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gravitation

The question has also been raised whether the action of gravitation is absolutely instantaneous.

3221The question whether this cause modifies gravitation admits of an easy test from observation.

2612On the other hand the enigmatical motion of the perihelion of Mercury has not yet found any plausible explanation except on the hypothesis that the gravitation of the sun diminishes at a rate slightly greater than that of the inverse square - the most simple modification being to suppose that instead of the exponent of the distance being exactly - 2, it is - 2.000 000 161 2.

123The 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.

1111The 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.

1111Gravitation Constant And Mean Density Of The Earth >>

89A good deal of this is transported by gravitation from Baku to Batum on the Black Sea by means of a pipe laid overland.

77A good deal of this is transported by gravitation from Baku to Batum on the Black Sea by means of a pipe laid overland.

77The 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.

65We might conceive the rapid motions of the heavenly bodies to result in some change either in the direction or amount of their gravitation towards each other at each moment; but such is not the case, even in the most rapidly moving bodies of the solar system.

41A misunderstanding as to the manner in which these should be dealt with was the immediate occasion of the publication by Hutchinson in 1724 of Moses's Principia, part i., in which Woodward's Natural History was bitterly ridiculed, his conduct with regard to the mineralogical specimens not obscurely characterized, and a refutation of the Newtonian doctrine of gravitation seriously attempted.

44He quotes as an instance that Newton in this way added to the planetary appearances contained in Kepler's laws the gravitation of the planets to the sun, as a notion of causality not contained in the appearances, and thus discovered that gravitation is the cause of the appearances.

45The flying body must act against gravitation, and elevate and carry itself forward at the expense of the air and of the force which resides in it, whatever that may be.

32The 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.

33The 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.

33In all the cases which have yet arisen in astronomy the extraneous forces are so small compared with the gravitation of the central body that the orbit is approximately an ellipse, and the preliminary computations, as well as all determinations in which a high degree of precision is not necessary, are made on the hypothesis of elliptic orbits.

35Newton's law of gravitation affords the most notable example of the process of verification of a law of force, and incidentally of the Galileo-Newton theory.

35Another way of stating the same thing is to say that we introduce, as a correction for the earth's rotation, a force called "centrifugal force," which combined with gravitation gives the weight of the body.

35The 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.

22In the case of the motion of the moon around the earth, assuming the gravitation of the latter to be subject to the modification in question, the annual motion of the moon's perigee should be greater by I 5" than the theoretical motion.

22The actual force between the particles arises in part from their mutual gravitation, which is inversely as the square of the distance.

22In front of this is a double series of stationary waves, the gravitation waves forming a series increasing in wave-length with their distance in front of the body, and the surface-tension waves or ripples diminishing in wave-length with their distance from the body, and both sets of waves rapidly diminishing in amplitude with their distance from the body.

22He also showed that the total gravitation of the earth, assumed as spherical, on external bodies, would be the same as if the earth's mass were concentrated in the centre.

23Another cause which might be supposed to modify the action of gravitation between two bodies would be the interposition of masses of matter between them, a cause which materially modifies the action of electrified bodies.

23What is done is to divide the resultant force due to gravitation into two components, one of which corresponds to this acceleration, while the other one is what is called the "weight" of the body.

23In the case of a particle falling directly towards the earth from rest at a very great distance we have C=o and, by Newtons Law of Gravitation, p/ai=g, where a is the earths radius.

23Nothing is more remarkable in the history of discovery than the manner in which Ampere seized upon the right clue which enabled him to disentangle the complicated phenomena of electrodynamics and to deduce them all as a consequence of one simple fundamental law, which occupies in electrodynamics the position of the Newtonian law of gravitation in physical astronomy.

23In the case of a particle falling directly towards the earth from rest at a very great distance we have C=o and, by Newtons Law of Gravitation, p/ai=g, where a is the earths radius.

23In 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.

24We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

12The limiting law expressing the behaviour of gases under varying temperature and pressure assumes the form pv= RT; so stated, this law is independent of chemical composition and may be regarded as a true physical law, just as much as the law of universal gravitation is a true law of physics.

12The absolute unit of force is employed here, and not the gravitation unit of hydrostatics; in a numerical application it is assumed that C.G.S.

12The law of gravitation is unique among the laws of nature, not only in its wide generality, taking the whole universe in its scope, but in the fact that, so far as yet known, it is absolutely unmodified by any condition or cause whatever.

12Hence arise the springs which run perennially, several of which have been collected into the gravitation water supplies of the Vignacourt and Fawara aqueducts.

12Reference should be made to the article Gravitation for an account of the methods employed to determine the "mean density of the earth."

12They were content with a knowledge of the truth of the principle of gravitation; instead of essaying to explain it further by the properties of a transmitting medium, they in fact modelled the whole of their natural philosophy on that principle, and tried to express all kinds of material interaction in terms of laws of direct mechanical attraction across space.

12Rasselas and Imlac, Nekayah and Pekuah, are evidently meant to be Abyssinians of the 18th century; for the Europe which Imlac describes is the Europe of the 18th century, and the inmates of the Happy Valley talk familiarly of that law of gravitation which Newton discovered and which was not fully received even at Cambridge till the 18th century.

12The 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.

12It 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.

12when the more general law of gravitation is shown to include the less general laws of planetary gravitation.

12The limiting law expressing the behaviour of gases under varying temperature and pressure assumes the form pv= RT; so stated, this law is independent of chemical composition and may be regarded as a true physical law, just as much as the law of universal gravitation is a true law of physics.

12The absolute unit of force is employed here, and not the gravitation unit of hydrostatics; in a numerical application it is assumed that C.G.S.

12The law of gravitation is unique among the laws of nature, not only in its wide generality, taking the whole universe in its scope, but in the fact that, so far as yet known, it is absolutely unmodified by any condition or cause whatever.

12when the more general law of gravitation is shown to include the less general laws of planetary gravitation.

12This is not inconsistent with the law of gravitation, for such estimates as have been made of planetary perturbations due to stars give results which are insignificant in comparison with quantities at present measurable.

13The investigation that brought about this result was probably the most laborious that had been made up to Airy's time in planetary theory, and represented the first specific improvement in the solar tables effected in England since the establishment of the theory of gravitation.

00He was the first to state clearly that the motions of the heavenly bodies must be regarded as a mechanical problem, and he approached in a remarkable manner the discovery of universal gravitation.

00The heading "Measurement of Dynamical Quantities" includes the topics units, measurements, and the constant of gravitation.

00During this period logarithms were invented, trigonometry and algebra developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation.

00It could hardly have been thought of before Sir Isaac Newton's discovery of the actual facts regarding universal gravitation.

00These precise conditions were afterwards demonstrated by Newton to follow necessarily from the law of gravitation.

00A re-examination of his previously considered hypotheses as to the cause of these phenomena was fruitless; the true theory was ultimately discovered by a pure accident, comparable in simplicity and importance with the association of a falling apple with the discovery of the principle of universal gravitation.

00In order to obtain the acid, a series of basins is constructed over the vents, and so arranged as to permit of the passage of water through them by gravitation.

00but commonly known as the "laws of motion"; T and the demonstration of the fact that the motions of the celestial bodies could be included in this theory by means of the law of universal gravitation.

00In a number of cases measures of the relative positions of the two stars, continued for many years, have shown that they are revolving about a common centre; when this is so there can be no doubt that they form a binary system, and that the two components move in elliptic orbits about the common centre of mass, controlled by their mutual gravitation.

00By far the simplest supposition open to us is that the functions are the same in all cases, the attractions differing merely by coefficients analogous to densities in the theory of gravitation.

00Now it is shown in hydrodynamics that she velocity of propagation of waves in deep water is that acquired by a heavy body falling through half the radius of the circle whose circumference is the wave-length, or _ f_X _ ga 27rT 'I ' v2- 2r 2r pn This velocity is a minimum when X=2.7r gp' and the minimum value is v= 4 - p g For waves whose length from crest to crest is greater than X, the principal force concerned in the motion is that of gravitation.

00If it were otherwise - if it were rescued from the law of gravitation on the one hand, and bereft of independent movement on the other, it would float about uncontrolled and uncontrollable like an ordinary balloon.

00Hence it comes by natural gravitation into the town at a pressure of five atmospheres, so that it supplies the highest parts of the town with abundant water.

00PROBLEM OF THREE BODIES, the problem of determining the motion of three bodies moving under no influence but that of their mutual gravitation.

00But in the sun's atmosphere gravitation alone is a misleading guide.

00condensing power of gravitation at the sun's borders is the pressure of radiation.

00- Any area, large or small, of the earth's surface from any part of which, if the ground were impermeable, water would flow by gravitation past any point in a natural watercourse is commonly known in Europe as the " hydrographic basin " above that point.

00Perennial springs of large volume rarely occur in Great Britain at a sufficient height to afford supplies by gravitation; but from the limestones of Italy and many other parts of the world very considerable volumes issue far above the sea-level, and are thus available, without pumping, for the supply of distant towns.

00Yet the hilly parts of the last-named country are rich in magnificent sites at sufficient altitudes for the supply of any parts by gravitation, and capable, if properly laid out, of affording a volume of water, throughout the driest seasons, far in excess of the probable demand for a long future.

00above the sea, may be made available for the supply of pure water by gravitation to any part of England.

00In the spring he had determined the attractions of masses, and thus completed the law of universal gravitation.

00He also wrote an Essay touching the Gravitation or Nongravitation of Fluid Bodies (1673); Difficiles Nugae, or Observations touching the Torricellian Experiment, &c. (1675); and a translation of the Life of Pomponius Atticus, by Cornelius Nepos (1677).

00It was this: from the observed perturbations of a known planet to deduce by calculation, assuming only Newton's law of gravitation, the mass and orbit of an unknown disturbing body.

00Its mathematical prediction was not only an unsurpassed intellectual feat; it showed also that Newton's law of gravitation, which Airy had almost called in question, prevailed even to the utmost bounds of the solar system.

00The most soluble of the constituents of crude coal gas is ammonia, 780 volumes of which are soluble in one volume of water at normal temperature and pressure, and the water in the hydraulic main absorbs a considerable quantity of this compound from the gas and helps to form the ammoniacal liquor, whilst, although the liquor is well agitated by the gas bubbling through it, a partial separation of tar from liquor is effected by gravitation.

00ROGER JOSEPH BOSCOVICH (1711?-1787) mathematician and natural philosopher, one of the earliest of foreign savants to adopt Newton's gravitation theory, was born at Ragusa in Dalmatia on the 18th of May 1711, according to the usual account, but ten years earlier according to Lalande (Eloge, 1792).

00Among these subjects were the transit of Mercury, the Aurora Borealis, the figure of the earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometer, various problems of spherical trigonometry, &c. In 1742 he was consulted, with other men of science, by the pope, Benedict XIV., as to the best means of securing the stability of the dome of St Peter's, Rome, in which a crack had been discovered.

00Modern theoretical astronomy, taken in the most limited sense, is based upon Celestial Mechanics, the science by which, using purely deductive mechanical methods, the laws of motion of the heavenly bodies are derived by deductive methods from their mutual gravitation towards each other.

00Celestial Mechanics is, strictly speaking, that branch of applied mathematics which, by deductive processes, derives the laws of motion of the heavenly bodies from their gravitation towards each other, or from the mutual action of the parts which form them.

00The science had its origin in the demonstration by Sir Isaac Newton that Kepler's three laws of planetary motion, and the law of gravitation, in the case of two bodies, could be mutually derived from each other.

00==Problem of Three Bodies== As soon as the general law of gravitation was fully apprehended, it became evident that, owing to the attraction of each planet upon all the others, the actual motion of the planets must deviate from their motion in an ellipse according to Kepler's laws.

00This numerical proportion, as being a necessary consequence of the law of gravitation, must prevail in every system under its sway.

00Gravitation was thus shown to be the sole influence governing the movements of planets and satellites; the figure of the rotating earth was successfully explained by its action on the minuter particles of matter; tides and the precession of the equinoxes proved amenable to reasonings based on the same principle; and it satisfactorily accounted as well for some of the chief lunar and planetary inequalities.

00The discovery, just one hundred years after the publication of Newton's Principia, of its dependence upon the slowly varying eccentricity of the earth's orbit signalized the removal of the last conspicuous obstacle to admitting the unqualified validity of the law of gravitation.

00After 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.

00The modern lunar theory began with Newton, and consists in determining the motion of the moon deductively from the theory of gravitation.

00In his lectures at the college de France he first publicly expounded the analytical theory of gravitation, and his timely patronage secured the services of J.

00The second conclusion is that, as a general rule, the incandescent heavenly bodies are not masses of solid or liquid matter as formerly assumed, but mainly masses either of gas, or of substances gaseous in their nature, so compressed by the gravitation of their superincumbent parts toward a common centre that their properties combine those of the three forms of matter known to us.

00The idea of a universal force of gravitation seems to have hovered on the borders of this great man's mind, without ever fully entering it.

00This notion, it is plain, tended rather towards Descartes's theory of vortices than towards Newton's theory of gravitation.

00inventors, and even at the present day processes are being patented, having for their object the boiling out of fruits with water or salt solutions, so as to facilitate the separation of the oil from the pulp by gravitation.

00The introduction and withdrawal of the charges in fusion furnaces is effected by gravitation, the solid masses of raw ore, fuel and flux being thrown in at the top, and flowing out of the furnace at the taphole or slag run at the bottom.

00gravitation of the moon might act upon all the substances in our sphere.

00All our digestive, blood and respiratory systems are needed to provide energy for muscle systems - again - to overcome gravitation!

00However, Newton's theory of universal gravitation is not fully worked out for another twenty years.

00Two geographical theories both written in the 1930s: Christaller's Theory of Central Places and Reilly's Law of retail gravitation.

00When it did so, sixteen years after Halleys death, Newtonian gravitation received a great boost and the comet was named after Halley.

00gravitation water which is brought from Hare Hill, 5 or 6 miles away.

00gravitation water supply.

00Despite the success of Newton's gravitation theory, he was not satisfied by the concept of the gravitation theory, he was not satisfied by the concept of the gravitational force.

00gravitation pull could influence individuals.

00gravitation field causes a falling object to accelerate toward the ground.

00They now match up with quantum mechanics and provide a totally satisfactory solution for quantum gravitation.

00Water There is a fairly plentiful supply of gravitation water.

00slop sinks with gravitation water supply.

00The investigation that brought about this result was probably the most laborious that had been made up to Airy's time in planetary theory, and represented the first specific improvement in the solar tables effected in England since the establishment of the theory of gravitation.

00ablatus, taken away), reducing or withdrawing; in astronomy a force which interferes between the moon and the earth to lessen the strength of gravitation is called "ablatitious," just as it is called "addititious" when it increases that strength.

00He was the first to state clearly that the motions of the heavenly bodies must be regarded as a mechanical problem, and he approached in a remarkable manner the discovery of universal gravitation.

00If the law of attraction is that of gravitation, the orbit is a conic section - ellipse, parabola or hyperbola - having the centre of attraction in one of its foci; and the motion takes place in accordance with Kepler's laws (see Astronomy).

00In all the cases which have yet arisen in astronomy the extraneous forces are so small compared with the gravitation of the central body that the orbit is approximately an ellipse, and the preliminary computations, as well as all determinations in which a high degree of precision is not necessary, are made on the hypothesis of elliptic orbits.

00We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

00The heading "Measurement of Dynamical Quantities" includes the topics units, measurements, and the constant of gravitation.

00During this period logarithms were invented, trigonometry and algebra developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation.

00In 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.

00The 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.

00The hollow bulb is worked into the shape it is intended to assume, partly by blowing, partly by gravitation, and partly by the workman's tool.

00As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.

002wr { a 0, dt2WE+2UC+ dz = o, dw dt - 2un+2v+ dH = 0, where H = fdp/p +V +1q 2, (7) 2 2 +v 2 2 (8) and the three terms in H may be called the pressure head, potential head, and head of velocity, when the gravitation unit is employed and Zq 2 is replaced by 1q 2 1 g.

00If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.

00The hydrodynamical equations with moving axes, taking into account the mutual gravitation of the liquid, become dp +4 p Ax+ du - vR {-wQ?

00From the drying floor on which the spent char is heaped up it falls by gravitation into the retorts.

00GRAVITATION (from Lat.

00The other was to show that the gravitation of the earth, following one and the same law with that of the sun, extended to the moon.

00He also showed that the total gravitation of the earth, assumed as spherical, on external bodies, would be the same as if the earth's mass were concentrated in the centre.

00But no conditions to which matter has ever been subjected, or under which it has ever been observed, have been found to influence its gravitation in the slightest degree.

00We might conceive the rapid motions of the heavenly bodies to result in some change either in the direction or amount of their gravitation towards each other at each moment; but such is not the case, even in the most rapidly moving bodies of the solar system.

00The question has also been raised whether the action of gravitation is absolutely instantaneous.

00Another cause which might be supposed to modify the action of gravitation between two bodies would be the interposition of masses of matter between them, a cause which materially modifies the action of electrified bodies.

00The question whether this cause modifies gravitation admits of an easy test from observation.

00On the other hand the enigmatical motion of the perihelion of Mercury has not yet found any plausible explanation except on the hypothesis that the gravitation of the sun diminishes at a rate slightly greater than that of the inverse square - the most simple modification being to suppose that instead of the exponent of the distance being exactly - 2, it is - 2.000 000 161 2.

00In the case of the motion of the moon around the earth, assuming the gravitation of the latter to be subject to the modification in question, the annual motion of the moon's perigee should be greater by I 5" than the theoretical motion.

00Gravitation Constant And Mean Density Of The Earth >>

00The 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.

00A misunderstanding as to the manner in which these should be dealt with was the immediate occasion of the publication by Hutchinson in 1724 of Moses's Principia, part i., in which Woodward's Natural History was bitterly ridiculed, his conduct with regard to the mineralogical specimens not obscurely characterized, and a refutation of the Newtonian doctrine of gravitation seriously attempted.

00Hence arise the springs which run perennially, several of which have been collected into the gravitation water supplies of the Vignacourt and Fawara aqueducts.

00Reference should be made to the article Gravitation for an account of the methods employed to determine the "mean density of the earth."

00Early in the 19th century Andrew Knight showed by experiment that the vertical growth of stems and roots is due to the influence of gravitation, and made other observations on the relation between the position assumed by plant organs and external directive forces, and later Dutrochet, H.

00The disciples of Newton maintained that in the fact of the mutual gravitation of the heavenly bodies, according to Newton's law, they had a complete quantitative account of their motions; and they endeavoured to follow out the path which Newton had opened up by investigating and measuring the attractions and repulsions of electrified and magnetic bodies, and the cohesive forces in the interior of bodies, without attempting to account for these forces.

00Newton himself, however, endeavoured to account for gravitation by differences of pressure in an aether; but he did not publish his theory, ` because he was not able from experiment and observation to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature.'

00It could hardly have been thought of before Sir Isaac Newton's discovery of the actual facts regarding universal gravitation.

00Although, however, gravitation has formed the most perfect instance of an influence completely expressible, up to the most extreme refinement of accuracy, in terms of laws of direct action across space, yet, as is well known, the author of this ideally simple and perfect theory held the view that it is not possible to conceive of direct mechanical action independent of means of transmission.

00They were content with a knowledge of the truth of the principle of gravitation; instead of essaying to explain it further by the properties of a transmitting medium, they in fact modelled the whole of their natural philosophy on that principle, and tried to express all kinds of material interaction in terms of laws of direct mechanical attraction across space.

00It must be a medium which can be effective for transmitting all the types of physical action known to us; it would be worse than no solution to have one medium to transmit gravitation, another to transmit electric effects, another to transmit light, and so on.

00This raises the further question as to whether the transmission of gravitation can be definitely recognized among the properties of an ultimate medium; if so, we know that it must be associated with some feature, perhaps very deep-seated, or on the other hand perhaps depending simply on incompressibility, which is not sensibly implicated in the electric and optical activities.

00But experience has shown that the mistakes, so far as there have been mistakes, are unimportant; and in practice even these are rectified by the natural gravitation of the mind of man to that which it finds most nourishing and most elevating.

00These precise conditions were afterwards demonstrated by Newton to follow necessarily from the law of gravitation.

00A re-examination of his previously considered hypotheses as to the cause of these phenomena was fruitless; the true theory was ultimately discovered by a pure accident, comparable in simplicity and importance with the association of a falling apple with the discovery of the principle of universal gravitation.

00He quotes as an instance that Newton in this way added to the planetary appearances contained in Kepler's laws the gravitation of the planets to the sun, as a notion of causality not contained in the appearances, and thus discovered that gravitation is the cause of the appearances.

00But 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.

00In order to obtain the acid, a series of basins is constructed over the vents, and so arranged as to permit of the passage of water through them by gravitation.

00but commonly known as the "laws of motion"; T and the demonstration of the fact that the motions of the celestial bodies could be included in this theory by means of the law of universal gravitation.

00Newton's law of gravitation affords the most notable example of the process of verification of a law of force, and incidentally of the Galileo-Newton theory.

00The work of translating the law of gravitation into the form of astronomical tables, and the comparison of these with observations, has been in progress ever since.

00The verification is sufficiently exact to establish the law of gravitation, as providing a statement of the motions of the bodies composing the solar system which is correct to a high degree of accuracy.

00What is done is to divide the resultant force due to gravitation into two components, one of which corresponds to this acceleration, while the other one is what is called the "weight" of the body.

00Another way of stating the same thing is to say that we introduce, as a correction for the earth's rotation, a force called "centrifugal force," which combined with gravitation gives the weight of the body.

00The effect of centrifugal force at the equator is to make the weight of a body there about .35% less than the value it would have if due to gravitation alone.

00This is not inconsistent with the law of gravitation, for such estimates as have been made of planetary perturbations due to stars give results which are insignificant in comparison with quantities at present measurable.

00It ascends the flow pipe by convection, where its onward journey would speedily end if it were not for the driving force of other molecules of water following, and the suction set up by the gravitation into the boiler of the cooled water by the return pipe.

0069-180), in 1678, was a new set of dialogues on physical questions, most of which he had treated in a similar fashion before; but now, in dealing with gravitation, he was able to fire a parting shot at Wallis; and one more demonstration of the equality of a straight line to the arc of a circle, thrown in at the end, appropriately closed the strangest warfare in which perverse thinker ever engaged.4 We must now turn back to trace the fortunes of Hobbes and his other doings in the last twenty years of his life.

00Rasselas and Imlac, Nekayah and Pekuah, are evidently meant to be Abyssinians of the 18th century; for the Europe which Imlac describes is the Europe of the 18th century, and the inmates of the Happy Valley talk familiarly of that law of gravitation which Newton discovered and which was not fully received even at Cambridge till the 18th century.

00By relinquishing her claim to the Belgian provinces and other outlying territories in western Germany, and by acquiescing in the establishment of Prussia in the Rhine provinces, she abdicated to Prussia her position as the bulwark of Germany against France, and hastened the process of her own gravitation towards the Slavonic East to which the final impetus was given in 1866.

00Instead of thought, we have perception; instead of dialectic, gravitation; instead of causation, sequence in time.

00In a number of cases measures of the relative positions of the two stars, continued for many years, have shown that they are revolving about a common centre; when this is so there can be no doubt that they form a binary system, and that the two components move in elliptic orbits about the common centre of mass, controlled by their mutual gravitation.

00The 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.

00It 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.

00It may be that these fainter components are still in the stage when the temperature is rising, and the luminosity is as yet comparatively small; but it is not impossible that the massive stars (owing to their greater gravitation) pass through the earlier stages of evolution more rapidly than the smaller stars.

00(See Gravitation.) The figure he gives for the specific gravity of the earth is 5.48, water being 1, but in fact the mean of the 29 results he records works out at 5.448 Other publications of his later years dealt with the height of an aurora seen in 1784 (Phil.

00Nothing is more remarkable in the history of discovery than the manner in which Ampere seized upon the right clue which enabled him to disentangle the complicated phenomena of electrodynamics and to deduce them all as a consequence of one simple fundamental law, which occupies in electrodynamics the position of the Newtonian law of gravitation in physical astronomy.

00The actual force between the particles arises in part from their mutual gravitation, which is inversely as the square of the distance.

00By far the simplest supposition open to us is that the functions are the same in all cases, the attractions differing merely by coefficients analogous to densities in the theory of gravitation.

00Now it is shown in hydrodynamics that she velocity of propagation of waves in deep water is that acquired by a heavy body falling through half the radius of the circle whose circumference is the wave-length, or _ f_X _ ga 27rT 'I ' v2- 2r 2r pn This velocity is a minimum when X=2.7r gp' and the minimum value is v= 4 - p g For waves whose length from crest to crest is greater than X, the principal force concerned in the motion is that of gravitation.

00In front of this is a double series of stationary waves, the gravitation waves forming a series increasing in wave-length with their distance in front of the body, and the surface-tension waves or ripples diminishing in wave-length with their distance from the body, and both sets of waves rapidly diminishing in amplitude with their distance from the body.

00The flying body must act against gravitation, and elevate and carry itself forward at the expense of the air and of the force which resides in it, whatever that may be.

00If it were otherwise - if it were rescued from the law of gravitation on the one hand, and bereft of independent movement on the other, it would float about uncontrolled and uncontrollable like an ordinary balloon.

00Hence it comes by natural gravitation into the town at a pressure of five atmospheres, so that it supplies the highest parts of the town with abundant water.

00PROBLEM OF THREE BODIES, the problem of determining the motion of three bodies moving under no influence but that of their mutual gravitation.

00But in the sun's atmosphere gravitation alone is a misleading guide.

00condensing power of gravitation at the sun's borders is the pressure of radiation.

00- Any area, large or small, of the earth's surface from any part of which, if the ground were impermeable, water would flow by gravitation past any point in a natural watercourse is commonly known in Europe as the " hydrographic basin " above that point.

00Perennial springs of large volume rarely occur in Great Britain at a sufficient height to afford supplies by gravitation; but from the limestones of Italy and many other parts of the world very considerable volumes issue far above the sea-level, and are thus available, without pumping, for the supply of distant towns.

00Yet the hilly parts of the last-named country are rich in magnificent sites at sufficient altitudes for the supply of any parts by gravitation, and capable, if properly laid out, of affording a volume of water, throughout the driest seasons, far in excess of the probable demand for a long future.

00above the sea, may be made available for the supply of pure water by gravitation to any part of England.

00In the spring he had determined the attractions of masses, and thus completed the law of universal gravitation.

00He also wrote an Essay touching the Gravitation or Nongravitation of Fluid Bodies (1673); Difficiles Nugae, or Observations touching the Torricellian Experiment, &c. (1675); and a translation of the Life of Pomponius Atticus, by Cornelius Nepos (1677).

00It was this: from the observed perturbations of a known planet to deduce by calculation, assuming only Newton's law of gravitation, the mass and orbit of an unknown disturbing body.

00Its mathematical prediction was not only an unsurpassed intellectual feat; it showed also that Newton's law of gravitation, which Airy had almost called in question, prevailed even to the utmost bounds of the solar system.

00The most soluble of the constituents of crude coal gas is ammonia, 780 volumes of which are soluble in one volume of water at normal temperature and pressure, and the water in the hydraulic main absorbs a considerable quantity of this compound from the gas and helps to form the ammoniacal liquor, whilst, although the liquor is well agitated by the gas bubbling through it, a partial separation of tar from liquor is effected by gravitation.

00ROGER JOSEPH BOSCOVICH (1711?-1787) mathematician and natural philosopher, one of the earliest of foreign savants to adopt Newton's gravitation theory, was born at Ragusa in Dalmatia on the 18th of May 1711, according to the usual account, but ten years earlier according to Lalande (Eloge, 1792).

00Among these subjects were the transit of Mercury, the Aurora Borealis, the figure of the earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometer, various problems of spherical trigonometry, &c. In 1742 he was consulted, with other men of science, by the pope, Benedict XIV., as to the best means of securing the stability of the dome of St Peter's, Rome, in which a crack had been discovered.

00Modern theoretical astronomy, taken in the most limited sense, is based upon Celestial Mechanics, the science by which, using purely deductive mechanical methods, the laws of motion of the heavenly bodies are derived by deductive methods from their mutual gravitation towards each other.

00Celestial Mechanics is, strictly speaking, that branch of applied mathematics which, by deductive processes, derives the laws of motion of the heavenly bodies from their gravitation towards each other, or from the mutual action of the parts which form them.

00The science had its origin in the demonstration by Sir Isaac Newton that Kepler's three laws of planetary motion, and the law of gravitation, in the case of two bodies, could be mutually derived from each other.

00==Problem of Three Bodies== As soon as the general law of gravitation was fully apprehended, it became evident that, owing to the attraction of each planet upon all the others, the actual motion of the planets must deviate from their motion in an ellipse according to Kepler's laws.

00This numerical proportion, as being a necessary consequence of the law of gravitation, must prevail in every system under its sway.

00Gravitation was thus shown to be the sole influence governing the movements of planets and satellites; the figure of the rotating earth was successfully explained by its action on the minuter particles of matter; tides and the precession of the equinoxes proved amenable to reasonings based on the same principle; and it satisfactorily accounted as well for some of the chief lunar and planetary inequalities.

00The discovery, just one hundred years after the publication of Newton's Principia, of its dependence upon the slowly varying eccentricity of the earth's orbit signalized the removal of the last conspicuous obstacle to admitting the unqualified validity of the law of gravitation.

00After 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.

00The modern lunar theory began with Newton, and consists in determining the motion of the moon deductively from the theory of gravitation.

00In his lectures at the college de France he first publicly expounded the analytical theory of gravitation, and his timely patronage secured the services of J.

00The second conclusion is that, as a general rule, the incandescent heavenly bodies are not masses of solid or liquid matter as formerly assumed, but mainly masses either of gas, or of substances gaseous in their nature, so compressed by the gravitation of their superincumbent parts toward a common centre that their properties combine those of the three forms of matter known to us.

00The idea of a universal force of gravitation seems to have hovered on the borders of this great man's mind, without ever fully entering it.

00This notion, it is plain, tended rather towards Descartes's theory of vortices than towards Newton's theory of gravitation.

00On this is based the great structure of celestial mechanics and the theory of universal gravitation; and in the elucidation of problems more directly concerned with astronomy, Kepler, Sir Isaac Newton and others discovered many properties of the conic sections (see Mechanics).

00inventors, and even at the present day processes are being patented, having for their object the boiling out of fruits with water or salt solutions, so as to facilitate the separation of the oil from the pulp by gravitation.

00The introduction and withdrawal of the charges in fusion furnaces is effected by gravitation, the solid masses of raw ore, fuel and flux being thrown in at the top, and flowing out of the furnace at the taphole or slag run at the bottom.

00Gravitation #1 and #2, produced solely by Rob Stow, ventured into the funky realms of Techno.

00The sand-pump descends by gravitation, and its fall is checked by pressing hack the lever, so as to throw the reel against a post which serves as a brake.

01As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.

01If homogeneous liquid is drawn off from a vessel so large that the motion at the free surface at a distance may be neglected, then Bernoulli's equation may be written H = PIP--z - F4 2 / 2g = P/ p +h, (8) where P denotes the atmospheric pressure and h the height of the free surface, a fundamental equation in hydraulics; a return has been made here to the gravitation unit of hydrostatics, and Oz is taken vertically upward.

01From the drying floor on which the spent char is heaped up it falls by gravitation into the retorts.

01Early in the 19th century Andrew Knight showed by experiment that the vertical growth of stems and roots is due to the influence of gravitation, and made other observations on the relation between the position assumed by plant organs and external directive forces, and later Dutrochet, H.

01This raises the further question as to whether the transmission of gravitation can be definitely recognized among the properties of an ultimate medium; if so, we know that it must be associated with some feature, perhaps very deep-seated, or on the other hand perhaps depending simply on incompressibility, which is not sensibly implicated in the electric and optical activities.

01But 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.

01The work of translating the law of gravitation into the form of astronomical tables, and the comparison of these with observations, has been in progress ever since.

01The effect of centrifugal force at the equator is to make the weight of a body there about .35% less than the value it would have if due to gravitation alone.

01By relinquishing her claim to the Belgian provinces and other outlying territories in western Germany, and by acquiescing in the establishment of Prussia in the Rhine provinces, she abdicated to Prussia her position as the bulwark of Germany against France, and hastened the process of her own gravitation towards the Slavonic East to which the final impetus was given in 1866.

01Instead of thought, we have perception; instead of dialectic, gravitation; instead of causation, sequence in time.

01The sand-pump descends by gravitation, and its fall is checked by pressing hack the lever, so as to throw the reel against a post which serves as a brake.

01The hollow bulb is worked into the shape it is intended to assume, partly by blowing, partly by gravitation, and partly by the workman's tool.

022wr { a 0, dt2WE+2UC+ dz = o, dw dt - 2un+2v+ dH = 0, where H = fdp/p +V +1q 2, (7) 2 2 +v 2 2 (8) and the three terms in H may be called the pressure head, potential head, and head of velocity, when the gravitation unit is employed and Zq 2 is replaced by 1q 2 1 g.

02The hydrodynamical equations with moving axes, taking into account the mutual gravitation of the liquid, become dp +4 p Ax+ du - vR {-wQ?

02The other was to show that the gravitation of the earth, following one and the same law with that of the sun, extended to the moon.

02Newton himself, however, endeavoured to account for gravitation by differences of pressure in an aether; but he did not publish his theory, ` because he was not able from experiment and observation to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature.'

02But experience has shown that the mistakes, so far as there have been mistakes, are unimportant; and in practice even these are rectified by the natural gravitation of the mind of man to that which it finds most nourishing and most elevating.

02The verification is sufficiently exact to establish the law of gravitation, as providing a statement of the motions of the bodies composing the solar system which is correct to a high degree of accuracy.

02It ascends the flow pipe by convection, where its onward journey would speedily end if it were not for the driving force of other molecules of water following, and the suction set up by the gravitation into the boiler of the cooled water by the return pipe.

02It may be that these fainter components are still in the stage when the temperature is rising, and the luminosity is as yet comparatively small; but it is not impossible that the massive stars (owing to their greater gravitation) pass through the earlier stages of evolution more rapidly than the smaller stars.

02But no conditions to which matter has ever been subjected, or under which it has ever been observed, have been found to influence its gravitation in the slightest degree.

03Although, however, gravitation has formed the most perfect instance of an influence completely expressible, up to the most extreme refinement of accuracy, in terms of laws of direct action across space, yet, as is well known, the author of this ideally simple and perfect theory held the view that it is not possible to conceive of direct mechanical action independent of means of transmission.

03It must be a medium which can be effective for transmitting all the types of physical action known to us; it would be worse than no solution to have one medium to transmit gravitation, another to transmit electric effects, another to transmit light, and so on.

03

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.