to Choice and Chance," Mess. Mth. 4, pp. 152-158, 193-200, (The continuation seems not to exist.)
[1869] F.F.E. Brünnow. Tables of Iris, computed with regard to the perturbations of Jupiter, Mars, and Saturn, including the perturbations depending on the square of the mass of Jupiter. Dublin: Asher & Co.
[1869] P.E. Chase. "On the mathematical probability of accidental linquistic resemblances," Am. Ph. S. T. 13, pp. 25-33.
[1869] M.W. Crofton. "Mr. Crofton On the Theory of Local Probability." L. Mth. S. P. 2, pp. 54-57.
[1869] Thomas Rowe Edmonds. "On the vital force according to age and the `English Life Tables'." Phil. Mag. (4) 38, 18-33.
[1869] A. de Morgan. "On the final law of drawings." J. Inst. Actuar., 14, 175-82.
[1869] Francis Galton. Hereditary Genius; an Inquiry into its Laws and Consequences. (London) See the Galton website.
[1869] B.A. Gould. Investigations in the military and anthropological statistics of American soldiers. New York.
[1869] William Matthew Makeham. "On the adjustment of premiums for life assurance in reference to extra risks." J. Inst. Actuar., 14, 159-64.
[1869] J.E. Oliver. "Mathematical Note on Linguisitc Resemblances." Transactions of the American Philosophical Society 13, pp. 69-72.
[1869] William A. Rogers. "On the variability of the personal equation in Transit observations," Amer. Jour. Sci. 47, pp. 297-307.
[1869] W. Walton. "On the expression of a certain function in the form of a series." Quart. J. Pure Appl. Math., 10, 87-93.
[1869] James C. Watson. "Method of least squares, Theory of the combination of observations, and determination of the most probable system of the elements from a series of observations," Chapter 7 of his Theoretical Astronomy (Philadelphia) pp. 360-425. The subject according to Gauss and Encke.
[1870] M.W. Crofton. "On the Proof of the Law of Errors of Observations," Phil. Trans. 160, pp. 175-188. Errrors are assumed to arise from the joint operation of a large number of small sources of error, positive and negative, not being equiprobable.
[1870] W. Lazarus. "On some problems in the theory of Probabilities," London Assur. Mag.(Journal of Actuaries) 15, pp. 244-257. A translation from the German.
[1870] C.S. Peirce. "On the Theory of Errors of Observation." Report US Coastal Survey during 1870. pp. 200-224. In the introduction new ideas are offered concerning a notation "suggested by the study of the logic of relations."
[1870] Charles S. Peirce. "Description of a notation for the logic of relations, resulting from an amplification of the conceptions of Boole's calculus of logic." Mem. Amer. Acad., 9, 317-78.
[1870-2] W. Sutton. "On Herr Wilhelm Lazarus's paper 'On some problems in the theory of probabilities'." J. Inst. Actuar., 15, 452-5; J. Inst. Actuar. 16, 151-2.
[1871] Cleveland Abbe. "A Historical Note on the Method of Least Squares." American J. Sci. 1, pp. 411-415. Discusses the discovery of the method by Adrain.
[1871] Arthur Cayley. "A `Smith's Prize' paper." 1870. Question 12. Oxf. Camb. & Dublin Mess. Math., 5, 199-200.
[1871] A. Frost. "General solution and extension of the problem of fifteen schoolgirls." Quart. J. Pure Appl. Math., 11, 26-37.
[1871] J.W.L. Glaisher. "On a Class of Definite Integrals." Philosophical Magazine 42, pp. 421-436. Includes an account of Kramp's, Bessel's, Encke's and other tables of the probability integral.
[1871] J. Hopkinson. "On the Calculation of Empyrical Formulae." Messenger. Mth. 2, pp. 65-67. A less accurate method than least squares is presented.
[1871] Isaac Todhunter. "On the method of least squares," Trans. Camb. Phil. Soc. 11, pp. 219-238. A demonstration of a result that Laplace gave without proof.
[1872] S.C. Chandler. "On the construction of a graduated table of mortality from a limited experience. J. Inst. Actuaries 17, pp. 161-171.
[1872] A. de Morgan. A budget of paradoxes.... London: Longmans, Green & Co.
[1872] J.W.L. Glaisher. "Remarks on certain portions of Laplace's Proof of the Method of Least Squares," Ph. Mg. 43, pp. 194-201. See Glaisher immediately below.
[1872] J.W.L. Glaisher. "On the Law of Facility of Errors of Observations, and on the Method of Least Squares," As. S. Mm. 39, pp. 75-124. According to Merriman, the most valuable of all theoretical memoirs.
[1872] J.W.L. Glaisher. "Remarks on a theorem in Laplace's Probabilités," Mess. Mth. 2, pp. 62-64.
[1872] J.W.L. Glaisher."The Method of Least Squares," Nature 6, pp. 140-141.
[1872] J.E. Hilgard. "An Application of an Exponential Function" Proceedings Amer. Assoc. Adv. Science for 1871, pp. 61-63. Concerns a statute relating to errors in coinage.
[1872] J.E. Hilgard. "On the verification of the probability function." Rep. Brit. Ass. Advance. Sci., 42, 21. No text printed.
[1872] T. Hopkinson. "On the calculation of empirical formulae." Mess. Math., 2 (2), 65-7.
[1872] James Clerk Maxwell. "On the geometrical mean distance of two figures in a plane." Trans. Royal Soc. Edinburgh, 26, 729-33.
[1872] James Meikle. Observations on the rate of mortality of assured lives, as experienced by ten assurance companies in Scotland, from 1815 to 1863. Edinburgh: Blackwood.
[1872] William Thomson. "The kinetic theory of the dissipation of energy." Proc. Roy. Soc. Edin., 8, 325-34.
[1872] W. Allen Whitworth. "Chance" Messenger of Mathematics 1, pp. 163-166.
[1872] W.S.B. Woolhouse. "On the Philosophy of Statistics." Journal Institute Actuaries and Assurance Magazine 17, pp. 37-56. A popular article largely copied from Quetelet.
[1873] Brown, Samuel. "On the application of the Binomial Law to Statistical Enquiries, illustrated by the Law of the growth of Man at different ages." Journal Institute Actuaries and Assurance Magazine 17, pp. 340-351.
[1873] W. Crookes. "On the Probability of Error in Experimental Research." Quarterly Journal of Science and Annals of Mining, Metallurgy 3 (Vol. 10 Old series), pp. 1-13. Contains formulas for weights taken from DeMorgan 1838. Applies this to the determination of the atomic weight of thallium.
[1873] E.L. De Forest. "On some Methods of Interpolation Applicable to the Graduation of Irregular Series, such as Tables of Mortality, &c, &c." Annual Report of the Board of Regents of the Smithsonian Institution for 1871, pp. 273-339. Continued in Ann. Rep. Smith. Inst. for 1873: "Additions to a Memoir on Methods etc.," 319-55
[1873] J.R. Eastman. "The frequency of the occurrence of the zero and the nine digits in the tenths of seconds as obtained from the chronographic record of transit observations," Wash. Ph. S. Bll. 1, pp. 85-87.
[1873] S. Newcomb. "A mechanical representation of a familiar problem," As. S. M. Not. 33, p. 573.
[1873] S. Newcomb. "Note on a mechanical representation of some cases in the methiod of least squares." Monthly Not. Roy. Astr. Soc., 33, 575.
[1873] E.J. Stone. "On the most Probable Result which can be derived from a number of direct Determinations of Assumed Equal Value," As. S. M. Not. 33, pp. 570-572. An argument that the arithmetic mean is the most probable result.
[1874] J.W. Berg. "Remarks on the influence of errors of observation on the determination of the orbit of a planet from three observations." Monthly Not. R. Astr. Soc., 34, 479-82. (Translation.)
[1874] De Forest, E.L. "Additions to a Memoir on Methods of Interpolation Applicable to the Graduation of Irregular Series."Annual Report of the Board of Regents of the Smithsonian Institution for 1873, pp. 319-353.
[1874] J.W.L. Glaisher. "On the probability of errors of different amounts in calculations, attributable to the uncertainty of the last figure through contraction," Mess. Mth. 3, pp. 59-61.
[1874] J.W.L. Glaisher. "Note on a question in probabilities connected with the performance of calculations in duplicate," Mess. Mth. 3, pp. 106-108.
[1874] J.W.L. Glaisher. "On the rejection of discordant observations." Monthly Notices of the Astronomical Society of London 33, pp. 391-402.
[1874] J.W.L. Glaisher. 'Note on a paper by Mr. Stone, "On the Rejection of Discordant Observations."' Monthly Notices of the Astronomical Society of London, 34, p. 251.
[1875] J.W.L. Glaisher. "Note on partitions." Phil. Mag., (4) 49, 307-11.
[1866] W.S. Jevons. "The mathematical theory of political economy." J.R. Statist. Soc., 37, 478-88.
[1875] William Matthew Makeham. "On an application of the theory of the composition of decremental forces" J. Inst. Actuar., 18, 317-22.
[1874] Jevons, Williams Stanley. The Principles of Science (New York) Several chapters give valuable remarks concerning the fundamental principles of least squares.
[1874] Monro, Cecil. J. "Note on the inversion of Bernoulli's theorem in probabilities." Proceedings of the London Mathematical Society 5, pp. 74-78, Errata pp. 145-146.
[1874] C.R. Powalky. "On the combination of the different results of various series of observations," As. S. M. Not. 34, pp. 476-479.
[1874] E.J. Stone. "On the rejection of discordant observations," As. S. M. Not. 34, pp. 9-15.
[1874] E.J. Stone. "Note on a Discussion relating to the rejection of Discordant Observations." Monthly Notices of the Astronomical Society of London 35, pp. 107-108.
[1874-80] J.W.L. Glaisher. "On the solution of the equations in the method of least squares," As. S. M. Not. 34, pp. 311-335; "On the method of least squares," Vol. 40 (1880) pp. 600-614; "Addition to a paper on the method of least squares," Vol. 41 (1881) pp. 18-23. A critical discussion of Gauss', Bessel's and Jacobi's methods for solving equations and determining weights.
[1875] Wilfred Airy. "On the Probable Errors of Levelling; with Rules for the Treatment of Accumulated Errors." Minutes of the Proceedings of the Institution of Civil Engineers. 44, pp. 174-192. Comments to the paper 193-203.
[1875] J.H. Baxter. Statistics, Medical and Antropological...of over a Million Recruits. Washington. Volume I and Volume II.
[1875] Theo. L. De Land. "Solution of a problem." Analyst, Des Moines (Ia), 2, 22-4.
[1875] Francis Galton. "Statistics by Intercomparison," Ph. Mg. 49, pp. 33-46. See the Galton website.
[1875] Artemas Martin. "Problem." Analyst, Des Moines (Ia), 2, 28.
[1875] Henry Wyldbore Rumsey. Essays and papers on some fallacies of statistics concerning life and death, health and disease.
[1875] P.G. Tait. "On a question of arrangements and probabilities." Proc. Roy. Soc. Edin., 24, 37-44.
[1875] A.J. Verney. "Principles of vital statistics." J. R. Statist. Soc., 38, 487-513.

Published in French
See also Bertrand.

[1866] Émile Adan. Probabilités du tir et appréciation des distances à la guerre. Bruxelles.
[1866] Émile Adan. "Essai sur les limites à poser à la mesure de précision des observations immédiates," Brux. Ac. Bll. 21, pp. 480-502.
[1867] Émile Adan. "Loi générale de la probabilité des erreurs étendue à tous les genres d'observations immédiates," Brux. Ac. Bll. 23, pp. 148-187.
[1867] C. Jordan "De quelques formules de probabilité," Comptes. Rendus. 65, pp. 993-994.
[1867] G. Wyrouboff. "Le certain et le probable. L'absolu et le relatif." La Philosophie positive:revue 1, pp. 165--182.
[1868] Le Boulengé. "Études de ballistique expérimentale," Mém. Acad. Belgique 20, pp. 1-94.
[1869] Faà de Bruno. Traité élémentaire du calcul des erreurs, avec des tables stéréotypées, ouvrage utile à ceux qui cultivent les sciences d'observation (Paris) According to Merriman, the tables are the best part. Cast into oblivion as soon as possible.
[1868] Clemente Cerri. Méthodes pour exécuter les opérations de la statistique. Section population, première partie. Recensement. Florence.
[1870] P. Mansion. "Sur le problème des partis," Brux Mm. Cour. (8). 21 (No. 1), pp. 1-13.
[1871] C. Simon. "Note sur la formule de Gompertz et sur son application au calcul des probabilités de la vie humaine." Bull. Sci. Math. Astr. Darboux, 2, 282-8.
[1872] J. Groulous. "Études sur les nombres." J. Inst. (Acad. & Soc. Sci. France) Sci. Math., Phys. Natur., 40, 253-4.
[1872] J. Groulous. "Sur une question de probabilité appliquée à la théorie des nombres." J. Inst. (Acad. & Soc. Sci. France) Sci. Math., Phys. Natur., 40, 253-4.
[1872] H. Laurent. "Consdérations sur le théoreme de J. Bernoulli." J. Actuair. Franç., 1, 287-307.
[1872] H. Laurent. "Application du calcul des probabilités à la vérification des répartions." J. Actuair. Franç., 1, 308-12.
[1872] C. Moreau. "Question 44." Nouv. Ann., 11 (2), 131-2.
[1872] C. Simon. "Exposition élémentaire des principes du calcul des probabilités." J. Actuair. Français, 1, 410-28.
[1873] Jahn, Sur la probabilité du tir et la méthode des moindres carrés. Paris.
[1873] C. Jordan. "Questions de probabilités," Par. S. Mth. Bll. 1, pp. 256-258, 281-282.
[1873] E. Jourffret. "Sur la probabilité du tir," Rv. Mar. 38, pp. 5-30, 523-544, 957-988. Vol. 42, (1874) pp. 665-680, 986-1021; Vol. 43 (1874) pp. 131-152.
[1873] E.P. Jouffret. Sur la methode des moindres carrés et ses applications dur tir. (Paris)
[1873-1874] E.P. Jouffret. "Sur la probabilité du tir," Rv. Mar. et Col. 38, pp. 5-30, 523-544, 957-988; Vol. 42, (1874) pp. 665-680, 986-1021; Vol. 43 (1874) pp. 131-152.
[1873] G.H. Halphen. "Sur un problème de probabilités." Par. S. Mth. Bll. 1, pp. 221-224.
[1873] Matthieu Paul Hermann Laurent. Traité du calcul des probabilités (Paris) This is meant to be an introduction to the study of Laplace.
[1873] H. Laurent. "Note sur un passage de la théorie analytique des probabilités," N.A. Mth. 12, pp. 176-179.
[1873] É. Lemoine. "Sur une question de probabilités," Par. S. Mth. Bll. 1, pp. 39-40.
[1873] Ernst Liouville. "Sur la statistique judicaire." Liouville's J. Math. Pures Appl. (1) 18, 145-64.
[1873] Terrier, "Sur la solution d'un problème de probabilité. Neuch. Bll. 9 pp. 441-443. Concerns an urn problem.
[1874] A. Badoureau. "Note sur problème des partis appliqée aux jeux de calcul," Par. Éc. Pol. J. 27, (cah. 44), pp. 123-132.
[1874] Louis Adolphe Bertillon. La démographie figurée de la France...Mortalité selon l'âge, le sexe, l'etat-civil, &c., en chaque département et pour la France entière comparée aux pays étrangers. Paris.
[1874] Émile Dormoy. "Théorie mathématique des assurances sur la vie." Journal des Actuaires Francais 3 pp. 284-299, 432-461.
[1874] Paul A.R. Janet. Probabilism. La Morale. Paris. English translation by Chapman (1883): Moral Probabilism. The theory of morals. New York, pp. 292-308.
[1874] Anton Meyer. "Cours de calcul des probabilités fait à l'Université de Liège de 1849 à 1857. (Published on the manuscripts of the author by F. Folie.) Mémoires de la Societé royale des sciences de Liège 4, Separate pagination. 446 pages.
[1874] Anton Meyer. "Calcul des Probabilités," Liége S. Sc. Mm. 4 (no. 2),
[1874] Anton Meyer. Cours de Calcul des Probabilités fait à l'université de Liége de 1849 à 1857. Edited by A. Folie. The proofs of Gauss 1809 and Hagen 1837 are given and also the investigations of Bienaymé 1852. There is a German translation by Emanuel Czuber: Vorlesungen über Wahrscheinlichkeitsrechnung von Dr. A. Meyer, (1879) Leipzig: Teubner.
[1875] J. Bertrand. "Addition à la Note relative au théorème de M. Bienaymé, insérée page 458," Comptes.Rendus. 81, p. 458, 491-492.
[1875] T.V. Charpentier. "Sur la nécessité d'instituer la logique du probable. Comptes Rendus Acad. Sci. Morales, 103 (1), 657-.680.
[1875] H.A.É. Faye. "Note accompagnant la présentation d'une Notice autographiée sur la méthode des moindres carrés," Comptes Rendus. 80, pp. 352-356. The exponential law is regarded as an empirical law established by experience.
[1875] F. Hélie. "Probabilité des résultats moyen des observations." Mém. de l'Artill. de la Marine.
[1875] Camille Jordan. "Questions de probabilités." Bull. Soc. Math. France, 1, 256-8, 281-2.
[1875] H. Laurent. "Sur la méthode des moindres carrés," Liouv. J. Mth. 1, pp. 75-80. A discussion of 1444 observations to deduce an empirical law of error.
[1875] Charles Ruchonnet. Éléments de calcul approximatif. 2nd ed. Paris: Gauthier-Villars. 4th ed. (1887): Paris: Lausanne.
[1875] G.V. Schiaparelli. "Sur le principe de la moyenne arithmétique." Astron. Nach. 87, col. 55-58.
[1875] Joseph Marie de Tilly. "Corréspondance." Nouv. Corréspondance Math., 6, 410-14.
[1875] Joseph Marie de Tilly. "Théorie mathématique des erreurs." Conférences militaires belges. Balistique. Bruxelles: Murquardt. pp. 155-225.
[1875] Joseph Mariede Tilly. "Note sur le principe de la moyenne arithmetique et sur son application à la théorie mathématique des erreurs." Nouv. Corres. Math. I, pp. 159-170.

Published in German

[1866] A. Börsch. "Ueber die mittlern Fehler der Resultate aus trigonometrischen Messungen," Arch. Math. Ps. 46, pp. 40-44. See Bessel 1816, Gauss 1816 and 1823, and Dedekind 1860.
[1866] F.G. Mehler. "Über die Entwicklung einer Funktion von beliebig vielen Variablen nach Laplace'schen Funktionen höherer Ordnung." J. reine angew. Math., 66, 161-76.
[1866] Gregor Mendel. "Versuche über Pflanzen-Hybriden." Verh. Naturforsch. Ver. Brünn, 4, 3-43. English translation in 1901: J.R. Hortic. Soc. 26, 1-32 and by J.H. Bennett, W. Bateson & R.A. Fisher (1965): Edinburg: Oliver & Boyd.
[1866] Leopold Natani. "Quadrate (Methode der kleinsten)," Hoffmann's Mathematisches Wörterbuch 5, pp. 16-33. Gauss' proof of 1808 and Hagen's of 1837 are presented and use is made of Wittstein's work of 1849.
[1866] R. Radau. "Ueber die persönlichen Gleichungen bei Beobachtungen derselben Erscheinungen durch verschiedene Beobachter," Reper. f. phys. Technik 1, pp. 202-218, 306-321; Vol. 2, pp. 115-156. See Peters 1861. This is a translation from the Moniteur scientifique for 1865, pp . 977- 985 of "Sur les erreurs personnelles."
[1866] Anton Winckler. "Allgemeine Sätze zur Theorie der unregelmässigen Beobachtungsfehler," Sitzungsberichte Akademie Wein 53, (Pt. 2), pp. 6-41. This investigates the relation between mean values of powers of errors and expressions for the probability of errors.
[1867] C.W. Baur. "Kleinere Mittheilungen (XXI Aufgabe aus der Wahrscheinlichkeitsrechnung: Paschen mit sechs Würfeln)," Z. Mth. Ps. 12, pp. 355-356.
[1867] K. Becker. "Zur Theorie der Sterbetafeln für ganze Bevölkerungen." Statist. Nachr., Oldenburg, 9.
[1867] R.F. A. Clebsch. "Ueber ein Problem der Forstwissenschaft," Crelle J. 67, pp. 248-265.
[1867] M.W. Drobisch. Die moralische Statistik und die menschliche Willensfreiheit. Leipzig.
[1867] G. Hagen. Grundzuüge der Wahrscheinlichkeits-Rechnung, 2nd ed. (Rewritten from 1837 edition)
[1867] Alb. von Miller-Hauenfels. "die Methode der kleinsten Quadrate." Oestr. Z. Brgw. 15, 181, 194. A work for mining engineers. Gives Gauss' first method of proof of method of least squares.
[1867] Ludwig Mattheissen. "Vermischtes aus dem Gebiete der Wahrscheinlichketisrechnung," Arch. Mth. Ps. 47, pp. 457-460.
[1867] L. Oettinger. "Ueber einige Probleme der Wahrscheinlichkeitsrechnung, ins Besondere über das Rouge et Noire und den Vortheil der Bank bei diesem Spiele. Ein Beitrag zur Wahrscheinlichkeitsrechnung," Crelle J. 67, pp. 327-380.
[1867] T. Wittstein. Mathematische Statistik und deren Anwendung auf National-Ökonomie und Versicherungs-Wissenschaft, Hanover. English translation by T.B. Sprague (1872): On mathematical statistics and its application to political economy and insurance. J. Inst. Actuar., 17, 178-89, 353-69, 417-35.
[1868] Ludwig Boltzmann. "Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten." Sitz.-ber. Math.-naturwiss. Kl. Kais. Akad. Wiss., 58, 517-60.
[1868] Ludwig Boltzmann. "Lösung eines mechaischen Problems." Sitz.-ber. Math.-naturwiss. Kl. Kais. Akad. Wiss., 58, 1035-44.
[1868] P.A. Hansen. "Von der Methode der kleinsten Quadrate im Allgemeinen und in ihrer Anwendung auf die Geodäsie," Abhandl. Sächsisch. Gesell. 13, pp. 571-806. Separately Leipzig. A valuable work for geodetic engineers. See 1871 and 1869 for supplements.
[1868] Friedrich Robert Helmert. "Studien über rationelle Vermessungen im Gebiete der höheren Geodäsie," Zeitschr. Math. u. Phys. 13, pp. 73-120, 163-186. See Jahrb Forschre. Math. 1, p. 389.
[1868] Richard Hencke. Ueber die Methode der kleinsten Quadrate. (Leipzig) Ed. 1894. A doctoral dissertation containing historical and critical information relating to least squares.
[1868] Georg Freidrich Knapp. Über die Ermittlung der Sterblichkeit aus den Aufzeichnungen der Bevölkerungs-Statistik. Leipzig.
[1868] Albert von Miller-Hauenfels. Höhere Markscheidekunst. Praktisch-theoretische Anleitung beim Marksscheiden die vermeidlichen Fehler zu umgehen, die unvermeidlichen aber in einfacher und streng wissenschaftlicher Weise zu verbessern. (Wien)
[1868] Hermann Scheffler. Sterblichkeit und Versicherungswesen. Braunschweig.
[1869] C.G.G. Andrä. "Schreiben... [om Bestemmelsen af den sandsynnlige Feil ved Hjaelp af Iagttagelsernes Diffentser]," Astron. Nachr. 74, col. 283-284. Objects to Jordan's (1869) method of computation of probable errors since the differences are not independent. See 1872 continuation.
[1869] P. A. Hansen. "Entwickelung eines neuen veränderten Verfahrens zur Ausgleichung eines Dreiecksnetzes mit besonderer Betrachtung des Falles in welchem gewisse Winkel voraus bestimmte Werthe bekommen sollen," Abhandl. Säschsisch. Gesell. 14, pp. 185-287.
[1869] Friedrich Robert Helmert. "Beiträge zur Theorie der Ausgleichung trigonometrischer Netze," Zeitschr. Math. u. Phys. 14, pp. 174-208.
[1869] Wilhelm Jordan. "Über die Bestimmung der Genauigkeit mehrfach wiederholter Beobachtungen einer Unbekannten," Astron. Nachr. 74, 209-226. Computation of probable errors using the set of differences between pairs of observations. See Andrä 1869.
[1869] Wilhelm Jordan. "Ueber die Bestimmung der Genauigkeit mehrfach wiederholter Beobachtungen einer Unbekannten," As. Nr. 74, pp. 209-226.
[1869] Georg Freidrich Knapp. Die Sterblichkeit in Sachsen nach amtlichen Quellen dargestellt. 2 parts.
[1869] J. Lüroth. "Bemerkung über die Bestimmung des wahrscheinlichen Fehlers," As. Nr. 73, col. 187-190. An extension of the formula given by Peters (1856). See Helmert 1876.
[1869] F. Minding. "Über eine bei Beobachtung der Sternschnuppen vorkommende Aufgabe der Wahrscheinlichkeitsrechnung." Bull. Acad. Imp. Sci. St Petersbourg, 13, 203-8.
[1870] J. Vinc. Goehlert. Statistische Untersuchungen über die Ehen. Wien.
[1870] M. Kanner. "Allgemeine Probleme der Wahrscheinlichkeitsrechnung und ihre Anwendung auf Fragen der Statistik." Annal. gesammt. Versich.-wesens, 1, no. 20-24. The first part (Nr. 20) is lacking.
[1870] M. Kanner. "Grundlage zu einer Theorie des mittleren Risiko bei Lebensversicherungen." J. Collegium Lebensversicherungs-Wissenschaft.
[1870] W. Sutton. "On Herr Wilhelm Lazarus's Paper 'On some problems in the theory of probabilities,'" I. Act. J. 15, pp. 452-455; Vol. 16 (1872), pp. 151-152.
[1870] Julius Weisbach. "Bestimmung der Rittellage einer Ebene aus mehr als drei gegebenen Puncten...," Der Civilingenieur: Zeitschrift für das Ingenieurwesen. 16, pp. 397-421.
[1870] W. Windelband. Die Lehren vom Zufall. Berlin.
[1871] E. Abbe. Gesammelte Abhandlungen. Vol. 1 (1904 printing)
[1871] Julius-Hermann Franke. Die Dreiecksnetze vierten ordnung als Grundlagen geodätischer Detail-Aufnahmen. (Munich)
[1871] J. Frischauf. "Zum Gebrauche der Zahlentafeln," Z. Mth. Ps. 16, pp. 178-179.
[1871] P.A. Hansen. "Fortgesetzte geodätische Untersuchungen, bestehend in zehn Supplementen zure Abhandlung von der Methode der kleinsten Quadrate im allgemeinen und in ihrer Anwendung auf die Geodäsie," Abhandl. Säschsisch. Gesell. 14, pp. 1-184.
[1871] K. Hattendorff. "Über die Ermittelung des Sterblichkeitsgesetzes aus gegebenen Beobachtungen." Nachr. König Ges. Wiss. Univ. Göttingen, 1871, 382-98.
[1871] W.Z. Jordan. "Ueber das Einschalten eines trigonometrischen Punktes in ein gegebenes Dreiecksnetz nach der Methode der kleinsten Quadrate," Z. Mth. Ps. 16, pp. 164-167.
[1871] M. Kanner. "Analytische Theorie der Ausgleichung von Sterblichkeitstafeln." Berstein. J. Collegium Lebensversicherung.-Wissenschaft. Berlin.
[1871] C.F.W. I. Karup. Theoretisch-praktisches Handbuch der Lebensversicherung. Leipzig.
[1871] W. Klinkerfues. "Die Berechnung einer Bahn aus einer grösseren Zahl von Beobachtungen nach der Methode der kleinsten Quadrate." Theoretische Astronomie (Braunschweig)
[1871] Georg Freidrich Knapp. Sie neuen Ansichten über Moralstatistik. Jena
[1871] F.A. Minding. "Zur Methode der kleinsten Quadrate." Bulletin de l'Académie Impériale des Sciences de St.-Pétersbourg. 16, pp. 305-308. On the solution of normal equations, determination of weights, etc.
[1871] C.F.W. Peters. "Quadrate der Zahlen von 1 bis 10,000." Astronomische Tafeln und Formeln. (Hamburg) An aid in the method of least squares.
[1871] Thorvald Thiele. "On a Mathematical Formula to express the Rate of Mortality throught the whole of Life, tested by a Series of Observations made use of by the Danish Life Insurance Company of 1871." Translated by T.B. Sprague. J. Inst. Actuaries 16, pp. 313- 329.
[1871] Chr. Wiener. "Ueber die möglichst genaue mechanische Rectification einees verzeichneten Curvenbogens, bestimmt auf der Grundlage der Wahrscheinlichkeitsrechnung," Z. Mth. Ps. 16, pp. 112-124.
[1872] C.G. Andrae. "Ueber die Bestimmung des wahrscheinlichen Fehlers durch die gegebenen Differenzen von m gleich genauen Beobachtungen einer Unbekannten," As. Nr. 79, pp. 257-272. An investigation of Jordan's method.
[1872] Friedrich Robert Helmert. Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate (Leipzig) The first and second proofs by Gauss are given. He regards the exponential law as proven by experience and the arithmetic mean is the most plausible value.
1872] Joseph Dienger. "Über einen Satz der Wahrscheinlichkeits-Rechnung." Abhandlungen der königl. böhmischen Gesellschaft der Wissenschaften, (1871-72) 5, pp. 44. Separate pagination.
[1872] Wilhelm Jordan. "Ueber die Bestimmung des Gewichts einer durch die Methode der kleinsten Quadrate bestimmten Unbekannten," Z. Mth. Ps. 17, pp. 350-352. A simplification of demonstrations of two methods.
[1871] Wilhelm Jordan. "Ueber die Genauigkeit eingacher geodätischer Operationen." Z. Mth. Ps. 17, pp. 397-427.
[1872] Wilhelm Jordan. "Verallgemeinerung eines Satzes der Methode der kleinsten Quadrate," Z. Mth. Ps. 18, pp. 116-120. On the solution of normal equations.
[1872] Wilhelm Jordan. "Ueber die Bestimmung des mittleren Fehlers duch Wiederholung der Beobachtungen." Astronomische Nachrichten 79, 219-222. On the method of deducing probable errors from pairwise differences. See Andrä 1872.
[1872] Wilhelm Jordan. "Vergleichung der Genauigkeit verschiedener Gradmessungen." Astronomische Nachrichten 80, 17-22. Gives the mean errors of 17 angle and 21 base line measurements.
[1872] Hermann Rumpen. Über den Zusammenhang der von Gauss begründeten Methode der kleinsten Quadrate (Bonn) Doctor's thesis. The conditions for minimum squares, etc., discussed by method of determinants.
[1872] O. Schömilch."Ueber die Bestimmung der Wahrscheinlichkeit eines Beobachtungsfehlers," Z. Mth. Ps. 17, pp. 87-88. Hershell's proof is taken from Thompson and Tait (1869) and pronounced "einfache und anschauliche" (simple and descriptive).
[1873] H. Seeliger. "Ueber die Jacobi'sche Auflösung eines Systems von Normalgleichungen mit drei Unbekannten." Astronomische Nachrichten 82, 249-252.
[1873] F.R. Helmert. "Bestimmung des mittlern Fehlers der Längenmessungen aus den Differenzen von Doppelmessungen," As. Nr. 81, pp. 49-52. A comparison of the common formulas with that of Zachariae (1872). He shows the latter is less accurate.
[1873] G. Zachariae. "Note betreffend die Bestimmung des mittleren Fehlers," As. Nr. 80, pp. 67-70. Without demonstration gives a new formula for the mean error of a base line measured in several portions. See Helmert and Jordan 1873.
[1873] Wilhem Jordan. "Ueber die Berechnung des mittleren Fehlers einer Basismessung," As. Nr. 81, col. 51-56. A criticism of Zachariae's formula.
[1873] G. Zachariae. "Ueber die Bestimmung des mittleren Fehlers einer in mehreren Theilen doppelt gemessenen Grundlinie." Astronomische Nachrichten 81, 225-228. A defence against Jordan 1873.
[1873] W. Scheibner."Ueber Mittelwerthe," Leip. B. 25, pp. 562-567.
[1873] Wilhelm Jordan. "Verallgemeinerung eines Satzes der Methode der kleinsten Quadrate." Zeitschrift für Mathematik und Physik 18, pp. 116-120.
[1874] P.L. von Seidel. "Ueber die Berechnung der wahrscheinlichsten Werthe solcher Unbekannten, zwischen welchen Bedingsungs-Gleichungen bestehen," As. Nr. 84, pp. 193-210. The conditional equations are regarded as having infinite weights and so lead to a new method of solution.
[1873] P.L. von Seidel. Münch. Ak. Ab. 11 (3rd Ab.) pp. 76-
[1874] Karl Becker. Zur Berechnung von Sterbetafeln an die Bevölkerungsstatistik zu stellende Anforderungen. Berlin.
[1874] Maurice Cantor. Historische Notizen über die Wahrscheinlichkeitsrechnung (Halle) Of no value.
[1874] G.Th. Fechner. "Ueber die Bestimmung des wahrscheinlichen Fehlers eines Beobachtungsmittels durch die Summe der einfachen Abweichungen," A. Ps. C. Jubelbd., pp. 66-81. This is an extract of a memoir published in Abhandl Sächs. Gesell. in 1875. See also Helmert 1876.
[1874] G.T. Fechner. Elemente der Psychophysic. Vol. 1 & Vol. 2.
[1874] P.A. Hansen. "Von der Bestimmung der Theilungsfehler eines gradlinigen Maassstabes." Abhandlungen der königlich Sächsischen Gesellschaft der Wissenschaften Mathematisch-Physischen Classe 15, pp. 525-668.
[1874] J. Hirschberg. Die mathematischen Grundlagen der medizinischen Statistik elementar dargestellt. Leipzig.
[1874] Wilhelm Jordan. Taschenbuch der praktische Geometrie (Pub. Metzler) In part I, the method of least squares is presented. According to Merriman, it is republished in 1877 as Elemente der Vermessungskunde. However, in 1877, there was published Handbuch der vermessungs-Kunde Volume I which deals with the method of least squares.
[1874] Georg F. Knapp. Theorie des Bevölkerungs-Wechsels. Braunschweig: Vieweg.
[1874] P.L. von Seidel. "Ueber ein Verfahren, die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineäre Gleichungen überhaupt, durch successive Annäherung aufzulösen." Abhandlungen der Mathematisch-Physicalishen Classe Akademie Wissenschaften. 11 (3rd Ab.) pp. 81-108.
[1875] Baeyer, "Ueber Fehlerbestimmung und Ausgleichung eines geometrischen Nivellements." Astronomische Nachrichten 86, 177-188. An application of Bessel's method for adjusting triangulation.
[1875] J. Dienger. "Die Laplace'sche methode der ausgleichung von beobachtungsfehlern bei zahlreichen beobachtungen," Wien Ak. D. 34 (Ab. 2), pp. 21-62. The method is extended to the case of several unknown quantities.
[1875] Ernst Engel. "Über Möglichkeit und Wirklichkeit." Philosophische Monatschefte, 8, 241-71.
[1875] G.Th. Fechner. "Ueber den Ausgangswerth der kleinsten Abweichungssumme." Abhandlungen der königlich sächsischen Gesellschaft der Wissenschaften mathematisch-physischen class 16, pp. 1-76. See Fechner 1874.
[1875] Wilhelm Julius Förster. Wahrheit und Wahrscheinlichkeit. Berlin.
[1875] Julius H. Franke. Die trigonometrische Punktbestimmung im Netz-Auschluss, mit besondere Rücksicht auf eine rationelle Fehler-Ausgleichung. München.
[1875] Joseph Haberl. Lehrbuch der politischen Arithmetik enhaltend die Wahrscheinlichkeits-Rechnung, die Zinzeszinsen-Rechnung, die Rückzahlungsformen von Anlehen, die Construction von Tilgungssplänen, die Lotterie-Anlehen und die Berechnung der in das Gebiet der Lebenversicherung gehörigen Fälle. Wien.
[1875] Friedrich Robert Helmert. "Ueber die formeln für den Durchschnittsfehler," As. Nr. 85, pp. 353-366. A discussion of the formula of Peters (1856) is discussed. A new formula for probable error is proposed. See Lüroth 1869 and Helmert 1876.
[1875] Friedrich Robert Helmert. "Ueber die Berechnung des wahrscheinlichen Fehlers aus einer endlichen Anzahl wahrer Beobachtungsfehler." Zeitschrift für Mathematik und Physik 20. pp. 300-303. A reply to Mees.
[1875] Franke, Julius Hermann. Die Trigonometrische Punktbestimmung im Netz-Anschluss, mit besonderer Rücksicht auf eine rationelle Fehler-Ausgleichung. Reference is given to graphical methods of adjustment but no sources are cited.
[1875] Leopold Natani.. Methode der kleinsten Quadrate (Berlin) Herschell's proof is given. The numerical examples concern striking a target.
[1875] Wilhelm Lexis. Einleitung in die Theorie der Bevölkerungsstatistik. Strassburg.
[1875] J. Lüroth. "Vergleichung von zwei Werthen des wahrscheinlichen Fehlers. Astr. Nachr., 87, 209-20.
[1875-76] R.A. Mees."Ueber die Berechnung des wahrscheinlichen Fehlers einer endlichen Zahl von Beobachtungen," Z. Mth. Ps. 20, pp. 145-152; Vol. 21 (1876), pp. 126- 128. Gauss' method (1816) is considered incorrect. See Helmert 1875.
[1878] G.Th. Fechner. "Ueber den Ausgangswerth der kleinsten Abweichungssumme, dessen Bestimmung, Verwendung und Verallgemeinerung," Leip. Mth. Ps. Ab. 11, pp. 1-76.

Published in Italian

[1866-7] L. Guala. Elementi di Statistica Italiana teorica e practica. 2 parts. Biella. Parte I (1866) & 1867.
[1867] F. Faà di Bruno. Cenni elementari sopra il calcolo degli errori, con tavole stereotipate. Torino. French translation 1869.
[1867] G. Palomba. Studi sulla scienza statistica.
[1867] F.P. Ruffini. "Del modo di calcolare il risultamento medio più osservazioni successive," Mod. Ac. Sc. Mm. 8, pp. 65-75.
[1867] G.V. Shiaparelli. "Sul modo di ricavare la vera espressione delle leggi della natura dalle curve empiriche." Effemeridi Astronomische Milano.
[1868] E. Paulo Frisiani. "Sulla più vantaggiosa combinazione delle osservazioni." Memorie dell' J.R. Instituto. Lombardo 11, pp. 1-21.
[1868] G.V. Shiaparelli. "Sul principio della media arithmetica nel calcolo dei resultati delle osservationi," Instit. Lombard. Rendiconti 1, pp. 771-778. A new demonstration of the validity of the method of least squares. See his paper of 1875.
[1869] A. Dorna. "Sulla Media Aritmetica vel calcolo di compensazione," Tor. At. Ac. Sc. 4, pp. 757-763. On Encke's demonstration of the arithmetic mean and on Schiaparelli 1868.
[1869] Pietro Maestri. Le pubblicazioni della Direzione di Statistica. Firenze.
[1869] A. Zuccagni-Orlandini. Elementi di statistica. Florence.
[1870] Paolo Frisiani. "Sulla più vantaggiosa combinazione delle osservazioni," Milano I. Lomb. Mm. 11, pp. 1-21. A proof of the method of least squares given that the arithmetic mean gives the most probable result.
[1870] G. Piantanida. L'arte e la scienza della statistica. Milano.
[1870] Giovanni Santini. "Compendiato esposizione del modo più vantaggiosa di resolvere una serie di equazioni lineari, risultanti da operationi tutti ugualmente probabili, per la determinazione degli elementi di una proposta teorica. Mem. Istit. Veneto 14, pp. 477-510.
[1871] C. Fiori. Del metodo statistico considerato specialmente nei suoi rapporti coi fatti della medicina.
[1871] Nicolò Lo Savio. Instituzioni di statistica teoretica e pratica. Bari.
[1872] E. Anelli. Saggio di Statistica.
[1872] Angelo Messedaglia. La statistica e i suoi metodi.
[1872] Emilio Morpurgo. La statistica e le scienze sociali. Florence.
[1874] A. Balletti. Le leggi sulla statistica e l'economia politica.
[1874] G.V. Shiaparelli. "Sul calculo di Laplace intorno alla probabilità delle orbite planetarie iperboliche." Rendiconti Reale Istituto Lomb. Sci Lett., (2) 7, 77-80.
[1875] Manfredo Bellati. "Intorno a un modo di semplificare in alcuni casi l'applicazione del metodo de'minimi quadrati al calcolo delle costanti empiriche," Ven. Atti del Reale Istituto. 33 (Issue 2), pp. 849-863.

Published in other languages

[1866] A. Steen. "Nogle Bemaerkninger om Sandsynlighedsregningens Anvendelse til at maale Styrken af de Aarsager, der begunstige et Phaenomen, som uafbrudt har vist sig gjentagne Gange," Kjöb. Ov. pp. 8-12.(Probabilities application to comparison of causes favoring a recurring phenomenon.)
[1867] C.C.G. Andrä. Den Danske Gradmaaling. Vol. I (Copenhagen), Vol. II (1873), Vol. 3 (1878), Vol. 4 (1884) The adjustment of indirect observations subject to conditional equations.
[1867] Adolph Steen. "Mathematiske theori af et hazardspil kaldet spekulation," Ts. Mth. 3, pp. 33-42.
[1868] L.V. Lorenz. "Løsning af en opgave i sandsynlighedsregning." (The solution of a problem in probability calculus.) Tidsskr. Math. Zeuthen, (2) 4, 139-43.
[1869] Thorvald Thiele. Undersogelse af Omlobsbevaegelsen i Dobelstjerne.
[1870] L. Neovius. Lärobok i minsta qvadrat-metoden. (Åbo)
[1871] Viktor Buniakovsky. "On a special kind of combinations occurring in problems connected with defects."Записки Императорской академіи наук, Volume 20, Issues 1-2, Separate pagination.
[1871] Anders N. Kiaer. Statistik Håndbog for Kongeriget Norge. 2 parts. Kristiana.
[1871] Thorvald Thiele. En mathematisk Formel for Dödeligheden. Kopenhagen: Reitzel.
[1871] C. Tychsen. "Svar paa en Foresporgsel." Tidsskr. Math. Zeuthen, (3) 1, 70.
[1871] G. Zachariae. Theorien om de mindste Quadraters-Methode (Nyborg)
[1871] G. Zachariae. Laerebog i Theorien om de mindste Quadraters-methode. Nyborg.
[1871] Karl C. Zachariae. De mindste Kvadraters Methode. Nyborg: Schönemann.
[1872] L. V. Lorenz. "Udjevning af Iagttagelsesfejl." Tidsskrift for mathematik 2, pp. 1-20; (af G. Zachariae) 97-103; "Bidrag til udjevningsproblemet." pp. 125-136. (Graduation of errors of observation.)
[1872] L. V. Lorenz. "Udjevning af iagttagelsesfejl," Ts. Mth. 2, pp.1-20, 125-135.
[1872] G. Zachariae. "Udjevning af iagttagelsesfejl," Ts. Mth. 2, pp. 97-103, 182-188.
[1873] Thorvald Thiele. Om en Tilnarmelses formel. Tidskr. Math. Zeuthen, 3 (3), 22.
[1873] Fab. J. Wrede. "Några anmärkningar r:orande minsta qvadratmetoden," Stock. Öfv. 30 (No. 8) pp. 3-34; "Ratelser och tillägg till afhandlingen: Några anmärkningar r:orande minsta qvadratmetoden,'" No. 10, pp. 21-90. The probable error is not always 0.6745 of the mean error, but varies with the number of unknown quantities. See Bienaymé 1852 and also Bessel 1838.
[1874] C. Tychsen. "Om Sandsynlighedsregningens Anvendelse til Lösningen af geometriske Problemer. (On the application of probability calculus to the solution of geometrical problems.) Tidsskr. Math. Zeuthen, (3) 4, 65-82.
[1875] P. van Geer. "Over het gebruik van determinanten bij de methode der kleinste kwadraten," N. Arch. Wisk. 1, pp. 179-188; Vol. 9 (1882), pp. 180-188; "Sur l'emploi des déterminants dans la méthode des moindres carrés, Arch. Neer. 12 (1877), pp. 229-240; Arch. Neer. 18 (1883), pp. 127-137.
[1875] D.J. Korteweg. "Over de waarschijnlijkheid van de verschillende mogelijke uitkomsten eener verkeizing waarbij stemmers van tweeërlei kleur zich bij loting in afdeelingen verdeelen," N. Arch. Wisk. 1, pp. 157-178; Vol. 2 (1876) pp. 40-61. French version (1877): "Sur la probabilité des divers résultats possibles d'une élection pour laquelle des votants des deux opinions différentes se partagent en sections par la voie du sort." Arch. Néerl. Sci. Exact. Nat., 12, 65-95.
[1875] S. Levänen. "Ett sannolikhetsproblem," Helsingf. Öfv. 17, pp. 112-120.
[1875] Ch.M.Schols. "Over de theorie de fouten in de ruimte en in het platte vlak," [On the errors in space and the plane] Amst. Ak. Vh. 15, pp. 1-70. Also translated "Théorie des erreurs dans le plan et dans l'espace," Ann. Ec. Polytech. Delft. 2 (1886), pp. 123-178.
[1876] Ch. M. Schols. "De interpolatie-formulae van Tchébychef volgens de methode der kleinste vierkanten." Verslagen en mededeelingen der koninklijke adademie van Wetenschappen 9, pp. 301-311. French version (1877): "La formule d'interpolation de Tchébycheff suivant la méthode des moindres carrés." Arch. Néerl. Sci. Exact. Nat., 12, 102-12.