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 correfponds 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.

earth, were one to another as Tor, TJOT, and 2 refpectively. Then, because as the dif tances are increased or diminished, the weights are diminished or increased in a duplicate ratio; the weights of equal bodies towards the fun, Jupiter, Saturn, and the earth, at the diftances 10000, 997, 791, and 109, from their centres, that is, at their very fuperficies, will be as 10000, 943, 529, and 435 refpectively.

COR. 2. Hence likewife we difcover the quantity of matter in the feveral planets. For their quantities of matter are as the forces of gravity at equal diftances from their centres, that is, in the fun, Jupiter, Saturn, and the carth, as I, To

the fun be taken greater or less than 10" 30", the quantity of matter in the earth must be aug. mented or diminished in the triplicate of that proportion.

COR. I. Therefore the force of gravity towards any whole planet, arifes from, and is compounded of, the forces of gravity towards all its parts. Magnetic and electric attractions afford us examples of this. For all attraction towards the whole, and respectively. If the parallax of arifes from the attractions towards the feveral parts. The thing may be easily underflood in gravity, if we confider a greater planet as formed of a number of leffer planets, meeting together in one globe. For hence it would appear that, the force of the whole muft arife from the forces of the component parts. If it be objected, that, according to this law, all bodies with us muft mutually gravitate one towards another, whereas no fuch gravitation anywhere appears; it is anfwered, that, fince the gravitation towards these bodies is to the gravitation towards the whole earth, as thefe bodies are to the whole earth, the gravitation towards them must be far lefs than to fall under the obfervation of our fenfes. (The experiments with regard to the attraction of mountains, however, have now further elucidated this point.)

COR. 2. The force of gravity towards the feveral equal particles of any body, is reciprocally as the fquare of the distance of places from the particles.

PROP. VII. In two spheres mutually gravitating each towards the other, if the matter, in places on all fides round about and equidiftant from the centres, is fimilar, the weight of either sphere towards the other will be reciprocally as the fquare of the diftance between their centres. For the demonftration of this, fee the Principia, book i. op. 75. and 76.

COR. 1. Hence we may find and compare together 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 fquares of their periodic times reciprocally; and their weights at the furfaces of the planets, or at any other diftances from their centres, are (by this prop.) greater or lefs, in the reciprocal duplicate proportion of the diftances. Thus, from the periodic times of Venus, revolving about the fun in 224d. 163h.; of the utmost circumjovial fatellite revolving about Jupiter in 16d. 16h.; of the Huygenian fatellite about Saturn in 15d. 223h.; and of the moon about the earth in 27d. 7h. 43'; compared with the inean distance of Venus from the fun, and with the greatest heliocentric elongations of the utmost circumjovial fatellite from Jupiter's centre, 8' 16"; of the Huygenian fatellite 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 diftances from the centres of the fun, of Jupiter, of Saturn, and of the arth, towards the fun, Jupiter, Saturn, and the

COR. 3. Hence alfo we find the denfities of the planets. For (by prop. 72. book 1.) the weights of equal and fimilar bodies towards fimilar spheres, are, at the furfaces of those spheres, as the diameters of the fpheres. And therefore the denfities of diffimilar fpheres are as those weights applied to the diameters of the spheres. But the true diameters of the fun, Jupiter, Saturi, and the earth, were one to another as 10000, 997, 791, and 109; and the weights towards the fame, as 10000, 943, 529, and 435 respectively; and therefore their denfities are as 100, 94, 67, and 400. The denfity of the earth, which comes out by this computation, does not depend upon the parallax of the fun, but is determined by the parallax of the moon, and therefore is here truly defined. The fun therefore is a little denfer than Jupiter, and Jupiter than Saturn, and the earth four times denfer than the fun; for the fun, by its great heat, is kept in a fort of a rarefied ftate. The moon alfo is denfer than the earth.

COR. 4. The fmaller the planets are, cæteris paribus, of fo much the greater denfity. For fo the powers of gravity on their feveral furfaces come nearer to equality. They are likewife, cateris paribus, of the greater denfity as they are nearer to the fun. So Jupiter is more denfe than Saturn, and the earth than Jupiter. For the planets were to be placed at different diftances from the fun, that, according to their degrees of denfity, they might enjoy a greater or lefs proportion of the fun'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 vapour. For the light of the fun, to which its heat is proportional, is seven times denfer in the orb of Mercury than with us; and by the thermometer Sir Ifaac found that a fevenfold heat of our fummer fun will make water boil. Nor are we to doubt that the matter of Mercury is adapted to its heat, and is therefore more denfe than the matter of our earth; fince, in a denfer matter, the operations of nature require a stronger heat.

It is fhown in the scholium of prop. 22. book 2. of the Principia, that, at the height of 200 miles above the earth, the air is more rare than it is at the fuperficies of the earth, in the ratio of 30 to 90000000000003998, or as 75ap0000000000 to 1

nearly.

54 who for debt were reduced to a state of flavery. By the laws of the XII. tables it was ordained, that infolvent debtors fhould 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 harfhly than the flaves themfelves. If one was indebted to feveral perfons, and could not within 60 days find a cautioner, his body, according to fome, but according to others his effects, might be cut in pieces, and divided among his creditors. This latter opinion feems by much the moft probable, as Livy mentions a law by which creditors had a right to attach the goods, but not the perfons of their debtors.

NEXOE, a fea-port of Denmark, on the E. coaft of the ille of Bornholm.

NEXON, a town of France, in the dep. of Upper Vienne; 15 miles SW. of Limoges.

(1.) * NEXT. adj. [next, Saxon, by a colloquial change from nebft or nybft, the fuperlative of neh or nyh; neeft, Scottifh.] 1. Neareft in place; immediately fucceeding in order.-Want fupplieth itfelf of what is next, and in many times the next way. Bacon.-

The queen already fat

High on a golden bed; her princely guest
Was next her fide; in order fat the reft. Dryden.
The next in place and punishment were they
Who prodigally throw their fouls away. Dryd.
2. Neareft in time.-

The good man warn'd us from his text,
That none could tell whofe turn fhould be the

next.

Gay. 3. Nearest in any gradation.-If the king himself had ftaid at London, or, which had been the next beft, kept his court at York, and fent the army on their proper errand, his enemies had been speedily fubdued. Clarendon.

O fortunate young man! at leaft your lays Are next to his. Dryden. -Finite and infinite, being by the mind looked on as modifications of expanfion and duration, the next thing to be confidered, is, how the mind comes by them. Locke.

That's a difficulty next to impoffible. Rowe. There, bleft with health, with business unperplext,

This life we relish, and ensure the next. Young. (2.) NEXT. adv. At the time or turn immediately fucceeding.

Th' unwary nymph
Defir'd of Jove, when next he fought her bed,
To grant a certain gift..
Addifon.
NEYBA, or NEYVA, a river of Hifpaniola,
which runs into the fea 25 m. W. of St Domingo.
NEYDORFF, a town of Germany, in Auftria;
7 miles WNW. of Falkenftein.

NEYERING, a river of Carniola, which runs into the Save, 2 miles N. of Buckenstein.

NEYKIRCHEN, 2 towns of Auftria: 1. fix miles SW. of Neuftatt: 2. four miles N. of Schwannaftatt.

NEYLAND. See NAYLAND.

NEYLEAU, a town of Franconia, in Culm

bach.

NEYMARKT, 2 towns of Auftria: 1. fix miles W. of Efferding: 2. three miles S. of Frieftatt. NEYPERG, a town of Germany, in Stiria. NEYRAC, a town of France, in the dep. of Aveiron, 18 miles N. of Phodez.

NEYSIDEL, a town of Auftria, 3 miles S. of Vienna.

NEYSTADT, a town of Auftria, 8 miles W. of Ips.

NEYSZE. See NEISSE, N° 1—3.

NEYTRECHT, a town of Upper Hungary, capital of a county of the fame name, with a bifhop's fee; feated on the Neitra, 40 miles NE. of Prefburg. Lon. 17. 49. E. Lat. 48. 28. N.

(1.) NEYVA, or NEYBA, a town of S. America, in Terra Firma, capital of a mountainous district in Popayan.

(2.) NEYVA. See NEYBA.

NÉZ, [Fr. i. e. Nofe or Face,] in geography, is ufed by the French for a cape or promontory: thus,

1. NEZ DE JOBOURG, a cape on the W. coaft of France, in the English Channel, 3 miles S. of Cape Anderville. Lon. 15. 43. E. of Ferro. Lat. 49. 40. N.

2. NEZ DE QUERQUEVILLE, a cape on the W. coaft of France, in the English Channel, 3 miles NW. of Cherburg.

NEZIN, a town of Ruffia, in Tchernigov. NEZITZA, a river of Ruffia, in Archangel, which runs into the Frozen Sea, 28 miles S. of

Ponoi.

NEZLET, a town of Egypt, 7 miles N. of Atfich.

NGAN-CHAN, a city of China, of the ift rank, in the province of Koei-tcheou. Its territory is well watered, and fertile, though very mountainous; and comprehends 3 cities of the 2d order, and 5 of the 3d, with feveral forts. It lies 1005 miles SSW. of Peking. Lon. 123. 17. E. Ferro. Lat. 26. 12. N.

NGAN-KING, a city of China, and capital of the W. part of the province of Kiang-nan. It is governed by a viceroy, who keeps a large garrifon in a fort built on the banks of the river Yang-tfe-kiang. Its fituation is delightful; its commerce and riches render it very confiderable; and every thing that goes from the S. part of China to Nan-king must pass through it. All the country belonging to it is level, pleasant, and fertile. It has under its jurisdiction 6 cities of the 3d clafs. It is 575 miles S. of Peking. Lon. 134. o. E. Ferro. Lat. 30. 37. N.

NGAN-LO, a city of China of the 1ft rank, in the prov. of Hou-Quang, on the banks of the river Han, in a fertile country. Its district contains 2 towns of the 2d rank, and 5 of the 3d. It lies 575 miles SW. of Peking. Lon. 129. 48. E. Lat. 31. 14. N.

NGAN-Y, a town of China of the 3d rank, in the prov. of Kiang-fi, 20 miles NW. of Nan-tchang, near a lake, whofe waters are as falt as those of the ocean, and from which much falt is extracted. NGO-HIEN, a town of China of the 3d clafs, in the prov. of Chang-tong.

NGO-KIA, a Chinefe drug, of which the compofition will no doubt appear as fingular as the NEYMARCK, a town of Auftria, 6 miles S. of numerous properties afcribed to it. In the province of Chang-tong, near Ngo-hien, is a well

Yps.

formed

the 3d rank. It is 537 miles SSE. of Peking. Lon. 136. 10. E. Ferro. Lat. 31. 2. N.

NIA, or UNIE, an island of Maritime Austria, in Dalmatia, W. of Ofero. It is 7 miles long, and has a fpacious and safe harbour.

NIAB, a town of Arabia, near the coaft of the Red Sea; 72 miles WSW. of Saab, and 58 N. of Abu-Arifch.

formed by nature, 70 feet in depth, which has a communication with fome fubterranean lake, or large refervoir. The water drawn from it is exceedingly clear, and much heavier than common; and if it be mixed with muddy water, it purifies it, and renders it limpid, by precipitating all its impurities to the bottom of the veffel. This water is employed in making the ngo-kia, which is a kind of glue procured from the skin of a black (1.) NIAGARA, a river of the United States, afs. The animal is killed and flayed, and the skin which flows from Lake ERIE, and runs by a NW. is fteeped for 5 days in water drawn from this courfe into the SW. end of Lake ONTARIO, conwell. It is then taken out, fcraped, and cleaned; ftituting part of the boundary between the United afterwards cut into fmall pieces, which are boiled States and Canada. It is 34 miles long, including over a flow fire, in fome of the fame water, until its meanders. About 20 miles below Lake Erie it is reduced to a jelly, which is ftrained, while is the great Cataract, called the Falls of Niagara, warm, through a cloth, to free it from all the which is juftly reckoned one of the greateft natugrofs matter. When this glue is cool, and has ac- ral curiofities in the world. These falls run from quired a confiftence, it is formed into fquare SSE. to NNW.; and the rock of the falls croffes cakes, upon which the Chinese imprint characters them not in a right line, but forms a kind of fiand coats of arms, or the figns of their fhops. gure like an hollow femicircle, or horfe-fhoe. This well is the only one of the kind in China; it Above the falls in the middle of the river, is an is always fhut, and fealed by the governor of the ifland called Grand Ifle, about 900 or 1000 feet place, until the customary day of making the em- long; the lower end of which is juft at the perperor's glue. This operation generally lafts from pendicular edge of the fall. On both fides of this the autumnal harvest till March. During that time island runs all the water that comes from the lakes the neighbouring people and merchants treat for of Canada; viz. Lakes Superior, Michigan, Huthe purchase of the glue with those who guard ron, and Erie. Before the water comes to this the well, and with the people who make it. The island, it runs but flowly compared with its molatter manufacture as much of it as they can, on tion afterwards, when it grows the most rapid in their own account, with this difference, that it is the world, running with a furprifing swiftnefs benot fo pure, and that they are lefs fcrupulous in fore it comes to the fall. It is perfectly white, examining whether the afs be fat or of a very and in many places is thrown high up into the air. black colour: however, all the glue made here is as At this ifland, the river divides into two channels; much efteemed at Peking as that which the man- the perpendicular defcent of the NE. channel, as darines who are on the spot tranfmit to court, and measured by Dr M'Cauflin, is 163 feet; that of to their friends. As this drug is in great requeft, and the NW. 143; the breadth of the cataract and as the quantity of it made at Ngo-hien is not fuf- ifland, above a mile. The water that runs down ficient to fupply the whole empire, people coun- on the W. fide is more rapid, in greater abunterfeit it elsewhere, and manufacture a fpurious dance, and whiter, than that on the E. fide; and kind from the skins of mules, horfes, and camels, feems almoft to outfly an arrow in swiftnefs. At and sometimes even from old bones. It is, how the principal fall, on looking up the river, one ever, easy to distinguish that which is genuine; it may fee that the water is every where exceedhas neither a bad fmell nor a difagreeable tafte ingly fteep, almoft like the fide of an hill; but when applied to the mouth; it is brittle and fri- upon looking at the fall itself, it is impoffible to able, and always of a deep black colour, fometimes exprefs the amazement it occafions. The height inclining to red. The qualities of the counterfeit of it, as measured by mathematical inftruments, kind are entirely different; both its tafte and fmell is exactly 137 feet; and when the water is come are difagreeable, and it is viscous and flabby even to the bottom, it jumps back to a very great when made of the fkin of a hog, which is that height in the air. The noife is heard at the dif which imitates the true kind beft. The Chinese tance of 45 miles. At fort Niagara, when they attribute a great number of virtues to this drug. hear the noife of the fall more loud than ordina They fay, that it diffolves phlegm, facilitates the ry, they are fure that a NE. wind will follow; motion of the lungs, gives free refpiration to thofe which is the more furprifing, as the fort lies SW. who breathe with difficulty, comforts the breaft, from the fall. Sometimes the fall makes a much increases the blood, ftops dyfenteries, provokes greater noife than at others; and this is held for arine, and ftrengthens children in the womb. an infallible fign of approaching rain or bad weaWithout warranting the truth of all these proper, ther. From the place where the water falls there ties, it appears, at least, certain, by the teftimony arifes a great quantity of vapour like very thick of the miffionaries, that this drug is ferviceable fmoke, infomuch that when viewed at a distance in all difeafes of the lungs. It is taken with a one would think that the Indians had fet the decoction of fimples, and fometimes in powder. forests on fire. These vapours rife high in the air NGOLA, king of Angola. See ANGOLA, f 3. when it is calm, but are difperfed by the wind NHING, a town of China of the 2d rank, in when it blows hard. In Sept. and Oct. fuch the prov. of Kiang-fi; 675 miles S. of Peking. quantities of dead water-fowl are found every morning below the fall, on the fhore, that the garrifon of the fort live chiefly upon them. Befides the fowls, they find feveral forts of dead fish, alfo deer, bears, and other animals which have

NHING-KOUE, a city of China, of the 1ft rank, in the prov. of Kiang-nan, in a mountainous country, famous for its paper manufactures, made from reeds. Its diftrift contains 6 towns of