The Karawanken railway, a direct connexion with Bohemia and the northern industrial provinces of Austria, is calculated to counteract the gravitation of traffic towards the German ports; while the Tauern railway constitutes the shortest route to the interior of Austria and to the south of Germany.
The most important are: (I) To express the time of describing an elliptic arc under the Newtonian law of gravitation in terms of the focal distances of the initial and final points, and the length of the chord joining them.
The meteors, whatever their dimensions, must have motions around the sun in obedience to the law of gravitation in the same manner as planets and comets - that is, in conic sections of which the sun is always at one focus.
In the appended treatise Sur la Cause de la pesanteur, he rejected gravitation as a universal quality of matter, although admitting the Newtonian theory of the planetary revolutions.
But Newton had already discovered beforehand in the mechanics of terrestrial bodies that gravitation constantly causes similar facts on the earth, and did not derive that cause from any logical ground beyond experience, any more than he did the third law of motion.
The question whether this cause modifies gravitation admits of an easy test from observation.
It was shown by Homer Lane that a mass of gas held in equilibrium by the mutual gravitation of its parts actually grows hotter through radiating heat; the heat gained by the resulting contraction more than counterbalances that lost by radiation.
The mutual gravitation of a large number of stars crowded in a comparatively small space must be considerable, and the individual stars must move in irregular orbits under their mutual attractions.
After the establishment of universal gravitation as the primary law of the celestial motions, the problem was reduced to that of integrating the differential equations of the moon's motion, and testing the completeness of the results by comparison with observation.
The time had come when the results obtained in the development and application of the law of gravitation by three generations of illustrious mathematicians might be presented from a single point of view.