...interference with ' the perennial Miracle of the Material World,' the law that in the planetary orbits the squares of the periodic times are as the cubes of the distances. In like manner, no moralist fancies that he can lay bare the ultimate causes of our power...

...motion of each planet is such, that it describes about the sun equal areas in equal times; and 3° that the squares of the periodic times are as the cubes of the greater axes of their orbits. Kepler, to whom wo owe these important discoveries, was born in 1571,...

...described by that line in the planet's motion round the sun are proportioned to the times employed, and the squares of the periodic times are as the cubes of the distances ; so in regard to the action of gravitation, the height is proportional to the square of...

...therefore, V Hence, if several bodies move in different ellipses, about the same force in the focus, the squares of the periodic times are as the cubes of the major axes. 235. The values of p and p being the same for the hyperbola as for the ellipse, it follows that...

...that line in its motion round the sun are proportional to the times employed in the motion, and that the squares of the periodic times are as the cubes of the distance. The first of these is a law of forms, the other two are laws of numbers. By their mutual...

...force in the centre. (5) A parahola with the centre of force in the focus. 9. In the planetary orbits the squares of the periodic times are as the cubes of the mean distances. Paper 3. DESCHANEL-S NATURAL PHILOSOPHY. PART I. 1. Enunciate the proposition known...

...that line in its motion round the sun are proportional to the lines employed in the motion ; (3) that the squares of the periodic times are as the cubes of the distances. character of all the higher laws of nature to assume the form of a precise quantitative...

...every orbit is circular, the position of the central body depending upon the ratio of the forces. 3rd. The squares of the periodic times are as the cubes of the radii. These laws, though not formally announced in the early part of this work, are fundamental, and...

...remains the same. But if several planets describe circular orbits uniformly round a common centre, and the squares of the periodic times are as the cubes of the radii of the orbits, it is clear that the accelerations of the several planets are inversely proportional...

...describe equal areas in equal times. 2d. The orbits are ellipses, with the Sun in one of the foci. 3d. The squares of the periodic times are as the cubes of the mean distances. Questions of identity to establish a minor premise are necessarily a part of scientific...