Probleme de Dynamique in Suite des Memoires de Mathematique et de Physique pp. 504-532, Annee 1747 [CONSERVATION OF ANGULAR MOMENTUM]

Amsterdam: Mortier, 1747. 1st Edition. FIRST EDITION OF D'ARCY'S PROPOSED AN EARLY VERSION OF THE CONCEPT OF CONSERVATION OF ANGULAR MOMENTUM FOR ORBITING BODIES. Extract in fine condition housed in a custom pamphlet case; text block complete.

"In physics, angular momentum is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant" (Wikipedia). "Seen another way, a rotational analogue of Newton's first law of motion might be written, "A rigid body continues in a state of uniform rotation unless acted by an external influence." Thus with no external influence to act upon it, the original angular momentum of the system remains constant" (BK101).

Patrick D'Arcy (1725-1779) was an Irish mathematician whose proposal of the concept of conservation of angular momentum included two postulates. "The first is a generalization of Kepler's second law. D'Arcy proposed that the areal velocity of any orbiting body of a particular mass is identical regardless of the radius of the orbit or the position in the orbit. Kepler's second law just proposed the conservation of areal velocity for a specific orbit.

"D'Arcy's second concept is that the orbital velocity of any body is inversely proportional to its mass. In other words, Mars has a higher orbital velocity than Earth would have at the same distance, and the ratio of orbital velocities of Earth and Mars at the same distance from the Sun would be the inverse of the ratio of their masses. These two concepts together comprise D'Arcy's ‘conservation of momentum for rotary motion,' and for orbiting bodies this is equivalent to ‘conservation of angular momentum'" (Wenner Collection). CONDITION & DETAILS: Extract in fine condition housed in custom pamphlet case gilt-lettered at the spine. The text block remains tightly bound. 6 plates. Bright and clean.