GRAVITY

, in Physics, the natural tendency or inclination of bodies towards the centre. And in this sense Gravity agrees with Centripetal force.

Gravity however is, by some, defined more generally as the natural tendency of one body towards another; and again by others still more generally as the mutual tendency of each body, and each particle of a body, towards all others: in which sense the word answers to what is more usually called Attraction. Indeed the terms Gravity, weight, centripetal force, and attraction, denote in effect all the same thing, only in different views and relations; all which however it is very common to confound, and use promiscuously. But, in propriety, when a body is considered as tending towards the earth, the force with which it so tends is called Gravity, Force of Gravity, or Gravitating Force; when the body is considered as immediately tending to the centre of the earth, it is called Centripetal Force; but when we consider the earth, or mass to which the body tends, it is called Attraction, or Attractive Force; and when it is considered in respect of an obstacle or another body in the way of its tendency, upon which it acts, it is called Weight.

Philosophers think differently on the subject of Gravity. Some consider it as an inactive property or innate power in bodies, by which they endeavour to join their centre. Others hold Gravity in this sense to be an occult quality, and to be exploded as such out of all sound philosophy. Newton, though he often calls it a vis, power, or property in bodies, yet explains himself, that he means nothing more by the word but the effect or phenomenon: he does not consider the principle, the cause by which bodies tend downwards, but the tendency itself, which is no occult quality, but a sensible phenomenon, be its causes what they may; whether a property essential to body, as some make it, or superadded to it, as others; or even an impulse of some body from without, as others.

It is a law of nature long observed, that all bodies near the earth have a Gravity or weight, or a tendency towards its centre, or at least perpendicular to its surface; which law the moderns, and especially Sir I. Newton, from certain observations have found to be much more extensive, and holding universally with respect to all known bodies and matter in nature. It is therefore at present acknowledged as a principle or law of nature, that all bodies, and all the particles of all bodies, mutually gravitate towards each other: from which single principle it is that Newton has happily deduced all the great phenomena of nature.

Hence Gravity may be distinguished into Particular and General.

Particular Gravity, is that which respects the earth, or by which bodies descend, or tend towards the centre of the earth; the phenomena or properties of which are as follow:

1. All circumterrestrial bodies do hereby tend towards a point, which is either accurately or very nearly the centre of magnitude of the terraqueous globe. No<*> that it is meant that there is really any virtue or charm in the point called the centre, by which it attracts bodies; but because this is the result of the gravitation of bodies towards all the parts of which the earth consists.

2. This point or centre is fixed within the earth, or at least has been so far as any authentic history reaches. For a consequence of its shifting, though ever so little,| would be the overflowing of the low lands on that side of the globe towards which it should approach. Dr. Halley suggests, that it would well account for the universal deluge, to have the centre of gravitation removed for a time towards the middle of the then inhabited world; for the change of its place but the 2000th part of the radius of the earth, or about 2 miles, would be sufficient to lay the tops of the highest hills under water.

3. In all places equidistant from the centre of the earth, the force of Gravity is nearly equal. Indeed all parts of the earth's surface are not at equal distances from the centre, because the equatorial parts are higher than the polar parts by about 17 miles; as has been proved by the necessity of making the pendulum shorter in those places, before it will swing seconds. In the new Petersburg Transactions, vol. 6 and 7, M. Krafft gives a formula for the proportion of Gravity in different latitudes on the earth's surface, which is this: ; where g denotes the Gravity at the equator, and y the Gravity under any other latitude l. On this subject, see also the articles Degree, and Earth.

4. Gravity equally affects all bodies, without regard either to their bulk, figure, or matter: so that, abstracting from the resistance of the medium, the most compact and loose, the greatest and smallest bodies would all descend through an equal space in the same time; as appears from the quick descent of very light bodies in an exhausted receiver. The space which bodies do actually fall, in vacuo, is 16 1/12 feet in the first second of time, in the latitude of London; and for other times, either greater or less than that, the spaces descended from rest are directly proportional to the squares of the times, while the falling body is not far from the earth's surface.

5. This power is the greatest at the earth's surface, from whence it decreases both upwards and downwards, but not both ways in the same proportion; for upwards the force of Gravity is less, or decreases, as the square of the distance from the centre increases, so that at a double distance from the centre, above the surface, the force would be only 1-4th of what it is at the surface; but below the surface, the power decreases in such sort that its intensity is in the direct ratio of the distance from the centre; so that at the distance of half a semidiameter from the centre, the force would be but half what it is at the surface; at 1/3 of a semidiameter the force would be 1/3, and so on.

6. As all bodies gravitate towards the earth, so does the earth equally gravitate towards all bodies; as well as all bodies towards particular parts of the earth, as hills, &c, which has been proved by the attraction a hill has upon a plumb line, insensibly drawing it aside.— Hence the gravitating force of entire bodies consists of those of all their parts: for by adding or taking away any part of the matter of a body, its Gravity is increased or decreased in the proportion cf the quantity of such portion to the whole mass. Hence also the gravitating powers of bodies, at the same distance from the centre, are proportional to the quantities of matter in the bodies.

General or Universal Gravity, is that by which all the planets tend to one another, and indeed by which all the bodies and particles of matter in the universe tend towards one another.

The existence of the same principle of Gravitation in the superior regions of the heavens, as on the earth, is one of the great discoveries of Newton, who made the proof of it as easy as that on the earth. At first it would seem this was only conjecture with him: he observed that all bodies near the earth, and in its atmosphere, had the property of tending directly towards it; he soon conjectured that it probably extended much higher than any distance to which we could reach, or make experiments; and so on, from one distance to another, till he at length saw no reason why it might not extend as far as to the moon, by means of which she might be retained in her orbit as a stone in a sling is retained by the hand; and if so, he next inferred why might not a similar principle exist in the other great bodies in the universe, the sun and all the other planets, both primary and secondary, which might all be retained in their orbits, and perform their revolutions, by means of the same universal principle of gravitation.

These conjectures he soon realized and verified by mathematical proofs. Kepler had found out, by contemplating the motions of the planets about the sun, that the area described by a line connecting the sun and planet, as this revolved in its orbit, was always proportional to the time of its description, or that it described equal areas in equal times, in whatever part of its orbit the planet might be, moving always so much the quicker as its distance from the sun was less. And it is also found that the satellites, or secondary planets, respect the same law in revolving about their primaries. But it was soon proved by Newton, that all bodies moving in any curve line described on a plane, and which, by radii drawn to any certain point, describe areas about the point proportional to the times, are impelled or acted on by some power tending towards that point. Confequently the power by which all these planets revolve, and are retained in their orbits, is directed to the centre about which they move, viz, the primary planets to the sun, and the satellites to their several primaries.

Again, Newton demonstrated, that if several bodies revolve with an equable motion in several circles about the same centre, and that if the squares<*> of their periodical times be in the same proportion as the cubes of their distances from the common centre, then the centripetal forces of the revolving bodies, by which they tend to their central body, will be in the reciprocal or inverse ratio of the squares of the distances. Or if bodies revolve in orbits approaching to circles, and the apses of those orbits be at rest, then also the centripetal forces of the revolving bodies will be reciprocally proportional to the squares of the distances. But it had been agreed on by the astronomers, and particularly Kepler, that both these cases obtain in all the planets. And therefore he inferred that the centripetal forces of all the planets are reciprocally proportional to the squares of the distances from the centres of their orbits.

Upon the whole it appears, that the planets are retained in their orbits by some power which is continually acting upon them: that this power is directed towards the centre of their orbits: that the intensity or efficacy of this power increases upon an approach| towards the centre, and diminishes on receding from the same, and that in the reciprocal duplicate ratio of the distances: and that, by comparing this centripetal force of the planets with the force of gravity on the earth, they are found to be perfectly alike, as may easily be shewn in various instances. For example, in the case of the moon, the nearest of all the planets. The rectilinear spaces described in any given time by a falling body, urged by any powers, reckoning from the beginning of its descent, are proportional to those powers. Consequently the centripetal force of the moon revolving in her orbit, will be to the force of Gravity on the surface of the earth, as the space which the moon would describe in falling during any small time, by her centripetal force towards the earth, if she had no circular motion at all, to the space a body near the earth would describe in falling by its Gravity towards the same.

Now by an easy calculation of those two spaces, it appears that the former force is to the latter, as the square of the semi-diameter of the earth is to the square of that of the moon's orbit. The moon's centripetal force therefore is equal to the force of Gravity; and consequently these forces are not different, but they are one and the same: for if they were different, bodies acted on by the two powers conjointly would fall towards the earth with a velocity double to that arising from the sole power of Gravity.

It is evident therefore that the moon's centripetal force, by which she is retained in her orbit, and prevented from running off in tangents, is the very power of Gravity of the earth extended thither. See Newton's Princip. lib. 1, prop. 45, cor. 2, and lib. 3, prop. 3; where the numeral calculation may be seen at full length.

The moon therefore gravitates towards the earth, and reciprocally the earth towards the moon. And this is also farther consirmed by the phenomena of the tides.

The like reasoning may also be applied to the other planets. For as the revolutions of the primary planets round the sun, and those of the satellites of Jupiter and Saturn round their primaries, are phenomena of the same kind with the revolution of the moon about the earth; and as the centripetal powers of the primary are directed towards the centre of the sun, and those of the satellites towards the centres of their primaries; and lastly as all these powers are reciprocally as the squares of the distances from the centres, it may safely be concluded that the power and cause are the same in all.

Therefore, as the moon gravitates towards the earth, and the earth towards the moon; so do all the secondaries to their primaries, and these to their secondaries; and so also do the primaries to the sun, and the sun to the primaries. Newton's Princip. lib. 3, prop. 4, 5, 6; Greg. Astron. lib. 1, sect. 7, prop. 46 and 47.

The laws of Universal Gravity are the same as thofe of bodies gravitating towards the earth, before laid down.

Cause of Gravity. Various theories have been advanced by the philosophers of different ages to account for this grand principle of Gravitation. The ancients, who were only acquainted with particular Gravity, or the tendency of sublu<*>ar bodies towards the earth, aimed no farther than a system that might answer the more obvious phenomena of it. However, some hints are sound concerning the Gravitation of celestial bodies in the account given of the doctrine of Thales and his successors; and it would seem that Pythagoras was still better acquainted with it, to which it is supposed he had a view in what he taught concerning the Harmony of the Spheres.

Aristotle and the Peripatetics content themselves with referring Gravity or weight to a native inclination in heavy bodies to be in their proper place or sphere, the centre of the earth. And Copernicus ascribes it to an innate principle in all parts of matter, by which, when separated from their wholes, they endeavour to return to them again the nearest way. In answer to Aristotle and his followers, who considered the centre of the earth as the centre of the universe, he observed that it was reasonable to think there was nothing peculiar to the earth in this principle of Gravity; that the parts of the sun, moon, and stars tended likewise to each other, and that their spherical figure was preserved in their various motions by this power. Copern. Revol. lib. 1, cap. 9. But neither of these systems assigns any physical cause of this great effect: they only amount to this, that bodies descend because they are inclined to descend.

Kepler, in his preface to the commentaries concerning the planet Mars, speaks of Gravity as of a power that was mutual between bodies, and says that the earth and moon tend towards each other, and would meet in a point so many times nearer to the earth than to the moon, as the earth is greater than the moon, if their motions did not hinder it. He adds, that the tides arise from the Gravity of the waters towards the moon. To him we also owe the important discovery of the analogy between the distances of the several planets from the sun, and the periods in which they complete their revolutions, viz, that the squares of their periodic times are always in the same proportion as the cubes of their mean distances from the sun. However, Kepler, Gassendi, Gilbert, and others, ascribe Gravity to a certain magnetic attraction of the earth; conceiving the earth to be one great magnet continually emitting effluvia, which take hold of all bodies, and draw them towards the earth. But this is inconfistent with the several phenomena.

Des Cartes and his followers, Rohault &c, attribute Gravity to an external impulse or trusion of some subtle matter. By the rotation of the earth, say they, all the parts and appendages of it necessarily endeavour to recede from the centre of rotation; but whence they cannot all actually recede, as there is no vacuum or space to receive them. But this hypothesis, founded on the supposition of a plenum, is overthrown by what has been since proved of the existence of a vacuum.

Dr. Hook inclines to an opinion much like that of Des Cartes. Gravity he thinks deducible from the action of a most subtle medium, which easily pervades and penetrates the most solid bodies; and which, by some motion it has, detrudes all earthly bodies from it, towards the centre of the earth. Vossius too, and many others, give partly into the Cartesian notion, and suppose Gravity to arise from the diurnal rotation of the earth round its axis.

Dr. Halley, despairing of any satisfactory theory,| chooses to have immediate recourse to the agency of the Deity. So Dr. Clarke, from a view of several properties of Gravity, concludes that it is no adventitious effect of any motion, or subtle matter, but an original and general law impressed by God on all matter, and preserved in it by some efficient power penetrating the very solid and intimate substance of it; being found always proportional, not to the surfaces of bodies or corpuscles, but to their solid quantity and contents. It should therefore be no more inquired why bodies gravitate, than how they came to be first put in motion. Annot. in Rohault. Phys. part 1, cap. 11.

Gravesande, in his Introduct. ad Philos. Newton. contends that the cause of Gravity is utterly unknown; and that we are to consider it no otherwise than as a law of nature originally and immediately impressed by the Creator, without any dependence on any second law or cause at all. Of this he thinks the three following considerations sufficient proof. 1. That Gravity requires the presence of the gravitating or attracting body: so the satellites of Jupiter, for ex. gravitate towards Jupiter, wherever he may be. 2. That the distance being supposed the same, the velocity with which bodies are moved by the force of Gravity, depends on the quantity of matter in the attracting body: and the velocity is not changed, whatever the mass of the gravitating body may be. 3. That if Gravity do depend on any known law of motion, it must be some impulse from an extraneous body; so that as Gravity is continual, a continual stroke must also be required. Now if there be any such matter continually striking on bodies, it must be fluid, and subtle enough to penetrate the substance of all bodies: but how shall a body subtle enough to penetrate the substance of the hardest bodies, and so rare as not sensibly to hinder the motion of bodies, be able to impel vast masses towards each other with such force? how does this force increase the ratio of the mass of the body, towards which the other body is moved? whence is it that all bodies move with the same velocity, the distance and body gravitated to being the same? can a fluid which only acts on the surface either of the bodies themselves, or their internal particles, communicate such a quantity of motion to bodies, which in all bodies shall exactly follow the proportion of the quantity of matter in them?

Mr. Cotes goes yet farther. Giving a view of Newton's philosophy, he asserts that Gravity is to be ranked among the primary qualities of all bodies; and deemed equally essential to matter as extension, mobility, or impenetrability. Præfat. ad Newt. Princip. But Newton himself disclaims this notion; and to shew that he does not take Gravity to be essential to bodies, he declares his opinion of the cause; choosing to propose it by way of query, not being yet sufficiently satissied about its experiments. Thus, after having shewn that there is a medium in nature vastly more subtle than air, by whose vibrations sound is propagated, by which light communicates heat to bodies, and by the different densities of which the refraction and reslection of light are performed; he proceeds to inquire: “Is not this medium much rarer within the dense bodies of the sun, stars, planets, and comets, than in the empty celestial spaces between them? and in passing from them to greater distances, doth it not grow denser and denser perpetually, and thereby cause the Gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to recede from the denser parts of the medium towards the rarer?

For if this medium be supposed rarer within the sun's body than at its surface, and rarer there than at the hundredth part of an inch from his body, and rarer there than at the fiftieth part of an inch from his body, and rarer there than at the orb of Saturn; I see no reason why the increase of density should stop any where, and not rather be continued through all distances from the Sun to Saturn, and beyond.

And though this increase of density may at great distances be exceeding slow; yet if the elastic force of this medium be exceeding great, it may suffice to impel bodies from the denser parts of the medium towards the rarer with all that power which we call Gravity.

And that the elastic force of this medium is exceeding great, may be gathered from the swiftness of its vibrations. Sounds move about 1140 English feet in a second of time, and in seven or eight minutes of time, they move about one hundred English miles: light moves from the Sun to us in about seven or eight minutes of time, which distance is about 70000000 English miles, supposing the horizontal parallax of the Sun to be about twelve seconds; and the vibrations, or pulses of this medium, that they may cause the alternate fits of easy transmission, and easy reslection, must be swifter than light, and by consequence above 700000 times swifter than sounds; and therefore the elastic force of this medium, in proportion to its density, must be above 700000 × 700000 (that is, above 490000000000) times greater than the elastic force of the air is in proportion to its density: for the velocities of the pulses of elastic mediums are in a subduplicate ratio of the elasticities and the rarities of the mediums taken together.

As Magnetism is stronger in small loadstones than in great ones, in proportion to their bulk; and Gravity is stronger on the surface of small planets, than those of great ones, in proportion to their bulk; and small bodies are agitated much more by electric attraction than great ones: so the smallness of the rays of light may contribute very much to the power of the agent by which they are refracted; and if any one should suppose, that æther (like our air) may contain particles which endeavour to recede from one another (for I do not know what this æther is), and that its particles are exceedingly smaller than those of air, or even than those of light; the exceeding smallness of such particles may contribute to the greatness of the force, by which they recede from one another, and thereby make that medium exceedingly more rare and elastic than air, and of consequence, exceedingly less able to resist the motions of projectiles, and exceedingly more able to press upon gross bodies by endeavouring to expand itself.” Optics, p. 325 &c.

, in Mechanics, denotes the conatus or tendency of bodies towards the centre of the earth.— That part of mechanics which considers the equilibrium| or motion of bodies arising from Gravity or weight, is particularly called statics.

Gravity in this view is distinguished into Absolute and Relative.

Absolute Gravity is that with which a body descends freely and perpendicularly through an unresisting medium. The laws of which see under Descent of Bodies, Acceleration, Motion, &c.

Relative Gravity is that with which a body descends on an inclined plane, or through a resisting medium, or as opposed by some other resistance. The laws of which see under the articles Inclined Plane, Descent, Fluid, Resistance, &c.

, in Hydrostatics. The laws of bodies gravitating in Fluids make the business of Hydrostatics.

Gravity is here divided into Absolute and Specific.

Absolute or True Gravity, is the whole force with which the body tends downwards.

Specific Gravity, is the relative, comparative, or apparent Gravity in any body, in respect of that of an equal bulk or magnitude of another body; denoting that Gravity or weight which is peculiar to each species or kind of body, and by which it is distinguished from all other kinds.

In this sense a body is said to be Specifically Heavier than another, when under the same bulk it contains a greater weight than that other; and reciprocally the latter is said to be Specifically Lighter than the former. Thus, if there be two equal spheres, each one foot in diameter; the one of lead, and the other of wood: since the leaden one is found heavier than the wooden one, it is said to be Specifically, or in Specie, Heavier; and the wooden one Specifically Lighter.

This kind of Gravity is by some called Relative; in opposition to Absolute Gravity, which increases in proportion to the quantity or mass of the body.

I. If two bodies be equal in bulk, their specific gravities are to each other as their weights, or as their densities.

II. If two bodies be of the same specific gravity or density, their absolute weights will be as their magnitudes or bulks.

III. In bodies of the same weight, the specific gravities are reciprocally as their bulks.

IV. The specific gravities of all bodies are in a ratio compounded of the direct ratio of their weights, and the reciprocal ratio of their magnitudes. And hence again the specific gravities are as the densities.

V. The absolute gravities or weights of bodies are in the compound ratio of their specific gravities and magnitudes or bulks.

VI. The magnitudes of bodies are directly as their weights, and reciprocally as their specific gravities.

VII. A body specifically heavier than a fluid, loses as much of its weight when immersed in it, as is equal to the weight of a quantity of the fluid of the same bulk or magnitude.

Hence, since the Specific Gravities are as the abso- lute gravities under the same bulk; the Specific Gravity of the fluid, will be to that of the body immerged, as the part of the weight lost by the solid, is to the whole weight.

And hence the Specific Gravities of fluids are as the weights lost by the same solid immerged in them.

VIII. To find the Specific Gravity of a Fluid, or of a Solid.—On one arm of a balance suspend a globe of lead by a fine thread, and to the other fasten an equal weight, which may just balance it in the open air. Immerge the globe into the fluid, and observe what weight balances it then, and consequently what weight is lost, which is proportional to the Specific Gravity as above. And thus the proportion of the Specific Gravity of one fluid to another is determined by immersing the globe successively in all the fluids, and observing the weights lost in each, which will be the proportions of the Specific Gravities of the fluids sought.

This same operation determines also the Specific Gravity of the solid immerged, whether it be a globe or of any other shape or bulk, supposing that of the fluid known. For the Specific Gravity of the fluid is to that of the solid, as the weight lost is to the whole weight.

Hence also may be found the Specific Gravity of a body that is lighter than the fluid, as follows:

IX. To find the Specific Gravity of a Solid that is lighter than the fluid, as water, in which it is put.—Annex to the lighter body another that is much heavier than the fluid, so as the compound mass may sink in the fluid. Weigh the heavier body and the compound mass separately, both in water and out of it; then find how much each loses in water, by subtracting its weight in water from its weight in air; and subtract the less of these remainders from the greater.

Then, As this last remainder, Is to the weight of the light body in air, So is the Specific Gravity of the fluid, To the Specific Gravity of that body.

X. The Specific Gravities of bodies of equal weight, are reciprocally proportional to the quantities of weight lost in the same fluid. And hence is found the ratio of the Specific Gravities of solids, by weighing in the same fluids, masses of them that weigh equally in air, and noting the weights lost by each.

The Specific Gravities of many kinds of bodies, both solid and fluid, have been determined by varioüs authors. Marinus Ghetaldus particularly tried the Specific Gravities of various bodies, especially metals; which were taken from thence by Oughtred. In the Philos. Trans. are several ample tables of them, by various authors, particularly those of Mr. Davis, vol. 45, p. 416, or Abr. vol. 10, p. 206. Some tables of them were also published by P. Mersenne, Muschenbroeck, Ward, Cotes, Emerson, Martin, &c.

It will be sufficient here to give those of some of the most usual bodies, that have been determined with the greater certainty. The numbers in this table express the number of Avoirdupois ounces in a cubic foot of each body, that of common water being just 1000 ounces, or 62 1/2 lb.|

These numbers being the weight of a cubic foot, or 1728 cubic inches, of each of the bodies, in Avoirdupois ounces, by proportion the quantity in any other weight, or the weight of any other quantity, may be readily known.

For ex. Required the content of an irregular block of common stone which weighs 1 cwt, or 112lb, or 1792 ounces. Here, as cubic inches the content.

Ex. 2. To find the weight of a block of granite, whose length is 63 feet, and breadth and thickness each 12 feet; being the dimensions of one of the stones, of granite, in the walls of Balbeck. Here, feet is the content of the stone; therefore as or 885 tons 18 cwt. 3 qrs. the weight of the stone.

XI. A body descends in a fluid specifically lighter. or ascends in a fluid specifically heavier, with a force equal to the difference between its weight and that of an equal bulk of the fluid.

XII. A body sinks in a fluid specifically heavier, so| far as that the weight of the body is equal to the weight of a quantity of the fluid of the same bulk as the part immersed. Hence, as the Specific Gravity of the fluid is to that of the body, so is the whole magnitude of the body, to the magnitude of the part immersed.

XIII. The Specific Gravities of equal solids are as their parts immerged in the same fluid.

The several theorems here delivered, are both demonstrable from the principles of mechanics, and are also equally conformable to experiment, which answers exactly to the calculation; as is abundantly evident from the courses of philosophical experiments, so frequently exhibited; where the laws of specific gravitation are well illustrated.

GREAT BEAR, one of the constellations in the northern hemisphere. See Ursa Major.

Great Circles, of the Globe or Sphere, are those whose planes pass through the centre, dividing it into two equal parts or hemispheres, and therefore having the same centre and diameter with the sphere itself. The principal of these are, the equator, the ecliptic, the horizon, the meridians, and the two colures.

Great-Circle Sailing, is the art of conducting a ship along the arc of a great circle. And it is also that part of the theory of navigation which treats of sailing in the arc of a great circle. See Navigation.