- Michell , J. 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 234 – 264 . A brief account of Michell's life and work is provided in A. Geikie, Memoir of John Michell (Cambridge, 1918); see also Clyde L. Hardin, ‘The Scientific Work of the Reverend John Michell’, Annals of Science, 22 (1966), 27–47. During the century following Newton's death, Michell was, according to Whittaker, ‘the only natural philosopher of distinction who lived and taught at Cambridge’; see E. Whittaker, History of the Theories of Aether and Electricity. The Classical Theories (London, 1951), p. 153.
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 243 – 243 .
- De Movire , A. 1738 . The Doctrine of Chances , 2nd edn. v – v . London An account of De Moivre's contributions to mathematics, which includes a section devoted to his work on probability, is to be found in I. Schneider, ‘Der Mathematiker Abraham de Moivre (1667–1754)’, Archive for History of Exact Sciences, 5 (1968–9), 177–317.
- Arbuthnot , J. 1710 . An Argument for Divine Providence, taken from the Constant Regularity observed in the Births of both Sexes . Phil. Trans. , 27 : 186 – 190 . Analyses of Arbuthnot's argument are given by I. Hacking in his Logic of Statistical Inference (Cambridge, 1965), pp. 75–81, and in his The Emergence of Probability (Cambridge, 1975), chapter 18.
- See Todhunter I. History of the Theory of Probability Cambridge 1865 222 223 for an account and references.
- Bayes , T. 1764 . Phil.-Trans. , 53 : 370 – 418 . An Essay towards Solving a Problem in the Doctrine of Chances
- Bayes . 1764 . An Essay towards Solving a Problem in the Doctrine of Chances . Phil.-Trans. , 53 : 374 – 374 .
- Boole , George . 1851 . On the Theory of Probabilities, and in particular on Michell's Problem of the Distribution of the Fixed Stars . Phil. Mag. , 1 : 521 – 530 . 4th series reprinted in G. Boole, Studies in Logic and Probability, edited by R. Rhees (London, 1952), 247–59. See also G. Boole, An Investigation of the Laws of Thought, on which are Founded the Mathematical Theories of Logic and Probability (London, 1854), pp. 364–8.
- Forbes , J.D. 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 401 – 427 . 3rd series (p. 424). For information about Forbes, see J. C. Shairp, P. G. Tait and A. Adams-Reilly, Life and Letters of James David Forbes, F.R.S. (London, 1873). Chapter 14 of this biography, written by Tait, contains an account of Forbes' work on the double star problem and prints some of the letters he received concerning the matter from such men as William Thomson, Bishop Terrot, George Airy, and Robert Leslie Ellis.
- See Fisher R.A. Statistical Methods and Scientific Inference Edinburgh 1956 37 40 I. Hacking, Logic of Statistical Inference (Cambridge, 1965), pp. 81–2.
- Some comments on the questions raised by Forbes' attack on Michell's reasoning are to be found in Garber Elizabeth Aspects of the Introduction of Probability into Physics Centaurus 1972 17 11 39
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 243 – 243 .
- In his introduction to Bayes' memoir, Richard Price drew attention to the explicit definitions of the words ‘chance’ and ‘probability’ that Bayes had provided. ‘His design herein’, Price wrote, ‘was to cut off all dispute about the meaning of the word, which in common language is used in different senses by persons of different opinions’. Bayes An Essay towards Solving a Problem in the Doctrine of Chances Phil.-Trans. 1764 53 375 375
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 243 – 243 .
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 243 – 234 .
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 244 – 245 .
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 246 – 246 .
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 247 – 249 .
- de Laplace , P.S. 1902 . A Philosophical Essay on Probabilities Edited by: Truscott , W.S. and Emory , F.L. 16 – 16 . New York
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 249 – 249 .
- Forbes , J.D. 1849 . On the alleged Evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, arising from their Proximity alone . Phil. Mag. , 35 : 132 – 133 . 3rd series (p. 132).
- Forbes . 1849 . On the alleged Evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, arising from their Proximity alone . Phil. Mag. , 35 : 132 – 132 . 3rd series One of the first critics of the view that every proposition must have some numerical probability was Forbes' correspondent Bishop Terrot. See Terrot, ‘On the possibility of combining two or more probabilities of the same event, so as to form one definite probability’, Transactions of the Royal Society of Edinburgh, 21 (1857); reprinted as Appendix C in G. Boole, Studies in Logic and Probability, edited by R. Rhees (London, 1952), pp. 487–96.
- Forbes . 1849 . On the alleged Evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, arising from their Proximity alone . Phil. Mag. , 35 : 132 – 132 . 3rd series Forbes is quoting from J. Herschel, Outlines of Astronomy (London, 1848), p. 565. See also J. M. Keynes, A Treatise on Probability (London, 1921), p. 296, where it is claimed that the invalidity of Michell's argument ‘becomes plain when we notice that he would still have a high probability for his conclusion even if only one binary star had been observed’.
- Herschel . 1848 . Outlines of Astronomy 564 – 564 . London
- 1850 . The Edinburgh Review Vol. 92 , 1 – 57 . (p. 36). The essay is a review of Quetelet's Lettres à S.A.R. le Duc règnant de Saxe-Cobourg et Gotha sur la Théorie des Probabilités appliquée aux Sciences Morales et Politiques (Brussels, 1846). Following the usual custom it was unsigned, though there was no mystery about its authorship. The importance of Herschel's expository essay in the formation of Maxwell's ideas about the relevance of statistics to the kinetic theory of gases was noticed by C. C. Gillispie, ‘Intellectual Factors in the Background of Analysis by Probabilities’, in Scientific Change, edited by A. C. Crombie (London, 1963), pp. 431–53. See also Garber (footnote 11), and I. Schneider, ‘Rudolph Clausius’ Beitrag zur Einführung wahrscheinlichkeitstheoretischer Methoden in die Physik der Gase nach 1856’, Archive for History of Exact Sciences, 14 (1974–5), 237–61, especially pp. 258ff.
- 1850 . The Edinburgh Review Vol. 92 , 36 – 37 . Herschel gives the credit for this argument not to Michell but to the Russian astronomer F. G. W. Struve, who had devised a slightly more elaborate way of calculating chances than that used by Michell. Whittaker (footnote 1), 153, observes that Michell's researches seem to have attracted little or no attention among his contemporaries and successors, who silently acquiesed when his discoveries were attributed to others.
- 1850 . The Edinburgh Review Vol. 92 , 37 – 37 .
- 1850 . The Edinburgh Review Vol. 92 , 36 – 36 .
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 404 – 404 . 3rd series
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 404 – 404 . 3rd series
- Hacking , I. 1975 . The Emergence of Probability 129 – 129 . Cambridge in says that English scientists in the eighteenth century ‘took a purely aleatory attitude to probability’. There is no reason to think that Michell was an exception to this generalization. In the light of subsequent developments, it might be urged that an epistemic attitude to probability is implicit in Bayes' work but, even if this is so, there is no indication that Michell recognised its relevance for his enquiries.
- De Morgan , A. 1817–45 . “ Theory of Probabilities ” . In Encyclopedia Metropolitana Vol. II , 393 – 476 . London 28 vols (p. 412). See also G. Boole, ‘Further Observations on the Theory of Probabilities’, Phil. Mag., 4th series, 2 (1851), reprinted in Boole (footnote 23), 260–7 (pp. 261–2).
- 1850 . The Edinburgh Review Vol. 92 , 32 – 32 . A comment by Terrot in a letter to Forbes, although it refers to Michell, is particularly apposite with respect to the reasoning of De Morgan and Herschel: ‘You hold as I do that he makes the atrocious blunder of saying that the antecedent improbability of an event is the consequent probability of its having a physical cause, e.g., that if the odds against throwing aces with two dice be 1 to 35, then (the aces having turned up) the odds for the dice being loaded or some equivalent cause is 35 to 1’. (Shairp, Tait, Adams-Reilly (footnote 9), 476.)
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 405 – 406 . 3rd series The difficulty with an epistemological interpretation of randomness or chance was pointed out by Poincaré. Responding to the suggestion that ‘chance is only a measure of our ignorance’ and that ‘fortuitous phenomena are, by definition, those whose laws we are ignorant of’, he asks: ‘When the first Chaldean shepherds followed with their eyes the movements of the stars, they did not yet know the laws of astronomy, but would they have dreamed of saying that the stars move by chance? If a modern physicist is studying a new phenomenon, and if he discovers its law on Tuesday, would he have said on Monday that the phenomenon was fortuitous?’ (H. Poincaré, Science and Method, translated by F. maitland (London, 1914), p. 65).
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 406 – 406 . 3rd series
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 406 – 406 . 3rd series See also Keynes (footnote 25), 302–3, where it is claimed, against Michell, that the improbability, however high, of an event before its occurrence or observation is no ground for attributing a high probability to any sufficient explanation of the event, since any other possible event may be equally improbable.
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 409 – 409 . 3rd series
- Michell . 1767 . An inquiry into the probable Parallax and Magnitude of the Fixed Stars from the quantity of Light which they afford to us, and the particular Circumstances of their Situation . Phil. Trans. , 57 : 243 – 243 .
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 417 – 417 . 3rd series
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 419 – 419 . 3rd series See also Keynes (footnote 25), 290–1. A definition of the term ‘random’, Keynes says, which leads to the conclusion ‘that there would be perfect randomness in the distribution of stars in the heavens…if they were disposed in an exact and symmetrical pattern' represents a ‘departure from ordinary usage’.
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 418 – 418 . 3rd series The argument is not convincing. Given the purpose for which Forbes wants to use his analogy, he should have compared the probability of obtaining the complete 1 … 100 arithmetical sequence with that of obtaining a sequence in which any one number is missing, and not with that of obtaining a sequence in which a particular number is missing.
- Lucas , J.R. 1970 . The Concept of Probability 112 – 125 . Oxford See also Keynes (footnote 25), chapter 24.
- Both Newton in his letter to Bentley, and Bentley himself in his Boyle Lectures, speak of an even distribution of matter as representing a ‘chaos’; see The Works of Richard Bentley, D. D. Dyce A. London 1838 III 153 154 3 vols 211. Neither would have subscribed to Forbes' view that ‘if we could form an idea of of utter confusion or material chaos, it would not surely be of anything in which uniformity would have a conspicuous share’ (Forbes (footnote 9), 420).
- Forbes . 1850 . On the alleged evidence for a Physical Connexion between Stars forming Binary or Multiple Groups, deduced from the Doctrine of Chances . Phil. Mag. , 37 : 416 – 416 . 3rd series
- Newton , Isaac . 1730 . Opticks , 4th edition London Query 31. Similar remarks are to be found in Newton's first letter to Bentley; see Dyce (footnote 45), 204–5.
- De Moivre , A. 1756 . The Doctrine of Chances , 3rd edn 253 – 253 . London
- See The Works of Richard Bentley, D. D. Dyce A. London 1838 III 153 154 3 vols 211.
- Ellis , Robert Leslie . who corresponded with Forbes about the star distribution problem, is sometimes spoken of as having been among the first to break away from a Laplacian interpretation of probability.
Annals of Science
Volume 39, 1982 - Issue 2