He attri the equator the Propofition where he gives this Table, that fuppofing the Denfity of the Parts of the Earth to increase from the Circumference to the Center, the Diminution of Gravity from the Pole to the Equator would also increase. XIV. Altho Newton feems inclined to believe, from the Obfervations he relates butes this in Prop. 20 on the lengthning of the Pendulum occafioned by the Heat in difference to the Regions of the Equator, that thefe Differences arrife from the different the heat at Temparature of the Places in which the Obfervations have been made, the which leng great Care and Attention employ'd in preferving the fame Degree of Heat thens the by means of the Thermometer in the experiments made fince Newton's pendulum Time on the Length of Pendulums in the different regions of the Earth proves in thofe re- that thefe Differences do not arife from this Caufe, and that the Decrease of Gravity from the Pole to the Equator exceeds the Proportion afperiments fign'd by Newton in his Table. gions but leater ex have fhewn that those In Effect the Lengths of the Pendulum Corrected by the Barometer and differences reduced to that of a Pendulum oscillating in a Medium without Resistance cannot arife are under the Equator, from the lengthing At Portobello Latitude, 9 Degrees, 439, 21 Lines, of the pen dulum pro duced by At litle Goave Latitude, 18 Degrees, 439, 47 At Pello Latitude, 484 50m 0, 26 the heat in thofe regi ons. 2, 06 Nowthe differences proportional to the Squares of the Sines of the Latitude, are 7, 24, 138, 205, which are lefs than what refults from Experiment. XV. Method At the End of Prop. 19. B. 3. Newton fhews how to find the Proportion given by of the Axes of a Planet whofe Density and diurnal Rotation are known, emNewton for finding ploying for Term of Comparison the Ratio discovered between the Axes of the ratio of the Earth; for whether the Bulk or Ray (r) of a Planet be greater or less the axes of than the Bulk or Ray (R) of the Earth, if its Denfity (d) be equal to the Denany planet. fity (D) of the Earth, and the Time (t) of its diurnal Rotation be equal to the Time (T) of the diurnal Rotation of the Earth, the fame Proportion will fubfift between the centrifugal Force and Gravity, and confequently between its Diameters as was found between the Axes of the Earth: But if its diurnal Rotation is more or less rapid than that of the Earth, the centrifugal Force of the Planet will be greater or less than the centrifugal Force of the Earth and confequently the Difference of the Axes of the Planet will be greatr R er or less than the difference of the Axes of the Earth in the Ratio of to TT tt (Cor. 2. Prop. 4.) and if the Density of the Planet be greater or less than the Denfity of the Earth, the Gravity on this Planet will be greater or less than the Gravity on the Earth, in the Ratio of dr to DR, and the Difference of the Axes of the Planet will be greater or less than the Difference of the Axes of the Earth, in Proportion as the Gravity on the Planet is lefs or greater than the Gravity on the Earth confequently in the Ratio to R dr DR wherefore if the Time of Rotation and Denfity of a Planet be different from that of the Earth, the Difference of the Axes of this Planet compared with its leffer Axis, is to the difference of the Axis of the Earth compared with its leffer Axis, as T to R which gives, X DXTT for the expreffion of the Difference of the Axes of the Planet. XVI. Determina. Hence the Difference of the diameters of Jupiter, for inftance whofe di- tion of the urnal Revolution and Density are known will be to its leffer Axis in the com- ratio of the pound Ratio of the Squares of the Times of the diurnal Revolution of the axes of Jupi Earth and Jupiter of the Denfities of the Earth and Jupiter, and the Difference ing to this 29 of the Axes of the Earth compared with its leffer Axis, that is, as X 400× to 1. that is, as 1. to 9 I neerly: Therefore the Diameter of 49 229 XVII. ter accord method. A very im why the flat This Method that Newton takes to explain a Depreffion towards the Poles Probable rea fon affigned of Jupiter less than that which refults in the Cafe of Homogenity feems by Newton very improbable,it is furprising that in Order to explain the flatnefs of the Figure of Jupiter, he has had recourse to a Cause whofe Effect would be much more fenfibly perceived on the Earth than in Jupiter, fince the Earth is much nearer the Sun than Jupiter. The Propofition of Clairaut that the Flatness diminishes as the Density increases towards the Center, furnishes a natural Explication of this Phenomenon in fuppofing Jupiter denfer towards the Center than at the Surface, an Hypothefis entirely confiftent with the Laws of Mechanicks. XVIII. nefs of the figure of Ju piter is lefs than what refults from theory. Why the ratio of the axes only of Jupiter the earth and As the two Principles neceffary for determining the Axes namely the diurnal Revolution and the Density, are known only in Jupiter, the Earth, the fun can and the Sun, these are the only celestial Bodies the Proportion of whofe Ax- be found. es can be discovered. How this Proportion has been discovered in the Earth tion of the and Jupiter has been already fhewn; the Difference of the Axes of the Sun The pronar is to its leffer Axis in the compounded Ratio of the Square of 1 to 27 diuraxes of the nil Revolution of the Earth to that of the Sun, of 400 to 100 Denfity of fun is too the Earth to that of the Sun, and 21, Difference of the Diameters of the inconfide - Earth compared to its leffer Axe, to 1, that is, as 5 to 1, a Differobferved. ence too inconfiderable to be observed. ble to be It was a long time that the 229 Theory of the Precession of the Equinoxes. I. For many Ages it had been thought that the Axis of the Farth durthought for ing its annual Revolution preferved the fame Pofition, and this Suppofition was very natural. For Theory fhews that this Parallelifm fhould refult axis of the from the two known Motions of the Earth, the annual and diurnal Motion; earth always and in Fact for a Number of Years this Parallelifim is fenfibly preserved. prefer ved its paralleli fm. But from the Continuance, and accuracy of Aftronomical Obfervations it has been discovered that the Poles of the Earth are not always directed to the fame fixed Stars, and of Confequence that the Axis of the Earth does not always remain parallel to itself. Hyparchus was the first who II. This Motion of the Axis of the Earth was first perceived by Hypparcbus; and afterwards established by Ptolomey who fixed this Motion to a perceived Degree in a hundred Years, fo that the entire Revolution of the Sphere of the fixed Stars from whence Ptolomey derived this appearance, was compoles of the pleated in 36000 Years; and it was generally believed in his Time that earth. at the Expiration of this Revolution called the great Year, the celestial Ptolemey Bodies would return to their primitive Pofition. the revoluti on of the fixed the duration of The Arabs difcovered that Ptolomey had made this Motion too flow, UIthis revolu- lughbeig fixed it to a Degree in 72 Years, and Modern Aftronomers by tion which fixing it to 51 annually have confirmed the Discovery of Ullughbeig; fo that the Revolution of the Poles of the Earth is compleated in 25920 Years. was called the great year, Ultughbeig corrected the time The equinoctial Points change their Places in the fame Time and by the afligned by fame Quantity as the Poles of the World, and it is this Motion of the Ftolomey Equinoctial Points which is called the Preceffion of the Equinoxes. volution. for this re Tho' the fixed Stars are immovable, at least in refpect of us, yet as the comThis regref- mon interfection of the Equator and Ecliptic Recedes, it is necessary that fion caufes the Stars which correfpond to thofe Points fhould continually appear to an apparent change their Places, and that they should feem to advance eftward, from the fixel whence it arrives, that their Longitudes, which is reckoned on the Ecliptic motion in flats. from the Beginning of Aries, or the vernal Interfection of the Equator and Ecliptic, continually increafes, and the fixed Stars appear to move in Confe- It is the quentia; but this Motion is only apparent and arifes from the Regreffion of caufe why the Equinoctial Points in a contrary Direction. the interfection of the equator and does not cor In Confequence of this Regreffion, all the Constellations of the Zodiac the ecliptic have changed their Places fince the Obfervations of the first Aftronomers; refpond to For the Constellation Aries, for Example, which in the Time of Hipparchus the fame correfponded to the vernal Intersection of the Equator and Ecliptic, is now ftars it did advanced into the Sign Taurus, and Taurus has paffed into Gemini, &c. and formerly, & thus they have taken the Place of each other, but the twelve Portions of the conftellatiEcliptic where these Constellations were formerly placed, ftill retain the ons of the fame Names they had in the Time of Hipparchus. VI. Before Newton the phyfical Cause of the Preceffion of the Equinoxes was utterly unkown, and we shall now proceed to fhew how he deduced this Motion from his Principle of universal Gravitation. that the zodiac have changed their places. We have seen that the Figure of the Earth is that of an oblate Spheroid, Flat towards the Poles and elevated towards the Equator. In Order to explain the Preceffion of the Equinoxes, Newton premifes 3 Lemmas, from Lemmas whence he deduces (Prop. 39. B. 3.) that this Revolution of the equinoctial with which Points is produced by the combined Actions of the Sun and Moon on the pro- out to detuberant Matter about the Earth's Equator. VII. Newton fets duce this motion from the principle of uni In the first Lemma he fuppofes all the Matter by which the Earth confidered as a Spheroid would exceed an infcribed Sphere, to be reduced to a ver fal gravi Ring investing the Equator, and collects the Sum of all the Efforts of the tation. Sun, on this Ring, to make it Revolve round its Axis which is the common Section of the Plane of the Ecliptic with the Plane paffing thro' the Center of the Earth, and Perpendicular to the ftraight Line connecting the Centers of the Earth and the Sun. In the second Lemma he investigates the Ratio between the Sum of all thofe Forces, and the Sum of the Forces exerted by the Sun on all the protuberant Parts of the Earth, exterior to the infcribed Sphere. In the third Lemma he compares the Quantity of the Motion of this Ring, placed at the Equator, with that of all the Parts of the Earth taken as a Sphere. VIII. To determine the Force of the Sun upon this Protuberant Matter about the Equator of the Earth, Newton affumes for Hypothefis, that if the Earth was anihilated, and that only this Ring remained, defcribing round the Sun the annual Orb, and revolving at the fame Time by its diurnal Motion round its Axe, inclined to the Ecliptic in an Angle of 23d 30m, the Motion Newton of the Equinoctial Points would be the fame, whether the Ring was fluid or composed of folid Matter. Newton after having inveftigated the Ratio of the Matter of this fuppofed Ring, that is, of the Protuberant Matter about the Equator, to the Matter of the Earth taken as a Sphere, and having found it [affuming the Ratio of the Axes of the Earth] to be as 459 to 52441, he proves that if the Earth and this Ring revolved together about the Diameter of thi Ring, the Motion (R) of the Ring would be to the Motion (T), of the interior Globe, or to the Motion of the Earth round its Axis, in a Proportion compounded of the Proportion 459 to 52441 of the Matter in the Ring to the Matter in the Earth, and of the Number 1000000 to the Number 800000, or as 4590 to 419528, (a) and confequently that the Motion (R) of the Ring would be to the Motion (R+T) of the Ring and the Globe, in the Ratio of 4590 to 424118. He found (Prop. 32. B. 3) that the mean Motion of the Nodes of the Moon in a Circular Orbit, is 20, 11, 46, in Antecedentia, in a Sydereal Year; and he proved (Cor. 16 Prop. 66) that if feveral Moons revolved round the Earth, the Motion of the Nodes of each of those Moons would be as their periodic Times. from whence he concludes that the Motion (n) of the Nodes of a Moon revolving near the Surface of the Earth confiders the in 234, 56m, would be to 20d 11 46, Motion (N) of the Nodes of our protuberant Moon in a Year, as 23h 56m, the Time of the Earth's diurnal Rotation, the equator to 27743, the periodic Time of the Moon, that is, as 1436 to 39343; of the ea th and by the Cor. of Prop. 66 the fame Proportions hold for the Motion of as a ring of the Nodes of an Affemblage of Moons furrounding the Earth, whether these hering to the Moons were feparate, and detached from each other, or if they coalefced globe of the fuppofing them liquified and forming a fluid Ring, or that the Ring became hard and inflexible. matter about moons ad earth. He deduces from this fuppofition the manner that the attraction of the fun on the ele vation at the equator causes the preceffion of the equi Doxes. Therefore, the protuberant Matter about the Equator of the Earth being confidered as a Ring of Moons adhering to the Earth, and revolving along with it, fince the Revolution (n) of the Nodes of fuch a Ring, is to the Revolution (N) of the Nodes of the Moon, as 1436 to 39343, (according to Cor. 16. Prop. 66.) and that the Motion (R) of the Ring is to the Sum of the Motions (T+R) of the Ring and the Globe to which it adheres, as 4590 to 424118; nxR is to N x T+R, as 1436 X 4590 to 39343 nxR X424118, or TR is to N, as 1436X4590 to 39343 × 424118; but it is demonstrated that the Sum of the Motions T+R of the Ring and the Globe to which it adheres is to the Motion (R) of the Ring as the Revolution (n) of the Nodes of this Ring to half the annual Motion [P.] of the Equinoctial Points of the Body compofed of the Ring and Globe to which it ad (a) The ratio of the motion of the ring to the motion of the interior globe affigned by Newton, is 4590 to 485223. which is erroneous as shall be shewn hereafter. |