EAR

EA R

ever its diameterfrom the earth.

from the rising and setting of tiie sun, moon, and slurshappen sooner to those who live-to the Si. and later to those livingto the W. and that more or less so, according to the distance. Soalso, going or sailing to the N. the north pole and northern starsbecome more elevated, and the.south pole and southern stars moredepressed ; the elevation uoitherlv increasing equally with the de-pression southerly ; and either ot them proportionable to the dis-tance gone. The same thing happens in going to the S. Besides,the oblique ascensions, desconsious, emersions, and amplitudes ofthe rising and setting of the sun and stars in every latitude, areagreeable to the earth’s spherical form : all which could not hap-pen if it were of any other figure. The roundness of the earth isfarther continued by Us having been often sailed round: tl.e lirsttime was in 1519 , when Fet'd. Magellan made the tour of the-whole globe in 1124 days. In 1557 Sir Francis Drake performedtire same in 1056 days; in 1536, Sir Thomas Cavendish performedit in 777 davs ; Simon Cordes, ol Rotterdam , in 1590, in 1575 days;in 1598, Oliver Noort , a Hollander, in 1077 days; Van Schoulen,in 1615, in 749 days; Jac. 1:1 eremites and John Ilnygens, in 1693,in 80-2 days : and m my others have since performed the samenavigation, particularly Anson, Bougainville , and Cook ; some-times sailing round by the E. sometimes by the W. till at lengththey arrived again in Europe , from whence they set out; ami inthecourse of their voyage, observed that all the phenomena, bothof the heavens and the earth, correspond to, and prove this sphe-rical figure. The natural cause of this sphericity of the globe is,according to Sir Isaac New ton, the great principle of attraction,■fcjth which the Creator has endued ail the matter in the universe;and by' which all bodies, and all the parts of bodies, mutually at-tract one another. 'I bis is also the cause of the sphericity of thedrops of rain, quicksilver, &c. 'I he inequality of the surface ofthe earth, by mountains and valleys, is notlimg considerable : thehighest eminence being scarce proportionably equivalent to theminutest protuberance on the stir nice of an orange. It differs how-ever, from a perfect sphere, Us shape being that of an oblate sphe-roid, so that the axis from pole to pole is less than the equatorialdiameter. What gave the first occasion to the discovery of thisfigure of the earth, were the observations of some French andEnglish philosophers in the East Indies, and other parts, who foundthat pendulums, the nearer they came to the equator, performedtheir vibrations slower: from whence it follows, that the velocityof the descent of bodies by gravity, is. less in countries nearer tothe equator; and consequently that those parts are farther removedfrom the centre of the earth, or from the common centre ofgravity. See the History of the Koval Academy of Sciences, by-Du Hamel ; p. 110 , 156,206; and 1’[list, de 1’Acad. Koy. 1700and 1701.—This circumstance put Huygens and Newton uponfinding out the cause, which they attributed to the revolution ofthe earth about its axis. If the earth were in a fluid state, its ro-tation round its axis would necessarily make it put on such a figure,because the centrifugal force being greatest towards the equator,the fiuid would there rise and swell most; and that its figurereally should be so now, seems necessary, to keep the sea in theequinoctial regions from overflowing the earth about those parts.See this curious subject well treated by Huygens, in his discourseDe Causa Gravitati«, p. 154, where he states the ratio of thepolar diameter to that of the equator, as 577 to 57S. And New-ton , in his Prinaipia, first pithiishctl in 1686 , demonstrates, fromthe theory of gravity, that the figure of the earth must be that ofan oblate "spheroid, generated by the rotation of an ellipse aboutits shortest diameter, provided all (lie parts of the earth were of anuniform density throughout; and that the proportion of the po-lar to the equatorial diameter of the earth, would be that of 6 SDto 692, or nearly that of 229, to 230, or as '9956522 to one.Tbis proportion of tne two diameters was calculated by Newlon inthe following manner: Having found that the centrifugal force atthe equator is one 2 S 9 lh of gravity, he assumes, as an hypothesis,that the axis of the earth is to the diameter of the equator as 100 to101 , and thence determines what must be the centrifugal force atthe equator to give the earth such a form; and finds it to he four5 t) 5 ths of gravity : then, by proportion, if a centrifugal force equalto four 505ths of gravity would make the earth higher at the equator■than at the poles by one hundredth of the whole he'ght at the poles.

VOL. II.— no. 69.

one 289th of gravity will make it higher,by a proportional excess, which by calculation is one 229 th of theheight at the poles ; and thus tie discover-al, that the diameter atthe equator is to the diameter at the poles, or the axis, as 230 to229. But this computation supposes the earth to be every where| of an uniform density; whereas if the earth is more dense near thecentre, then bodies at the poles will be more attracted by thisadditional matter being nearer; and therefore the excess of thesemidiameter of the equator, above the semi-axis, w ill be different.According to this proportion between the two diameters, Newton1 farther computes, from the diilerent measures of a degree, that the| equatorial diameter will exceed the polar by 34 miles and onc-I filth. Nevertheless, Messrs. Cassini, both father and son, the one: in 1701, and the other in 1713, attempted to prove, in the Me-moirs of the Royal Academy of Sciences, that the earth was anoblong spheroid: and in 1718 M. Cassini again undertook, fromobservations, to shew that, on the contrary, the longest diameterpasses through the poles; which gave occasion for Mr. John Ber-noulli , in his “ Essai d'tme Nouvelle Physique Celeste,” printedat Paris in 1735, to triumph over the British philosopher, appre-hending that these observations would invalidate what Newton haddemonstrated. And hi 1720, M. De Mairan advanced argumentssupposed to be strengthened by geometrical demonstrations, far-ther to confirm the assertions ot Cassini. Butin 1735, two com-panies of mathematicians were employed, one for a northern, andanother fora southern expedition, the result of whose observationsanti measurement plainly proved that the earth was flatted at thepoles. The proportion of tiie equatorial diameter to the polar, asstated by Hie gentlemen employed on the northern expedition formeasuring a degree of the meridian, is as 1 to 0.9891 ; by theSpanish mathematicians as 266 to 265, or as 1 to 0.99624: by M.Bouguer as 179 to 17S, or as 1 to 0.99441. As to all conclusions,however, deduced from the length of pendulums in different places,it is to be observed, that they proceed upon the supposition of theuniform density of the earth, which is a very improbable circum-stance; as justly observed by Dr. Horsley in his letter to Capt.Phipps: “ You finish your article, he concludes, relating to thependulum with saying, ‘ that these observations give a figure ofthe earth nearer to Sir l<vac Newton ’s computation, than anvothers that have hitherto been made ;’ and then you state the severalfigures given, as you imagine, by former observations, and byyour own. Now it is very true, that if the meridian- be ellipses,or if the figure of the earth Ire that of a spheroid generated by therevolution of an ellipsis, turning on its shorter axis, the particularfigure, or the ellipticity of the generating ellipsis, which your ob-servations give, is nearer to what Sir Isaac Newton saith it shouldbe, if the globe were homogeneous, than any that can he derivedfrom former observations. But yet it is not what you imagine.Taking the gain of the pendulum in latitude 79° 50' exactly as youstate it, the difference between tiie equatorial and the polar diame-ter is about as much less than the Newtonian computation makes it,and the hypothesis of homogeneity would require, as you reckonit, to be greater. The proportion of 212 to 211 should in-deed, according to your observations, be the proportion of theforce that acts upon the pendulum at tiie poles, to the force actingupon it at tiie equator. But this is by no means the same with tiieproportion of tiie equatorial diameter to the polar. If the globewere homogeneous, the equatorial diameter would exceed thepolar by one 230th of the length of the latter: and the polar forcewould also exceed the equatorial by the like part. But if thedifference between tiie polar and equatorial force lie greater thanone230lh, (which may be the case in an heterogeneous globe, andseems to be tiie ease in ours), then the dillerence of the diametersshould, according to theory, lie less titan one 230th, :md vice| versa. I confess this is by no means obvious at first sight; so farjj otherwise, that the mistake, which you have fallen into, was once|i very general. Many of the best mathematicians were misled by| too implicit a reliance upon the authority of Newton , who hadcerfainlv confined his investigations to the homogeneous spheroid,and had" though! about the heterogeneous only in a loo.-e andgeneral way. The late Mr. Clairault was (be first who set thematter li^ht, in his elegant and subtle treatise on tiie figure of tiieearth. 'I hat work hath now' been many years in the hands ofI mathematicians, among whom 1 imagine there are none, whoi! have considered the subject attentively, that do not acquiesce injl 3 L the-

vary, according to tiie greater or less distanceThe spherical figure of the earth is also evinced

1 a centrifugal force that is