|Hutton, Charles Mathematical and Philosophical Dictionary 1795|
, in Mechanics. See Wheel.
Rota Aristotelica, or Aristotle's Wheel, denotes a celebrated problem in mechanics, concerning the motion or rotation of a wheel about its axis; so called because first noticed by Aristotle.
The difficulty is this. While a circle makes a revolution on its centre, advancing at the same time in a right line along a plane, it describes, on that plane, a right line which is equal to its circumference. Now if this circle, which may be called the deferent, carry with it another smaller circle, concentric with it, like the nave of a coach wheel; then this little circle, or nave, will describe a line in the time of the revolution, which shall be equal to that of the large wheel or circumference itself; because its centre advances in a right line as fast as that of the wheel does, being in reality the same with it.
The solution given by Aristotle, is no more than a good explication of the difficulty.
Galileo, who next attempted it, has recourse to an infinite number of infinitely little vacuities in the right line described by the two circles; and imagines that the little circle never applies its circumference to those vacuities; but in reality only applies it to a line equal to its own circumference; though it appears to have applied it to a much larger. But all this is nothing to the purpose.
Tacquet will have it, that the little circle, making its rotation more slowly than the great one, does on that account describe a line longer than its own circumference; yet without applying any point of its circumference to more than one point of its base. But this is no more satisfactory than the former.
After the fruitless attempts of so many great men, M. Dortous de Meyran, a French gentleman, had the good fortune to hit upon a solution, which he sent to the Academy of Sciences; where being examined by Mess. de Louville and Soulmon, appointed for that purpose, they made their report that it was satisfactory. The solution is to this effect:
The wheel of a coach is only acted on, or drawn in a right line; its rotation or circular motion arises purely from the resistance of the ground upon which it is applied. Now this resistance is equal to the force which draws the wheel in the right line, inasmuch as it defeats that direction; of consequence the causes of the two motions, the one right and the other circular, are equal. And hence the wheel describes a right line on the ground equal to its circumference.
As for the nave of the wheel, the case is otherwise. It is drawn in a right line by the same force as the wheel; but it only turns round because the wheel does so, and can only turn in the same time with it. Hence it follows, that its circular velocity is less than that of the wheel, in the ratio of the two circumferences; and therefore its circular motion is less than the rectilinear one. Since then it necessarily describes a right line equal to that of the wheel, it can only do it partly by sliding, and partly by revolving, the sliding part being more or less as the nave itself is smaller or larger. See Cycloid.
, Rolling, in Mechanics. See ROLLING.
, in Geometry, the circumvolution of a surface round an immoveable line, called the axis of Rotation. By such Rotation of planes, the figures of certain regular solids are formed or generated. Such as, a cylinder by the Rotation of a rectangle, a cone by the Rotation of a triangle, a sphere or globe by the Rotation of a semicircle, &c.
The method of cubing solids that are generated by such Rotation, is laid down by Mr. Demoivre, in his specimen of the use of the doctrine of fluxions, Philos. Trans. numb. 216; and indeed by most of the writers on Fluxions. In every such solid, all the sections perpendicular to the axis are circles, and therefore the fluxion of the solid, at any section, is equal to that circle multiplied by the fluxion of the axis. So that, if x denote an absciss of that axis, and y an ordinate to it in the revolving plane, which will also be the radius of that circle; then, n being put for 3.1416, the area of the circle is ny2, and consequently the fluxion of the solid is ny2x.; the fluent of which will be the content of the solid.
Such solid may also be expressed in terms of the generating plane and its centre of gravity; for the solid is always equal to the product arising from the generating plane multiplied by the path of its centre of gravity, or by the line described by that centre in the Rotation of the plane. And this theorem is general, by whatever kind of motion the plane is moved, in describing a solid.
, Revolution, in Astronomy. See REVOLUTION.
Diurnal Rotation. See Diurnal, and Earth.
, or Rotundo, in Architecture, popular term for any building that is round both within and withoutside, whether it be a church, hall, a saloon, a vestibule, or the like.
, Roundness, Rotundity, the property of a circle and sphere or globe &c.
, an ingenious English mathematician and philosopher, was fellow of Magdalen College, Cambridge, and afterwards Rector of Anderby in Lincolnshire, in the gift of that society. He was a constant attendant at the meetings of the Spalding Society, and was a man of a great philosophical habit and turn of mind, though of a cheerful and companionable disposition. He had a good genius for mechanical contrivances in particular. In 1738 he printed at Cambridge, in 8vo, A Compendious System of Natural Philosophy, in 2 vols 8vo; a very ingenious work, which has gone through several editions. He had also two pieces inserted in the Philosophical Transactions, viz, 1. A Description of a Barometer wherein the Scale of Variation may be increased at pleasure; vol. 38, pa. 39. And 2. Direction for making a Machine for finding the Roots of Equations universally, with the Manner of using it; vol. 60, pa. 240.—Mr. Rowning died at his lodgings in Carey-street near Lincoln's-Inn Fields, the latter end of November 1771, at 72 years of age.
Though a very ingenious and pleasant man, he had but an unpromising and forbidding appearance: he was tall, stooping in the shoulders, and of a sallow downlooking countenance.
ROYAL Oak, Robur Carolinum, in Astronomy, one of the new southern constellations, the stars of