SONING.

In his second book Sir Isaac Newton treats of the properties of fluids, and their powers of resistance; and lays down such principles as entirely overthrow the doctrine of Des Cartes's vortices, which was the fashionable system in his time. In the third book he begins particularly to treat of the natural phenomena, and apply them to the mathematical principles formerly demonstrated; and, as a necessary preliminary to this part, he lays down the following rules for reasoning in natural philosophy:-1. We are to admit no more causes of natural things than such as are both true and sufficient to explain their natural appearances. 2. Therefore to the same natural effects we must always assign, as far as possible, the same causes. 3. The qualities of bodies which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. 4. In experimental philosophy, we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

The phenomena first considered are, 1. That the satellites of Jupiter, by radii drawn to the centre of their primary, describe areas proportional to the times of the description; and that their periodic times, the fixed stars being at rest, are in the sesquiplicate ratio of their distances from its centre. 2. The same thing is likewise observed of the phenomena of Saturn. 3. The five primary planets, Mercury, Venus, Mars, Jupiter, and Saturn, with their several orbits, encompass the sun. 4. The fixed stars being supposed at rest, the periodic times of the five primary planets, and of the earth about the sun, are in the sesquiplicate proportion of their mean distances from the sun. 5. The primary planets, by radii drawn to the earth, describe areas no ways proportionable to the times: but the areas which they describe by radi drawn to the sun are proportional to the times of description. 6. The moon, by a radius drawn to the centre of the earth, describes an area proportional to the time of description. All these phenomena are undeniable from astronomical observations, and are explained at large under the article ASTRONOMY. The mathematical demonstrations are next applied by Sir Isaac Newton in the following propositions:

Prop. I. The forces by which the satellites of Jupiter are continually drawn off from rectilinear motions, and retained in their proper orbits, tend to the centre of that planet; and are reciprocally as the squares of the distances of those satellites from that centre. The former part of this proposition appears from theor. II. or III. and the latter from cor. 6, of theor. V., and the same thing we are to understand of the satellites

of Saturn.

Prop. II. The forces by which the primary planets are continually drawn off from rectilinear

tend to the sun; and are reciprocally as the squares of the distances from the sun's centre. The former part of this proposition is manifest from phenomenon 5, just mentioned, and from theor. II.; the latter from the phenomenon 4, and cor. 6, of theor. IV. But this part of the proposition is with great accuracy deducible from the quiescence of the aphelion points. For a very small aberration from the reciprocal duplicate proportion would produce a motion of the apsides, sensible in every single revolution, and in many of them enormously great.

Prop. III. The force by which the moon is retained in its orbit tends towards the earth, and is reciprocally as the square of the distance of its place from the centre of the earth. The former part of this proposition is evident from phenomenon 5, and theor. II.; the latter from phenomenon 6, and theor. II. or III. It is also evident from the very slow motion of the moon's apogee; which, in every single revolution, amounting but to 3° 3′ in consequentia, may be neglected: and this more fully appears from the next proposition.

Prop. IV. The moon gravitates towards the earth, and by the force of gravity is continually drawn off from a rectilinear motion, and retained in its orbit.-The mean distance of the moon from the earth in the syzigies in semidiameters of the latter is about 60}. Let us assume the mean distance of 60 semidiameters in the syzigies; and suppose one revolution of the moon in respect of the fixed stars to be completed in 27 d. 7 h. 43 m., as astronomers have determined; and the circumference of the earth to amount to 123,249,600 Paris feet. Now, if we imagine the moon, deprived of all her motion, to be let go, so as to descend towards the earth with the impulse of all that force by which it is retained in its orbit, it will, in the space of one minute of time, describe in its fall 151 Paris feet. For the versed sine of that are which the moon, in the space of one minute of time, describes by its mean motion at the distance of 60 semidiameters of the Earth, is nearly 15 Paris feet; or, more accurately, 15 feet 1 inch and 1 line 3. Wherefore, since that force, in approaching to the earth, increases in the reciprocal duplicate proportion of the distance; and, upon that account, at the surface of the earth is 60 x 60 times greater than at the moon; a body in our regions, falling with that force, ought, in the space of one minute of time, to describe 60 × 60 × 15 Paris feet; and, in the space of one second of time, to describe 15, of those feet; or, more accurately, 15 feet 1 inch 1 line. And with this very force we actually find that bodies here on earth do really descend.-For a pendulum oscillating seconds in the latitude of Paris, will be 3 Paris feet and 8 lines in length, as Mr. Huygens has observed. And the space which a heavy body describes, by falling one second of time, is to half the length of the pendulum in the duplicate ratio of the circumference of the circle to its diameter; and is therefore 15 Paris feet 1 inch 1 line 3. And therefore the force by which the moon is retained in its orbit, becomes, at the very surface of the earth, equal to the force of

gravity which we observe in heavy bodies there. And therefore (by rules 1 and 2) the force by which the moon is retained in its orbit is that very same force which we commonly call gravity. For, were gravity another force different from that, then bodies descending to the earth with the joint impulse of both forces would fall with a double velocity, and, in the space of one second of time, would describe 30 Paris feet; altogether against experience.

The demonstration of this proposition may be more diffusely explained after the following manner: Suppose several moons to revolve about the earth, as in the system of Jupiter or Saturn, the periodic times of those moons would (by the argument of induction) observe the same law which Kepler found to obtain among the planets; and therefore their centripetal forces would be reciprocally as the squares of the distances from the centre of the earth, by prop. I. Now, if the lowest of these were very small, and were so near the earth as almost to touch the tops of the highest mountains, the centripetal force thereof, retaining it in its orbit, would be very nearly equal to the weights of any terrestrial bodies that should be found upon the tops of these mountains; as may be known from the foregoing calculation. Therefore, if the same little moon should be deserted by its centrifugal force that carries it through its orbit, it would descend to the earth; and that with the same velocity as heavy bodies do actually descend with upon the tops of those very mountains, because of the equality of forces that obliges them both to descend. And if the force by which that lowest moon would descend were different from that of gravity, and if that moon were to gravitate towards the earth, as we find terrestrial bodies do on the tops of mountains, it would then descend with twice the velocity, as being impelled by both these forces conspiring together. Therefore, since both these forces, that is, the gravity of heavy bodies, and the centripetal forces of the moons, respect the centre of the earth, and are similar and equal between themselves, they will (by rules 1 and 2) have the same cause. And therefore the force which retains the moon in its orbit is that very force which we commonly call gravity; because, other wise, this little moon at the top of a mountain must either be without gravity, or fall twice as swiftly as heavy bodies use to do.

Having thus demonstrated that the moon is retained in its orbit by its gravitation towards the earth, it is easy to apply the same demonstration to the motions of the other secondary planets, and of the primary planets round the sun, and thus to show that gravitation prevails throughout the whole creation. After which Sir Isaac proceeds to show from the same principles, that the heavenly bodies gravitate towards each other, and contain different quantities of matter, or have different densities in proportion to their

bulks.

Prop. V. All bodies gravitate towards every planet; and the weight of bodies towards the same planet, at equal distances from its centre, are proportional to the quantities of matter they

contain.

It has been confirmed by many experiments,

that all sorts of heavy bodies (allowance being made for the inequality of retardation by some small resistance of the air) descend to the earth from equal heights in equal times; and that equality of times we may distinguish to a great accuracy by the help of pendulums. Sir Isaac Newton tried the thing in gold, silver, lead, glass, sand, common salt, wood, water, and wheat. He provided two wooden boxes, round and equal, filled the one with wood, and suspended an equal weight of gold in the centre of oscillation of the other. The boxes hanging by equal threads of eleven feet, made a couple of pendulums, perfectly equal in weight and figure, and equally receiving the resistance of the air. And, placing the one by the other, he observed them to play together forwards and backwards, for a long time, with equal vibrations. And therefore the quantity of matter in the gold was to the quantity of matter in the wood, as the action of the motive force (or vis motrix) upon all the gold to the action of the same upon all the wood; that is, as the weight of the one to the weight of the other. And the like happened in the other bodies.

By these experiments, in bodies of the same weight, he could manifestly have discovered a difference of matter less than the thousandth part of the whole, had any such been. But, without all doubt, the nature of gravity towards the planets, is the same as towards the earth. For, should we imagine our terrestrial bodies removed to the orb of the moon, and there, together with the moon, deprived of all motion, to be let go, so as to fall together towards the earth; it is certain, from what we have demonstrated before, that, in equal times, they would describe equal spaces with the moon, and of consequence are to the moon, in quantity of matter, as their weights to its weight. Since the satellites of Jupiter perform their revolutions in times which observe the sesquiplicate proportion of their distances from Jupiter's centre, their accelerative gravities towards Jupiter will be reciprocally as the squares of their distances from Jupiter's centre; that is, equal at equal distances. And therefore, these satellites, if supposed to fall towards Jupiter from equal heights, would describe equal spaces in equal times, in like manner as heavy bodies do on our earth. And by the same argument, if the circumsolar planets were supposed to be let fall at equal distances from the sun, they would, in their descent towards the sun, describe equal spaces in equal times. But forces, which equally accelerate unequal bodies, must be as those bodies: that is to say, the weights of the planets towards the sun must be as their quantities of matter.

Further, that the weights of Jupiter and of his satellites towards the sun are proportional to the several quantities of their matter, appears from the exceedingly regular motions of the satellites. For, if some of those bodies were more strongly attracted to the sun in proportion to their quantity of matter than others, the motions of the satellites would be disturbed by that inequality of attraction. If at equal distances from the sun, any satellite, in proportion to the quantity of its matter, did gravitate towards the sun with a force greater than Jupiter in proportion to his

1.

according to any given proportion, suppose of d to e; then the distance between the centres of the sun and the satellite's orbit would be always greater than the distance between the centres of the sun and of Jupiter nearly in the subduplicate of that proportion. And, if the satellite gravitated towards the sun with a force less in the proportion of e to d, the distance of the centre of the satellite's orb from the sun would be less than the distance of the centre of Jupiter's from the sun in the subduplicate of the same proportion. Therefore, if at equal distances from the sun the accelerative gravity of any satellite towards the sun were greater or less than the accelerating gravity of Jupiter towards the sun but by part of the whole gravity, the distance of the centre of the satellite's orbit from the sun would be greater or less than the distance of Jupiter from the sun byth part of the whole distance; that is, by a fifth part of the distance of the utmost satellite from the centre of Jupiter; an eccentricity of the orbit which would be very sensible. But the orbits of the satellites are concentric to Jupiter; therefore the accelerative gravities of Jupiter, and of all satellites, towards the sun, are equal among themselves. And, by the same argument, the weight of Saturn and of his satellites towards the sun, at equal distances from the sun, are as their several quantities of matter; and the weights of the moon and of the earth towards the sun are either none, or accurately proportional to the masses of matter which they contain. But further, the weights of all the parts of every planet towards any other planet are one to another as the matter in the several parts. For if some parts gravitated more, others less, than in proportion to the quantity of their matter; then the whole planet, according to the sort of parts with which it most abounds, would gravitate more or less than in proportion to the quantity of matter in the whole. Nor is it of any moment whether these parts are external or internal. For if, as an instance, we should imagine the terrestrial bodies with us to be raised up to the orb of the moon, to be there compared with its body; if the weights of such bodies were to the weights of the external parts of the moon as the quantities of matter in the one and in the other respectively, but to the weights of the internal parts in a greater or less proportion; then likewise the weights of those bodies would be, to the weight of the whole moon in a greater or less proportion; against what we have showed above.

Cor. 1. Hence the weights of bodies do not depend upon their forms and textures. For, if the weights could be altered with the forms, they would be greater or less, according to the variety of forms in equal matter; altogether against experience.

Cor. 2. Universally all bodies al ont the earth gravitate towards the earth; and the welds of ail, at equal distances from the earth's centre, are as the quantities of matter which they se verally contain. This is the quality of all bodies within the reach of our experitaents; and, therefore (by rule 3), to be affirmed of all bodies whatsoever. If ether, or any other body, were erber altogether void of gravity, or were to gravitate less in proportion to its quantity of matter; then, because

(according to Aristotle, Des Cartes, and others) there is no difference betwixt that and other bodies, but in mere form of matter, by a successive change from form to form, it might be changed at last into a body of the same condition with those which gravitate most in proportion to their quantity of matter; and, on the other hand, the heaviest bodies, acquiring the first form of that body, might by degrees quite lose their gravity. And therefore the weights would depend upon the forms of bodies, and with those forms might be changed, contrary to what was proved in the preceding corollary.

Cor. 3. All spaces are not equally full. For, if all spaces were equally full, then the specific gravity of the fluid which fills the region of the air, on account of the extreme density of the matter, would fall nothing short of the specific gravity of quick-silver or gold, or any other the most dense body; and, therefore, neither gold, nor any other body, could descend in air. For bodies do not descend in fluids, unless they are specifically heavier than the fluids. And, if the quantity of matter in a given space can by any rarefaction be diminished, what should hinder a diminution to infinity?

Cor. 4. If all the solid particles of all bodies are of the same density, nor can be rarefied without pores, a void space or vacuum must be granted. (By bodies of the same density, our author means those whose vires inertia are in the proportion of their bulks.)

Prop. VI. That there is a power of gravity tending to all bodies, proportional to the several quantities of matter which they contain. That all the planets mutually gravitate one towards another, we have prove before; as well as that the force of gravity towards every one of them, considered apart, is reciprocally as the square of the distance of places from the centre of the planet. And thence it follows that the gravity tending towards all the planets is proportional to the matter which they contain. Moreover, since all the parts of any planet A gravitate towards any other planet B, and the gravity of every part is to the gravity of the whole as the matter of the part to the matter of the whole; and (by law 3) to every action corresponds an equal re-action: therefore the planet B will, on the other hand, gravitate towards all the parts of the planet A; and its gravity towards any one part will be to the gravity towards the whole as the matter of the part to the matter of the whole. Q. E. D.

Cor. 1. Therefore the force of gravity towards any whole planet arises from, and is compounded of, the forces of gravity towards all its parts. Magnetic and electric attractions afford us examples of this. Frail atractie is towards the whole arise from the attractions towards the several parts. The thing may be early understood in gravity, if we consider a greater planet as formed of a number of lesser planets, meeting together in one globe. For hence it would appear that the force of the whole must arise from the forces of the component parts. If it be objected that, according to this law, all bodies with us must mutually gravitate one towards another, whereas no such gravitation any where appears; it is answered that, since the ravitation towards these

bodies is to the gravitation towards the whole earth as these bodies are to the whole earth, the gravitation towards them must be far less than to fall under the observation of our senses. (The experiments with regard to the attraction of mountains, however, have now further elucidated this point.)

Cor. 2. The force of gravity towards the several equal particles of any body is reciprocally as the square of the distance of places from the particles.

Prop. VII. In two spheres mutually gravita ing each towards the other, if the matter, in places on all sides round about and equidistant from the centres, is similar, the weight of either sphere towards the other will be reciprocally as the square of the distance between their centres. For the demonstration of this, see the Principia, book i. prop. 75 and 76.

Cor. 1. Hence we may find and compare to gether the weights of bodies towards different planets. For the weights of bodies revolving in circles about planets are as the diameters of the circles directly, and the squares of their periodic times reciprocally; and their weights at the surfaces of the planets, or at any other distances from their centres, are (by this prop.) greater or less, in the reciprocal duplicate proportion of the distances. Thus, from the periodic times of Venus, revolving about the sun in 224 d. 16 h.; of the utmost circumjovial satellite revolving about Jupiter in 16 d. 16h.; of the Huygenian satellite about Saturn in 15 d. 223 h.; and of the moon about the earth in 27 d. 7h. 43 m.; compared with the mean distance of Venus from the sun, and with the greatest heliocentric elongations of the utmost circumjovial satellite from Jupiter's centre, 8′ 16′′; of the Huygenian satellite from the centre of Saturn 5′ 4′′; and of the moon from the earth, 10′ 33′′: by computation our author found that the weight of equal bodies at equal distances from the centres of the sun, of Jupiter, of Saturn, and of the earth, towards the sun, Jupiter, Saturn, and the earth, were one to another as 1967, 3021, and 1695 respectively. Then, because as the distances are increased or diminished the weights are diminished or increased in a duplicate ratio; the weights of equal bodies towards the sun, Jupiter, Saturn, and the earth, at the distances 10,000, 997, 791, and 109, from their centres, that is, at their very superficies, will be as 10,000, 943, 529, and 435, respectively.

Cor. 2. Hence likewise we discover the quantity of matter in the several planets. For their quantities of matter are as the forces of gravity at equal distances from their centres, that is, in the sun, Jupiter, Saturn, and the earth, as 1,, ਨੇ, and To respectively. If the parallax of the sun be taken greater or less than 10′′ 30′′", the quantity of matter in the earth must be augmented or diminished in the triplicate of that proportion.

Cor. 3. Hence also we find the densities of the planets. For (by prop. LXXII., book i.) the weights of equal and similar bodies towards similar spheres, are, at the surfaces of those spheres as the diameters of the spheres. And

therefore the densities of dissimilar spheres are as those weights applied to the diameters of the spheres. But the true diameters of the sun, Jupiter, Saturn, and the earth, were one to another as 10,000, 997, 791, and 109; and the weights towards the same, as 10,000, 943, 529, and 435, respectively; and therefore their densities are as 100, 94, 67, and 400. The density of the earth, which comes out by this computation, does not depend upon the parallax of the sun, but is determined by the parallax of the moon, and therefore is here truly defined. The sun, therefore, is a little denser than Jupiter, and Jupiter than Saturn, and the earth four times denser than the sun; for the sun, by its great heat, is kept in a sort of a rarefied state. The moon also is denser than the earth.

Cor. 4. The smaller the planets are, cæteris paribus, of so much the greater density. For so the powers of gravity on their several surfaces come nearer to equality. They are, likewise, cateris paribus, of the greater density as they are nearer to the sun. So Jupiter is more dense than Saturn, and the earth than Jupiter. For the planets were to be placed at different distances from the sun, that, according to their degrees of density, they might enjoy a greater or less proportion of the sun's heat. Our water, if it were removed as far as the orb of Saturn, would be converted into ice; and in the orb of Mercury, would quickly fly away in vapor. For the light of the sun, to which its heat is proportional, is seven times denser in the orb of Mercury than with us; and by the thermometer Sir Isaac found that a seven-fold heat of our summer sun will make water boil. Nor are we to doubt that the matter of Mercury is adapted to its heat, and is therefore more dense than the matter of our earth; since, in a denser matter, the operations of nature require a stronger heat.

It is shown in the scholium of prop. XXII. book ii. of the Principia, that, at the height of 200 miles above the earth, the air is more rare than it is at the superficies of the earth, in the ratio of 30 to 0-0000000000003298, or as 75000000000000 to 1 nearly. And hence the planet Jupiter, revolving in a medium of the same density with that superior air, would not lose by the resistances of the medium the 1,000,000th part of its motion in 1,000,000 years. In the spaces near the earth the resistance is produced only by the air, exhalations, and vapors. When these are carefully exhausted by the air-pump from under the receiver, heavy bodies fall within the receiver with perfect freedom, and without the least sensible resistance; gold itself, and the lightest down, let fall together, will descend with equal velocity; and though they fall through a space of four, six, and eight feet, they will come to the bottom at the same time; as appears from experiments that have often been made. And therefore, the celestial regions being perfectly void of air and exhalations, the planets and comets, meeting no sensible resistance in those spaces, will continue their motions through them for an immense space of time.

NEW YEAR'S GIFTS. Nonius Marcellus refers the origin of new year's gifts among the Romans to Titus Tatius, king of the Sabines, who reigned at Rome conjointly with Romulus, and who having considered as a good omen a present of some branches cut in a wood consecrated to Strenia, the goddess of strength, which he received on the first day of the new year, authorised this custom afterwards, and gave to these presents the name of strenar. The Romans on that day celebrated a festival in honor of Janus, and sent presents to one another of figs, dates, honey, &c., to show their friends that they wished them a happy and agreeable life. Clients, or those who were under the protection of the great, carried presents of this kind to their patrons, adding to them a small piece of silver. Under Augustus, the senate, the knights, and the people, presented such gifts to him, and in his absence deposited them in the capitol. Of the succeeding princes some adopted this custom and others abolished it; but it always continued among the people. The early Christians condemned it, because it appeared to be a relique of Paganism, and a species of superstition; but, when it became nothing more than a mark of esteem, the church ceased to disapprove

of it.

NEXI, in Roman antiquity, persons free-born, who for debt were reduced to a state of slavery, By the laws of the XII. tables it was ordained, that insolvent debtors should be given up to their creditors to be bound in fetters and cords, whence they were called Nexi; and, though they did not entirely lose the rights of freemen, yet they were often treated more harshly than the slaves themselves.

NEXT, adj. & adv. Sax. next, nepre; the superlatives of nep or nyp, Goth, and Dan. næst; Tent, nechst. Nighest or nearest, in time, place, or degree; at the time or term immediately preceding.

Want supplieth itself of what is next, and many times the next way.

Bacon.

If the king himself had staid at London, or, which had been the next best, kept his court at York, and sent the army on their proper errand, his enemies had been speedily subdued." Clarendon.

The queen already sat

High on a golden bed; her princely guest
Was next her side, in order sat the rest.
Dryden.

O fortunate young man! at least your lays,
Are next to his, and claim the second praise. Id.
Finite and infinite, being by the mind looked on
as modifications of expansion and duration, the next

was born at Sarre Louis in 1769, and entered as a private into a regiment of hussars. At the beginning of the revolution he was made a captain, and served with distinction at Nerwinde and Valenciennes. His address and bravery first attracted the notice of Kleber, under whom he became an adjutant-general. He was next made general of a division, and commanded the French cavalry during the invasion of Switzerland in 1798, when he is said to have behaved with considerable humanity to the unfortunate inhabitants of that country. The following year he distinguished himself under Massena ; and shared, in 1800, in the victories of Moreau at Moeskirch and Hohenlinden. In 1804 he received the bâton of marshal; and the following year gained the battle to which he owed the title of duke of Elchingen. He was next employed against the Prussians and Russians, in Friedland, and the British in the peninsula, where he showed skill in retreating before our distinguished Commander from Portugal. In 1812 he was present in Russia at the terrible battle of Mojaisk, where he commanded the centre of the French army, and obtained the further title of prince of Moskwa. Having afterwards lost the battle of Dennewitz, in Germany, he retired to Paris in disgrace; but was soon again employed. He had justly earned the character of a brave leader, whatever were his principles, and afterwards contributed to induce the emperor to resign, and to retire to Elba. He was one of the first of the imperial generals who submitted to the Bourbons, and thus preserved his titles and pensions. In 1815, when Buonaparte escaped from Elba, Ney was at his estate in the country, and received orders to repair to his government of Bescançon. He went to Paris, making strong protestations of loyalty to the king, and promised it is said to bring back the disturber of Europe in an iron cage. then proceeded towards Lyons; but instead of attacking the invader he joined his standard. His subsequent career was as unfortunate as this conduct was unprincipled. He followed his old master to Waterloo, and being afterwards arrested was tried by a commission as a traitor to Louis XVIII., and shot.

He

NIAGARA, a river of North America, issuing from the north-east end of lake Erie, and flowing into lake Ontario. It forms the boundary between the United States and Upper Canada, and its course, which is nearly north, is thirty-six miles in length, and varies in breadth from half a mile to a league. For the first few miles from

them.

Locke. Rowe.

Desired of Jove, when neat he sought her bed,

To grant a certain gift.

Addison's Ovid. The good man warned us from his text That none could tell whose turn should be the next. Gay.

There, blest with health, with business unperplext,

This life we relish, and ensure the next.

Young.

NEY, MARSHAL, a celebrated general and peer of France, under the Imperial government. He