|Rights||No Copyright - United States (NoC-US)|
|Publisher||Digitized by J. Willard Marriott Library, University of Utah|
I lethirt I QRAT1TATIOK, AJ50 CfiNRiPU- 1 GAL FORCES. I PT9BSON.PE.ATT, B tHiCKUxia or nit vxitbisitt or csorr, K Mhitrut instU TabcmatU, at.Q. S. L. din. on M Monday ntninj, forth IQfA, i860, ORArmitoii lea force exerted between etery ptlcl of matter, In thefiinTTerse. Tw'o or nivre jwrticles or. Haaoa of .matter, plact-d In tentact. have a mutual tendency to prcs thiin kItm towardi each , other's centra. This Pto mroU ojiial dud rn'-oppocile' direction,- koweTer great may be tho differenco lu the qMntitlej of matter; forylnstancc, onn ponud t exerts tho same pressure Jupon tho tmr-- we of the tartb, as the earth exorta upon thq jne pound weighty and aar b two, forw nrao ta'dlrectloM .oppoeUo- to each? other:, the two wales mrtit remain at tesr. i I .i ot.' r exerted a greater force I -,tt the,r 'l pressures, then S. ;rnp6urided of these1 "'different I w,";,, ncccwarlly mowe.-riIth unl wly accelleraUd' raoUon, ,ln.the direction of i6? 8ratr pressure. This may be represented I iw,?',c,t,. vessels of. equal weight In cod- Pff ?n opposite dlrecllonsr If the S!? ,,tma, oh tha two boat8 equal, I tSLfP '.to 41 rMt5 U the SiPf "tatce- over the other, there will not I t?. I,,'' fore U Mertodi I ni?-7'''ad.B,te" o'c matter, Jiot only I WkSn wwofjpressura when In.ontact,but I ySsh?" ' manifest a mutual rw I Ss?i'0w ach other. By -vlrtbo of th I S rMtralrlftdi iher will mbvo I uSiS Jf,h &er jrtlh uniformly aceel- I aW7?oUo?- wasff of matter. eleTatcd I uV' lh BeHm will rise to rrieet I Will il i ? "Ues of tho two" moving bodies I tkat u i.T proportional to their jmasses- I Imm:i masses of tbb tw'omovlnjj bodies I irlll?!l'h?l!.veIodt5c towards tach other I tkalrln11 tnaa of one body ds twice I fflta :"?.tttw velocity. will be one-halfj I win fiKft"' greater, its velocity I SLMWI-IMU mass Is one hundred I 3rsk'TH!ftu velocity will be the oue-hnn- I vuami? Hhat of the smallet, Ae. The I atty of motion in raoring body it equal to th relochy multiplied Into tho 'mm', hence, when two bodies move toward each other by hS' ? lVstvWUtrrfr their quaa. tltlfcs o motloa are aly( exactly equah Thereforo, when, they mcet,tbey wUI mUtuX destroy; rtch others' otW,, end temJfii at rrat. ; - -Jh1?4.,lt!,.ltK PercjtlTetl, thst the fbrca of gravity Is exhibited In two rnys; oamelK hi pressoro and by .motion.. : Both' of these $ fects are used to measuro the force. When &h.V l 1,Muie.4 b Prepare, tho. result is called weight, ondie represented by tho num. per of ounces, pound, tons, &c. Whea it is messured by motion, tho result is determined byth,snace thtougliblehabody more, by grnTltatIoa,lB a given time.' WtorT drabn tra ed, by . cartful expertmentsttthat every kind of aatten near the sutfwd of the ntU' la equal times, when the resistance of the atmosphere and 'other dUt'utUnces are removed.' re-moved.' , ,' '. t --.' i- , '". r?ce through which one tody falls from , tUte of rest tbardj,ftnother la' tio 'second m,l l Monbmical measuro of gmvi- i0D? "P250 ,a wna" estimated in Inches or .fsot. Tho space threugh whlch abody falls I9S Inches, in one second. , nv;,!i In adopting thlt measttr "bf'the force of I 'aWty, there are three xhlcs which should be well nnderstbpd and carefully "observed,- "s by nrfut of -iUgrwtUdwn moot tokatitTtAotittt in tmt ttcondf does not dtptruf upin tht wu'ifrth't or. rwr; ltd it thi tam vTuUettri puiyM Hi vmiiftiii ' dalandtartthtnoitek -. '-'X- ,-' - -Thustho So. gratlUtfs towards JupHeir. and. the earth graTitafes iowntds,; Jupiter rdws but though th inaia of the, sua. I"JJ80S51 limes greater than thp.mas8 !of the earth, yet tho gravitation, of, the former' towards Jupiter is; exactly, equal tb tho gravitation of the latter towards hl'r when "the -Sun-mid; earth are equally dlatant from hlmj, In 'oth'erwor Js; tho Sun and earth, when at -equal' distances from Jupiter, movo through tho same number of inches or parts of Indies towards Jiipiter Irt one second of time ' And such must always Be the cose, whatcyer may be tho differences of tho mosses of any number of.-TnoIng: bodies towardsanother bodyi ,. J. - BWb psijtm tpact through uhU Im'iu'by tmr gravitation, tune toiearJi. ahoifitr-- in mt retwid u proportional to Me mm pftht lalttrjf Ihe du'.ariu Mutetn tht former and Mt& nrtunh'tfy 'tamii ' , ' Thus, iMho.-mass'. towards which r -body gravitates is dblcd;. quadrupled,'. tti.S the number of inches which the gtaVItatlng body will pass: over In one.second,.wH. bb"doubl4;; quadrupled. &s; Suppose .that-;tho jSuu and Juplterare at; equal ;dlstarcci. front" Saturn; as the Sun cootiins :l(M8 . times more tudtWr than Jupiter, then whateirtriiiay be tho num-herof num-herof Inch.ei.tlirougUiwhlch Saturn may: era". vltate towards Jupiter In oheseCond pfttmo. lt' will gmvttato towards;, llib iSun ,' in .the isaiue X'SUHIUJltJaAhi-i (antes ffravitati tencardt int hody, iht .- ipata JpaUtd 'mtrlbifihe'orfiUti ,wMM.-oid.:4 time, iiiU.liiin; wruly'pnporiiotidl iojthi i'tfaan xfcthtir distancd fromikilalUr SC- -X'--'; v'V,Ur.V: v lsThus1," if the idUtance bf 3the.".iurfacbbf the earth frbr4"iis.centrobe' cUed'il,iahd .tHe space pasted.-, over' by n, falling; body near xt he r'surfai'b t Is. sixteen. feet Jtt.a second of . tlrao, then , at twlco" tho . -.distance frotn,tlie; centre, of the' earth," a body would fall ouo-fourth of sixteen feet In oao second. At three times .the distance, a body would., fall one-ninth ot sixteen ftet. ). At four -times the' distance bno-sixtceQth .of sixteen' feet, or: one foot.-vAt, sixty times. the distance romjtne. centre of the earth; to -lf: surfacc,',br -atl the distance of. the tooon. a body would fall, in oao srtohd,-the onVJ.thlrty.slx .hundiedth part tof slxteenjf or'r about , bno-tweiitleth; part , of an Inch, , ,Tlie Bub, being 400tlmes, more, dis-tant dis-tant tharf the moon"; falU towards the' earth in oner'ecoria, the. lilfiO.OOOlh1 part of the l20tb of (in lnch.equal to the l-3,200,000th part of an Inch. While Ncptuno, Uibp SO. timet mora, dUtant than tho Bun. falls towards the. earth iri one second the UOOOth partof the 14;200, 000th of an tbcti, wbkh Is equal tb the 1.2,880,-OUO.OOOth 1.2,880,-OUO.OOOth partcf an theh. l'erhops this audience may Inquire how this law of gravity Is known to be true? Bow is it known that tho force called gravitation decreases as the square of tho distance Inefcisw? Who has ascended the heights of heaven to experiment upon this force? Who has observed any phenomena by which he could exactly determine the fractions of on inch through which bodies would (fall towards tho earth la one second of time at the voBt distances of tho moon Sun and planetsf The answer Is, that all mauklnd, of every age, havo beheld the phenomena which include tho dU' Accessary for the solution of this grand problem. Ail have beheld tho moon drcllng Itst-lf around the earth, at the distance of about 210,000 miles, or at the distance of CO semi-diameters of the. earth from its centre. All might have known thai a body must move In a straight line, when once pnt in raotlpn, unless deflected from that straight line by soma force. All might have known, that the orbit or path of the moon was curved towards tho earth, being defleited every mo mcntfroiuftstrsight Hue, called Its tangent, Into a curved lino. All might have known,-by known,-by a shnpla calculation, the Cxa?t amount of this" deviation from tbb tangent tb the curve In dno second of time.. Yot, strarig It may appear, this simple phenomenon, though observed ob-served for thousands of years, wMnot comprO' hcniled till the Immortal Newton, some two centuries i2tft, solved tho simple problem. We:say, simpla problem, bccauso.lt (s now so easily poltcdf but In the days of Newton it was considered the greatest discovery that over was unfolded to the mind of man. Thus we ice that the tamo force which makes a stones fall 103 Inches ttf one second, causes the moo-i to fU 8800 times less, during tlw same time; If gravitation did not vary In its Intensity with thb distance, then tho moon would fall with thesamevelocHyas astonenear the earth's surface; If the velocities reated merelyasthedUtance.then the moon, being CO semMhvmetersf iha earth distant, would fall 00 times slower? but its filing velocity It known to be 60 times CO. or 3(500 times wower, beings M before statod, only about the l-20tn of an Inch in a second. The mean ecmi-dlamctcr of the carlo, ts about S350.2 mile: tho mean distance of the tun" Is about 93,000,000 milts. The .latter dls-tance dls-tance divided by tho former "gives a quotlenlof 24080; Mist It, the sun's distance Is fcqual to 31080 Mml-dlameters'of the- e&rtb;thls squared or multiplied Into Itself Is equal to 680,219,021. If the sun. contained only the same amount of matter as tho earth, Ihen Uio latter would be deflected from the tangent of Its orbit Into a onnre towards tho sun with a'Teloelty 680,. 270,921 timet Jets p? second than that of a falling body near the earth surface: hut Ob servailon proves that, the earth' falls towards the sua with artelodty sevirl Mdre ffi SMS? grM,'f ;r,ta dsliM fm tho tai gent of Its orbit being about the 1-Sth cf oh inch pewecoBd; or, more accurately, the earth Novr. UC80,279t92l bef dtv ded by 1.4! the ?oMtI?LtW,lt 88?.,651?that & ttertf ; contains 889tC6t timet mbte waiter" than the wrA - onlyi ejjual to' that .of . the ' .NcptW.Wlng-absui 30 times the distant 'A' P'aaet, twic tho .olstanca of, 'the earth from.the tun. will fall fourtlmes less distance I o i ono tecond; at three timet iho distance, Its failfpg velocity, will be nlne.tlmct lesV, at four t met the distance,, tlxtten tlmesles:t tea timet ;th dUtonrt,. oao, hmidred timet lest; SC.. SC. ''- "'. the. lav of graVltatloUi and ,detcrmjneil a 'proper 'pro-per measure of its orcc fof any given quanU ty or matter; and for ,any.: given distance, ncxti Jet us examlno the r,flaturo of .those, opposing forces by which the planets. and'satellltce Vra prevented fron; falling to ono.cbrnmbii centre. an ray lirsUecture,' I pointed, out thVhrlncU pie of the composition, of. force and motions; that a bodyocUd updhbytwostobe' w.ould mofo ..IiV.r; direction .Iriterntedlate.: between 1, ,mLr. ifonopftho WomotlonsMs'untform.- ptoduces thq aceelleratlon; ,. 1 : "i , ...f All.the planei irand BatelllteVof -0?r-MStVra aro under .the Influence of a projcctlld: force. br aforeeich; andtheu ceased to,:nct; the" siimd os powder cease to nctupoii'a ball, after' the Wmem of explosion. WHhout-a.,reslstlBR medium, or tqme other .extroiicout cause, tba'- planetary .bodies must have continued tomore for ever ri the straight line In -which WKpr jeeted, . But gravitation every moment deflects thtm ft?2S! tLi H'2ht Une; into .curYlltrtcar orbUs.,-iThe nature of these orbits wilKdepcnd upon the, lnttuelty. and airectloiof -the'twb forces,-; t ., ' f,;;-'LiiV-',.'' ,ll- jSlfiJthomotlonarlsiog"' frqro thb' projcetloa rlsnt right -angle Mo - thb i : wbtl arising from gravitation; and if tho'veloclty. of the;jbrmerl pxactly,-propbrtloned to: that "of the latter, to as to keep the body at , all tlmctf f Mb? a.,.4i'ni from thb centre.lti, orbit .will be a circle.', v " , , - ' ,.; ' ' " "2rid.f- Tbough the projectile Vcl6clty.:is 'exi! actly. such, as woul J fprodncoa clrcularr.orblt wheonopcrattoff A rlght;angles.f tolthb .' cenJ traL force, yet,if;;opemtlngt an acuta or ob-iSf?'anglo,totheUttcf:iori:tIjitv4 ob-iSf?'anglo,totheUttcf:iori:tIjitv4 velocity will bo equal, to that of Its prclccUon?'- 3rd, If n body be projected at right angles to therbehtrtV,foico,VHh a velocity, insufficient to prUco.'A'Vclrouiar'orbli, U;w)U' descrlbd.an lltpsb of which the. polnt of projcctloB 'wlll.. be the aphelion." .c-jr f: ,v" Tat ,. : 4th If a;bbdy be.projectotl nt rlght angle to the central forco.wltti.it velocity BOmowhat' too great for the central force to deflect It'into a circle. lt.wlll revplvala irn' ellipse of. which tlie point of projection' will, betbo perihelion. ! '. Oth;:if a body be projected laa Hne making t au acute, ot obtuse angle with the direction o( the central forceaud with; a .'velocity some, what smaller or greater than, that which (if at the same distance,' and acting at right angles); wouldr;produce ;;drcl, dt.TvJU describo' an ellipse; iiV "" ,.... - Cthv'IL the projectile velocity, is .equal - to; that which the Uxly would.ocqulrb in. falling froni the point of projection to tho sun. It will dcrcrtbe a curve, called a parabola; the body, in this case, would fbllow one of the branches of this curve with a retarded velocity far beyond the limits of oursolar system, never to return to It again.- 7th. If tho projcclUe velocity Is. greater than that which a body,. would acquire la following fol-lowing front the point of projection to the sun. It would describo a curve called a hyperbola. As the branch of this curve in which the body Is moving, extends, lika the parabola, to an inOnlte distance, the body never could return again to the solar system. : The circle, ellipse, parabola, and hyperbola, . are the only possible orbits or curves In which bodies can move under the Influence of projectile pro-jectile and gravitating forces. At driven distance,-there is only one velocity velo-city of projection, which will produce a circular circu-lar orbit; and there Is only oao velocity which Will describo a parabola; but there is sn infinite infi-nite rnminer of velocities which will produce an InGnite number of elliptic orbits between a straight line and a circle. And there Is also au Infinite number of velocities which will causa bodies to describe an infinite number of hyperbolic. currcs'.bf different forms. All the planets and satellites of our system describo ellipses which do not vury much from circles. Some of the comets describe, ellipses very eccentric: and tome of them are supposed to describe parabolas and hyperbolas. Let us next determine measure for projectile projec-tile forces, that they may be properly adjusted to dhy given central lorccs. For Jhe Bake of simplifying onr statements. Ictus suppose bodies to movu in circles around central forces. It is required to determine whateQect different, velocities and distances will have In relation to central farces Let nstrlng one foot long 1kj attached to ball of lead of tho weight of ono pound; let It be whirled arouud in a horizon tal.plane. and it will have a tendency to recede, from tho centre: cen-tre: the greater the velocity of revolution, tho grcster will bo the force pulling upon the string In a direction outwards from the centre Thfa.ia called the centrifugal force,. When the string petfb'mt a revolution In 1.00352 seconds, it will become stretched, by tho circular , velocity, ve-locity, qual to the force of itt weight, that Is, centrifugal force will be equal to one pound : Let the' vlocityof revolution, which generates one pound ofj-cntrifual force, be represented by ono. Suppose tho string connecting the ball vrllh the centre, to bo varied In Its length, while Its velocity icroatiw the same, what will be the law of fores exerted upon tho strjngf Both expcrlment.and calculation demonstrate that, IRA tt tame vtfycitu, Iht tentrifugalforc varia inxauly at thttmgCh fjtht ttrinfc Kxaroplcs: A string ono foot, long, with a certain velocity, generates a centrifugal force of one pound:, Attring, two feet long, gives a forcsof half of a pound; three fed long, one-third one-third of a pound; ten feet long, one-tenth of a pound, Ac, Ac. , Tb philosophy of this la w will be seen by tht a body reval ing wUh Is deflected from the tangent to the curve lfetgh a Me oaly half a. great; la liffig "?i1Vkt Ikrough which the nearer bodyi. tfeK4. AMimtlrfictthedUtn;o,thtt" fewstott k oaly ae-thlrd of that of the ncarwt bwly. At ten tlKW.lho distance the deflection ttaIroftenlbof lhatpftho, nearest bbdy, .TlW forcej exerted tipon the sttlng belae at iho deflectlbbs; and thedeflectloot bef, teg fayetwlya tho distances; therefore, the cHtrtfgal furce mustbo lavertely a the dls-taaces.- ,r V',t .'-f , : Vett, suppose thai tlrt'veloclly of'tho revol v bur ball to he varied, while titer length of tbb string, couutctlng it with tho centre,? remains tk. What will bu the law of force teTtei.m tha-a4tlaT', I thkj bite; at fa the former, both experiment and mathematical calculation prove that, " ' Whitjhikwhiiftht Urtnj'rmalh tts W Va etatrffirgalfarctvariti dirttStuatlhitrntartaflht tttoatjt. : . ; Kxamples: A etrlug cap foot, long, with; a teloctty equal to one, generates a centrifugal fore equal to one noundt If tha im.t.ii t J? of thottrlpg; Is aado to rbvolvevwlth r twice the velocltyi the fbreer exerted upoh.rtbe tlrlngiwllllmfoarpoundtf If the "velocity Is ture . times n, ercaV."h'e; string -wlir' -be tohed.Btn.eippunds! it; the revolving velocity I nve. tlmw as grJat, tho tension b thettrlng i1?U.t,,t?.cnlr?,v? WHSMf the-circtilar , ve-locltypfthe. ve-locltypfthe. bilt it ?00 times. M- greut; thb ftrcpexcrted upon thOiitrlng- wiIlrbo' 800,000 Tho reason of this jaw Will "bo perccfycil by . trilectlngv:that body; revolving ri,a circle I wlthTelocitycqual tp pnei'willbe.defleeted; in h given tlme,'frbm the taugentofltt orbit ,to the uurro; through a space 'wble&may.- be jrenresent.cd by one.1 - With twlcii the rcvolvinK velocity; Mie deflection; la the sambftlmerwIU wfpurt times otVar; wjth ihtico times lli0"r ulvlng ycIocIty,,tho:deflectiori4"rom- thb tan.' gnt, in,thp-iumetime;wll, bo, nlnpj timet ok forr Ap., Ac: Tho deflections being' at thb square, of the; .velocity therefOTO.tho central w;iCVhIch produce these deflections, must bs as . the square . 'of the velocities:, but1 in circles tho central andcntrlfugal forces, ba lMtoeacIrotltiiratid are, equal; thereforo. tbe rtrifngal.forces must bb as tho'jtquare of the vCiPclth. 4., ' ' .. ' i bcchtral fbrce'wlth two timet "the "rci Wty. muat be four 'Um'esiJw gteat; a body," under Its Influence, .must,fli;from Its tangent four times rtft fann tho;:SamV:tld(orfTjiu?Ine the first half of the tlmc,lt,wllivaii through onerpartof ,j,0 tp9 i0','ontt-;.oUMtbr of the whole; during, thelost.hali'of tho: Mme,.it tf iii fall through three times e . much 'spacbi Xhercfoie,. during tho whole time ;thb omouni orspace.fallen' througli fronY.tho' Ungcnt will be equal to'.thfesijm. of -th' spaces, fallen through during the. two equal Interval of Urae, that is, equal to four . 'f " gtsat, andtho fall ot deflection from.' the .tangent .tan-gent must be nine time as far; for. dating the tint .third of the. time, the deflection will . be one part b( the space equal tb one-ninth of the whole;' the ncxt;thlrd of -the ,tlmc' the body will bedeOccted through-three 'parts more; : and the last third pfthe;tJme, ltiMU be" deflected through Ovb parts moie: one, three; and- five, IHng added tcgothcr,; will b equal to nlnb. These are. the. phllosoph&all.reatont wHy the - deflections and forces vary, directly at tho nquar'o of the yclocltle. V.; By a combination of these .two laws' wo .obi tain a law stlH tDoie gener!, applicable to any given length of tlio string, ana to any given vtloclty ,of. tho; whirling ball. , Tb a lawr may be expressed 'as'fpitows: Cf.? " ."f. endi, and intrtrulg at their lengtla. " '- - ExampIi-s A- string, one. foot long, having a velocity, of one, will exert a force, of tension, equal to ,bhb -pound. A string, four feet long, irltb ono'ponnd weight attached, and whirling with a velocity of tlx, will exert a centrifugal force equal to nine pounds. A weight of one pound, Attached to ft string ten feet long, and whirled tvlth velocity equal to, twenty, will generate a centrifugal force equal to forty pounds. A string, 400 feet long,, attached to tha same weight, and having a; revolving velocity equal to thirty will, stretch tho string' equal to two and a quarter joudiIs. To determine thc utruo?t tension that can be Imparted to A string of given strength. Wlithlherength ofitrixgt tittadiloanj invert lyatihe tquart qf. their length, then tht greatett ft-wring ft-wring vtlocitiei which they trill admit of, will vary at the invent tguate root of their lenitkt. Examples:. I. A weight, attached to a string of a certain given strength, ono foot long, anil revolving with a velocity represented by one, will support, ot its greatest possible tension, before breaking, a centrifugal force represented by one. 2. A string four times aslong will, according to tho assumed hypothesis, be sixteen times weaker (one slxtei-nth being tho Inverse square of its length); and the greatest reyalvii.g ye. loclty which Itcbri endure will bo half (half being the Inverse square root of Its length). The string, representing the control force, being be-ing sixteen timet weaker, tho centrifugal force, necessary to lalanc. It. must a)J be sixteen tiroes weaker: but the length four and velocity half will exactly generate a centrl fogal force equal to 1-10. I a. If the Btrlpg be 400 tinys as long, that of i tho first example, the assumed hypothesis : would make it JC0.C. 0 times weaker (1-1C0,. : OOOth.belng; the Inverse square of its length); niid thegreatest circular velocity, which it Is l.cttpablo of eridurlng, will be equnl to l-20th (1-201U being the invtro square root of Its length). In this case, the greatest possible tension which' the itrlng will endure is the iMCp.OOOfhpartortbstin. the first example: hut the length 400 and velocity l-20th will i exacliygeherafe this force of tension, i These simple- mechanical laws ore applicable . to the revolving wheels of machinery. If the trengthoftheiokes,orof"thepthermatcrlalsof wheels, and their diameters, bo known, the exact revolving velocities, which they are cap-able cap-able of enduring, can, by these laws, be calculated. calcu-lated. But,- tha moat iptercsttug exlilUtloii of these laws, will be teen in their application to the celestial .machinery of the. Universe If a one-pound ball'be attached to a string reaching from tho centre of the earth to Its equatorial surface, Its. length wbuld 8.9C2 81 miles, which would be equal to 20,928,037 feet. If this weight be A hlrled round the centre of tht earth, so at to complete one revolution In 83 minutes and22 seconds, it will generate a centrifugal force equal to one pound, 'yblrh bo- j ; ing exactly equal to Its weight, the ball would j f.-i . ,,.; .. ., ..ji W exact W UlMiced betwecB th lbf forces, and. would hate bo .tadeacy to fall, hut would continue to circulate around the wth aTlb at Its velocity continued tho ' Ibavo already ttattd tht,a ball of one pound . weight, attached to a strlmr baa foot jongt would geBerateaceritrlfogal fere fel tplu. felghtjlf it U made to rsvohe Obcs tound In 1.09362 eeconds. -f?w' if J."" rfWt 6 the scml-cKamcter Oftheearth. ovthotqusre root -of 20,023,637 feet (which i is equa to 4,674.230), it mnlrt-plied mnlrt-plied Into I 0M&2 . seconds, the product, wilt be equal to I002aecoftdt (which h eqaal to S3 talBtitet and 22 tecoad): thlt, thetefbw hi the preclto limp In' which ;a body vtoald tavolre arounA tha eartKclote tolls tnrfabo. 1 v7 .Now, the moon is about-$ srml diaatetm ft th erthd,tot, thesqiwre root of which it equal to 7,7r tkl multiplied Into i082 JrcondtwlU bo equal to 38746 seconds (equal to lOhpurt 46 mlnutct,45 secoadt, If gravit&Uoa were the tame at. all distaacet thla would ba the periodic lime of, the taboa; but her period I about- 27 daytf therefore, her velocity must be about tlin I.fiOlh nf Wl.nt It m'.M u theJuppoBitlon that gravitation, retained 4he , iame lutfnUyftt.all distances": but the ten. slots pf struct, when the dhtancc arolhe tamearaas tho. square oftbo velocttlet:4he ttluaro of 1.60 it equal to 1-8G00: hecee, tha cetitrifugaliorce fat tho'dltlancb "of the., mbon it only; .the :I-8(J00th part pr what it it .at the surfttco of. thb earth; Therefore, st tho centrl. trlfugnl ;,and Centripetal forcca in-ctrclet are mnuh RvitatlonimUtt' W 8600 times lest at the'dntauce of the . lunar;brh than: It k at the surface of tho earthr 1 " " ' "-j'-f v V-5 .-('Let the earth nod moor be. connected' by si Jttlng.whoto length may, be rcprcscnWd ; by 11 let. tha moon be.whlrled around thbeiirth wlth' a veloclly-,of ilimlfei in li ,secondt;.;audUi tho centrifugal force thus generated. bo" trpres ented .by 1 i, It It reqUlfed f o fihd what centrl-fiignlfprcp.Wouldbb.geberated.lf'-them weixi connected' with the Sub by a atrlng'ioo limes lpngr,,and -mode to whirl around hlin ItbavetocUy ,of 30 miles lillj teconikr -iBy.tho jawof tbo, dktance,1hc centrifugal force oa Moi tension of ttib string would be 4P0 times, weaker,' than' when -revolving around I fhpeanh; bUt,by'he law of the square or the : velocity tho teusfoaon the ttr'mk .would be 900 tlrars greater; by divldlng the latter number by tho former; the quotent will be 2i; hence the centrifugal forc,wh!ch tho rabon generates in revolving around the Sun in company with lt prlmaryi'l'. Z '(tlme8jgreatcr, than that gencratcd .by lher "revolution -mfound' thb earth.- ' .jAS'lPT- - ? -Therefore, If tha tensions of thb strings reprer echt the gravitation of the moon,. fit w to tho earth and then to the Sih.the. force of gravlr latloa to. the latter, though 400 - timet more distant;., .It': Z tlmcsgrcater lh"an'to tbi former: but gravllatlba Increases at the square of the distance dccrcaacs: lot 400. bo : squared trajUjUnUlaioJtKclfj-the f product twin b thoy were brought 4oaZrMi woon to 2t timet ICO.000 ara 1qWto8wrrrtfajttr rtprqicnU the wholo forcc of Ura.Sun nt com. pared wlth ihat of hbtartb, when both bodies are placed at equal distances froni ...the . inoon. .l"herefore,if " large", scales.wcre constructed; Standing upon" the moo"n; arid USOO.OOOearths .'were placed In one' scale, and .ther'Bun ln,the fether. thcy Vwbuld," lu their-pressure towards thq lunar'orb, balance each other. Theso.num? bert 'aroMiscd 'ui "convenient. for Jllnstratloo; but areabt sufficiently exact vfof astronomical pnrposcs.j,- , -4-. . -V The mechanical law which I hnvcixplalned constltuto ,h perfect balance In which to ac-. Ciirafely dotermlne the .comparative, weights 'of worlds. . 'fho; astronomer of the present day Is is imlllar with the process of weighing worlds" 'a thb, chemist v. It x la weighing tho Ingredients which "enUr.'.dhto; hit' com: pound;. ; ' v 'i; 4 - Is. I hive already continued my lecture to an unusual length, or I would polottpnt Home other lnterestlm? applications of these rohder-ful rohder-ful mechanical laws.' The exact mathematical adjustments of tho Various, forces of nature the consummate wisdom and skill exhibited In every department of the universe, accessible to finite minds the. omnipotent power and. grandcor.dlsplavcd In the construction of the magnificent machinery of creation proclaim the majesty, and glory of Htm who formed and governs the mighty fabric.