Physical Demonstration of the Earth's Motion of Rotation, pp. 575-578) (Foucault) + On the Theory of Probabilities, and in Particular on Mitchell's Problem of the Distribution of the Fixed Stars, pp. 521-530, (Boole) in The London, Edinburgh and Dublin Philosophical Magazine, Fourth Series, Vol. 1, 1851 [FOUCAULT'S PENDULUM + BOOLE'S FIRST PAPER ON THE LOGIC OF PROBABILITY]

London, 1851. FIRST DESCRIPTION IN ENGLISH of FOUCAULT'S 1st MECHANICAL DEMONSTRATION OF THE EARTH'S ROTATION, FOUCAULT'S PENDULUM. Also included is BOOLE'S FIRST PAPER ON THE LOGIC OF PROBABILITY.

FOUCAULT: Copernicus explained the daily diurnal rotation of the earth on its polar axis in 1543, however it was Foucault, 300 years later, who first demonstrated it. "On February 3, 1851, a 32-year-old Frenchman—who'd dropped out of medical school and dabbled in photography—definitively demonstrated that the Earth indeed rotated, surprising the Parisian scientific establishment. Acting on a hunch, Léon Foucault determined he could use a pendulum to illustrate the effect of the Earth's movement. He called together a group of scientists, enticing them with a note declaring, "You are invited to see the Earth turn." Foucault hung a pendulum from the ceiling of the Meridian Room of the Paris Observatory. As it swept through the air, it traced a pattern that effectively proved the world was spinning about an axis...

"According to the American Physical Society, Foucault suspended from the Pantheon's lofty dome a 61-pound brass bob on a 220-foot cable. As it swung back and forth, the pointed end of the bob traced lines in sand that had been poured on a wooden platform. Over time, the angle of these lines changed, suggesting to audience members that the direction of the pendulum's travel was shifting under the influence of an unperceived rotational motion—that of Earth. Foucault's pendulum had moved according to his sine law which predicts how much a pendulum's path will distort each day based on its latitude (Smithsonian). Foucault stated his sine law as: The rate of rotation of the pendulum can be stated mathematically as equal to the rate of rotation of the Earth times the sine of the number of degrees of latitude.

"Absent any exterior forces, a pendulum would swing back and forth in a single plane forever—there would be no gradual angular shift. But the Earth is rotating, so the story isn't that simple. Since all points on Earth's surface rotate as a unit, it follows that those located on the wider portions of the planet—nearer to the equator—must cover more meters each second (i.e., go faster) to "keep up" with the points tracing smaller circles each day at the extreme northern and southern latitudes. Though they don't feel it, a person standing in Ecuador, is moving with appreciably higher velocity than one in Iceland" (ibid).

The Foucault paper in this volume includes the English translation of his first paper published in French; it also contains an extensive description of his demonstration as described by those present (and at which some fainted).

BOOLE: 1st edition of Boole's first paper on probability, here applying his theory of probabilities to the problem of the distribution of fixed stars. This work first "seems to be 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. A Prelude to the Digital Age).

As Boole stated: "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" (p. 524). This paper marks the beginning of his seminal later work, Laws of Thought. CONDITION: Complete. Octavo. Bears only tiny ex-libris tamp on title page. Rebound in three-quarter morocco over contemporary marbled boards; marbled endpapers. Gilt-lettered & tooled spine; 5 compartments. Bright and clean throughout. Fine condition.