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Show IIAW OF ELANETAUY jxQTA.-xo jxQTA.-xo xnE iDiToii or . 4KB tisies. Sir- Permit mo .tq announce! to the wrltl, througlj your;valuabJo pnpor, an astronomlcar diSQQvery, mado by juo on tuo eleventh, day o November, j 184.. Firmly believing, from- my j earlv youth, that the diurnal motions oHhe planets yrcvb tho results of Home , ,, hidden law, I endeavored, rtt different i times, to discover tho same, so aq to determine the' periods, ofdtation by calculation instead jE observation, j After man; fruitless, researches in rc-) rc-) 8&4 to tho.'original causes' oE planet-) planet-) wyrojapnj .raffled by'.;tho, indica-, I uons of certam,hyp'theset6.6eek. for I axof rotaUon co.nnec'tcd vr,Uh.4he I masses and diamStera -of tho 'planois or, ia other, ords5witUtheir doflslticsY ThfiBo tnywtjgationsrosaltctl in 'the oevelopmehttilidfollbwrng beautiful, law ' ' ' '' ' ITuB'ctJjJEJiobTSf "inn densities OF niK4 WiXNEtS Mf Ah TI?E. SQUAllG soots Oi'iu&iij!nipDs'pir koAtion OrwliicWambupfs tQ the same tiling J "-The squares op the cube roots 0 .th densities ob -tub ;tt ahets aie as tubib, periods- 01? -rotation j But as the densities of 'globes aroJ proportional4o their masses'or quantity quanti-ty of niatter,'diVidc by thfefr yolumtis 1 or Kythe' cubes oTvtheir diajne't'ers, jt folbff8b( thisjawj'that tho totation of the planets,,)ionsideredrti3 spheres, proportional to" Ihejf .maisi'S q.nd ,di-ameters;" ,di-ameters;" J;Tho; Mi "therefore,, may bo H '?Prsodn.ierrai-o';tho masses and ataeters,:a9.folloVst , Int 8iPni;8,or. TiiEiR;niAMKKasjJinn s' TBpJEniODa OR HOTATIOK, Xo express, thislaw ingoneral alge-oraical alge-oraical lofmulai applicable to the -periods of theotation'-df all tho, primary planets- lot' M,; D, T,'v represent, re-pectively re-pectively the mass;.dianiel;cr;.nnd to-"tiTe to-"tiTe period of the-earthy ;mV let m, d,.p, jrcprcsent'iho.lriass, diametei', a;nd ! rotative period :ti any1 planqt? then wo will have dr iri ternia of tho densities 'nd periods, thuV , j , "' , J i. ,'- - " Or, jf tho earth1 "rotattvo period. amT density bo each, talten q..jinity of l,1 thctii ' . (Itr.) (Planet's density), -rota tivc, period. "! ;, . As tho rotative periodai dop'enupoa thff,rnsa,(5S.and didmotora Of .tho llan ,cts,' any fcrrortf entering, into theso eloJ nenfd byvtho, -;imperf ection; Ofiotserr vatibnj'wll'nccbssarily. affect thoalcur latcd periods'o;rotaUoa.1nl'a tionatdcigreeei. "fyjM'L -' Thoasses'm'nd vdiath'cte,rs'd the pia'nob;': ;aro' ;otlypptoatoldb1H . tniried iAstroriomcrs-diffcrtan "regard to-tho, amount oEHhio. elchi'erii'y'cU it". ,rs"'pIeasing''td'nbVUlia great 'number $ , ob"c'rA;ationsfcpnGne fliOi'crrorsiwithitt.V Tho'inasse8. andiaraeters; in tliqifolr-towirtg. tliqifolr-towirtg. tabid are,- jjerhaps, a npaj ;tho trutji,. as, tho imperfeciions tit past obr' Sei-vatioujrill allow: us to approimatoV; Mercury 'd,0G87f3M0 S4 OS'OO iVijnusH 6,00335 l7flb0 23 2l?f Jarth ' "JIWWO'O - 7923.S 3 500.00 Jiliiys b:1463't ' 100.26,24 7 2$, JUptter .. 371,75470 dOi'DSt H&l 12' Saturn! HMsSlOTOtfiO' ,108017 Uranus 20;62fiJ9 3450D 0 30 00 Ntptrie 2C767ll3J500 . ,9 35 32 v TJk periods of '"rotation, in the 4th ;C,olunin,OEytKifl4AU; jb'yfthe-atd qf,',fdrmu1a Tsing thcf; cIcmcntsiri"the.'iJn'dJE cplunras. hFScula'iio'PlJ are pecisely the sara'd'","as 'the observed1, pcnqdsVBb1 far as; the JatVcr-jtavc1 bebh ascertained.. ',iliodiaractcV oE' .Neptune js probably proba-bly .not ye t known: wi i thin-icyeraftlipu-sandu miles -Jdr ah error .of'dbseuvation' of ;thrt'.6r tenths pf.,a;sccohd of ort'orc, wouldj;;at - that, great distance, prpdu'cb an errbr of i over 4000 miles in tile calculated cal-culated diameter of the planet. I'ho saind statement is equally applicable to the determination of the mass.1 An crrdf of observation On tho dimensions of the orbit b Ncptunb's , satellite, 1 though it should be only a. small jor-r tiori of a second of nn arc, yet would produce; a great difference in tho calcu-rlated. calcu-rlated. ma$s I It will be seen by the formula which ' I lisivo given, that if tho rotation is ' known by observaUon, tho ratio of the raass and diajneter can bo calculated; and that i dny ttto of the elements arb known, tho third can bo detcruiinqd. . Whether tho law of planetary rotation rota-tion can, ho ..extended, to tho rotatiyo pcriods.pt the satellites, attending the ' four exterior plmiets o tho solar sys-J tcm, is not known It- is supposed' by somo, from observation that tho periods pe-riods of tho rotatiotf of tho atolhtos aw equal to their periods of revolution j around!theirprimaric: hut this needs conGrmationlby fnrther observation b greater perfections and. "accuracy tlian wjiat the present powers q tuff teles'-: copd seem capable of affording. From tho masses and diameters o, tho four satellites of Jupiter, as given , inllorschel's "Outlines o Astronomy' jl find, by tho application of tholaw of ' rotation tho following rclativo ot pro-iportional pro-iportional periods. (Assuming thq I period of the rotation p tho 1st satel-v 'lite, nearest tp the planot?, to bo equal to unity or 1) Juplltr't J'ropbriijftal PtrioJ of SiltU'ttet; RoMwnfat.eaUulaledi . 1st. " " "i;0OQQOOO00 ' '2nd. ": ' 780'47B4q3 "3rd. 1.635188852 4th. j I.37.55550S3 1 If it bo true, that tho rotative periods , of theso satellites aro equal to tuo po-triods po-triods o their revolutions, then tho law 'does not apparently nold good for this ' secondary systbm, unless, tho diameters - and i masses-are affected with cpnsider-Jablo cpnsider-Jablo errors; if .the" apparent ungulai . diamctbir of the 2nd. satollite bo re- duqed thoonc-twciitieth ot a, second of an arc, it. woul4 rctluco thq real diatne-: ter HO milqs, which, would gtva a calculated period ,o. rotation, nch aa should, cxist.in order to.correspbnd 1n-o' cisojy with tho ratio of. thq pbridds Of ireyolution in their orbits. In tlib cases of tho Urd or 4th.aatclHt(, tHbro would liavo to be a. reatcf , corrbction liii ; or- dr to make thtf rptatfVo . and orbitual "periods; of thq sime length..-! A.mistalio of asmalf fraction of, a. Second, of an arc, mlght'casily bo made in the' ap-pardfit ap-pardfit Aiigdlar' !didmqter8' -Likewise as the masses aro deduced .from b-.. 6citip63 ot thp ramiitp perturhaons' whicfi thtf fiatcljitca exercise upon'1 each other,' it :i$ evident ;thatft;minuto error M tnclt observations; would'giycftj muclilgrcater; 'error, -m''lib.;calcuiatbdl masses; Th'drcforoi iriasscs.,and diamb-ter diamb-ter might bo assumed iyitliin thq limitt 'o .unavoidable VertbrsVAvhicU 'buld 'giv6 calculated p'drfodsfrptatibn for tlio'fou? fltollitea,'6f the "same jength-as. jength-as. ilielrbtbltiial orToidst J i hqWtrpnpnicrcann aJltdjXier- ccivo that, thjVrpraal6loia! h ibWe. hat, anaVagduir to'tudrfdnb" .discpyerqd by Kepler, Icbniieptirig tlio'orKtriSl' Iperjo'ds of 'tlio FicaYcolybd4ter w'j.tli ; tlfeiH aistqnceafrbnT. their" lrcqntrc,.-df i;moion.i .When ICeper,s,iawv"was(, dt's-'! cpycrcdf tWwtancesQE-'tjbdplaiibts were.-;vbrywimperfcctlyiinowu;bn wlihstandiugtlid;' ojr.thcsje, dita'i -he clcariy "percerved the Relation between isthem'tmd tho eriotlio'eyqltf- ; tiori$-around the sum So .iikqwjseVin 'this; new discovery, no ono can f ail-W ;seo the relation existing betwettt tiuf density of, planets and. their diurnal jq: tatidiis, no'twiihstantliug tho f braietofe-1 niciit is so' imperfectly' ascortaihcdl With, the' most sincbro desire Tbf'tW dovclopcmcntrind diffusion of iisofdl. ikuowlotiCvJtjattbsm ntpstilmmblp-Bcrvant: ... t i.-, 42lslingtd,iiYerpoolAugust'2l .,"r,v" .J P.c8.,I(frrt, Jan. and),186Q, To.tiTe EoiTja oralis IoujTtBEiii, 3 'OciTi.tMKf-TIie above I copy, of 1. a -leUer written bym fo ibVs "Lbnoii Timeii''-1l yoit copetderfit wortby.ot an insertion 'inlyow paper, It Is atyour-difgoaal,'- ; , t ; Ojwom Vslktt, Sen. |