...greater than that of the nearer, in the fefquiplicate ratio of the diftances from the Sun; that is, the Squares of the Periodic Times are as the Cubes of the diftances from the Sun. Which things are to be underftood after the like manner concerning the Secondary...

...Mathematically demonftrated : If feveral Bodies revolve with an equable Motion in concentric Circles, and the Squares of the Periodic Times are as the Cubes of the Diftances from the common Centre 5 the Centripetal Forces will be reciprocally as the Squares of the...

...Mathematically demonftrated : If fcveral Bodice revolve with an equable Motion in concentric Circles, and the Squares of the Periodic Times are as the Cubes of the Diftances from the common Centre $ the Centripe• tal Forces will be reciprocally as the Squares of...

...body, U the velocity in a circle, radiua^i, then ^''rrt^ M. LA PLAQE shews that the law of Kepler, viz. that the squares of the periodic times are as the cubes of the axes, U not rigorous, and only obtains in as much as the mutual action of the planets, and their action...

...centripetal forces are as the distances of the revolving bodies from the centres of the circles. When the squares of the periodic times are as the cubes of the rays of the circles, and, consequently, the velocities in the subduplicate ratio of these rays inversely,...

...of the planets, the respective real distances of the whole may be found by means of Kepler's law, " that the squares of the periodic times are as the " cubes of their mean distances from the son." DISTANCE, apparent, in optics, is that distance .which we judge...

...satellites move in circular orbits, we may take 44",23 for the true distance, without much error; hence, as the squares of the periodic times are as the cubes of the distances, the distance of the first satellite comes out 33",09. The synodic revolutions were here...

...general harmony and universal law, which all the other moving bodies in the system observe ; namely, that the squares of the periodic times are as the cubes of the distances; but if the sun moves round the earth, that law is destroyed, and the general order of symmetry...

...general harmony and universal law, which all the other moving bodies in the system observe ; namely, that the squares of the periodic times are as the cubes of the distances ; but if the sun move* round the earth, that law is destroyed, and the general order of symmetry...

...their motions always conforming to the law discovered by Kepler, but first demonstrated by Newton, that the squares of the periodic times are as the cubes of the respective mean distances from the sun, or focal body. 3. The time of performing1 their revolutions...