Show reo ree arto I 1 LI U baz S a J I 1 t bwy rf p gravitation auel and ceneri centri v 1 1 f u 5 al forces BY PRATT 7 sen before tho the or of tho the r j formal institute at the deseret university on wednesday kven even yui yuu lui nast lith 1875 1 jl I 1 tj M n eke it ro gwo IWO l WO ata manifestations faring facing bodies universal tendency bf worlds ta other three laws of dis I 1 covered 1 or va P U Q AT F 0 va A n t af 0 n f s alioto gravity cy of worlds to moe in straight lines instead of curved orbil orbits curvilinear orbits of liotis orbits possible biffl icycle 4 rc 6 ebell ellipse apse parabola and I 1 hyperbola percola hy under unda what circumstances dachis dachia each is produs 6 d L 9 of P projectile tactile forces 10 by Wl whirling weights V I revolving worlds TT laio jaio of distance and mid velocity greloch Tr cloch eloch maht of 4 I 1 lu 2 an of rut aut wisdom ay a ji povl P aw cr i u 1 gravitation is a force 0 exert X ert erl cd treon treen ff een eon particles ail all of matter in tl two or par at int ift lid aes ees ont ort r matter I 1 placed in n lit itt tit have havo ol 01 ti mutual edl V fow rownY ards erds ds eadle 1 jhc rs centers this preg pres ilo lia great teeny the quan matter is equal and luf iff op bb instance jn tance dge dae pound pou nd weight tiie the tile same bame e pres pren stir tiro upon tile tho surface of bf ill til the 0 earth aa as the earth exerts the gue que one pound bound weight andas and as the wo two forces pie pip su in directions opposite id td each other tile the two bodies must re bui lul f h i 1 faaiu arrest idono moio 1 tini duct janci hof matter exerted a arpa ter another in lri their theli pres ures urea then tho the bodies compounded of bf these dlf dif different feren t kinds would bohld with a accelerated motion in ithe tolfe direction of tho the greater pressure imaki ba represented by two balcam vessels ves sels sela oc ot equal weight in contact opposite directions if ther theT orca bf steam on mhd two boats is equale equate they will r remain i e 1 nt t rest if tho the force 0 of one there pro preponderate neerav s olef over tho the other there wl cju V ba tonly no only but a motion gre gro greater itter atton foych Is T 2 particles and n masses of or fait dilt mab mat ekr r not onie only exert emert the for foree force af pres prea nry urd when in contact but bat when epa rad they manifest a mutual 1 ar gravitation tot tosy yards trdy othen other by virttie of thi farce whenn cheri nobre nobie nol nob restrained they will towards lyach llach other with a ta a accelerated motion if a mass of mat otei oter elevated above tho the tha stir surface face of uha utho earh earth is at liberty to move id itt will cfall if all ali towards the surface w while lle lie ile the tho earth at the bame same amo time lime will hie nhe rie fo meet R it but the velocities of tho the c two moving c i bodies wili will be inversely proportion nai nal tb their masses that Is if the masses of the two moving bodies arol aroi equal their velocities to towards ards aeh aph ather will be e equal bif the 1116 abasi mass of une abne body boby is twice that of 11 Ah the othor nAhor 1 lwe ife velocity esthe wili will be 61 one 1 liala halfwit it ro mass mm is thred 0 tj anres wes mes li greater reafer its velocity will be one ono hird d if it its mass is I 1 one om hundred tl inie gc ator its velocity wll wil be and 1 n hundredth edth laatt pa tt of that of the smal leir etc u i the quat quai quantity ity aind arnd fion flon in a amov dg body bodi is 19 equal to ahovelo kat nat eity efty city multiplied into the tho m mass mals MS ghenco ih enco when two bodies budles ave move towards each other by virtue of weir their mutual gravitation their quantities of motion are always exactly equal t therefore when they meet they willmuth Will mutually Mutu ally nily destroy each others motions and remain at ret test d arthus rT aithus hus it will be perceived thau thai the force foree of gravitation is 19 exhibited in jil two ways namely by pressure and by mot motion loff both of these these of docta are used to measure the force whon when gravity is ig measured by p pres res guie gure suie the result is called weight v klina and is Te represented presented by the number s W V ounces pounds bons tons etc when it is measured by motion the result is determined by the space through vj body moves by gravitation etin dennin efin a given tine time newton nawton demon W st rated ba b careful experiments tini tint overy lind kind bl bf coatter near surf aco acoy pa p the earth faiia fails falla fra ftp talo nt tato 0 of resti reli through fui ful spaces pages ingual q u J times timis when resists resistance noo ace th the atmosphere and mid other rheid auces ances are removed S 3 the space phrot through igi oiye otye body fallstrom falls from a state of rest TOW or towards another in one seep g 0 time Is one of the astronomical measures of gravitation T tho space is usually liiv estimated 1 in indies af pf or feet the toe space through which ja a body falls fails frem fram reit rest in ln this tiei latitude is sixteen feet and one inch ar inches in one second 4 in adopting this measure of the force of gravity ther thera dare oare are three laws which should be e well antler uller stood and garer carefully ully obe observed nou rou 11 t FIRST firsa LA ewt v vie wie space through ond ons baily bod by idi virtue of bf its ils ave jud towards another in ono one second does upon the mass rass of vib yorm former ar out but is the i same aine whatever mav may ba 60 its il mass if the distances ard aye the same i thus tho the he sun bun gravitates towards jupiter au piter hild and the hartli gravitates towards jupiter also but bt though the mass of tho the sun is isM limes times times greater thair the ruas rias s of bf the earth I 1 yet the gravitation of the former towards jupiter is 19 exactly estial al to 0 the gra gravitation ra t boft of ot the latter iatter latt r towards wal wai ds clim him bim flim when wh n the sun and earth are equally distant from him aim in other the sein sun and earth whenn when at distances from mom jupiter Jb piter moyo mow through the tue ahle s same samo mb number of bf inches or ok parts of inches towards jupiter Su Piter in ona hib nib aft corid i of or time and such m ja was ways bo hd the thecae I 1 ehte far ver vermay may be the differences of bf the K masses of any number of moving t boi bot bodies iles lles to wards another body I 1 8 SECOND cond law bac spage space kvaca bodies by their J gravit aiton moue move cowards abita t r j pi n p ane ang second na bodt to tha massif dv fm latter between the former fOrpe rana rand I 1 win the same thus thug if im uhe nikia ti which a body gravitated is doubled ac chenu aber which rul rui pass over oter in one ona pw iii doubled dou doa bled bied sc suppose that chesun and are at crual distances C S from fram satini as the sun san con cou contains thins lois lols 1018 1013 marc more matter than then them whatever vermay may be ze the number e if through whish saturn may gravitate gnavi tate byards buds ards a jupiter in xia meo moo or time it w wall 1 in theace time 1013 ulca numbe cumbe ot inches i tamb lawa af sentral hodies borms eat pat tessar differ ii mt ent distant distances s gravitate graci towards mi body the spaces grazes passed ger mer by the rier ow oho second of time will be eilt eill p n I 1 ol IQ the square of their mir distances faiai M uie vie tj it fatter latter A 1 thus if it the distance Alstan cent of i the of the earth froin froni its cen centre trebe trebo be called band land 1 and the space passed over by py a falling dody body near the surface is 10 16 feenin a saco second dudot of tinli time c then at let twice du such buch elf cil distance arora abd tbd of the earth a body would fall one fourth of 16 infect feet in second at three times limes anali such distance n body would fall one ninth of IG f feet abt at four mica timea the ditta distance hice fice onh sixteenth of or ar one foot at atsitty sixty times the distance or sixty radii of the earth which is a ditl lucora than the moons distance a body would laii jall inanc ong ond second the oue one thirty dreth 10 feet or about one awed aleth pait part of an inch the sun being in bun nan round a numbers nearly too 00 times diore more distant irom from the carth earth than the falls towards the the tho earth the one hundred kundred and band sixty thousandth part of the tho bno bweni bieth of an inch which is equal to to the thirty two hundred thousandth part pt of t an inch la in one second of time tame IV while lenca neptune tune being thirty times more inore distant from the narth earth rth than thin the sun san falls towards ardi arai the earth in im alic one second DW goo times less lesi than that of tho the sun SUB or the tho two thousand eight dight hundred and eighty millionth part of an inch 0 pi this audience phy inquire how hov this law of gravity is to be true how liow Is 9 it known that thit tha the force called decreases dOeA aa tho square of the distance increases who has ascended the ahe adi heights aghta of heaven hearen to experiment apon upon this force who at the vast a t distances of ot the moon sun and und planets has observed any phenomena ex aitt jy determine the fractions of bf an inch through which bodies would fall fail towards s the earth in one second of time the answer is that all mankind of ertry ase hayd hard hate have beh beheld id the tha phenomena which incle include e the data ecca necea mecca saty sary for por or the tho solution of this grand problem iem leu all haye have beheld behold the moon clr eln circling clink itself around the earthal ear that at the distance ja round nai nui numbers abers of bf about miles or at ht the distance 6 from the earths centre centie of GO semi bemi diameters ol 01 the tha earth AH all might hate have known thata body a straight line when ohice onee once put in motion unless deflected from that straight line by some force all might have known that thit the orbit or path af the moon was curved towards the earth being deflected every moment from a straight line called its tangent tang cati into lato i a curved jin lin all ali might have known by a sirarpe the exact amount of this 1 d I laa kat wl from the tangent to the curve in 0 oli oni second of time yet strange as it lumaya may this simple phenomenon though observed foi for thor thou a a of years was not nov comprehended till the immortal newton some two awo ago solved the simple problem simple problem because it is now dow so ho easily solved tat in the days bt bf newton ndwton it wis ws considered discovery ass 19 to the tho toland 91 p 1 man M n a n hils hiis us iyo F foree force rca rea which makes tn ices iced haton hnton cfall IM inches lii iii ene one ne see sec bud causes the moba moon to fall timed times less athi e same time if gravitation did not yra tra vary tary in its intensity with she tho distance nce n ce then moan would fall with the same velocity t Y aa i a fatone near tbt earths gun bur surface N nce ace at if ae he velocities Oc decrease reise merely I 1 95 is the dist distance a nap then the tho moon being CO 60 semi bemi deaul rd op 0 f the tho earth distant would gould fall fail CO 60 times S a 1 oy Z ot but its falling velocity Is isk known to td belo beio times CO 60 or times blo bio slower if e r is before stated state donly only about the one gre twentieth bf aninch cli olg lna ina in A second dhe zhe the m mean ofin aemi diameter of tho the earth Is about ut miles jahe he mean distance of the san accordine accordia accor dins toted to the llew taine Is alles th dis tance divided by the former gives a quo tient of thatis e Is wei wel equal to bemi semi diameters of otlee the earth tarth thil thi squar bauar Ei LUara luard tidor or multiplied itself elf eif Is equal to if it the san ban cont contained alq c d only tm the same bame andouin of or matter as is the earth then the iatter latter would be deflected from irom the tangent of ils its orbit into a curve towards he the un ath a velb velocity city eity times less par per second than thit that of a falling filling body bodi ncr the carthy earthy K surface but observation proves that the narth falls towards the sun shri with avith a velocity several beveral hundred thousand timed greater than it would on the tse abord above supposition its iti deviation from the tangent of Us its orbit tewfig being about the one eighth of an sec see tards id id or more accurately jalis jails towards the suha about 1697 1607 times slower glower than x astone wee falls near the sni sui face of I 1 the 4 q earth now if bo divided by GW the quotient will be bb about GO that egv 0 s the san contains conta Ws times more matter than tho earth and thus the barth earth falls towards tho sa jl times faster than thin it would woud if the mass masa of the sun san were only equal to that of the eirts lacing abbat ulmes times B the als tance e othe of learh nom rom the sun suni falls falli towards W the tho tatter latter with a velocity about timid id ICES than he of the ca rth that luminary A planet abet telco jhb distance of the arth arial fridh the toe sun will fall lall towards him hila four jess ai stanco at tareo times the distance tits falling irel oci ocl i tydvill ty wiil wili be bd nine rimo timea times les less s asfour at jour times tha distance c sixteen timen times d less at ten time times ono hundred gilbs less ac ci ac c centrifugal oth oth As behave amli Led the aw an a proper measure of its forme force for any given quantity matt matter matten bri and ana for any given distance next let lot ns us inquire into in to the nature of thoad op by which ho be planets and satellites atel lites are ape falling to common centre 7 every eveny y in mathematician 1 athe maU clan olan A is wall W 11 acquainted mitlon quain ted bilth the idlof law of anc gic the c composition ot p of forces and ana motions if abbody Is acted upon a by b y two forces it will generally rally nally I 1 areu S resultant I 1 ta nt motion intermediate in durec or bethon between tho the directions woud would haval resulted from the action of cither forcer singly instance if a ball bail be bc projected on plane piane jc ice its I 1 path would be bb line brot trot 11 lithe inthe the same came lali lall hll bi be bloed by E strong wind at hight right angles tb its projection or path athi it would 0 uld deviate irom ii straight inq line i iu to ton n r I 1 lri f atho ha ball be attached at to od dard cord loo 1001 feet long annd and the other extremity i be fas fastened f cr ed to a pivot loo feet mom nom rom the straight ilde which the ball Is describing bj of its projection the ball will immediately deviate from such straight li line fidor or ils its its formen former path arid will db describe scribe centre of motion in this tha case there are two urd forces which produce the circular motion one is ulu ih Q projectile or propelling force th the bothen bothEr other Is the c central br or pulling forceps force foree of the siring the fint tint flet I 1 imparts m ar ts the impulse br or progression daggres and t then en ceases to act thee the second acts continually and uniformly from a central point as steam or gravitation the space through which tho the body would travel ins in ina a straight line in ift bone tone se second corid is A proper measure of the projectile force the perpendicular di distance standa from the ahe end iud ot of such ench straight line reaching the curvey at pe the end iid ild of bf one oue second la Is the irue measure of bf the fall towards the centre sali sail thola thUla hels held and satellites of bf our system are under the mhd of a projectile force or a forme force which originally gave them motion ceased eased to acu ack lct act the game same as powder ceases to act upon a bally ball bail after the tho moment ent of explosion U without a |