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It was one of the axioms of the Aristotelian mechanics, that the heavier of two falling bodies would reach the ground sooner than the other, and that their velocities would be proportional to their weights. Galileo attacked the arguments by which this opinion was supported; and when he found his reasoning ineffectual, he appealed to direct experiment.

If the earth stood still, or if light spent no time on the road from the stars, such an effect would not exist. Its amount represents the proportion between the velocities with which the earth and the light-rays pursue their respective journeys. This proportion is, roughly, one to ten thousand.

They knew now that the young, live sun, out there in space, was speeding toward them, their combined velocities equalling more than 100 miles each second. And they knew that there were not seven, but nine planets circling about that sun.

Acting on his suggestion, Brandes and Benzenberg, two students at the University of Göttingen, began in 1798 to determine the heights of falling stars by simultaneous observations at a distance. They soon found that they move with planetary velocities in the most elevated regions of our atmosphere, and by the ascertainment of this fact laid a foundation of distinct knowledge regarding them.

Certain differential equations can be found, which hold at every instant for every particle of the system, and which, given the configuration and velocities at one instant, or the configurations at two instants, render the configuration at any other earlier or later instant theoretically calculable.

The smaller was on a near-collision course with reference to the larger, although their relative velocities were not great. At precisely the right time, the smaller drifted by the larger, only a few hundred yards away. The weakness of the gravitational fields generated between the two caused only a slight change of orbit on the part of both bodies. Then they began to separate.

Hitting a ship in space at ultralight velocities was something else again. Young Kraybo could play baseball blindfolded, but he wasn't yet capable of making the master guesses that would protect a merchantship like the Naipor. But what was the matter with him? He had, of course, a fire-control computer to help him swing and aim his guns, but he didn't seem to be able to depend on his guesswork.

If life is not always poetical, it is at least metrical. Periodicity rules over the mental experience of man, according to the path of the orbit of his thoughts. Distances are not gauged, ellipses not measured, velocities not ascertained, times not known. Nevertheless, the recurrence is sure.

A O is the virtual train-arm; let the center, A, of the cross move to the position B, then since the angles A O B at the center, and A C B in the circumference, stand on the same arc, A B, the former is double the latter, showing that the cross revolves twice round the center O during each rotation of C; and since A C B = A D B, C and D rotate with equal velocities, and these rotations and the revolution about O have the same direction.

The Captain was quite as busy, but in a different way. Pulling out his tablets, he reviewed his calculations regarding the motion of projectiles, their velocities, ranges and paths, their retardations and their accelerations, jotting down the figures with a rapidity wonderful to behold.