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primary planets ; and of the primary planets, air, is this, that all bodies fall equal spaces with respect to the Sun.
in equal times; but the nature of gravity or As to the Moon, the proposition is thus weight, no doubt, is the same on the other proved: the Moon's mean distance is 60 planets as on the Earth. semidiameters of the Earth; her period, Suppose, e.gr. such bodies raised to the with regard to the fixed stars, is 27 days, surface of the Moon, and together with the 7 hours, 43 minutes; and the Earth's cir. Moon deprived at once of all progressive cumference 123,249,600 Paris feet. Now, motion, and dropped towards the Earth : supposing the Moon to have lost all her it is shewn, that in equal times they will motion, and to be let drop to the Earth, describe equal spaces with the Moon; and with the power which retains her in her therefore, that their qnantity of matter is orbit, in the space of one minute she will to that of the Moon, as their weights to its fall 1512 Paris feet; the arch she describes weight. in her mean motion, at the distance of 60 Add, that since Jupiter's satellites rediameters of the Earth, being the versed volve in times that are in a sesquiplicate sign of 151' Paris feet. Hence, as the ratio of their distances from the centre of power, as it approaches the Earth, increases Jupiter, and consequently at equal distances in a duplicate ratio of the distance in from Jupiter, their accelerating gravities versely; so as at the surface of the Earth are equal ; therefore, falling equal altitudes it is 60 x 60 greater than at the Moon; a in equal times, they will describe equal body falling with that force in our region spaces ; just as in heavy bodies on our Earth. must, in a minutes time, describe the And the same argument will hold of the prispace of 60 X 60 X 1512 Paris feet, or mary planets with regard to the Sun, and 15 Paris feet in the space of one second. the powers whereby unequal bodies are
But this is the rate at which bodies fall equally accelerated are as the bodies, i.e. by their gravity at the surface of our Earth; the weights are as the quantities of matter as Huygens has demonstrated by experi- in the planets, and the weight of the primary ments with pendulums. Consequently, the and secondary planets towards the Sun, are power whereby the Moon is retained in as the quantities of matter in the planets her orbit, is the very same we call gravity; and satellites. for, if they were different, a body, falling And hence are several corollaries drawn with both powers together, would descend relating to the weights of bodies on the surwith double the velocity, and in a second face of the Earth, magnetism, and the exist. of time describe 304 feet.
ence of a vacuum. As to the other secondary planets, their V. Gravity extends itself towards all bo. phenomena, with respect to their primary dies, and is in proportion to the quantity of ,ones, being of the same kind with those of matter in each. the Moon about the Earth, it is argued by That all planets gravitate towards each analogy, that they depend on the same other has been already shewn; likewise, causes; it being a rule or axiom all philoso- that the gravity towards any one, considerphers agree to, that effects of the same kind ed apart, is reciprocally as the squares of have the same causes. Again, attraction its distance from the centre of the planet ; is always mutual, i. c. the reaction is equal consequently, gravity is proportionable to to the action : consequently the primary the matter therein. Further, as all the parts planets gravitate towards their secondary of any planet, A, gravitate towards another ones, the Earth towards the Moon, and the planet, B; and the gravity of any part is to Sun towards them all. And this gravity, the gravity of the whole, as the matter of with regard to each several planet, is re. the part to the matter of the whole; and as ciprocally as the square of its distance from reaction is equal to action : the planet B will the centre of gravity. See ATTRACTION, gravitate towards all the parts of the planet
A; and its gravity towards any part will be IV. All bodies gravitate towards all the to its gravity towards the whole, as the planets; and their weight towards any one matter of the part to the matter of the planet, at equal distances from the centre whole. Hence we derive the methods of of the planet, is proportional to the quantity finding and comparing weights of bodies toof matter in each.
wards different planets; of finding the quanFor the law of the descent of heavy bodies tity of matter in the several planets, and towards the Earth, setting aside their un. their densities ; since the weights of equal equal retardation from the resistance of the bodies, revolving about planets, are as the
diameter of their orbits directly, and as the of those two planets, their orbits will be'a aqnares of the periodical times inversely; little disturbed. The Earth's orbit too is and the weights at any distance from the sensibly disturbed by the action of the centre of the planet are greater or less in a Moon; and the common centre of the two duplicate ratio of their distances inversely. describes an ellipsis round the Sun placed in And since the quantities of matter in the the umbilicus ; and, with a radius drawn to planets are as their powers at equal dis- the centre of the Sun, describes areas protances from their centres: and, lastly, since portionable to the times. See Earth, &c. the weights of equal and homogeneous bo- VIII. The aphelia and nodes of the planets dies towards homogeneous spheres are, at are at rest, excepting for some inconsider. the surfaces of the spheres, as the diameters able irregularities arising from the action of of those spheres ; and conseqnently, the the revolving planets and comets. Consedensities of heterogeneous bodies are as the quently, as the fixed stars retain their posiweights at the diameters of the spheres. tion to the aphelia and nodes, they too are
VI. The common centre of gravity of the at rest. Snn, and all the planets is al rest; and the IX. The axis, or polar diameter, of the Sun, though always in motion, yet never planets is less than the equatorial diameter, recedes far from the common centre of all The planets, had they no diurnal rotation, the planets.
would be spheres, as having an equal graFor the matter in the Sun being to that vity on every side: but by this rotation the in Jupiter as 1033 to 1; aud Jupiter's dis parts receding from the axis endeavour to tance from the Sun to the semi-diameter of rise towards the equator, which, if the mat. the Sun in a ratio somewhat bigger; the com- ter they consist of be fluid, will be affected mon centre of gravity of Jupiter and the very sensibly. Accordingly, Jupiter, whose Sun will be a point a little withont the Sun's density is found not much to exceed that of surface; and by the same means, the com- water on our globe, is observed by astronomon centre of Saturn and the Sun will be a mers to be considerably less between the point a little within the Sun's surface; and two poles than from east to west. And, on the common centre of the Earth, and all the the same principle, unless our Earth were planets, will be scarce one diameter of the higher at the equator than towards the Sun distant from the centre thereof; but the poles, the sea would rise under the equator, centre is always at rest; therefore, thongh and overflow all near it. But this figure of the Sun will have a motion this and that the Earth Sir Isaac Newton proves likewise way, according to the various situations of a posteriori, from the oscillations of penduthe planets, yet it can never recede far lams being slower and smaller in the equi. from the centre; so that the common centre noctial, than in the polar parts of the globe. of gravity of the Earth, Sun, and Planets, See EARTH. may be esteemed the centre of the whole X. All the Moon's motions, and all the world. See PLANET.
inequalities of these motions, follow from VII. The planets move in ellipses that have these principles, e. gr. her unequal velocity, their foci in the centre of the Sun; and de. and that of hier nodes and apogee in the scribe areas proportionable to their times. syzygies and quadratures; the differences This we have already laid down a posteriori in her excentricity and her variation. See as a phenomenon ; and now that the prin. Moon. ciple of the heavenly motions is shewn, we XI. From the inequalities of the lunar deiluce it therefroin a priori. Thus, since motions, we can deduce the several inequa. the weights of the planets towards the Sun lities in the motions of the satellites. are reciprocally as the squares of their dis. XII. From these principles, particularly lances from the centre of the Sun ; if the the action of the Sun and Moon upon the Sun were at rest, and the other planets did Earth, it follows, that we must have tides, or not act on each other, their orbits would be that the sea must swell and subside twice elliptical, having the Sm in the common every day. See TIDES. umbilicus, and would describe areas propor. XIII. Hence, likewise, follows the whole tionable to the tiines; but the mutual actions theory of comets, as that they are above the of the planets are very small, and may be region of the Moon, and in the planetary well thrown aside.
spaces; that they shine by the Sun's light, Ludeed, the action of Jupiter on Saturn is reflected from them; that they move in of some consequepce; and bence, accord. conic sections, whose umbilici are in the ing to the different simnation and distances centre of the Sun; and, by radü drawn to the Sun, describe areas proportional to the a jury lias found a verdict directly against times; that the orbits, or trajectories, are evidence; but where there has been evivery nearly parabola's ; that their bodies dence as to the fact in doubt, on both sides, are solid, compact, &c. like those of the the court will not interfere. It is also planets, and must therefore acquire an im- granted where damages have been given mense heat in their perihelia ; that their beyond the ordinary measure of justice; tails are exhalations arising from and en- and where the party bas been surprised by compassing them like atmospheres. See some evidence which he has snbsequently ASTRONOMY.
the means of answering, but had not at the NEW trial, in law. Formerly the only re- trial. It is always refused where the damedy for a reversal of a verdict unduly given, mages do not exceed 101. was by writ of attaint; but this course is now NICANDRIA, in botany, so named from justly exploded, and a new trial is granted Nicander of Colophon, a genus of the De. upon application to the court from which candria Monogynia class and order. Ersen. the cause issued.
tial character : calyx turbinate, coloured, A new trial, in many cases, may. be abso- four-parted; corolla one-petalled, ten-cleft; lutely necessary. But it is not granted germ encircled with a membranaceons ring; upon nice and formal objections, whichrdostigma peltate, orbieular, six-rayed ; berry not go to the real merits ; nor where the roundish, six-grooved, three-celled, manyscales of evidence. hang nearly equat. It is seeded. There is one species, viz. N. amara, generally upon some misdirection by the a native of the large forest of Guiana. judge to the jury, in point of law, or where
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