Một tài liệu kinh điển, một quyển sách như KInh Thánh của khoa học. Người mang ánh sáng đến cho nhân loại, nhà vật lý, nhà toán học, nhà triết học,...Isaac Newton, trình bày những nguyên lý cơ bản nhất của vật lý, cơ học cổ điển, với ba định lí Newton. Tài liệu còn nhiều phần phụ lục hay, như phần các đường cong bậc ba. Xin nói rằng, dù đã học xong chưa trình thạc sĩ về toán, tôi cũng chỉ mới được làm quen với những đường và mặt bậc hai. Nhưng, từ thời Niu tơn, cách đây 5, 6 thế kỷ mà ông đã có những nghiên cứu đầy đủ, và phân loại tất cả các đường cong bậc ba. Sự vĩ đại của trí tuệ ông là không thể tưởng tượn nổi. Tuy vậy, với một khoảng cách xa về thời gian, tiếng Anh trong tài liệu là loại tiếng Anh không giống như bây giờ. Nếu ai có ý muốn đọc qua, sẽ vấp phải những khó khăn nhất định về ngôn ngữ. Xin chân thành cảm ơn.
MATH.-STAT SIM ISAAC MIBWf OM NEWTON S PRINCIPIA THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY, BY SIR ISAAC NEWTON; TRANSLATED INTO ENGLISH BY ANDREW MOTTE TO WHICH ADDKTV IS NEWTON S SYSTEM OF THE WORLD With a Portrait taken from the Bust in the Royal Observatory at ; Greenwich FIRST AMERICAN EDITION, CAREFULLY REVISED AND CORRECTED, WITH A LIFE OF THE AUTHOR, BY PI W CHITTENDEN, M A., &e NEW-YORK PUBLISHED BY DANIEL ADEE, 45 LIBERTY STREET p*- Kntered according to Act of Congress, in the year 1846, by DANIEL ADEE 3!Ltht Clerk s Office ut tiie TWuey * Lockwoof, Stom 16 Spruce St N Y Southern Oisli:ct Court of New-York CONTENTS OF THE SYSTEM OF THE WORLD 674 fke precession of the equinoxes, and the libratory motion of the axes of the earth and planet That the greatest tides happen in the syzygies of the luminaries, the least in their quadratures; and that at the third hour after the appulse of the moon to the meridian of the place Bat that out of the syzygies and quadratures those greatest and least tides deviate a little from , ? that third hour towards the third hour after the appulse of the sun to the meridian, tides are greatest when the luminaries are in their perigees, That the That the That out tides are greatest about the equinoxes, of the equator the tides are greater and less alternately, That, by the conservation of the impressed motion, the difference of the tides that hence is diminished ; 535 536 536 536 537 and may happen that the greatest inensti ual tide will be the third after the syzygy, 5:38 Thit the motio is of the sea may be retarded by impediments in its channels, 538 That from the impediments of channels and shores various phenomena arite, as that the sea 539 may flow but once every day, it That the times of the tides within the channels of rivers are more unequal than in the ocean, hat the tides are greater in greater and deeper seas; greater on the shores of continents than (1 islands in the middle of the sea; and yet greater in shallow bays that open with wide inlets to the sea, * The force of the sun to disturb the motions of the moon, computed from the foregoing principks, The force of the sun to move the sea computed, The height of the tide under the equator arising from the force of the sun computed, The height of the tides under the parallels arising from the sun s force computed, The proportion of the tides under the equator, in the syzygies and quadratures, arising from the joint forces of both sun and moon, The force of the moon to excite tides, and the height of the water thence arising, computed, That those forces of the sun and moon are scarcely ?en?ible by any other effect beside the tides which they raise in The same proved from their parallax in latitude, The same proved otherwise by the parallax, From the light of the comets heads it is proved that they descend to the orbit of Saturn, And also below the orb of Jupiter, and sometimes below the orb of the earth, The same proved from the extraordinary splendor of their tails when they are near the sun, The same proved from the light of their heads, as being greater, c&teris paribus, when they come near to the sun, The same confirmed by the great number of comets seen in the region of the sun, This also confirmed by the greater magnitude and splendor of the tails after the conjunction of the heads with the sun than before, That That from the atmospheres of the comets, the air and vapour in the celestial spaces is of an immense rarity and that a small quan tity of vapour may be sufficient to explain all the phtcnomena of the tails of comets, After what manner the tails of comets may arise from the atmospheres of their heads That the tails indeed arise from those atmospheres, proved from several of their pheenomena, That comets sometimes descend below the orbit of Mercury, proved from their tails, That the comets move in conic sections, having one focus in the centre of the sun, and by radii the tails arise 545 545 547 547 547 548 549 550 550 551 551 553 555 555 556 ; Irawn "~*" 540 542 543 543 544 546 the sea, That the body of the moon is about six times more dense than the body of the sun, That the moon is more dense than the earth in a ratio of about three to two, Of the distance ot the fixed stars, That the comets, as o ten as they become visible to us, are nearer than Jupiter, proved from their parallax in longitude, 540 to that centre 561 describe areas proportional to the times, * That those conic sections are near to parabolas, proved from the velocity of the comets, In what space of time cornets describing parabolic trajectories pass through the sphere orbis magnus, 561 of the At what time comets enter into and pass out of the sphere of the vrbis magnus, With what velocity the comets of 1680 passed through the sphere of the orbis magnus, That these were not two, but one and the same comet In what orbit and with what velocity this comet was carried through the heavens described more exactly, With what velocity corsets are carried, shewed by more examples, The investigation of the trajectory of comets proposed, Lemmas premised to the solution of the problem, The problem resolved, 558 559 559 560 562 563 564 * ~i 564 565 566" 567 57C INDEX TO THE PRINC1PIA j their prsecession the cause of that motion shewn, the quantity of that motion computed from the causes, density at any height, collected by Prop XXII, Book II, and " A.IR, its of one semi-diameter of the earth, shewn, its elastic force, what cause it may be attributed 413 4oJ its density at the height 489 302 to, gravity compared with that of water, its -l^t by experiments of pendulums, the same more accurately by experiments of falling bodies, and a theory, ANGLE S of contact not all of the same kind, but some infinitely less than others, " its resistance, collected " 315 353 101 172, 173 APSIDES, their motion shewn, AREAS which revolving bodies, by radii drawn to the centre of force describe, compared with the times of description, 103, 105, 106, 195, As, the mathematical signification of this word defined, ATTRACTION " of all bodies demonstrated, the certainty of this demonstration shewn, the cause or manner thereof no where defined common the " by the author, and all the planets, centre of gravity of the earth, sun, firmed by Cor 2, Prop XIV, Book HI, the common centre of gravity of the earth and " is 507 at rest, 401 moon goes round distance from the earth and from the moon, the common centre of gravity of many bodies does not alter by the actions of the bodies among themselves, of the forces by which revolving bodies are retained " the orbis 402 magnus, 452 its state of motion or rest 87 in their orbits, the description of areas, how found by the given velocities of the revolving bodies, CIRCLE, by what law of centripetal force tending to any given point " how indicated by its circumference higher than the moon, and their distance " how ir the- planetary regions, of shine by the sun " 110 be collected very nearly by observations, them observed in the hemisphere towards the sun than phere; and how this comes to pa?s, more " may 107 108,111,114 465,486 460 described, sort of planets, not meteors, COMETS, a " 401 in the opposite hemis 464 from them, 464 surrounded with vast atmospheres, 463, 465 those which come nearest to the sun probably the least, 4P5 why they are not comprehended within a zodia like the planets, but move differently into all parts of the heavens, 502 502 may sometimes fall into the sun, and afford a new supply of fire, " s light reflected " " " , the use of them hinted, move " in conic sections, 492 having their foci in the sun centre, and by radii drawn to the in ellipses if they come round again s sun describe areas proportional to the times Move in their orbits, but these ellipses will be near to parabolas, COMET " " S 466 parabolic trajectory found from three observations given, corrected when found, place in a parabola found to a given time, velocity compared with the velocity of the planets, 472 495 466 JoMKTs TAILS " " " " * >7 384 its CENTRE, 2(!<> 100 " " 466 489 directed from the sun, brightest and large>t immediately after their passage through the neighbour hood of the sun, their wonderful rarity, and nature, what space of time they ascend from their origin in 7V their heads, 487 490 46S 490 INDEX TO THE PRINCIPIA 576 r?OMET of the years 1664 and 1665 the observations of its motion compared with the theory, u of the years 1680 and 1681 observations of its motion, its motion computed in a parabolic orbit, in an elliptic orbit, " " " its trajectory, and of the year 1682 " its tail its in the several parts of its orbit, delineated, motion compared with the theory, 496 474 478 479 484 500- seems to have appeared in the year 1607, and likely to return again after a period of l 75 years, of the year 1683 its motion compared with the theory, of the year 1723 its motion compared with the theory, CONIC SECTIONS, by what law of centripetal force tending to any given point they scribed by revolving bodies, 501,502 499 " " the geometrical description of when the foci are not given, " " when the CURVATURE CURVES of figures foci may are given, and geometrically irrational, DESCENT 131 147 157 184 its rectification, 185 " CYLINDER, 125 125 271, 423 estimated, distinguished into geometrically rational " 501 be de centres or asymptotes are given, how CYCLOID, or EPICYCLOID, " them when the * its evoluta, the attraction of a cylinder composed of attracting particles, rocally as the square of the distances, whose forces are recip 239 of heavy bodies in vacuo, how much it is, and ascent of bodies in resisting mediums, 405 252,265,281,283,345 DESCENT or ASCENT rectilinear, the spaces described, the times of decription, and the velocities acquired in such ascent or descent, compared, on the supposition of any EARTH, " " kind of centripetal force, 160 dimension by Norwood, by Picart, and by Cassini, 405 its figure discovered, with the proportion of its diameters, and the meattire of the degrees upon the meridian, 405, 40?) the excess of its height at the equator above its height at the poles, 407, 412 its " " its greatest its mean and semi-diameter, the globe of the earth more dense than " the nutation of " 407 was entirely water, 400 magnus demonstrated, 413 498 if it its axis, the annual motion thereof in the orbis " 407 least semi-diameter, the eccentricity thereof how much, the motion of its aphelion how much, " " 452 404 ELLIPSES, by what law of centripetal force tending to the centre of the figure it is described by a it is described by a 114 revolving body, " by what law of centripetal force tending revolving body to the focus of the figure 116 FLUID, the definition thereof, FLUIDS, the laws of their density and compression shewn, their motion in running out at a hole in a vessel determined, 108 293 " FORCES, their composition and resolution, " " " v M 84 attractive forces of spherical bodies, composed of particles attracting according to any law, determined, attractive forces of bodies not spherical, composed of particles attracting according to 218 any law, determined, the invention of the centripetal forces, 233 about an immoveable centre " 331 in any when a body is revolved in a non-resisting space 103, 116 orbit, the centripetal forces tending to any point by which any figure may be described by a revolving body being given, the centripetal forces tending to any other point by which the same figure may be described in the same periodic time are also given, lie the centripetal forces by which any figure is described by a revolving body being given, there are given the forces by which a new figure may be described, if the ordinates are augmented or diminished in any given ratio, or the angle of their inclination be any how changed, the periodic time remaining the same, centripetal forces decreasing in the duplicate proportion of the distances, may be described by them, 116 what figures 120 9f - INDEX TO THE PRINCIPIA FomcE, centripetal 577 74 75 76 force defined, the absolute quantity of centripetal force defined, the accelerative quantity of the same defined, " M w the mutive quantity of the same 76 defined, the proportion thereof to any known force how collected, a centripetal force that if reciprocally as the cube of the ordinate tending to a vastly remote centre of lorce will ca.use a body to move in any given conic section, " " a centripetal " force that is move in an hyperbola, centrifugal force of bodies on the earth s equator, GOD, his nature, ClaAviTY mutual between the earth and its parts, * of a different nature from magnetical force, the cause of it not assigned, 243 how 405 506 great, the pi anets, from the surfaces of the planets " 393 all upwards decreases in the duplicate ratio of the dis tances from the centre, 400 same downwards decreases nearly in the simple ratio of the same, tends towards all b dies, ami is proportional to the quantity of matter in each, is the force by which the moon is retained in its orbit, the same proved by an accurate calculus, is the force by which the primary planets and the satellites of Jupiter and Saturn are 400 fruin the " " " " " how great in Mercury, how great in the comet of 1680, when in its HEAVENS are void of any sensible re.-iotauce, 401, " " perihelion, 391 453 112 486 400 , 445, 492; and, therefore, of almost poreal fluid whatever, suffer light to pass " 397 393 retained in their orbits, iron rod increases in length by heat, of the sun, how great at different distances from the sun, HEAT, an " 94" 397 507 " tends towards 114 as the cube of the ordinate tending to a vastly remote centre of force will cau^e a body to " 109 through them without any refraction, , 486 any cor 355 356 485 HYDROSTATICS, the principles thereof delivered, SYPERBOLA, by what law of centrifugal force tending from the centre of the figure it is described by a revolving body, by what law of centrifugal force tending from the focus of the figure it is described by a revolving body, by what law of o* itripetal force tending to the focus of the figure it is described 293 116 " 117 " by a HYPOTHESES JUPITER, " " " its its of revi living its apparent diameter, its true diameter, attractive t rce, how " its the weights of " its density, its quantity of matter, " " " " " fjlOHT, " " " u " " rejected from this philosophy, 508 388 388 periodic time, distance from the sun, " " 118 body, what kind oever bi dies on 386 399 398 399 great, its surface, 399 perturbation by Saturn, how much, the proportion of its diameters exhibited by computation, and comf tared with observations, its rotation about the cause of its its belts axis, in 409 what time performed, hinted at, 409 409 445 246 propagation not instantaneous, its velocity different in different mediums, a certain reflection it sometimes suffers explained*, its 24J5 245 refraction explained, refraction is not made in the single point of incidence, an incurvation of light about the extremities of bodies observed by experiments, not caused by the agitation of any ethereal medium, 243 247 its ANETIC 399 403 its 24fc 368 94,304,397,454 force, 37 578 INDEX TO THE PRINCIPIA WARS, " its 3^ periodic time, distance from the sun, the motion of its aphelion, its " MATTER, quantity of matter defined, its msinsita its ." define! 73 74 impressed force defined, 74 its extension, hardness, impenetrability, mobility, rta inertia:, gravity, subtle mattir of Descartes ii quired how discovered, its ., METHOD of distance from the sun, first and its aphelion, last ratios, " differential, same analytical order, of finding the quadratures of all curves very nearly true, ot converging series applied to the solution of difficult problems, " of transforming figures into others of the of fluxions, " MOON, demonstrated, the inclination of its orbit to the ecliptic greatest in the syzygies of the " " " " " " " " " its librations explained, its mean apparent " tt " " by calculation, its its surface, density, quantity of matter, its mean distance from the earth, tained therein, its how many greatest sem>diameters experiments of pendulums, or any statical or hydrostatical observations, periodic time, the time of its synodical revolution, its motions, and the inequalities of the more slowly, in a dilated 261 447 448 208 45.) 405 453 453 453 453 453 453 454 its revolves 95 141 of the earth how many mean semi-diameter?, its force to move the sea how great, in 389 405 node with the ^un, its not perceptible " diameter, true diameter, weight of bodies on 94 388 271 430 and least in the quadratures, the figure of its body collected 385 320 into, MECHANICAL POWERS explained and MERCURY, its periodic time, the ruotion of 339 4^/5 its " " < 449 452 454 422 same derived from their causes, when the earth is in its perihelion 413, 144 orbit, ; and more swiftly in the aphelion the f-ame, its orbit being contracted, 413, 444, 445 revolves more slowly, in a dilated orbit, when tl.e apogteon is in the syzygies with the sun and more swiftly, in a contracted orbit, when the apogaeon is in the quadratures, 445 ; " more slowly, in a dilated orbit, when the node is in the syzygies with the sun and more swiftly, in a contracted orbit, when the node is in the quadratures, moves slower in its quadratures with the sun, swifter in the syzygies; and by a radius drawn to the earth describes an area, in the case less in proportion to the time, in the revolves ; " fir.<t last case greater, " " the inequality of those areas computed, its orbit is more curve, and goes farther from the earth in the u " first orbit i? less m< 415 " eccentricity greatest when the apogaeon in the syzygies with the sun its is in the quadratures, nodes move more slowly when the earth : in the syzygies with the sun is in its aphelion, helion, * its nodes are at rest ratures in their syzygies with the sun, and goes back ; is same * 423 414,445 apogaeon goes forward most swiftly when ward in the quadratures, its its 423 peri helion, " 413 420 curve, " 44G case; in the last case and comes nearer to the earth, the figure of this orbit, and the proportion of its diameters collected by computation, a method of finding the moon s distance from the earth by its horary motion, its apogaenn moves more slowly when the earth is in its re swiftly in the aphelion, its and more least when 414, 44l the 414, 44C swiftly in the peri 414,445 quad and go back most ; swiftly in the 41-1 INDEX TO THE PRINCIPIA MOON, the motions of the nodes and the inequalities of its motions 579 computed from the theory of 427,430,434,436 gravity, the same from a different principle, the variations of the inclination computed from the theory of gravity, " 437 the equ.ti3ns of the moon s motions for astronomical uses, the unnual equation of the moon s mean motion, the first semi-annual equation of the same, " " " 441, 443 445 445 443 447 447 448 425 445 the second serai-annual equation of the same, the first equation of the moon s centre, " " the second equation of the " MOON S first moon s centre, variation, the annual equation of the mean motion of the semi-annual equation of the same, " " its apogee, 447 447 the semi-annual equation of its eccentricity, the annual equation of the mean motion of its nodes, the seini-annual equation of the same, " " " the seini-anuual equation of the inclination of the orbit to the ecliptic, the method of fixing the theory of the lunar motions from observations, " " MOTION, its quantity defined, absolute and relative, 445 437 444 464 73 78 absolute and relative, the separation of one from the other possible, demonstrated by " .* an example laws thereof; " " " of concurring bodies after their reflection, by of bodies in eccentric sections, in " " " " " " moveub!e orbits, of very small bodies agitated by centripetal forces tending to each part of some very great body, 233 of bodies resisted in the ratio of the velocities, in the duplicate ratio of the velocity, 251 258 280 partly in the simple and partly in the duplicate ratio of the same, of bodies proceeding by their vis insita alone in resisting mediums, 251, 258, 259, 280, 281, 330 of bodies ascending or descending in right lines in resisting mediums, and acted on by " " an uniform force of gravity, 252,265,281,283 of bodies projected in resisting mediums, and acted on by an uniform force of gravity, 255, 268 287 in of bodies revolving resisting mediums, " u of funependulous bodies in resisting mediums, resistance of fluids, " and " 41 propagated through of fluids after the " fluids, manner of a 304 323 356 370 84 246 247, 248 vortex, or circular, MOTIONS, composition and resolution of them, " collected, in given superficies, and of the reciprocal motion of pendulums, of bodies tending to each other with centripetal forces, " OVALS what experiments 82 83 91 116 172 183 194 for optic uses, the method of finding them a general solution of Cartesius s problem, which Cartesius concealed, off from a given place with a given velocity according to a given right line, when the centripetal force is recipro cally as the square of the distance, and the absolute quantity of that force is known, of those which are described by bodies when the centripetal force is reciprocally as the OBBITS, the invention of those which are described by bodies going " cube of the distance, of those which are described " PARABOLA., by what law 114, 171, 176 by bodies agitated by any centripetal forces whatever, of centripetal force tending to the focus of the figure the same may be described, their properties explained, the diverse length? of isochronous 120 pendulums in different latitudes themselves, both by observations and by the theory of gravity, defined, and distinguished into absolute and relative, of bodies moving in conic sections 168 186, 190, 304 PENDULUMS, PLACE PLACES 123 409 to 413 78 found to any assigned time, not carried about by corporeal vortices, compared among 153 378 INDEX TO THE PRINCIPIA ">$() PLANET*, their peri diet imes, their distances " * the a t helia " and nodes of their orbits almost rest, the " " 339 405 their orbits determined, way of finding their places in their orbit?, their density suited to the heat they receive from the sun, their diurnal revolutions equable " 3gg .* from the tun, 406 347 to 350 their axes less than the diameters that stand upon them at right angles, PLANETS, PRIMARY, surround the sun, move in ellipses whose focus is in the sun s centre by radii drawn to the sun describe areas proportional to the times, 400 406 406 " 387 " 403 388, 403 revolve in periodic times that are in the sesquiplicate proportion of the dis tances from the sun, 387 are retained in their orbits by a force of gravity which respects the sun, and is reciprocally as the square of the distance from the sun s centre, 389, 393 PLANETS, SECONDARY, move in ellipses having their focus in the centre of the primary, by radii drawn to their primary describe areas proportional times PROBLEM KEPLEHIAN, 413 to the 386,387,390 revolve in periodic times that are in the sesquiplicate proportion of their distances from the primary, 386, 387 solved by the trochoid and by approximations, 157 to 160 of the ancients, of four lines, related by Pappus, and attempted by Car135 tesius, by an algebraic calculus solved by a geometrical composition, PROJECTILES move in parabolas when the resistance of the medium is taken away, 91, 115, 243, 273 their motions in re.-isting mediums, 255, 268 PULSES of the air, by which sounds are propagated, their intervals or breadths determined, 368, 370 these intervals in sounds " made by open pipes probably equal to twice the length of the 370 pipes, QUADRATURES general of oval figures not to be obtained by finite terms, QUALITIES of bodies how discovered, and when to be supposed universal, RESISTANCE, the quantity thereof in mediums not continued, 153 38-1 329 in continued " in mediums, mediums of any kind whatever, of mediums 40f 3.i as their density, cceteris paribus, 320, 321, 324, 329, 344 353 in the duplicate proportion of the velocity of the bodies resisted, ccrteris j.ari- is is is 258, 314, 374, 329, 3J4, 35 i bus, Ct in the duplicate proportion of the diameters of spherical bodies resisted, cceteris paribus 317, 31 8, 329, 34-1 of fluids threefold, arises either from the inactivity of the fluid matter, or the te nacity of its parts, or friction, " the resistance found in " " in " " " " " " almost 286 kind, 321, 35* cannot be diminished by the subtilty of the parts of the fluid, if the density remain, 355 of a globe, what proportion it bears to that of a cylinder, in mediums not continued, 327 fluids, all of the first 343 compressed mediums, mediums not continued, of a globe in 329 344 in compressed mediums, how found by experiments, to a frustum oi a cone, how made the least possible, what kind of solid it is that meets with the least, RESISTANCES, the theory thereof confirmed by experiments of pendulums, by experiments of fa-lling bodies, REST, true and relative, 345 to 328 329 313 345 " to 321 to of philosophy, SATELLITES, the greatest heliocentric elongation of Jupiter s satellites, the greatest heliocentric elongation of the Huygenian satellite from Saturn " " 356 78 RULES " 355 38-! 387 s centre 398 the periodic times of Jupiter s satellites, and their distances from his centre, 386, 387 the periodic times of Saturn s satellites, and their distances from his centre, 387, 388 the inequalities of the motions of the satellites of Jupiter and Saturn derived from the motions of the moon, SM^UIPLICATE proportion defined, 413 101 INDEX TO THE PRINCIPLE SATURN, " its its " periodic time, distance from the sun, its * apparent diameter, true diameter, its attractive force, how great, the weight of bodies on its surface, " its " " " " its density, its quantity of matter, of the earth to be its SHADOW perturbation by the approach of Jupiter the apparent diameter of its ring, " " 388 388 388 399 398 399 399 augmented in lunar how great, eclipses, because of the refraction of the at 44? mosphere, SUUNDS, their nature explained, 360,363,365,366,367,368,369 359 368 not propagated in directum, ( caused by the agitation of the " their velocity " air, mputed, by the theory in summer than winter, cease immediately, when the motion of the sonorous body ceases, somewhat " " Sf ACE, 368, 369 c< m swifter how augmented " 370 365 370 in speaking trumpets, absolute and relative, not equally full " 399 403 388 78, 79 396 SPHEROID, the attraction of the same when the forces of its particles are reciprocally as the 239 a given angle, by what law of centripetal force tending to the centre thereof it may be described by a revolving body, 107, 287, 291 SPIRIT pervading all bodies, and concealed within them, hinted at, as required to solve a great 508 many phsenomena of Nature, squares of the distances SPIRAL cutting all its radii in STARS, the fixed -tars demonstrated , their twinkling " what to be at rest, to be ascribed to, 404 487 new stars, whence they may arise, SUBSTANCES of all things unknown, 502 507 " m SUN, >ves round the common centre of gravity of all the planets, its revolution about its axis " " " its mean apparent its true diameter, horizontal parallax, its diameter, " its attractive force the weight " " <.f how bodies on great, its " its quantity of matter, " its force to disturb the motions of the its force to move " tli? 448 the sea, 415, 448, 449 78, 79 relative, astronomical equation thereof proved by pendulum clocks, and the eclipses of Jupiter proved, or that all spaces (if said to be full) are not equally full, VELOCITIES of bodies moving in conic sections, whore the centripetal force tends to the focus, VELOCITY, the greatest that a globe falling in a resisting medium can acquire, " s satellites, " 121 its 388 its 388 periodic time, distance from the sun, the motion of its aphelion, 405 centre, as the quantities of " 79 396 344 VOHTICES, their nature and constitution examined, W.AVES, the velocity with which they are propagated on the superficies of stagnant water, WEIGHTS of bodies towards the sun, the earth, or any planet, are, at equal distances from the 399 399 A VACUUM VENUS, 398 391, 419 moon, of the sea derived from their cause, TIMF, absolute and 403 399 surface, density, " 453 398 its TIDES 405 398 has a menstrual parallax, " 401 * the periodic time of " matter 361 394 in the bodies, they not depend upon the forms and textures of bodies of bodies in different regions of the earth found out, and compared together, 504 395 409 NON-CIRCULAT1NQ RETURN Astronomy/Mathematics/Statistics Library 100 Evans Hall LOAN PERIOD DAYS 642-3381 U.C BERKELEY LIBRARIES