Miscellaneous 1851

Miscellaneous Investigations 1851-1865

The study of least squares continues to dominate the literature. The study of sensation by Fechner begins the era of Psychophysics. Quetelet continues his work. Note also the applications to the US Coastal Survey.

Publications are sorted by language and then year of publication.

Publications in English
See also separately Charles Schott.

[1851] George Biddle Airy "On a Question of Probabilities which occurs in the use of a fixed collimator for the Verification of the Constancy of Position of an Azimuth circle. Report of the ... Meeting of the British Association for the Advancement of Science (2nd part) pp. 1-2.[1851] Can the Theory of Errors be applied to quantities for which the errors are the result of observation and also of the formulas used?
[1851] George Biddle Airy "On the Weights to be given to the separate Results for Terrestrial Longitudes, determined by Observations of Transits of the Moon and Fixed Stars," Mem. Astron. Soc. London 19, pp. 213-229. Weight is the reciprocal of the square of probable error.
[1851] William Fishburn Donkin. "Prof. Donkin on certain Questions relating to the Theory of Probabilities," Ph. Mg. 1 pp. 353-367, 458-465; Vol. 2 (1851) pp. 55-60. He offers critical remarks on the Theory of Least Squares. See Ellis 1850 and Herschel 1850.
[1851] Charles Hughes Terrot. "An Attempt to compare the Exact and Popular Estimates of Probability," Edinb. R.S. P. 2 pp. 228-230.
[1851] Charles Hughes Terrot. "On Probable Inference," Edinb. R.S.P. 2 pp. 288-290.
[1852] R.R. Anstice. "On a problem in combinations." Camb. & Dublin Math. J., 7, 279-92; 8, 149-54.
[1852] Arthur Cayley. "Demonstration of a theorem relating to the products of sums of squares." Phil. Mag., (4) 4, 515-19.
[1852] W. Orchard. "Petersburg Problem," Assur. Mg. 2 pp. 185. (Two pages are lacking after the article in this scan. The article is complete.)
[1852] Peter Hardy "Some Considerations in the Theories of Combinations, Probabilities, and Life Contingencies." The Assurance Magazine, Vol. 2, No. 2, pp. 151-159. Concluded in Vol. 2, No. 3, pp. 259-270.
[1852] Frederick Hendricks. Contributions to the history of insurance and of the theory of life contingencies. London: Layton. Also in The Assurance Magazine 2, 121-150, 222-258; The Assurance Magazine 3 (1853), 93-120.
[1852-62] T.P. Kirkman. "On the puzzle of fifteen young ladies." Phil. Mag., (4) 3, 526-7; Phil. Mag. (4) 23, 198-204.
[1852] T.P. Kirkman. "Theorems in the doctrine of combinations." Phil. Mag. (4) 4, 209.
[1852] Benjamin Peirce. "Criterion for the rejection of doubtful observations," Gould As. J. 2, pp. 161-163. See Gould 1855, Chauvenet 1864, Airy and Winlock 1856, Stone 1868 and especially Glaisher 1872 and 1873.
[1853] Arthur Cayley. "Note on a question in the Theory of Probabilities." Philosophical Magazine. 6 p. 259.
[1853] T.P. Kirkman. "Note on combinations." Phil. Mag. (4) 5, 11-12.
[1853] T.P. Kirkman. "Theorems on combinations." Camb. & Dublin Math. J. 8, 38-45.
[1853] C.J. Hargreaves. "On the valuation of life contingencies by means of tables of single and joint lives." Phil. Mag. (4) 5, 39-45.
[1853] Charles Hughes Terrot. "On the summation of a compound series and its application to a problem in probabilities." Trans. Royal. Soc. Edin., 20, 541-5.
[1854] Robert Leslie Ellis "Remarks on the fundamental principle of the theory of probabilities." Transactions of the Cambridge Philosophical Society 9, pp. 605.
[1854] G. Scott. "Calculation of the Odds of throwing any specified Number with Two, Three, Four or more Dice," Assur. Mg. 4 pp. 247-249.
[1854] H. Wibraham. "On the Theory of Chances developed in Professor Boole's 'Laws of Thought.'" Ph. Mg. 7 pp. 465-476.
[1855] A.D. Bache. "Comparison of the reduction of horizontal angles by the method of dependent directions and of dependant angular quantities, by the method of least squares," Rep. Coast Survey U.S. for 1854, pp. 63*-70*.
[1855] Benjamin Apthorp Gould. "Report... containing directions and tables for the use of Peirce's Criterion for the Rejection of Doubtful Observations," Rep. Coast Survey U.S. for 1854, pp. 131*-138*. Reprinted with different title in Gould As. J. 4, pp. 81-87.
[1855] William A. Guy. "On the Analogy existing between the aggregate Effects of the Operations of the Human Will and the Results commonly attributed to Chance." The Assurance Magazine, and Journal of the Institute of Actuaries, Vol. 5, No. 4, pp. 315-323.
[1855] Hilgard. "Discussion of the probable error of observation with a twenty-six in ch portable transit..." Rep. Coast Sur. U.S. for 1854. p. 121*.
[1855] Humphrey Lloyd. "On the mean results of observations," Transactions of Royal Irish Academy 22, pp. 61-73; abstract in Proceedings of the Royal Irish Academy 4, pp. 180-183. (Presented in 1848.)
[1855] Benjamin Peirce. "Report on the Determination of Longitude by Moon Culminations," Rep. Coast Sur. U.S. for 1854, pp. 109*-120*.
[1856] George Biddle Airy "Letter from .... [Remarks on Peirce's Criterion] Gould As. J. 4 pp. 137-138. The Criterion are opposed.
[1856] George P. Bond. "On the Use of Equivalent Factors in the Method of Least Squares." Memoirs of the American Academy of Arts and Sciences 6, pp. 179-212.
[1856] R.L. Ellis. "Remarks on the fundamental principle of the theory of probabilities." Trans. Camb. Phil. Soc., 9 (4), 605-7.
[1856] Benjamin Apthorp Gould."On Peirce's Criterion for the Rejection of Doubtful Observations, with Tables for facilitating it application," Gould As. J. 4 pp. 81-87.
[1856] John Paterson. "Investigation and calculation of the results of a process of causation." Proc. Amer. Ass. Advance. Sci., 1856, 29-49.
[1856] Charles Hughes Terrot. "On the Possibility of combining two or more Probabilities of the same Event so as to form one Definite Probability," Edinb. R. S. T. 21 pp. 369-376.
[1856] Joseph Winlock. "On Professor Airy's objections to Peirce's criterion," Gould As. J. 4, pp. 145-147. Airy's (1856) objections are considered in detail.
[1857] George P. Bond. "On the use of Equivalent Factors in the Method of Least Squares." Am. Ac. Mm. 6 pp. 179-212.
[1857] S. Brown. "On the advantages to statistical science of a uniform decimal system of measures weights and coins, throughout the world." J. Inst. Actuar., 7, 37-42.
[1857] William Fishburn Donkin. "On an analogy relating to the theory of probabilities, and on the principle of the method of least squares," QJ Mth. 1 pp. 152-162. Deduces the exponential law of error. See Glaisher Mem. Astron. Soc. Lond. Vol. 39, p. 118.
[1857] Charles Hughes Terrot. "On the summation of a compound series and its application to a problem in probabilities." Proc. Royal. Soc. Edin., 3, 173-5.
[1857] Charles Hughes Terrot. "On the possibility of combining two or more independent probabilities of the same Event, so as to form one Definite Probability," Edinb. R. S. P. 3 pp. 366-7.
[1857-60] Simon Newcomb. (Discussion of objections raised by Mr. Mill and others, against Laplace's presentation of the doctrine of probabilities.) Am. Ac. P. 4 (1857-60) pp. 433-440.
[1858] Clarke. Ordnance Trigonometrical Survey of Great Britain and Ireland. Account of the Observations and Calculations of the Prinicpal Triangulations and of the Figure, Dimensions and mean Specific Gravity of the Earth as derived therefrom. (London) The triangulation is adjusted by the method of least squares.
[1859] W.P.G. Bartlett "Theory of the distribution of points on a line." Mathematical Monthly 1, pp. 84-87.
[1859] R. Campbell. "On a test for ascertaining whether an observed degree of uniformity, or the reverse, in tables of statistics is to be looked upon as remarkable." Ph. Mg. 18, pp. 359-368.
[1859] W. Farr. "On the construction of life-tables, illustrated by a new life-table for healthy districts of England." Phil. Trans. 149, 837-78.
[1859-61] Simon Newcomb. "Notes on the Theory of Probabilities,"Camb. (M.) Mth. M. 1 (1859) pp. 136-139, 233-235, 331-335; Vol. 2 (1860) pp. 134-140, 272-275; Vol. 3 (1861) pp. 119-125, 343-349.
[1860] R. Campbell. "On a test for ascertaining whether an observed degree of uniformity, or the reverse, in tables of statistics is to be looked upon as remarkable." J. Inst. Act. 8, pp. 316-327.
[1860] Simon Newcomb. "Notes on the theory of probabilities" Math. Mon. 2, pp. 134-140.
[1860] Benjamin Peirce. "Cyclic solutions of the school-girls' puzzles." Astr. J., 6, 169-74.
[1860] J. Wrottesley. "On the application of the calculus of probabilities to the results of the measures of the positions and distance of double stars." Proc. Roy. Soc., 10, 133-46.
[1860-1] Benjamin Gompertz. "On one uniform law of mortality from birth to extreme old age, and on the law of sickness." Proc. 4th Session Int. Statist. Congress (London) Rep., 454-62.
[[1861] George Biddle Airy On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations. (London) 2nd ed. 1875. Airy consulted only Laplace and thus it is unreadable.
[1861] Augustus de Morgan "On the Theory of Errors of Observation." Transactions of the Cambridge Philosophical Society 10, pp. 409-427
1861] William Spottiswoode. "On Typical Mountain Ranges; an application of the Calculus of Probabilities to Physical Geography," Gg. S. J. 31 pp. 149-154.
[1861] J.J. Sylvester. "Note on the historical origin of the unsymmetrical six-valued functions of six letters." Phil. Mag., (4) 21, 369-77.
[1861] J.J. Sylvester. "On a problem in tactic which serves to disclose the existence of a four-valued function of three sets of three letters each." Phil. Mag. (4) 21, 515-20.
[1861] J.J. Sylvester. "Remark on the tactic of 9 elements." Phil. Mag., (4) 22, 144-9.
[1861] J.J. Sylvester. "On a generalization of a theorem of Cauchy on arrangements." Phil. Mag., (4) 22, 378-82.
[1861] W.S.B. Woolhouse. "On Rev. T.P. Kirkman's problem representing certain triadic arrangements of fifteen symbols." Phil. Mag., (4) 21, 510-15.
[1862] W.P.G. Bartlett. "On the empirical interpolation of observations in physics and chemistry," American Journal of Science 34, pp. 27-33.
[1862] Arthur Cayley. "On a question in the theory of probabilities," Ph. Mg. 23 pp. 352-365, 470-471.
[1862] Benjamin Gompertz. A supplement to two papers published in the Transactions of the Royal Society "On the Science connected with Human Mortality" the one published in 1820, the other in 1825. Phil. Trans. 152 (1), 511-60.
[1862] Charles Hughes Terrot. "On the average value of human testimony." Proc. Roy. Soc. Edin., 4, 87-8.
[1862] W.J. Thomson. "On the constitution of society in this country, with reference to the proportion which male life bears relatively to female life and the effect of an excess of female life." Proc. Roy. Soc. Edin., 4, 583-603.
[1862] W.S.B. Woolhouse. "On triadic combinations of 15 symbols." Ladys' and Gentleman's Diary, 1862, 84-8. (Also: London Assurance Magazine, 10, 275-81.)
[1863] Arthur Cayley. "On a tactical theorem relating to the triads of fifteen things." Phil. Mag. (4) 25, 59-61.
[1863] P.E. Chase. "On the mathematical probability of accidental linguistic resemblances." Transactions of the American Philosophical Society 13 (1869), pp. 25-33.
[1863] William Chauvenet. Method of Least Squares. Appendix to Manual of Spherical and Practical Astronomy, Volume 1, Volume 2, pp. 469-566; tables 593-599. Appendix and related tables reprinted as A Treatise on the Method of Least Squares. (1868) Abridgment of Encke 1832. See also Peirce's Criterion of 1852 and 1856.
[1863] R.L. Ellis. The mathematical and other writings of R.L.E. Edited by W. Walton. Cambridge: Deighton Bell & Co.
[1863] W.S.B. Woolhouse. "On triadic combinations." Ladys' and Gentleman's Diary, 1863, 79-80.
[1864] T.K. Abbott. "On the Probability of Testimony and Arguments," Ph. Mg. 28 pp. 12-25.
[1864] J. Matthews Duncan. "On the variations of the fertility and fecundity of women according to age." Trans. Roy. Soc. Edinburgh, 23, 475-90.
[1864] Augustus de Morgan "On the Theory of the Errors of Observation," Trans. Camb. Phil. Soc. 10, pp. 409-427. Valuable contribution to the theory of the arithmetic mean. He suggests the name "critical error" rather than "probable error."
[1864] W.S.B. Woolhouse. "On Interpolation, Summation, and the Adjustment of Numerical Tables," Lond. Assurance Mag. 11, pp. 61-88, 300-332; Vol. 12, pp. 136-175.
[1864] T. Zakharov. The Numerical Relations of the Population of China... Hong Kong.
[1865] Robert Brünnow. "The Method of Least Squares," Spherical Astronomy (1st English ed. from 2nd German).
[1865] Arthur Cayley. "On a problem of geometrical permutation." Phil. Mag. (4) 30, 370-2.
[1865] W.S. Jevons. "On the variation of prices and the value of the currency since 1782." J.R. Statist. Soc., 28, 294-320.
[1865] James Joseph Sylvester. "On a special class of questions in the Theory of Probabilities." Report of the Annual Meeting of the British Association for the Advancement of Science 35 (1866), pp. 8- 9.
[1865] P.G. Tait. "On the Law of Frequency of Error," Trans. Soc. Edinb. 24 (1867), p. 139-146. The idea and algebraic work is similar to Quetelet 1846. See Glaisher 1872.
[1865] Isaac Todhunter. "On the Method of Least Squares," Camb. Ph. S. T. 11 pp. 219-238. (1871)
[1865] Isaac Todhunter. A History of the Mathematical Theory of Probability from the time of Pascal to that of Laplace. Cambridge and London.

Publications in French

See also Quetelet and Bertrand.

[1851] Antoine Augustine Cournot. Essai sur les fondements de nos connaissances et sur les caractères de la critique philosophique. Paris: Hachette. German translation by H. Schmuse (1849) Braunschweig.
[1851] P. Hossard. "Note sur la méthode des moindres carrés," Nouv. Annal. Math. 10 pp. 456-460. The proof of Ivory 1825 is rediscovered.
[1851] Alexandre C. Moreau de Jonnés. Statistique des peuples de l'antiquité. 2 tom. Paris. Tome Premier, Tome Second.
[1852] Biver. Théorie des moindres carrés établie par l'analyse pure. (Bruxelles)
[1852] J. Liouville. "Rapport sur un Mémoire de M. Jules Bienaymé, Inspecteur général des Finances, concernant le probabilité des erreurs d'apreès la méthode des moindres carrés," Liouv. J. Mth. 17 pp. 31-32.
[1852] L.A.J. Quetelet, "Sur quelques propietés curieuses que présentent les résultats d'une série d'observations,...," Bull. Acad. Belgique, 19, Pt. 2, pp. 303-317. It is illustrated with meteorological data.
[1852] Jean Baptiste Joseph Liagre "Sur la valeur la plus probable d'un côte géoésique commun à deux triangulations," Bull. Acad. Belgique, 19, Pt. 1, pp. 513-534. An example from 1849 Baeyer is discussed.
[1852] Jean Baptiste Joseph Liagre "Sur la loi de répartition des hauteurs barométriques,par rapport à la hauteur moyenne," Bull. Acad. Belgique 19, Pt. 2, pp. 502-513. The law is shown to agree with the exponential law of error.
[1852] Jean Baptiste Joseph Liagre. Calcul des Probabilités et Théorie des Erreurs, avec des Applications Sciences d'Observation en Géneral et al la Géodesie en particular. Bruxelles: Muquardt. (2nd ed 1879).
[1852] É. Roger. "Solution d'un problème de probabilités," Liouv. J. Mth. 17 pp. 202- 208.
[1853] P.E. Biver. "Théorie analytique des moindres carrés," Liouv. J. Mth. 18 pp. 169-200. This follows the method of Encke 1832.
[1853] A. Jamar. Théorie des probabilités. Bruxelles.
[1853] Jean Baptiste Joseph Liagre "Sur l'erreur probable d'un passage observé à la lunette méridienne de l'Observatoire royal de Bruxelles." Bull. Acad. Belgique, 20, Pt. 2, pp. 303-312
[1853] Jean Baptiste Joseph Liagre Calcul des probabilités et la théorie des erreurs, avec des applications aux sciences d'observation en general, et à la géodésie en particular. Bruxelles.
[1854] Édouard Cornaz. "Recherches statistiques sur la fréquence comparative des couleurs de l'iris." Ann. oculist., 31, 251-80.
[1854] Hélie. Mémoire sur la probabilité du tir des projectiles de l'artillerie navale. (Paris) 2nd ed. 1856. Here bound in the Commission de Gâvre Année 1854.
[1855] Joseph Louis Bertrand. Sur la méthode des moindres carrés. Mémoires sur la combinason des observations, par Ch. Fr. Gauss. (Paris) This is a translation of the Latin memoirs of Gauss.
[1855] Joseph Louis Bertrand. "Sur la méthode des moindres carrés. (Lettre à M. Elie de Beaumont, accompagnant l'envoi d'un exemplaire de la traduction des Mémoires de Gauss.)" C.R. Acad. Sci. Paris, 40 pp. 1190-1192.
[1855] E.N. Gaucherel. "Note sur les erreurs relatives et absolues" Nouvelles annales de mathématiques 1re série, tome 14, pp. 145-150.
[1855] Jean Baptiste Joseph Liagre "Sur la probabilité de l'existence d'une cause d'erreur regulière dans une série d'observations," Bull. Acad. Belgique, 22, Pt. 2, pp. 9-13, 15-54. A valuable theoretical discussion.
[1856] F. Brioschi. "Sur les séries qui donnent le nombre de racine réelles des équations algébriques à une or plusieurs inconnues." Nouv. Ann. Math., 16, 264-86.
[1856] B. Jaufroid. "Théorèmes sur les erreurs relatives," N.A. Mth. 15 pp. 154-157.
[1856] Alexandre C. Moreau de Jonnés. Éléments de Statistique... 2nd édition. Paris.
[1856] Jean Brasseur. "Review on 'Note contenant une démonstration nouvelle du théorème de Bernoulli', par M.A. Meyer." Brux. Ac. Bull 23, pp. 349 - 350.
[1856] Ch. Dufour. "Sur certaines erreurs en matière d'observation." Bulletin de la Société vaudoise des sciences naturelles. Vol. 5, pp. 99-100.
[1856] Anton Meyer "Note sur le théorème inverse de Bernoulli," Brux. Ac. Bull. 23 pp. 148-158.
[1857] Babinet and Housel. Calculs pratiques appliqués aux sciences d'observations (Paris) Two pages are given over to the method of least squares.
[1857] Louis Adolphe Bertillon. Conclusions statisiques contre les détracteurs de la vaccine précédées d'un essai sur la méthode statistique appliquée à l'etude de l'homme. Paris.
[1857] I. Didion. "Mémoire sur la probabilité du tir des projectiles." Comptes Rendus Acad. Sci., Paris, 45. 85-89.
[1857] Jean Baptiste Joseph Liagre "Note sur la mesure de précision des observations méridiennes faites à l'Observatoire royal de Bruxelles," Bull. Acad. Belgique, 3, pp. 330-338.
[1857] Anton Meyer. Essai sur une exposition nouvelle de la théorie analytique des probabilités à posteriori. Liège.
[1858] Is. Didion. Calcul des probabilités appliqué au tir des projectiles. (Paris) See Sonnet's Dictionaire des mathématiques appliquées, (Paris, 1867). pp. 1103-1108.
[1858] P. M. Jullien SJ, "Sur la probabilité des erreurs dans la summe ou dans la moyenne de plusieurs observations," Tortolini A. 1 pp. 76-88, 149-155, 227-237. Errors subject to a constant law are discussed.
[1858] Élie Ritter. Manual théoretique de l'application de la méthode des moindres carrés au calcul des observations. (Paris) Textbook following Gauss' first demonstration.
[1859] Noël Germinal Pondra & Paul Michel Hossard. Question de probabilité résolue par la géometrie, etc. Paris.
[1859] Ch. Renouvier. L'homme: la raison, la passion, la liberté, la certitude, la probabilité morale. Paris.
[1860] E. Barbier."Note sur le problème de l'aiguille et le jeu du joint courvert," Liouville J. 5 pp. 273-286.
[1861] M. Block. Puissance comparée des divers états de l'Europe. Edition française, 2pt. German version: Die Machtstellung der europäischen Staaten. 2 pt. Gotha. Volume 2 is the atlas.
[1862] R. Blazejarski. "Solution Elementaire d'une question de probabilités," N.A. Mth. 1 pp. 131-132.
[1862] E. Brassinne. "Sur le calcul des moyennes entre plusieurs observations," Toul. Mm. Ac. 6 pp. 421-426.
[1862] Alfred P. de Courcy. Essai sur les lois du hasard, suivi d'études sur les assurances. Paris.
[1863] Louis-Adolphe Bertillon. "De la mèthode dans l'anthropologie à propos de l'influence es milieux sur la coloration des téguments." Bull. Soc. Anthropologie Paris 4, pp. 223-242.
[1864] Liagre, J.B.J. "Solution d'unde question de probabilités." Bulletins de l'Academie Royale des Sciences,... Belgique 17, pp. 365-370.

Publications in German

[1851] Franz Friedrich Ernst Brünnow. Lehrbuch der sphärischen Astronomie. Mit einem Vorwort von J.F. Encke. Berlin. 5th ed. 1881. English translation 1865 from 2nd German edition.
[1851] Ingen. Denszler. "Ueber den Fundamentalsatz der Methode der kleinsten Quadrate," Mittheil. Gesell. Zürich 2, pp. 110-118.
[1852] Joseph Dienger. "Ueber die Ausgleichung der Beobachtungsfehler," Archiv. Math. u. Phys. Vol. 18, pp. 149-193; Vol. 19, pp. 211-227.
[1852] Joseph Dienger. "Ueber die Bestimmung des Gewichts der nach der Methode der kleinsten Quadrate erhaltenen wahrscheinlichsten Werthe der Unbekannten, wenn Bedingungsgleichungen vorhanden sind," Grunert Arch. 19 pp. 197-202.
[1852] P.A. Hansen. "Allgemeine Auflösung eines beliebigen Systems von linearischen Gleichungen." Leipzig Abh., 1. 84-122.
[1852] Hartner. Handbuch der niedern Geodäsie, nebst einem Anhange über die Elemente der Markscheidekunst. (Wien). 2nd ed. 1856, 4th 1872. See also Bürsch.
[1852] L. Oettinger. Die Wahrscheinlichkeits-Rechnung. Berlin: Reimer.
[1853] Anon. Tafeln zur Berechnung der Wahrscheinlichkeit des Vorkommens von Beobachtungsfehler. Berline, lith. 00. 11.
[1853] J.F. Encke. "Über die Anwendung der Wahrscheinlichkeitsrechnung auf Beobachtungen." Berliner Astr. Jb. 1853, 310-51.
[1853] Johann August Grunert "Elementare Betrachtungen über die Bildung der Bedingungsgleichungen aus gegebenen Beobachtunge," Archiv. Math. u. Phys. 21, pp. 453-486. "Bedingungsgleichungen" or "Equations of conditions" is here not used in its usual sense.
[1853] J. Steiner. "Combinatorische Aufgabe." J. reine angew. Math., 45, 181-2.
[1853] Hugo Franz von Brachelli. Die Staaten Europa's in kurzer statistischer Darstellung. Brünn.
[1854] H. d'Arrest. "Beitrag zur Methode der kleinsten Quadrate," Bericht. Sächsich. Gesell., 6 (Leipsig B.) pp. 133-136. Astron. Nachr. 41, col. 35-40. Observes six new geometrical properties of the probability curve and obtains its equation by a mechanical idea.
[1854] F. Escherich. Hygienisch-statistische Studien über die lebensdauer in verschiedenen Ständen. Würzburg.
[1854] Goehlert. Untersuchungen über das Sexualverhältniss der Geborenen.
[1855] Franz Friedrich Ernst Brünnow. Tafeln der Flora, mit Berücksichtigung der Störungen durch Jupiter und Saturn. Berlin.
[1855] R. Dedekind. "Bemerkungen zu einer Aufgabe der Wahrscheinlichkeitsrechnung," Crelle J. 50 pp. 268-276.
[1855] Christian Ludwig Gerling "Ueber die Schätzung des mittleren Fehlers directer Beobachtungen," Grunert Arch. 25 pp. 219-222. Corrections to his book of 1843.
[1855] Phillip L. Seidel. "Bemerkungen über den Zusammenhang zwischen dem Bildungsgesetze eines Kettenbruches und der Art des Fortgangs seiner Näherungsbrüche. Abhand. Akad. Wiss. Mth. Ps. 7, pp. 559-602.
[1856] E.A. Jonâk. Theorie der Statistik in Grundzügen. Wien.
[1856] A. Kunzek. Studien aus der höheren Physik. Wien.
[1856] C.A.F. Peters. "Ueber die Bestimmung des wahrscheinlichen Fehlers einer Beobachtung aus den Abweichungen der Beobachtungen von ihrem arithmetischen Mittel," Astro. Nachr. 44, col. 29-32. Trans. in Rep. Coast Sur. U.S. for 1856, pp. 307-308 by Schott. For his formula see also Lüroth 1869 and Helmert 1875.
[1856] J.J. Vorländer. "Ueber die Genauigkeit der Längenmessungen mit der Messkette auf verschiedenen Bodenarten," Zeitschrift Math. u. Phys., 1, pp. 142-159. See Börsch 1863.
[1857] Andrä. "Fehlerbestimmung bei der Auflösung der Pothenot'schen Aufgabe mit dem Messtische," Astron. Nachr. 47, col. 193-202. Points for which the probabilities of error are equal have an ellipse for locus.
[1857] d'Arrest. "Schreiben ...[über die Berechnung der Gewichte]. Astron. Nachr. 47, col. 17-20. Connects weights with determinants.
[1857] Baur. ______________ Programm des Stuttgarter Polytechnikursus für 1857. Concerns the determination of weights.
[1857] Cantor, M. "Ueber Normalstellen." Zeitschrift für Mathematik und Physik 2, pp. 410-412.
[1857] Joseph Dienger. Ausgleichung der Beobachtungsfehler nach der Methode der kleinsten Quadratssummen. Mit zahlreichen Anwendung, namentlich auf geodätische Messungen, Braunschweig. An excellent elementary text following Gauss 1809. See Dienger 1852.
[1857] E. Engel. Die Productions- und Consumptionsverhältnisse des Königreichs Sachsen. Zeitschrift Statistischen. Bureaus des Königlich Sächsischen Min. des Inneren, nos. 8 & 9. Reprinted Bull. Int. Statist. Inst., 9 (1), 54 pp.
[1857] Georg Friedrich Kolb. Handbuch der vergleichenden Statistik. Zurich.
[1857] Joseph Petzval. "Fortsetzung des Berichtes über optische Untersuchungen," Sitzungsberichte der Mathematisch-Naturwissenschaftliche Klasse Königliche Akademie der Wissenschaften, Wien 24, pp. 129-144. The method of least squares does not apply to Optics.
[1857] Sawitsch. Die Anwendung der Wahrscheinlichkeitstheorie auf die Berechnung der Beobachtungen und geodätsche Messungen, oder die Methode der kleinsten Quadrate. (Russian) German ed. 1863.
[1857] Vorländer. "Ueber das geodätische Vorwärts-Einschneiden," Zeitschrift Math. u. Phys. 2, pp. 299-316.
[1857] Zech. Einladung zur akademischen Feier des Geburtstags des Königs von Württemberg, nebst einger Abhandlung zur Methode der kleinsten Quadrate. (Tübingen). The first exhaustive discussion of the adjustment of indirect observations subject to conditional equations. See Jordan, Elemente der Vermessungskunde (Stuttgart, 1877) p. 6.
[1858] Johann August Grunert "Drei Grössen x, y, z deren Summe die gegebene Grösse s ist, sind durch Messung bestimmt worden, und man habe dadurch für diese drei Grössen respective die Werthe a, b, c erhalten. Da diese Werthe mit Beobachtungsfehler behaftet sind, und ihre Summe also im Allgemeinen nicht genau s ist, so soll man dieselben so verbessern, dass die verbesserten Werthe genaus die Summe s geben, und die Summe der Quadrate der Verbesserungen ein Minimum ist." Archiv Math. u. Phys. 31, pp 479-481.
[1858] Kohler. Die Landesvermessung des Königsreichs Württemberg (Stuttgard) Applications of the method of least squares are located in an Appendix.
[1858] Richelot. "Bermerkungen zur Theorie der Maxima und Minima." Astr. Nachr. 48 (no. 1146), 273-86.
[1858] Schindler. Ueber Fehler bei der Berechnung eines ebenen Dreiecks. (Prag)
[1858] von Andrae, "Fehler bestimmung bei der Auflösung der Pothenot'schen Aufgabe mit dem Messtische." Astronomische Nachrichten 47 No. 1117, Columns 193-202.
[1858] J.J. Voränder. "Zur praktischen Geometrie," Zeitschrift. Math. u. Phys. 3, pp. 189-193. On the adjustment of a quadrilateral.
[1858] J.J. Voränder. "Bemerkungen über das numerische Eliminiren bei geodatischen Operationem," Zeitschrift. Math. u. Phys. 3, pp. 16-22. On shortening computations.
[1858] Christian Ludwig Gerling "Bemerkungen über das indirecte Eliminirem bei geodätischen Arbeiten," Zeitschrift Math. u. Phys. 3, 377-382. See the preceding article by Voränder.
[1858] J.J. Vorländer. Ausgleichung der Fehler polygonometrischer Messungen. (Leipzig).
[1858] Joseph Dienger. "Ueber die Ermittelung des wahrscheinlichen Fehlers bei Längenmessungen," Grunert Arch. 31 pp. 225-228. He opposes the method of Voränder given in the preceding book.
[1859] C. Bremiker. Das Risiko bei Lebensversicherungen. Berlin.
[1859] Richard Dedekind. "Mathematische Mittheilungen," Zür. Vjschr. 4 pp. 356-365; Vol. 5 (1860) pp. 66-88.
[1859-61] J. E. Wappaeus. Allgemeine Bevölkerungsstatistik. Vorlesungen. 2 vols. Leipzig. Erster Theil and Zweiter Theil.
[1860] Baeyer. Wissenschaftliche Begründung der Rechnungsmethoden des Centralbureaus der europäischen Gradmessung: I. Die Methode der kleinsten Quadrate. II. Die Anwendung derselben auf Geodäsie.
[1860] Richard Dedekind. "Ueber die Bestimmung der Präcision einer Beobachtungsmethode nach der Methode der kleinsten Quadrate." Vierteljahrs Gesell. Zürich 5, pp. 76-83. The most probable measure of precision is found. See Börsch 1866.
[1860] A. Erman. "Ueber Herrn Bunakowskji's mechanisches Mittel zur Ausführung der Rechnungen, welche die Methode der kleinsten Quadrate erfordert," Erman Arch. Rs. 19 pp. 1-12.
[1860] Gustav Fechner. Elemente der Psychophysik. Vol. 1 and Vol. 2. Leipzig:Breitkopf und Härtel.
[1860] Philipp Fischer. Grundzüge des auf menschliche Sterblichkeit gegründeten Versicherungswesens. 2 parts. Oppenheim am Rhein, Darmstadt.
[1860] Peter Merian. Die Mathematiker Bernoulli. Basel. Biographies of the mathematical Bernoullis.
[1861] M. Block. Bevölkerung des Französischen Kaiserreichs in ihren wichtigsten statistischen Verhältnissen dargestellt. Gotha.
[1861] C. W. Borchardt. "Ueber Interpolation nach der Methode der kleinsten Quadrate," Crelle's Jour. Math. 58, pp. 270-272. On Chebyshev's method. See 1858 and 1859.
[1861] G.T. Fechner. "über die Correctionen bezüglich der Genaouigkeitsbestimmung der Beobachtungen, der Bestimmung der Schwankungen meteorologischer Einzelwerthe um ihren Mittelwerth, und der psychophysischen Massbestimmungen nach der Methode der mittleren Fehler," Leip. B. 13 pp. 57-113.
[1861] Christian Ludwig Gerling "Notiz in Betreff der Prioritäts-Verhältnisse in Beziehung auf die Methode der kleinsten Quadrate," Nachr. Gesell. Göttingen for 1861, pp. 273-275.
[1861] Christian A. F. Peters. Ueber die Bestimmung des Längenunterschiedes zwischen Alton und Schwerin. (Altona) Contains a detailed history of the discovery of the personal equation. See Radau 1866.
[1861] A. Winckler. "Ueber den mittlern Fehler der Kettenmessungen," Zeitschr. Math. u. Phys. 6, pp. 109-119. An excellent paper.
[1861] August Zillmer. Die mathematischen Rechnungen bei Lebens- und Renten-Versicherungen. Berlin.
[1862] Christian Ludwig Gerling "Ueber Genauigkeit der Funcionen bedingter Beobachtungen," Grunert Arch. J. 38 pp. 379-381. Additions and corrections to his book.
[1862] Segnitz, E. "Einige Bemerkungen über die Berechnung der sogenannten Mittel und deren Anwendung in den Erfahrungswissenschaften." Zeitschrift für Mathematik und Physik 7, pp. 65-74.
[1862] Ludwig Siedel. "Ueber die Verallgemeinerung eines Satzes aus der Theorie der Potenzreihen." Sitzungsber. Baiersch. Acad., 2, pp. 91- 97.
[1862] Hugo Franz von Brachelli. Dreissig statistische Tabellen über alle Länder und Staaten der Erde.
[1862] Albert Wild. Die Grundsätze der Wahrscheinlichkeits-Rechnung und ihre Anwendungen. München.
[1862] Albert Wild. Die Leibrenten-Lebensversicherungs und Renten-Anstalten. München, Augsburg.
[1862] Albert Wild.. Die öffentlichen Glücks-Spiele mit Einschluss der Lotterie-Anlehen, oder Anleitung zur Berechnung der Vortheile, Nachtheile,... bei dem Spielen. München, Augsburg.
[1862] Albert Wild. Politische Rechnungs. Wissenschaft-Anleitung zu allen im Staatsleben vorommenden Berechnungen durch Beispile erläutert. München.
[1862] Albert Wild.. Probleme der Statistik im Zusammenhange mit der politischen Rechnungs-Wissenschaft, und mit besondereer Brücksichtigung der statistischen Tabellen über Mortalitätsverhältnisse. München.
[1863] Ernst Abbe. Über die Gesetzmässigkeit in der Vertheilung der Fehler bei Beobachtungsreihen. (Jena) Dissertation. Reprinted in Gesammelte Abhandlungen Vol. 2, pp. 55-81.
[1863] Otto Börsch. "Ueber die Genauigkeit der Winkel- und Linien-Messungen," Zeitschr. Math. u. Phys. 8, pp. 321-341. Discusses precision of angle and linear measurements. See Vorländer 1856 and Hartner 1852.
[1863] W. I. Freeden. Die Praxis der Methode der kleinsten Quadrate für die Bedürfnisse der Anfänger bearbeitet. Vol 1 (Braunschweig). An excellent little book.
[1863] A. Kurz. "Ueber der Methode der kleinsten Quadrate," Vierteljahrsschr. Gesel. Zürich 8, pp. 225-240.
[1863] Ludwig Seidel. "Ueber eine Anwendung der Wahrscheinlichkeitsrechnung bezüglich auf die Schwankungen in den Durchsichtigkeitserhältnissen der Luft." Sitzungsberichte der Königl. Bayerischen Akademie der Wissenschaften, Part. 2. pp. 320-350.
[1863] Ludwig Seidel. "Resultate photometrischer Messungen an 208 der vorzüglichen Fixsterne." Abhand. Akad. Wiss. Mth. Ps. 9, Abt. pp. 419-609.
[1864] Elwin Bruno Chrisotffel. "Ueber die Bestimmung einer Oberfläche durch lokale Messungen auf derselben," Journal für die reine und angewandte Mathematik 64, pp. 194-209. [See also Bestimmung einer Oberfläche durch lokale Messungen. (Berlin)]
[1864] A. Wagner. Die Gesetzmässigkeit in den scheinbar willkürlichen menschlichen Handlungen vom Standpunkt der Statistik. Hamburg.
[1865] Gooss, Johann Wilhelm. Zur Begründung der methode der kleinsten Quadrate. pp. 32. A doctor's thesis. He deduces the exponential law from the assumptions that the curve is symmetric, it is asymptotic to the x-axis, that the equation is simple, etc.
[1865] Ernst Gusmann. Statistische Untersuchungen über die Mortalitätsverhältnisse im ärtzlichen Stande. Tubingen.
[1865] Fr. Oesterlen. Handbuch der medicinischen Statistik. Tübingen.
[1865] Albert Wild.. Die europäischen Lotterie-Anlehen. Rosenheim und Leipzig.

Publications in Italian

[1852] A. Bordoni. "Sulle Probabilità," Mil. G. I. Lomb. 4 pp. 31-63.
[1853] Alessio Iginio. Saggio teorico di Statistica.
[1856-57] Bellavitis, G. "Considerazioni su la teoria della probabilità." Atti dell'i R. Istituto veneto di scienze, lettere ed arti, Ser. 3, Vol. 2 pp. 299-319.
[1856] O. Viola. Discussioni per una teoria di statistica.
[1857] N. Castagna. Della Statistica.
[1857] Placido de Luca. Principii elementari di Statistica. Naples.
[1857] Giacomo Racioppi. Del principio e del limite della statistica. Naples.
[1858] F. Casorati. "Intorno ad alcuni puncti della theoria dei minini quadrati," Tortolini A. 1 pp. 329-343. Discusses the use of determinants.
[1858] F. Maggiore-Perni. Della compilazione e della materia statistica.
[1861] G. Vanneschi. Elementi di statistica.
[1863] Gaetano Caporale. Lezioni poplari di Statistica teorico-pratica.
[1864] Francesco Protonotari. L'idea moderna della statistica. Firenze.

Publications in Dutch, Latin, Swedish, Russian &c.

[1854] Ludwig M. Merz. De theoria probabilitatis adhibita in physicam. Monachii.
[1857] L. A. Colding. "Fremstilling af en approximeret Mindste-Quadrat-Methode," Kjöb. Ov. 5, pp. 52-59.
[1857] F.J. Wrede. "Några anmärkningar rörande minsta qvadratmethodens tillämpning," Stockh. Öfv. 14 pp 73-81. On the error ellipse.
[1857-61] G.R. Dahlander. "Om felfördelningen vid bestämmande af en punkts läge i rymden," Stockh. Öfv. 14 pp. 405-409; "Bidrag till läran om geometriska betydelsen af felfördelning efter minsta qvadratmethoden," Vol. 15 (1858) pp. 49-54; "Om felfördelninge efter minsta qvadratmethoden vid bestämmande af en punkts sannolika läge uppå ett plan eller i rymden," Vol. 18 (1861) pp. 63-66.
[1860] C.G. von Andrae. "Udvidelse af en af Laplace i Mécanique celeste angivet Methode for Bestemmelsen af en unbekjendt Störrelse ved givne unmiddelbare Jagttagelser," Oversigt af Kgl. Danske Videnskabernes Selskabs over Forhandligen (Copenhagen) pp. 198-225.
[1860] Frans Wilhelm Hultmann. Minsta Qvadratmetoden. Stockholm.
[1861] P. Freuchen. "Om Udførelsen af Bereguingerne ved Anvendelsen af de mindste Kvadraters Method," Mth. Ts. 3 pp. 81-102. (On the computation in connection with the application of the method of least squares.)
[1862] Tsinguer. "Théorie élémentaire de la méthode des moindres carrés." Mosc. Bull. S. Nt. 35 (pt. 2) pp. 446-64.
[1862] Hendrik Arend Wijnne. De leer der waarschijnlijkheid in hare toepassing op het dagelijksche leven.
[1863] R. Lobatto. "Over de waarschijnlijkheid van gemiddelde uitkomsten uit een groot aantal waarnemingen. Archief. Wisk. Genoots 2, pp. 96-127.