John Herschel, John Stuart Mill and William Whewell: The uses of hypotheses
In 1767, just three years after the appearance of Thomas Bayes's solution of his problem in the 'doctrine of chances', the Royal Society published in its Philosophical Transactions an essay which attempted to apply that 'doctr ine ' to the question whether Newton's law of gravity extends to and governs the behaviour of the stars. Its author was John Michell, who has been described as the only natural philosopher of distinction working in Cambridge during the hundred years following Newton's death. His reasoning was that, if the stars were gravitationally attracted to one another, there would be more binary stars, and more clusters of stars, than would otherwise be the case. Of course, astronomers were aware that certain stars appeared close together, either as pairs or as clusters, but this in itself is of little significance because optically close stars can still be physically remote from each other. Observations of stars rotating about a fixed centre would suffice, but telescopes available at the time were insufficiently sensitive to enable astronomers to report such observations. So what Michell did was to construct a probable argument: 'The argument I intend to make use of', he said, 'is of that kind, which infers either design, or some general law, from a general analogy, and the greatness of the odds against things having been in the present situation, if it were not owing to some such cause'. He began his argument by calculating a numerical value for the probability that, if we were to scatter at random all the stars equal in brightness to the pair forming Beta-Capricorni, there would appear any two as close to each other as that pair. The small value of this probability, reinforced by other calculations relating to other pairs and clusters, led Michell to conclude that 'we may . . . with the highest probability conclude (the odds against the contrary opinion being many million millions to one) that the stars are really collected together in clusters in some places . . . to whatever cause this may be owing, whether to their mutual gravitation, or to some other law or appointment of the creator ' (Michell 1767: 243, 249).