## "On the Theory of Probabilities, and in particular on Mitchell's Problem of the Distribution of the Fixed Stars" (Boole) and “Physical Demonstration of the Earth's Motion of Rotation” (Wheatstone) in The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 1,1851, pp. 521-530; 572-578

FIRST EDITION of George Boole’s first paper on probability, marking his earliest published work on a subject he would continue to develop until in 1854 he published his highly influential An Investigation of The Laws of Thought on which are founded the Mathematical Theories of Logic and Probabilities. Laws of Thought, as the work is known presents “probability theory as an excellent topic to illustrate the power of his algebra of logic” – an argument whose origins lie in this 1851 paper (Stanford Encyclopedia of Philosophy).

On the Theory of Probabilities “seems to have been the first mention, by any author, of the close connection, both in essence and in form, between logic and probability and indeed of the dependence of the theory of probability on an underlying mathematical theory of logic" (MacHale, George Boole). Boole writes: ““Although the immediate business of the theory of probabilities is with the frequency of the occurrence of events, and although it therefore borrows some of its elements from the science of number, yet as the expression of the occurrence of those events, and also of the relations, of whatever kind, which connect them, is the office of language, the common instrument of reason, so the theory of probabilities must bear some definite relation to logic” (Phil Mag, 1, 1851, p. 524).

Boole’s interest in probabilities had been sparked by reading a 1767 Philosophical Transactions paper by John Michell [also Mitchell], a natural philosopher and clergyman responsible for a number of important and visionary insights into astronomy, gravitation, and optics. In the Phil Trans paper entitled An Inquiry into the Probable Parallax and Magnitude of the Fixed Stars, Michell “estimates that if the stars were just scattered randomly on the celestial sphere then the probability that the Pleiades would be grouped together in the sky is 1 part in 500,000. So he concluded that the Pleiades must be a stellar system in its own right---this is the first known application of statistics to astronomy” (Detweiler, Newtonian Black Holes, 1998).

The other spark to Boole’s interest took the form of what he referred to as ‘general doctrine…of the day’ – a mathematical issue that appeared in a theological debate that had been making the rounds: “was the existence of multiple star systems due just to chance, or would such systems be so unlikely to form by chance that their observed existence ‘proved’ the intervention of a ‘Creator’?” (Nahin, The Logician and the Engineer, 6.3).

Given his interest in Michell’s earlier work as well as the theological debate of his own contemporaries, in the 1851 paper Boole applies his theory of probabilities to the problem of the distribution of fixed stars. This problem had been "creating considerable discussion among mathematicians and astronomers. Professor Boole felt much interest in it, both because of its intrinsic importance, and because of its close connection with a class of speculations in the pursuit of which he had long been engaged" (Robert Vaughan and Henry Allon, The British Quarterly Review, vol 44).

Boole's paper articulates the origin of his thinking on probability and logic, marking the beginning of a thought process that would culminate in his seminal 1854 Laws of Thought. En route, he was able to answer to John Michell’s fixed star problem. ALSO INCLUDED is Wheatstone’s “Physical Demonstration of the Earth’s Motion of Rotation,” the first description in English of Foucault’s famous pendulum experiment demonstrating and proving that the rotation of the earth. Item #621

CONDITION & DETAILS: London: Taylor & Francis. (8.5 x 5.5 inches; 213 x 138mm). Complete. [viii], 592, [4]. Plates and in-text illustrations throughout. Ex-libris bearing a discreet stamp on the title page. Handsomely, solidly, and tightly bound in three quarter brown calf over marbled paper boards. Five gilt-ruled raised bands at the spine; gilt armorial devices in the compartments. Gilt-lettered red and black morocco spine labels. Very slight age toning within; bright and clean. Near fine condition.

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Price:
$775.00
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