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(^.ZUftfJ^m^J^l^u^^ n.au/raaie rum y/vWif
Bene ^erenutl, Hominnza enim Teftig>ia -video.
FIRST VOLUME
OF THt
INSTRUCTIONS
».
GIVEN IN THE
DRAWING SCHOOL
sstablishe:d by the
DUBLIN-S.OCIETr,
Puritiant to their Resolution of the Fourth of February, 1768;
To enable Youth to become Proficients in the different Branches of that Art, and to purfue with Succefs, geogra- phical, NAUTICAL, mechanical, COMMERCIAL, and
MILITARY Studies.
Under the Direfition of JOSEPH PENN, heretofore Profeflbr of Philosophy in the Unrverfity of Nauts.
^id munut Reipuhlie0 majut aut meliut afftrre poffumut, juamft Jw ventutm b*ne BrUJUamut f Cicero.
DUBLIN: Printed by Alex. M'Culloh, in Henry-ftreet, M,DCC>LXIX.
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AUSPICIIS FREDER/CI HARVETf Episcopi Derrensis Supreme Curiae, &c. Promovemte Societate Dublikensk FAVEN TIBUS JO SEP HO HENRr, ROGER PALMER et GULIELMO DEANE,
ArMIG^RIS* OMNIGENiE ErUDI'TIONIS MJECENATIBUS.
Jojipbus Fenn olim in Academia Nanatenfi Philofophiae Profeflfory purs et mixts Matnefeos Elementa digeiEt et publicavit^ in ufum Scholae ad propagandas Ar- tes in Hibernia fundatc.
Anno Chrifti M,DCC,LXVIII, die iv Menfis Februarii.
A. Rt. Hon. Earl of Antrim Rt. Hon. Lord Annaiy Rt. Hon. Earl of Ancram Hon. Francis Annifley Clement Archer, M D. Merryn Arcbdall, Efq ; Benedid Arthnre, Efq; Mr. John Atkinion MTilliamAnfHcU.Efq; Mr. Hillary Andoe Mr. }ohn Auftin Mr. Thomas Atidm.
Rt. Hon. Earlof Bcdive Rt. Hon. Earl of BeUamont Rt. Hon. William Brownlow Sir Lucius O'Brien, Bart. Sir Charles Bingham^ Bart. Rev. Dr. Benfon Rev. Dean Bourke Conftantine Barbor, M. D. David M'Bride, M. D. John Bourke, Efq; Bcllingham Boyle, Efq ; Walter Butler, Efq;
Dominick Bourke, Efq ; John Blenherhaflet, Efq; Thomas Burroughs, Efq ; David Burleigh^ Efq ; John Bonham, Efq; Francis Booker, Efq ; Robert Birch, Efq : Matthew Bailie, Efq ; John Blackwood. Efq ; Rev. Mr. John Ball Mr. Richard Bartlet Mr. John Boulder Rev. John Bowdcn^ D. D.
I'
r
f>i^
hi
SUBSCRIBERS
Wiliiam Bury, Efq^ Mr. Patrick Cullen
Rupert Baibor, h!4 ; Mr.Maurice Coliiii
Hon. Georgt Barncwall, Efq; Mr. Samuel Collins
Mn Thomas Broughali Mr, John Gafper battier Mr. JoJm Bloomfield Md Edward Beaty Mii William Becby M4 Henry Blenerhaflet Mil H.Bradley Mr^ Thomas Brow n Mr. George Begg Mr« Jofeph Barecroft Mr; Richard Bolton Mr. Richard Blood Mr, Lawrence Brync Mr. Chriftopher Brigg?.
Rt. H. Lord Vif. Clanwilliam
Mr. Richard Cranfield Mr. Richard Cowan Mr. George Carncrofi Mr. }ohn CarroO Daniel Cooke, M. D. Mr. liaac Ctmon Mr. WiUiam Cox Mr. Richard Connel Mr. Hugh Chambers.
D. Rt. Rev. Lord fip. of Down Rev. Dr. Darby Nehemiah Donnellan^ Efq ; William Dunn^ Efq; Arthur Dawfon, Efq : Henry Dillon^ Efq;
Rt Rev. Lord Bp. of Clonfert Edward Denny, Efq ; Sir James CaldweU, Bart. William Deveniih, Efq;
#Sir Paul Crofbic William Doyle, Efq;
fion. Francis Caulfeild Edward Donovan, Efq;
John Cro(bie Dennis Daly, Efq ;
Lomas Quffc, Efq; Henry Doyle, Efq;
Rev. Maurice Crolbie, D. D. Henry Dunkin, Efq ; Rev. Henry Candler, L.L. D. George Da wfon, Efq;
Rev. Dean Coote Matthew Carter, M. D. George Cleghorn, M. D* Jojbn Curry, M. D.. Rev John Conner, P. T. C. D. Rev Angnftus Calvert A. M. Arthur Craven, Efq; *
Capt. St. Claire John Cook, Efq; John Carden, Efq ; Andrew Caldwell, Efq-; Robeg Clements, Efq ; Stratford Canning, Efq ; Andrew Crawford, Efq James piulfeild, Efq ; Lawrence Crofbie, Efq ; Hugh Carmichael, Efq ; John Coningham, Efq ; John Conway Colthurft, Efq ; Henry Cope, Efq; Edmond Coftclo, Efq ; Thomas Caulfeild, Efq; Mi. Edward Cnllcn, T.C. D.
Robert Day, A. M. Dennis Doran; Efq> James Duncan, £fq ; Mr. Purdon Drew Alea^der M 'DonncI, Efq ; Mr. Jofeph Dioderici Mr. Henry Darjey Mr. Robert Deey Mr. SiiTon Darling Mr. John Dawfbn Mr. Hugh r&niel Mr. George Darley.
£. John JEnfor, Efq ; JohnEnery, Efq; John Edwards, T. C. D. John Evans, Efq; J. Echlin, Efq ;
F.
NAMES.
Thomas Fitzgrrald, E(q$ Robert Fit^j^cfa*d, Efq; Thomas Fic/.gibbon, Efq; Thomas Fofter, Efq j Thomas Franks, El'q ; Auguftine Fitzgjiald, E(q; . George Faulkner, Eiq; , Capuin Feild John Ferral^ M. D. Rev. Mr. Fetberfton Rev. Dr. Thomas Fofior Mr. William Feild Richard French, Efq; Thomas Forfeith, Efq.
G. Sir Duke Gif&rd, Bart. Luke Gardiner, Efq ; Sackviile Gardiner, £(q; Benjamin Geal Efq ; ' Thomas ^Soodlet, Efq; WUUamGun, £{q; Thomas St. Gwige, Efq ; William Grogan, Efq; Henry Gore, Efq ; Thomas Gledftane, EXq; Rev. Mr. Gtattan Rev. Mr. John Graves, A. B. Mr.Ponf.Gouldft>ury, T.CD. Mr. Luke George, A. B. Mr. Anthony Grayfon Mr. Charles Giilefpie Mr. Thomas M'Guite Mr. John Grant Mr. Daniel M'Gufty.
H. Rt. H. John Hely Hutchinfon Hon. Mr. Juftice Henn Rev. Dean Harman Claude Hamilton, Efq; Peter Hohnes, Efq; KaneO'Hara, Efq; Edward Herbert Efq ; WiUiam Hamilton, Efq; Charles O'Hara, Efq; John Hobfbn, Efq ; John Hatch, Efq ;
"1
Rt. H.Sir WiUiam Fownes, Bt. Mr. Guftavus HamUtoo Henry Flood, Efq;. Henry Hamilton, E^;
John Fitzgibbon, Efq ; Thomas Hartley, Efq ;
John Fofier, Efq; Francis HamUton, Efq;
F" ■""
SUBS
Sackville HamilCoii, Efq;
Gorges Edmund Howftfd, E<q ;
Rev. Mr. Richard Hopkins
Mr. Willtani Holt, A. M.
Mr. TKonas Hoieit T. C. D.
James Edward Hamilton, Efq ;
Mafter Chaifet Hamilton
Mr. William Hickey
Sanael Hayes, Efq ;
Mr. Robert Hunter
Mr. William Huthchinfon
Mr. F. Heoey
Mr. Thomas Harding
MeC }of. and Ben. Houghton
Mr. John Hardy
Mr. James Homidge
Mr. David Hay
David Hartley, Efq;
Mr. Kobert Hunter.
I. 9t« John Jeflfi!ryes. Biq ; Rev. Mr. Daniel Jkduou ficnjamin Johnibn, Bfq ; Charles Inncsj £i^ ; Bdr* RobcSft Jaffiay
K. Rt. Hon. Earl of KingAon Maurice Keating, Efq; Redmond Kane, E(q : Thomas Kelly, Efq; I>ennis Krlly, Efq ; Anthpny King Efq ; Jofeph Keen, Efq; Rev. Mr. Andrew King Rev. Mr. Kerr Mr. Gilbert Ki)bee
L. Rt. Hon. Lord Lifford, Lord
High Chancellor Rt. Hon. Earl of Lanefborough Rt. Rev. Lord Bp. of Limerick Rev. Dean Letablere Edward Lucas, Efq ; Walter Laurence, Efq ; Richard Levinge Efq ; IXivid Latouche, Efq ; John Latouche, Eiq; Guftavus Lambart, Efq ; Robert LongficU, Efq,
CRIBERST NA
William Ludlow, Efq; Thomas Lee, Efq; John Lee, £iq ; Charles Levinge, Efq; Charles Powei Leflie, Ffq ; Henry L' Eftrange, Efq ; Hugh Lyons, Elq ; Thomas Litton, Efq ; William Lane, Efq ; David Diggi Latouche« A. M. John Lamy, A. B. Mr. Charles Lbam,
M. Right Hon. Earl of Miltown Rt. H. Lord Vif. Mountgarrtt Rt. H. Lord Vif. Mount-Caihel Rt. Rev. Lord Bp. of Mcath Rt. H. Sir Thomas Maud, Bt. Sir Capel MoUyaeaux, Bart. Hon. Barry Maxwell Colonal Maiba Dr. George Maconchy Paul Meredith, Efq : JuftinMacCarthy, Efq; Thomas Maunfell, Efq ; Ftancis Matthew, Efq; Alexander Montgomery, fifq; Arthur Maguire, Efq; Charles Mofs, Efq; John Monk Mafon, Efq; . Arthur Mahon, Efq ; George Monro, A. B. Rev. Edward Moore Rev. R. Murray, S. F. T. C. D Mr. Thomas Moife William Mofle, T. C. D. Mr. Chriftopher Moyers Mr. Thomas Morris Mt, Hugh Murphy Mr. Robert Moifct, A. B. Mr. Thomas Mulock A. M. Mr. Dominick Mahon Mr. John Moran Mr. John Maddock Mr. George Maguire . Mr. Richard Mellin Mr. George Maquay.
N. Sir Edward Newenham
MES.
Edward Noy, Efq ; Braughill Ncwburgh, Efq ; Mr. Walter Nngent.
O. George Ogle,Efq; Cook Otway, Efq ; AbleOnge, Efq;
P. Rt Hon. Lord Vif. Powcrfcourt Sir William Parfons, Bart. Rev. Dr. Kene Pciceval Roger Palmer, Efq ; Chriflopher Palkce, Efq f John Prefloo. Efq ; Park Pepper Efq ; Robert Phibbs Efq; William Pleafants, A. B. Mr. William Penrofe Mr. James Paynofe John Prendergaft, £(q ; Edward Pfgot Efq; Mr. Jofcph Parker Mr. Richard Pike.
a
Henry Quin, M. D.
R. Hon. Mr. Juftice R<A)infon Colonel Rofs Rev. Dean Ryder John Rochfort, Efq ; George Rochfort, Efq ; Andrew Ram« Efq ; Richard Reddy, Efq ; Thomas Rynd, Efq : Mr. James Rynd, T. C. D. Mr. William Rynd, T. C. D. Mr. James Reed, T. C. D. James Rainsford, Efq; Richard Robbins, Efq ; Mr. Chriftophcr Rielly Mf . Thomas Robinfon, T.C.D. Mr. John Read Mr. Henry Roche Mr. John Reilly Mr. William Reilly Mr. Jofeph Rooke.
S. Rt. Hon. LK>rd Southwell Rt. Hon. Lord Stopford
SUB
Hon. Mr. Jufticc Smith ^iT George Savillc, Bart. Sir Annclly Stewart, Bart. Hon. Rob. Hen. Southwell Hon. Hugh Skeflington Bowen Southwell, Efq ; John Smyth, Efq; Chirle3 Smyth, Elq ; Ralph Smyth, Efq; William Smyth, Efq ; William Smyth, Efq ; Thomas Smyth, Efq; Jofeph Story, Efq ; . William Swift, Efq ; John Stewart, Efq; Henry Stewart, Efq ; Charles Stewart, Efq ; Mark Sinnet, Efq ; Ge. Lewis Shewbridgc^ A. Mr. Edward Strcttell Mr. John Sheppey Mr. Patrick Sherry Mr. Thomas Sherwood Mr. Frederick Stock Mr. William Sweetman Mr. Thomi^ i^mifke Mf. John Sewitd
SCRIBERS NA Mr. William Sliannon Mr. Samuel Simpfon Mr. Edward Scriven Mr. William Sweetman Mr. John Seat on.
T.
R. Hon. Philip Tifdal
William Tighe, Efq ;
Richard To wnihend, E(q;
William Talbot, Efq ;
John Tunnadine, Efq ;
Wentworth Thewlefs, Efq;
Charles Tottenham, Efq;
Robert Thorp, Efq ;
Riley Towers, Efq ;
Ed. Badham Thorhhill, Efq ;
Eyre Trench, Efq; . Richard Talbot, Efq ; ^' Charles Tarrant, Efq ;
Mr. Theophilus Thomfon
Mr. Arthur Thomas.
Agmondifham VcCcy, Efq ; Rev. Dr. Vance John ViLars^ M. D^
M E S..
John Ufher. E(q;
Mr. Henry Upton.
W. Rt. Hon. Earl of Weftmeath Rt. Hon. Earl of Wandesfbrd Sir Richard Wolfely, Bart. Rev. Tho. Wilfun, S.F. T.C.D. Bernard Ward, Efq; Charles WiUiam WaU, Efq; Edivard Wilmot. Efq; Hans Wood, Efq ; Ralph Ward, Efq ; Robert Waller, Efq; Mark Whyte, Efq ; John Wetherall, Efq; Meredith Workman, Efq; John Whitingham, Efq ; Stephen Wybrants, Efq ; Rev. Mr. John Wync Rev. John Waller, F. T. C. D. Jofeph Walker, Efq ; Mr. John Wilfon Mr. Samuel Whytc Charles WaU Efq ; Mr. William Williamibn.
Z. Mr. Mark Zouch;
PLAN of the Instructions given in the Drawing-School eflablijbed by the DUBLIN SOCIETT^ to enable Youth to become Proficients in the different Branches of that Art, and to purfue nuith Succefs geographical, nautical, mechanical, commercial or military In^ qutries^
VOiftvete y /' Ignorance font les deux Sources empoijonnees ditourier Dei- fordres, y les plus grands Fleaux de la Socieie.
THE EdacatioiT of Youth is conddered in all Countries as the Ob- je3 which intereds mod imn^ediately the Happinefs of Families, as well as that of the State. To t^his ]End, the, ablei^ Hanc)^ 4re errlptb)!- ed in forming Plans, of Inftrui&ion,^ > ^the belt calc;u)ated. ^r the .various Pirofeflions of Life> atid Societies are formed> coo[ipoied of Men'diftinr giiUhed, as well by their Birth and Rank, as by their Experience and Knowledge, under whofe InfpeAion> and by whofe Care they are carried into Execution, by Perfons of acknowledged Abilities iji their different Departments: And thus the Education of Youth is conduced, from their earKeft Years, in a Manner the beft fuited to engage their Minds in the Love of ufeftil Knowledge, t<s^ improvo their Underftandings, to form their Tafte and ripen, their Judgments, to fix in them an Habit of Thinking with Steadinefs and Attention^ to promote their Addrefs and Penetration, and to raife their Ambition to excel in their refpedive Provinces.
However neceffary fuch Regulations may appear to every reafpnable Perfon, however wifhed for by every Parent who feels the Lofs of a pro* per Education in his own Pra3ice ; never thelefs they -had not been even thought of ID this Country^ where that Extent of Knowledge^ requifite
Wife Regu* laciont rtlar tive to the Education of Youth, in England, Scotland, and other Parts of Eu^ rope.
Fatal Conic auencci re- niltina from the Ncgle€l ofthisOhica
IV COURSEOF
to prepare Youth to appear with Dignity in the virioas Enoployments of Life» or to enable them to bring to Perfe^on the different Arfsfbr whtefi they are defigned^ being not attended to ; Education was regarded as a puerile Objed, and of Courfe abandoned to illiterate Perfon^y who from their illiberal and mechanic Methods of teaching gave Youth little or no Information.
To remove fo general and well grounded a Complaint, it wa&propofed
that the Youth of this Kingdom fliouki receive in the Dcawiiig^Scbool
eftabliihed by the DuBLiN-SociETTy the Inftrudions neceOkry to ena-
ble them to become Proficients in the different Branches of that Art, and
^^[^"^ to purfue with Succefs, geographical, nautical, mechanical, commercial
School eftal or military Enquiries : in this View, an Abftrad of the following Plans
a^^in" were delivered to their Secretaries and Treafurer in the Month of Ofto-
IjpHon of ber, 1 764, to be laid before the Society ; and to prevent an Undertaking of
Xe Dublin- National Utility^ to be defeated through the Suggeftions of .Defign or Ig-
oTifmmr "^^rance, the Plans were printed ; which being received by the Public
FoMmcjuM with general Approbation, the DuBLTN-Soci£TY,purfuant to the Report
TupplMdthii of their Committee appointed to examine into the Merit of the Plans,
^^•^' and the Charader of the Propofer, refolved, the 4th of February, 1 768,
that they fliould be carried into Execution by the Author, under their
immediate Infpedion.
Tbe PLANS an as follow.
I.
PLAN of a Courfe of pure Mathematicks, abfolutely neq^flary for the right underftanding any Branches of pradical Mathematicks in their Application to geographical, nautical^ mechanical, commerciaU and military Enquiries.
!!• PL AN of the phyfical and moral Syftem of the Worlds including the Inftrudions relative to young Noblemen aud Gentlemen of For- \ tune.
ni.
PLAN of the military Art, including the Jnftrudions relative to Engineers, Gentlemen of the Artillery, and, in general^ to all Land<- Officers.
IV. P l^ A N of the merchantile Arts, or the Inftru Aions relative to thofe who are intended for Trade.
PLAN
MATBEMATCKS. V
V.
PLAN of the naval Art| including the InftruAions relative to Ship-Suiders, Sea-Oflicers, and to all rhore concerned in the Bufinefa of the Sea.
VI.
P L A N of a School of Mechanic Arts, where all Artifts» fuch ai Architedst Painters* Sculptors, Engravers, Clock-maken, bfc. receive ThcYomk the Inftmdions in Geometry, PcrfpeSive, Staticks, Dynamicks, Phy- of this King ficks, f^c. which fuit their reipefiive Profeflions, and may contribute to ^TtT ofThe improve their Tafte and their Talents. moftimpor-
Thofc Flaws have convinced the Noblemen and Gentlemen of For- **J?}'Ji"?i tune of this Kingdom, that their Children, and in general, the Youth l^^} \ '' of this OmntTy, were deftitute of the moft important Means of In* ftrudton, and would ever be deftitute of them, until they had refolved that Men of Grenios and Education fliould be encouraged to appear as Teachers.
PLAN »fa'C^ur/e of pupe MafbematickSf abfoliitely neceffary for the right undirftunding any Bp^fucbes of pruHhal Matbematicks in tbeir Ap- plication to gt^grapbicaly nautnal, mecbanical, commercial, and military Inquiries.
FiX futcfuamin univerfa Matbefi itaiificile aUt arduum occurrere poffe, quo non in^enjo fete per banc Methodum penetrare liceat.
1.
PURE Mathematicks comprehend Arithmetick, and Geometry. Pradical Mathematicks, their Application to particular Objtds, as the Laws of Equilibrium, and Motion of folid and fluid Bodies, the Motion of the heaveqly Bodies, (jfc. they extend to all Branches of MaiS^- ktuiMm Knowledge, and ftren$;thenihg our inteltedual Powers, by form- ticks tng in the Mind an Habit of Thinking clofely, and Reafoning accurate- ly, ferve to bring to Perfeaioti, with an entire Certitude, all Arts which Man can acquire by his Reafon alone. It is therefore of the higheft. Importance, that the Youth * of this Country (hould be me- thodically hrou^t acquainted with a Courfe of pure Mathematicks, to -^ ferve as an Introdudion to fuch Branches of Knowledge as are requifite to qualify them for their future Stations in Life. The Noblemen and Gentlemen of Fortune, therefore, have iinanimoufly refolved, that fuch a Courfe (hould be given on the rlioft approved Plan, in the Drawiko School eftablifhed under their Infpedion, by a Perfon, who, on ac- count of the Readinefs and Knowledge he has acquired in thefe Matters, during the many Years that he has made them his principal Occupation^ is qualified for making the Entry to thofe abftrufe Sciences, acceflabte to the meaneft Capacity.
* The proper Ace to conmcace thii Coivfe is 14*
-^
yi . COURSEOP
II.
Method of As to ihe Method of teaching Mathcmaticks, the fynthctic Method thcmitiM^** being neceflary to dircover the principal Properties of geometrical Figures, which cannot be rightly deduced but from their Formation, and iuiting Beginners, who, little accuflomed to what demands a ferious Attention, fland in Need of having their Imagination helped by fenfible Objeds, fuch as Figures, and by a certain Detail in the Demonflralions, is fol* lowed in the Elements (a). But as this Method, when applied to any other Refearch, attains its Point, but after many Windings and per- plexing Circuits, viz, by multiplying Figures, by defcribing a vaft many Lines and Arches, whofe Pofition and Angles are carefully to be ob- ' TW <5 h ^^^^^^* ^"^ ^y drawing from thefe Operations a great Number of in* 't^k Method cidental Propofitions which are fo many Acceffaries to the Subjed ; and fliouU not very few having Courage enough, or even are capable of fo earned an Se^^hi^'he Application as is neceflary to follow the Thread of fuch complicated fimplc EJe Demondrations : afterwards a Method more eafy and le(s fatiguing to raenci. the Attention is purfued. This Method is the analitic Art, the inge-
nious Artifice of reducing Problems to the moft fimpie and eafieft Calculations that the QueAion propofed can admit of; it is the uni- verfal Key of Mathematicks, and has opened the Door to a great .Num- ber of Perfons, to whom it would be ever fliut, without its Help ; by its Means, Art fupplies <jreniu8, and Genius, aided by Art fo ufefuU has had Succefles that it would never have obtained by its own Force alone ; it is by it that the Theory of curve Lines have been unfold- ed, and have been diftributed in .different Orders, Clafles, Genders, and Species, which as in an Arfenal, where Arms are properly arrang- ed, puts us in a State of chufmg readily thofe which ferve in the Re- The Anali- ^o^u^^^'n ^^ ^ Problem propofed, either in Mathematicks, Afironomy* tick Method Opticks, ijc. It j» it which has conduced the great Sir I/aac Newtam ••^'^of to the ^wonderful Difcoveries he has made, and enabled the Men of ticarpifcwe Genius, who have come after him, to improve them. The Method of ries. Fluxions, both dirtGt and inverfe, is only an Extention of it, the firfi be*
(t) It is for ihe(e Reafont that in all the puKGc matJiematical Schools eftabliihed ia Ei^gf^ad, Scodaod, &c. the Mafters commeocc their Courfes by the ElemenU of Geometry ; we /hall only inftancc that of Edinbnrgh, ^here a bandred young Gentlemen attend from the 6rft of Kovember to the firft of AugnA? u>«l are divided into 6ve dalTes, in each of which the Mafter employs a full Hour every Day. ^n ^^ ^^^ o^ lowed Claft, he teaches the firft fix Books of Euclid's Elements, plain Trigonometry, pra^cal Geometry, the ElemenU of Fortification, and an IntroduAion to Algebn. The fecond Cbfi ftudies Algebra, the i itfa and itth Books of Euclid, fpherical Trigonometry, conic SeAions, and the general Principles of Aftronomy. The third Cials goes on m Aftronomy and PerfpeAive, read a Pirt of Sir Ifaac Newron's Principia, and have a Courfe of Kxperimcnts for illuftrating them, performed and explained to theiA : the Mafter afterwards reads and demonftrates the £leme«:s of Fluxions. Tho.e in the fburth Clah read a Syftem of Fluxions, the DoArme of Chances, and the reft of Newton's Principia, .with the Improvements they hate received fnm the united Efibrti of the ftrft MaUiematicians of Europe.
MATHEMATICKS. VJI
ing ihe Aft ef finding Magnitudes infinitely fmall, which are the Elc-* ments of finite Magnitudes;^ the feccnd the Art of finding again, bv the Means of Magnitudes infinitely fmally the finite Quantities to whicfi they belong ; the firll as it were refolves a Q^antityi the lad reilores it to its firft State ; but what one refolves, the other does not always reindatey and it is only by anaiitic Artifices that it has been brought to any Degree of Pcrfedion, and perhaps, in Time, will be rendertd univerfal, and at the fame Time more umple. What cannot we ex- ped, in this RefpeS, from the united and conftant Application of the firft Mathematicians in Europe^ who, not content to make ufe of this fublime Art, in ail their Difcoveries, have perfeded the Art itftlf, and continue r9 to do.
This Method has alfo the Advantage of Clearnefs and Evidence, and HuthcAd- the Brevity that accompanies it every where does not require too ftrong vanugeor' an Attention. A few Years moderate Studv fttflices to raifc a Perfon, IJ^Jnw' of Ibme Talents, above thefe Geniufes who were the Admiration of aoi J^IX^. Antiquity ; and we have feen a young Man of Sixteen, publifh a Work, CTrait^ des Courbes d double Courbure par Clairaut) that Arabimedet would have wiihed to have compofed at the End of his Days. The Teacher of Math«maticks, 'therefore, fhould be acquainted with the difFerent Pieces upon the anaiitic Art, difperfed in the Works of the moft eminent Mathematicians, make a judicious Choice of the mofl ge- neral and eiTentlal Methods, and lead his Pupils, as it were, by the Hand, in the intricate Roads of the Labyrinth of Calculation ; that by this Means Beginners, exempted from that clofe Attention of Mind, which would give them a Diftafte for a Science they are defirous to at- tain, and methodically brought acquainted with all its preliminary Prin- ciples, might be enabled in a fhoit Time, not only to underfland the Writings of. the mofl eminent Mathematician?, but, rei!eding on their Method of Proceeding, to make Difcoveries honourable to themfelves and ufefu! to the Public.
III. Arithmetick comprehends the Art of Numbering and Algebra, confe- ^^^ ^^. . quently is diftinguiihed into particular and univerfal Arithmetick, becaufe meckk du- the Demonflrattons which are made by Algebra are general, and nothing ^^^ ^^^ can be proved by Numbers but by Induaion. The Nature and Forma- Veiled?" tion of Numbers are clearly dated, from whence the Manner of ptr- forming the principal Operations, as Addition, Subtrafiion, Multipli- cation and Divifion are deduced. The Explication of the Signs and Symbols ufed in Algebra follow, and the Method of reducing, add- ing* fubtrading,' multiplying, dividing, algebraic Quantities fimple atS compound. This prepares the Way for the Theory of vulgar, algebraical and decimal Fradions, where the Nature^ Value^ K&n^
VIII CaURSEOP
Manner of campnriitg ihtm, tnd their OperatiofiiSy ire carefidtj nil- folded. The Compofition and Rerolution of Qyancitics conies after, including the Method of raifing Quantities to any Power, extracting of Roots, the Manner of performing upon the Roott of imperfed Powers, radical or incommenfurable Quantities, the various Operations of which they are fufceptible. The Compofition and Refolution of Quantities being finilhed, the Dodrine of Equations prefents itfelf next, where foWn«Eqt- ^^^^^ Genefis, the Nature and Number of their Roots, the difierent tiom. Redu£bions and Transformations that are in Ufe, the Manner of foiving
them, and the Rules imagined for this Purpofe, fuch as Tranfpofition, Multiplication, Divifion, Subftitmion, and the Exlradion of their Roots, are accurately treated. After having confidered Qyantiticfs in themfelves, it remains to examine their Relations ; this Do3rine comprehends arith- metical and geomerrical Ratios, Proportions add Progreflions: The Theory of Series follow, where their Pormationi Methods for difcorer- ing their Convergency, or Divergency, the Operations of which they are fufceptible, their Reveriion, Summation, their tJfe in the Irtveffi- The Natiiff S*^^^" ^* *^^ Roots of Equations, Conftnidion of Logarithms, Wr. are ana^Lawiof taught. In fine, the Art of G>mbinations, and its Application for de- chtnce. termining the Degrees of Probability in civil, moral and political Enqpit- rics are difclofed. Ars cujus Ufus et NeceKus ita unhtrfale ejty utjine ilUf nee Sapientia Pbllofopbiy nee HiRwici Exa^itudo, nee Medici Dex^ teritas^ aut Politici Prudentiaf conjifiere queut. Omnis enim borvm Lahr in conjedando, et omnis Conje^ra in Trutinandis Caufarum CompUxiam^ bus aut CoMbinationibus verjatur.
tv. Divifionof GEOMETRY is divided into Elementary, TRAKseiKPE>7TAt>
Geometiy and SuBLIME.
u^, Tiin- '^^ ^P^" '^ Youth an accurate and eafy Method for acquiring a rcendentcl Knowledge of the Elements of Geometry, all the I^ropofitions in Euclid and Su- (a) in the Order they are found in the beft Editions, are retained with
blimc,
(0 '* PMTfffCUityititht'MMhodaikrFortti of Iteafonifig, it the ptfeiilitf Okar^ftcnftlc €f •* Eddies Etfeaiciic<« TttX, is iiitdrpolac«d by CXbpfttiUi and CUtiilt, ttmMkVM by Herigoile mA << Barrow, or dmraved by T-a(f<{uet and Derdialei. but of the OH|iiMl^ kaaded down t<^ ut by ** Antiquity. His Cemonftrations being conducted with the molt exprefs Defign of reduciow *• xht Principles ailbinedto the fewf^fk KniMber, atid moft e?ident thirt ndght be, and in 1 1i^ ** tbod the moft nanirali as it U the trtc^ condocive towirdta inft mid cdrnpieteCdtaMVlaiioiL " of the Sabfed, by beginnina with fuch Particulars as are -moft eafily coooehred, and flow aoft ** reiulily from theTrincipIes laid down ; thence by gradually proceeding to (iich as are more ob- ^ (hire, arid reqdh^ a longftt dhaiii of AtgvfMent, tt^ have Ai^t^M^beeii regafM hi all A^dbL *' as tfato moft ^xMk in their Kind." Such-i* the Jadgmem Hit the &0YAJU^80Cl£TY, Ao have expreif*d at the lame Tine thar Ditfrke to the new modelled £lemenci that aCpreleat every wh«re abbund ; and it the illiberal and ffttfdunic Mc!thods of teadfiilg thoft! moft fet^ Aftf- whicKistabeho)>ed, wfltiH^er be coUktciMhcad ia dit niUHcMoblt i&£DcU^:ad€M- land, Aec.
MATHEMATICKS. IX
atl poffible Attention} as alfo the Forniy Connedion and Accuracy of his Demonftrations. The eflential Parts of his Propofitions being fet Methodical forth with all the Cicarnefs imaginable, the Senfe of his Reafoning arc ^J^*^ J|J^ explained and placed in fo advantageous a Light* that the Eye the lead Eiements^f attentive may perceive them. To render thefe Elements ftill more eafy, Eufl'<l •« the different Operations and Arguments eflential to a good Demonftra- *^«*^***- tion» are diftinguiflied in feveral feparate Articles ; and as Beginners, in . order to make a Progrefs in the Study of Mathematicks, fhould apply themfelves chiefly to difcover the Connexion and Relation of the differ- ent Proportions, to form a juft Idea of the Number and Qualities of the Arguments, which ferve to eftablifh a new Truth ; in fine, to dif- cover all the intrinficalPartsofa Demonftration, which it being impofftble for them to do without knowing what enters into the CompoHtion of a Theorem and Problem, Firft, The Preparation and Demonftration are diftinguiihed from each other. Secondly, The Propofition being fet down, what is fuppofed in this Propofition is made known under the Title of Hypothecs, and what is aifirnaed, under that of Thefis. Third- ly, All the Operations neceffary to make known Truths, ferve as a Proof to an unknown one, are ranged in feparate Articles. Fourthly, The Foundation of each Propofition relative to the Figure, which forms the Minor of the Argument, are made known by Citations, and a marginal Citation recalls the Truths already demonftrated, which is the Major : In one Word, nothing is omitted which may fix the Attention of Be- ginners, make them perceive the Chain, and teach them to follow the Thread of geometrical Reafoning.
V.
Tranfcendental Gcometrv prefuppofes the algebraic Calulation; it com- Tranfcen- mences by the Solution of the Problems of the fecond Degree by Means of ^"^y.^^*^ the Right-line and Circle : This Theory produces important and curious Remarks upon the pofitive and negative Roots, upon the Pofition of the Lines which exprefs them, upon the different Solutions that a Pro- blem is fufceptible of; from thence they pafs to the general Principles in what it of the Application of Algebra to curve Lines, which confift, Firft, ^^^^ ^ In explaining how the Relation between the Ordinates and Abciffes of a Curve is reprefented by an Equation. Secondly, How by folving this Equation we difcover the Courfe of the Curve, its different Branches, and its Afymptots, Thirdly, The Manner of finding by the direft Me- thod of Fluxions, the Tangents, the Points of Maxima, and Minima. Fourthly, How the Areas of Curves are found by the inverfc Method of Fluxions.
The Conic SeSions follow; the bcft Method of treating them is to Beft Method confider them as Lines of the fecond Order, to divide them into ^^^^f^ their Species. When the moft fimple Equations of the Parabola, tions.
COURSE OF
The differ- rnc Ord.n of Curves.
Sublime O^ometry.
Its DivifioD.
/
What the firft Part compre- hends.
Ellipfei and Hyperbola are found, then it is eafily ihewn that thele Curves are generated in the Cone. The Conic Sedions are terminated by the Sohition of the Problems of the third and fourth Degree^ by the Means of thefe Curves.
The Conic Sedions being finiihed> they pafs to CurretW a fuperior Order* beginning by the Theory of multiple Points> of Points of Inflec^ tiont Points of contrary Infledion* of Serpentment, (Jc. Thefe Theo* ries are founded partly upon the fimple algebraic Calculation^ and partly on the dired Method of Fluxions. Then they are brought acquainted livith the Theory of the Evolute and Cauftiques by Refledion and Re« fra£^ion. They afterwards enter into a Detail of the Curves of diflFerent Orders, ailigning their Clafles, Species, and principal Properties^ treat- ing more amply of the bed known, as the Folium> the Conchoid, the Ciflbid, e^r.
The mechanic Curves follow the geometrical ones, beginning by the exponential Curves, which are a mean Species between the geometrical Curves and the mechanical ones ; afterwards having laid down the ge- neral Principles of the Conftnidion of mechanic Curves, by the Memos of their fluxional Equations, and the Quadrature of Curves, they enter into the Detail of the beft known, as the Spiral, the Qyadratrice, the Cycloid, the Trochoid, i^c.
VI.
Sublime Geometry comprehends the inverie Method of Fluxions, and its Application to the Quadrature, and Redification of Curves, the cubing of Solids, (Jc.
Fluxional Quantities, involve one or more variable Quantities ; the natural Divifion therefore of the inverfe Method of Fluxions is into the Method of finding the Fluents of fluxionary Qgaatities, containing one variable Quantity, or involving two or more variable Qjiantities ; the Rule for finding the Fluents of fluxional Quantities of the moft fimple Form, is laid down, then applied to diflFerent Cafes, which are nxxe compofed, and the DifSculties which fome Times occur, and which em* barrafs Beginners, are Iblved.
Thefe Refearches prepare the Way for finding the Fluents of fluxional Binomials, and Trinomials, rational Fra£iions, and fuch fluxional Qinuw tities as can be reduced to the Form of rational Fradions $ from thoice they pafs to the Method of finding the Fluents of fuch fluxional Quan- tities which fuppofe the Re&ification of the Ellipfe and Hyperbola, as well as the fluxional Quantities, whofe Fluents depend on the Quadra- ture of the Curves of the third Order ; in fine, the Refearches which Mr. Newton has given in his Quadrature of Curves, relative to the Qjja- drature of Curves whofe Equations arc compofed ef three or four Terms ;
MATHEMATICKS. XI
And this firft Part is terminated by the Methods of finding the Fluents of fluzionaU logarithnoieticaU and exponential QyantitieSf and thofe which are affed^ with many Signs of Integration^ and the various Me- thods of Approximation^ for the Solution of ProblemSf which can be reduced to the Qjiadrature of Curves*
The fecond Part of the inverfe Method of Fluxions* which treats of fluxional Qjiantitiesy including two or more variable Qyantities* com- mences by ihewing how to find the Fluents of fuch fluxional Quantities as require no previous Preparation; the Methods for knowing and ^
fiiftinguiihing thefe Quantities or Equations ; afterwards they pafs to the Methods of finding the Fluents of fluxional Quantities, which have f^oSd ftrt need of being prepared by fome particular Operation, and as this Oper- comDrc* ation confifts moft commonly in Separating the indeterminate Q^ntities, ^^ after being taught how to conftruft diflFerential Equations, in which the indeterminate Qgantities are feparated, they enter into the Detail of the different Methods for feparating die variable Quantities in a propofed Equation, either %j Multiplication, Divifion, or Transformations, be- ing Ihewed their Application, firft to homogeneous Equations, and after being taught how to conftnid thefe Equations in all Cafes, the Manner of r^ucing Equations to their Form is then explained. How the Me- thod of indeterminate Co-eflicients can be employed for finding the Fluents of fluxional Equations, including a certain Number of variable ^^antities, and how by this Method, the Fluent can be determined by certain Conditions given of a fluxional Equation. Fluxional Qjiantities ^f diflFerent Orders follow ; it is fhewn, firft, that fluxional Equations of the third Order, have three Fluents of the fecond Order, but the laft Fluent of a fluxionary Equation of any Order is fimple ; then the vari- ous Methods magined by the raoft eminent Mathematieians for finding thefe Fluetits, fuppofing the Fbxion of any one variable Quantity con- fttaitf are explained, and the Whole, in fine, terminated by the Applica- tion of this Do£b'ine to the Qsiadrature and Rectification of Curves, CttlMng of Solids, &!r.
vii.
Such is the Plan of a Courfe of pure Mathematicks traced by New^ Condufion. t^Hj improved by CoteSfBernffulfyf Euler, QairauU D^Jiemiett, M*Laurin, Stff^fon, Fontain, * &c. which ferves as a Bafis to the Inftrudions re- qoifite to qualify Youth to appear with Dignity in the different Employ- ments of Life, or to enable them in Time, To bring to Perfedion the various Arts for which they are intended.
* Qtisdratiira currarmn, kamoiiia mcDilvanmii ftc
XII
SYSTEM OF THE
PLAN of the Syflem of the Pbyftcal and Moral Worlds including the Infirufiions relative to young Noblemen and Gentlemen of Fortune.
P L AN of the Syflem of tbe Pbyftcal World.
Nubem pellente matbefty
UtiJity of the Study of the Sy- ftem of the World.
Is t Prc- iervative againft the PaifioDi.
Leads to
Virtue.
Clauflra patent calif rerumque immobilis ordo: fam fuperum penetrare domoi, atque ardua call Scandercf fublimis genii concefjit acumen. I.
STUDY in general is necefiary to Mankind, and eflentially contri« butcs to the Happincfs of thofc who have experienced that adive Curiofity which induceth them to penetrate the Wonders of Nature. It is, bcfides, a Prefervative agatnft the Diforders of thePaf&ons; a kind of Study therefore which elevates the Mind, which applies it ciofely, confcquently, which furniflies the moft affured, arms againft the Dangers we fpeak of, merits particular DiftinSion. " It is not " fufficient, fays Seneca^ to know what wt owe to our Country, to our " Family, to our Friends, and to ourfelves, if we have not Strength of " Mind to perform thofe Duties, it is not fufficient to eftablifli Precepts^ ** we muft remove Impediments, ut ad prcecepta qua damus pofpt animus " ire, folvendus eft. (Epift. 95.) Nothing anfwers better this Purpofe than the Application to the Study of the Syftem of the World ; the Wonders which are difcovered captivate the Mind, and occupy it in a noble Manner; they elevate the Imagination, improve. the Underftand- ing, and fatiate the Heart : The greateft Philofophers of Antiquity have been of this Opinion. Pytbagoras was accuftomed to fay, that Men ftiould have but two Studies, that of Natutc, to enlighten their Undcrftandings, and of Virtue to regulate their Hearts ; in eflFca to be- come virtuous, not through Wcaknefs but by Principle, wc muft be able to reflea and think ciofely ; we muft by Dint of Study be delivered from Prejudices which makes us err in our Judgments, and which are fo many Impediments to the Progrefs of our Reafon, and the Improve- ment of our Mind. Plato held the Study of Nature in the higheft Efteem ; he even goes fo far as to fay, that Eyes were given to Man to contemplate the Heavens : To which alludes the following Paflage of Ovid.
Finxit in effigiem moderantum cunffa deorum,
Pronaque cum fpeUant animalia cetera terram,
Os bomini fublime dedity ccelumque tueri
Jufptf et ereflos ad fidera toller e vultus.
r
PHYSICAL WORLD. XIII
II.
The Poets who have illuftratcd Greece and ItaJy^ and whore Works J* cdcbm- arc now fare of Immortality, were pcrfcSly acquainted with the Hca- pj^,^* vens, and this Knowledge has been the Source of many Beauties in their Works : Homer, Hejiad, Aratusy among the Greeks : Horace^ Virgilf Ovidf Lucretius, Manilius, Lucan, Claudian, among the Latins ; make life of it in feveral Places, and have expreflfed a fingular Admiration for this Science.
Ovid after having anounced in his Fafti, that he propofes celebrating the Principles on which the Divifion of the Roman Year is founded, enters on his Subjed by the following pompous Elogium of the firft Difcoverers of the Syftem of the World.
Felices MnimoSf quibus bac cognofcere primis^
Ihque domos Juperas fcandere curafuit, Credibile eft illos pariter vitiijque locifque,
Altius bumanis exeruiffe caput. Ncn venus out vinum fuhlimia pe^ora f regit ^
Officiumvefori fnilitiaque labor. Nee levis ambit io perfufaque gloria fuco,
JUagnarumve fames Jollicitavit opum, , Mmvoere oculis diftantia Jydera noftris^ • JEtberaque ingenio fuppo/uere Juo. • Sic petitur cctlum,
Claudian in the following Verfcs, celebrates Arcbimedes on his Inven- tion of a Sphere admirably contrived to reprefent the celeftial Motions.
Jupiter in parvo cum cerneret atbera vitro,
Rjfitf et adjuperos talia di^a dedit : Huccine mortalis progrejfa potentia cura I
Jam meus ihfragili luditur orbe labor. Jura poli, rerumque fidem legejque deorum
Ecce Syracujius tranjiulit Arte fenex ; Inclufus Variis famulatur fpiritus ^ftris,
Et vivum certis motibus urget opus ; Percurrit proprium mentitus JignUer, annum,
Etjknulata novo Cyntbia menfe redit : Jamque Juum volvens audax induftria mundum
Gaudet, ct bumanajidera mentc regit.
XIV SYSTEMOFTHE
yirgil feems defirous of renouncing all other Study^ to contemplate the Wonders of Nature.
Me vero primum dukes ante omnia mufttf ^arum facra fero ingenti percujfus amore, Accipiant, calijue vias et Jydera monjirent DefeBus foils varies, lunaque labor es, Unde tremor terrisf qua vi maria alta tumefcani Ohjicibus ruptis, rurfufque injeipfa refidant^ ^id tantum oceano properent ft tingerefoles
Hybernif vel quee tardis mora noBibus obftet
Felix qui potuit rerum congnojcere eaufas.
Ceor. n. 475.
La Fontaine imiutes the Regrets of Virgil in a niafterly Manner^ where he fays^
^andponrront les neuf/ieurs loin des cours et dee villes, i^occuper tout entier^ €t m' ^prendre des deux Les divers mouvements inconnus d nosyeux, Les noms et les vertues de ces clartes errantes.
Songe dun habitant da MogoL
Foltaire, the firft Poet of our Age^ has teftified in many Parts of hji Worksi his Tafte for Aftronomy» and his Efteem for Aflronomersy whom he has celebrated in the fineft Poetry. What he fays of Newton b worthy of Auention.
Confidens du Tres Haul, Subjlances eternellesp ^i parez de vos feux, qui couvrez des vos aUes, Le trone ou votre maitre eft ajfis parmis vous : Paries I du grand Newton n^etiez vous point jakax.
To which we can only oppofe what Pope has faid on the fame Sub- jeft:
Nature and Nature's Laws lay hid in Night ; God faid» Let Newton be^ and all was Light
The great Geniufes of every Species have been furprized at the In- difference which Men fliew for the Spedacle of Nature* Tajo puts Refledions in the Mouth of Rsnaldo, which merit to be recitedfor the Inftrudion of thofe to whom the fame Reproach may be applied ; it is at the Time when marching before Day towaixls Mount Olivet^ he con- templates the Beauty of the Firmament.
PHYSICALWORLD. XV
Cm gU occbs alzati contempUndo intorno, $uinci notturne r quindi matutim Bellezze^ incorruptibili e divine \ Fraftftejfo penfavOf o quanta belle Lucif il tempio celefie in Je ragunat Ha iljuo gran carro il de^ Pauratajtelle Spiega la notte^ e Pargentata Luna \ Ma non i cbi vagbeggi o quejlaf o quelle ; E miriam not torbida luce e bruna, Cb*un girar ffoccbi, un balenar di rifo Scopre in breve confin difragil vifo.
Jerus. Cant, xviii. Si. I2, 13.
HI.
The Knowledge of the Syflem of the World has delivered us from E^reOi the Apprehenfions which Ignorance occafions ; can we rccal without 7***^nit!ce Compaifion> the Stupidity of thofe People, who believed that by making ofthTsyf. a great Noife when the Moon waa eclipfed> this Godders received R^'ic^'*^^^ from her Sufferances^ or that Eclipfcs were produced by Inchantments (a) ? JJ^^j^
Cvmfrufira refonant JEra auxiltaria Luna. Met. iv. 333. Canfuj et e Curru Lunam deducere tentant, Etfaceretft non JEra repulfa fonent. Tib. El 8.
The Knowledge of the Syftem of the World has diflipated the Errors of The Koow- Aftrology, by whofe fooliih Prediaioos Mankind had been fo long abufed. s^l^^^^ The Mbmture of 1 1869 fliould have covered with Shame the Aftrologcrs the World erf Europe i they were all, Chriftians, Jews and Arabians, united to **f*^*%*' anounce, fevcn Yean before, by Letters pobliihed throughout Europe^ ^n In a Conjundion of all the Planets, which would be attended with fuch Aftrok>gy. terrible Ravages^ that a general Diflblution of Nature was much to be drettded^ fo that nothing Kefs than the End of the World was expeded : this Year nttcwithftanding pafled as others. But a hundred Lies, each M well atteftedy would not be fufficient to wain ignorant and credulous Men frem the Prejudices of their Infancy. It was neccflary that a Spi- rit of Philofophy, and Refearch, ihould fpread itfelf among Mankind, ■open their Underftandings, unveil the Limits of Nature, and accuftom them not to be terrified without Examination, and without Proof.
IV.
The CometS) as it is well known, were one of the great ObjeSs of Terror which die Knowledge of the Syftem of the World has, in fine,
(a) ScBCCSy Upolit, 7S7. Tacit Ann, Fhitarch In Fcridc, et de dcfcQa Oracalorum.
XVI
The Know ledffcofthe Svftem of the World ufeful in Geography and Naviff a tioD, ana confequent lyofthe greateftim portance to there King domi.
SYSTEM OF THE
removed. It is not without Concern wc find fuch (Irangc Prejudices in the fineft Poem of the laft Age, whereby they are iranfmitted to the iateft Pofterity.
^al colle cbiome fanguinoje borende%
Splender comfta fuol per Varia adufiay
Che i regni muta^ ei fieri morti adduce^
Ai purperei tiranni infaufia luce. Jerus. Lib. 7. St. 52.
The Charms of Poetry are aduaily employed in a Manner more phi- lofophical and ufefuU witnefs the following fine Pafiage.
Cometet que Pon craint a legal du tonnerref Cejfez d*epouvanter les peuples de la terre ; Dans une Ellipfe immenje acbevez voire courst Retn9nteZ9 de/cendez pres de V afire des jours ; Lancez vos feux, volez, et revenant fans cejfe% Des monies epuifez ranimez la vielleffe.
Thus the profound Study of the Syftem of the World has dlflipated abfurd Prejudices, and re-eftabli(bed human Reafon in its inalienable
Rights,
V.
To the Knowledge of the Syftem of the World, are owing the Im- provements in Cofmography, Geography, and Navigation ; the Obfer- vation of the Height of the Pole, taught Men that the Earth was rounds the Eclipfes of the Moon taught how to determine the Longitudes of the different Countries of the World, or their mutual Diftancet from Eaft to Weft. The Difcovery of the Satellites of JupiteTf has contri- buted more effe&ually to improve geographical or marine Charts, than ten thoufand Years Navigation ; and when their Theory will be better known, the Method of Longitudes will be ftill more exafi and niore eafy. The Extent of the Mediterranean was almoft unknown in 160O9 and To-Day, is as exadly determined as that of England or Ireland. By it the new World was difcovered. Cbrlfiopber Columbus had a more intimate Knowledge of the Sphere, than any Man of his Time, Hnce it gave him that Certainty, and infpired him with that Confidence with which he dire&ed his Courfe towards 4he Weft, certain to rejoin by the Eaft the Continent of Afia^ or to find a new one. And nothing feems to be wiftied for, to render Navigation more perfe£l and fecure, but a Method for finding with Eafe, the Longitude at Sea, which is now ob- tained by the Means of the Moon : And if the Navigators of thi$ Kingdom were initiated in Aftronomy, by able Teachers^ as is praftifed
PHYSICAL WORLD. XVfl
in other Parts of Europe, their Eftimation would approach within twenty Miles of the 'JVuth, whilft in ordinary Voyages, the Uncertainty amounts to more than three hundred Leagues, by which the Lives and Fortunes of Tboufands are endangered. The Utility therefore of the Marine to thofe Kingdoms, where Empire, Power, Commerce, even Peace and War, are decided at Sea, proves that of the Knowledge of the Syftem of the World.
VI.
The adual State of the Laws, and of the ecdefiaftical Adminiftra- The Refor tion, is cffentially conneded with the Syftera of the World ; St. A- "^'^*'^ gujline recommended the Study of it particularly for this Reafon; St. dJaepend* Hypp^Ute applied himfelf to it, as alfo many Fathers of the Church, cd on it. notwithftanding our Kalendar was in fuch a State of Imperfedion, that the Jews and Turks were afloniihed at our Ignorance. Nicholas V, Lton X, Cffc. had formed a Defign of re-eftabli(hing Order in the Ka- lendar, but there were at that Time no Philofophers, whofe Reputa- tion merited fufficient Confidence. Gregory the Xlllth, governed at a Time when the Sciences began to be cultivated, and he alone had the Honour of this Reformation.
VII.
Agriculture borrowed formerly from the Motions of the celeftial iinfeflilia Bodies, its Rules and its Indications ; Job, Heftod, Varro, Eudoxus, Agrkukuir* Aratujf Ovid, jMmy» Columella, Manilius, iurnidi a thoufand Proofs of it. The Pleyades, Arflurus, Orion, Syrius, gave to Greece and Egypt the Signal of the different Works ; the rifing of Syrius anounced to the Greeks the Harveft ; to the Egyptians the overflowing of the Nile. The Kalendar anfwers this Purpofe adualy.
VIII.
Ancient Chronology deduces from the Knowledge and Calculation of is the Fomi Eciipfes, the moft fixed Points which can be found, and in remote Times ^^^^ ^^ we find but Obfcurity. The Cbinefe Chronology is entirely founded up- ^^ ^ on Eciipfes, and we would have no Uncertainty in the ancient HiAory of Nations as to the Dates, if there were always Philofophers. (See the Art of verifying Dates.)
It is from the Syftem of the World we borrow the Divifion of Time, Fnrnlftef and the Art of regulating Clocks and Watches ; and it may be faid, the Meuis that the Order and Multitude of our Affairs, our Duties, our Amufe- ^J^,^jf inents, our Tafte, for Eicadtiefs and'Precifion, our Habitudes have ren- dered this Meafiire of "Time almoft indifpenfabie, and has placed it in the Number of the Keceflaries of Life; if inftead of Clocks and Watches, Meridians and folar t)ial$ are traced, it is an Advantage that the Knowledge of the Syftem of the World has procured us. Dial-
XVIII
SYSTEM OF THE
Is i:^erui in
ling being the Application of fpherical Trigonometry ; a ProjeAion of the Sphere upon a Plane, or a Se^ion of a Cone» according to ^he Forms given to a Dial.
X.
The Knowledge of the Changes of the Air, Winds, Rain, dry Wea- ther, Motions of the Thermometer, Barometer, have certainly an eflfen- tial and immediate Relation with the Health of the human Body ; the Knowledge of the Syftem of the World will be of fenfible Utility, when, by repeated Obfervations, the phyfical Influences of the Sun and Moon upon the Atmofphere, and the Revolutions which refult will be diP> covered. Galen advifes the Sick not to call to their Afliftance Phyfici- ans, who are not acquainted with the Motions of the celcftial Bodies, becaufe Remedies given at unfeafonable Times are ufelefs or hurtful, and the ableft Phyficians of our Days are convinced, that the Attradions which elevate the Waters of the Ocean twice a Day, influence the State of the Atmofphere, and that the Crifis and Paroxifms of Diforders cor^^ refpond with the Situation of the Moon in refped of the Equator, Sy- figies, aijd Apfides. See Mead, Ho/man, &c.
XI.
Thofe Advantages which refult from the Knowledge of the Syftem of the World, has caufed it to be cultivated and held in fmgular Efleem by
all the civilized People of the Earth. The ancient Kings of Perfia,
tiou of the and the Priefts of Egypt f were always chofen amongft the mofi expert ^^^*^ in this Science. The Kings of Lacedemon had always Philofophers in their Council. Alexander was always accompanied by them in hist mtli^ tary Expeditions, aiyl Jrijlotle gave him &r\€t Charge to do nothing without their Advice. It is well known how much Ptolemeus the fecond King of Egypt^ encouraged this Science ; in his Time flouriftied Hypar* cbuSf Cdlimacbut, ApolloniuSf Aratus^ Biorif TbeocriteSf Conon, yulius Cafar was very curious in making Experiments and Obfervations, as ii appears by the Difcourfe which Lucan makes him hold with Acbore^ Prieft of Egypt, at the Feaft of Cleopatrs.
Caltivated in all Aeei by aU the cmlized Na
' Media inter preliafemper
Stellarum ccelique plagis fuperifque vacavi. Nee meus Eudoxi vincetur faflibus annus.
Phar.
Has beenF the favorite- Study of €rcat Pri
rnacet.
The Emperor Tiberius applied himfelf to the Study of the Syftem of the World, as Suetonius relates ; the Emperor Claudius forefaw there would be an Eclipfe the Day of his Anniverfary, and fearing it might occaiion Commotions at Rome, he ordered an Advertifement to be pub- liftied, in which he explains the Circumftances, and the Caufes of this Phenomenon. It was cultivated particularly by the Emperors AdriQ^
PHYSICALWORLD. XIX
msd S^erus^ by Cbarlemagnet by Leon V, Emperor of ConJLantmopIe^ by Alpbonfo X, King of CafliU^ by Frederick II, Emperor of the • Wejty .by CVi//y> AlmamoTiy the Prince Uluheigbi and many other Monarchs of
Among the Heroes who alfo cultivated it, are reckoned Mahomet II, Conqueror of the Greek Empire; the Emperor Charles V, and Lewis XIV. In fine, the Eftabiifliments of diflFerent Philofophical Societies in Eng^ Jandf Scotland, France, Italy, Germany, Poland, Sweden, Rujpa, &c. have ^iven the Monarchs, Nobility, and Gentrv of thofe Countries, a Tafle for the more refined Pleafures attending the Study of the Sciences, and particularly of the Syftem of the World, an Example worthy to be imi- tated by thofe of this Kingdom.
XII. PabUck
Befides thofe renowned Societies which have all contributed to the f^JJ^.^ Progrefs of every Branch of human Knowledge, and particularly of the b the dif- Syftem of the World, there has been eftabliftied in the different Parts of ferentPaftt Europe public Schools, conduced by Men of fuperior Talents and Abi- for^SftSft lities, who make it their Bufmefs to guide and in(lru3 the young No- log young bility and Gentry in this noble Science, and furnifh thofe who difcovcr Noblemen fingular Difpofitions with every Means of Improvement. men^fFo-
An illuftrious Englijbman, Henry Saville, founded in the Univerfity of tune in what Oxford two Schools, which have been oi vaft Utility to England \ the J^?'^*^ Mailers have been Men all eminent in this Science, John Bainbridge in ilLworid. 1619, John Greaves in 1643, Seth Ward, Chrijlopher Wren, Edward Foundation Bernard \Xk 1673, David Gregory in 1691, Brigg^ Wallis, and 7. Caf- of Henry well in 1 708, Keill in 1 7 1 2, Hornjby, &c. ^ Savilfc.
The Schools eftablilhcd at Cambridge, among whofe Mafters were Founda- Barrow, Newton, Cotes, Wijion, Smyth, and Long, all celebrated Aftro- ^^^ ^^
tlOmtTS. and^ncaj.
The School of Grejham at BiJhops^Gate in London, which has cflen- college of ttally contributed to the Progrefs of Aftronomy ; among the Mafters of Grefliam. this School were Doftor Hook, and other eminent Men.
The Royal mathematical School at Cbrift's-Hofpital, where Hodgfon, *^'^["*1 Rohertfon, &c. have bred up a great Number of expert Navigators and ©f chrift^a Aftronomers. Hofpitai.
The Schools of Edinburgh, Glafgow, and Aberdeen, are known all Mathcmati ever Europe \ the Nobility, and Gentlemen of Fortune of Scotland, fu- cal Schools perintending them, and taking every Method of encouraging both Maf- ^ Scotland. tcrs and Students to Affiduity and Attention, to go through their refpec- tive Talks with Alacrity and Spirit; the Names of Gregory, M^Laurin, Stuart, Simp/on, &c. the famous Mafters, will never be forgotten.
* He ordered the Works of Ptolemey to be tranflated into Latin, and publickfy to be taught alKapkt.
XX
The Royal College.
Obrerrato ries and SchooUof Experimen tal Philofo phy.
Of CafTel.
Of Urani bourg.
OfDantzick
Of Copcn lugen.
Of Pekio.
SYSTEM OF THE
The Royal School of France^ founded by Francis I, has cfTentially con- tributed to the Progrefs of the Knowledge of the Syftcm of the World. Orancet Fine\ Stadiusj Morin, Gajfendu de la Hire, de Lifle^ who were fucceflively Mafters of it, have been celebrated Aftrononiers, lie.
XIII.
Experiments and Obfervations are the Foundation of all real Knonr- ledge, thofe which ferve as a Bafis to the Difcoveries relative to the Syftem of the World, are made and learned in Experimental Schools and Obfcrvatories : The firft Obfervatory of any^^lebrity, was built by William V, Landgrave of Heffe, where he colled^d all the Inftm- ments. Machines, Models, l£c, which were known in his Time, and put it under the Diredion of Rotbman and Byrgius, the firft an Aftroso- mcr, the fecond an expert Inftrument-Maker : The Duke of Bro^lio, General of the French Army, having rendered himfelf Mafter of Cafftl in 1 760, took a Copy of the Obfervations and Experiments made ia this Obfervatory, and depofited it in the Library of the Academy.
Frederick L King of Denmark^ being informed of the fingular Merit qf Ticbo Brake, granted him the Ifland of Venufia, oppofite Copenhagen^ and built for him the Caftle of Uranibourgb, fumiihed it with the larg- eft, and the moft perfeS Inftruments, and gave Peniions to a Number of Obfervers, Calculators, and Experiment- Makers, to aflift him, which enabled him in the Space of 16 Years, to lay the Foundation of the Sys- tem of the World, in a Manner more (table, than was ever before ef- feSed. The moft eminent Men took Pleafure in vifiting this incom- parable Philofopher : • The King of Scotland going to efpoufe the Prin-. cefs Jnne, Sifter of the King of Denmark, pafled into the Ifland of VertufU with all his Court, and was fo charmed at the Operations and Succets of T!^ycho, that he compofed his Elogium in Latin Poetry : So much > Merit raifed him Enemies, and the Death of King Frederick II, (iimilh- ed them the Means of fucceeding in their Machinations. A Minifter called Walchendorp, (whofe Name ftiould be devoted to the Execration of the Learned of all Ages) deprived him of his Ifland of Venujia, and forbad him to continue at Copenhagen his Experiments and Obfervations.
XIV.
The firft Obfervatory of the laft Age, was that of Hevelius, eftab- liflied at Dantzick ; it is defcribed in his great Work, intitled, Macbina CeU/tis.
The Aftronomical Tower of Copenhagen was finifhed in 1656, built by Chrijlian IV, at the Solicitation of Longomontanui.
There has been an Experimental School and Obfervatory at Peiin thefe 400 Years, built on the Walls of the City : Father Verbiejl be- ing made Prefident of the Tribunal of Mathematicks in 1669, obtained of the Emperor Cam-hj, that all the European Inftruments, Machines,
PHYSICALWORLD. XXI
Modelsj Efff. Ihould be added to thofc wiih which it was already furnlfli- cd. (See the Defcription of China by DubalJ.J There has been made there a vaft Colledion of ufeful Experiments and Obfervations^ a Copy of which is depofitcd in the French Academy.
XV.
The Royal Obfervatory of England was built by CbarlesIL under the The Royal Dtr^ion of Sir J, Moore, four Miles from London, to the Eaftward Obferruoiy upon a high Hill : It will be for ever famous by the immortal Labours JJlitS*^" of Flamjlead, Halley, and Bradley ; Flamftead was put in Poffeffion of this School at Obfervatory in 1676, where, during the Space of 33 Years, he made ^'?°*j'* a prodigious Number of Obfervations contained in his Hiftory of the ftmou. by Heavens: HaUej fuccetded him, and was, without Doubt, the greateft (he Labours Aftronomer England produced ; at the Age of Twenty he went to the ifJliy'^d'* Ifland of St. Helen, to form a Catalogue of the Southern Stars, which Btt^t^ he published in 1679 ; then he went to Dantzick to confer with Hevelius, he travelled aHb through Italy and France for his Improvement; in 1683 he publiflied his Theory of the Variation of the Magnetic Needle ; in 1686 he fuperintended the Impreffiori of the Prineipia Matbematica Phi- lofofia Naturalis, which its immortal Author could not refolve with him- felf to publifli. The fame Year he publilhed his Hiftory of the Trade Winds; in 1698 he received the Command of a Vcffel to traverfe the Atalantic Ocean, and vifit the Englijb Settlements, in order to difcover vrhether the Variation of the Magnetic Needle, found by Experiment, agreed with his Theory, and to attempt new Difcoveries ; he advanced as ht as 52 Degrees South Latitude, where the Ice impeded his further Progrefs ; he vifited the Coaft of Brajil, the Canaries, the Iflands of Cdpe Verde, Barbadoes, fire, and found every where the Variation of the Compafs comformabte to his Theory; in 1701 he was commiflioned to traverfe the Englijb Channel, to obferve the Tides, and to take a Survey of the Coafts ; in 1 708 he vifited the Ports of Triejie and Boccari in the Gulph of Venice, and repaired the firft, accompanied by the chief In- gincer of the Emperor; he publiflied in 1705 the Return of the Comets of which he was the firft Difcovcrer; and we have feen in 1759 the Accompliftiment of his Prediftion ; in 171 3 he was made Secretary of the Royal Society ; he examined the difFerenL^ethods for finding the Longitude at Sea, and proved that thofe whiJi depend on the Obferva- tions of the Moon were the only pradicable ones, and as 'thofe Me- thods required accurate Tables of this Planet, which did not differ from Obfervation more than two Minutes, he fet about reSifying them, hav- ing difcovered that to obtain this Point it was fufficient to determine, every Day during 18 Years, the Place of the Moon by Obfervation, and to know how much the Tables differed from it, the Errors every Period afterwards being the fame, and returning in the fame Order : It was
XXII
Other Obfer vatories and Experimen tal Schools in £DgUa<l.
Thofc of .Edinburgh,
The Royal Oblervatory of Paris.
Other Ob (crvatories and Expcri mental Schools in France.
Of Nurem berg in 1678.
Of Leiden in 1690.
STSTEM OF THE
in 1 722 that this courageous Aftronomcr, in the 65th Year of his Age, undertook this immcnfe Work, and after having completed it, and pub- liflied the Succefs ot his Lab( urs for foretelling accurately the Moon's Place, and deducing the Longitude at Sea; we loft this great Man the 25th of January 1742. Bradley fuccccded him, who inriched Allrorcmy with his Difcoveries and accurate Obfervations. He dc,parre. hi^ Life ihe I3ih of July 1762, in the 70th Year of his Age. M. Majkelne, his Succeflbr, continues his Obfervations witli the moft adive 2^eal and happy Difpofitions.
The Royal Obfervatory not being fufficient for all thofc who parfuc the Study of natural Phiiofophy, there has been formed feveral Obfcrva- tories in London and the different Parts of England^ for Fxample, the Obfervatory of Sberburn near Oxford, where the Lord MacUsfieldy late Prefident of the Royal Society, M.HornJby^ &c. have made Experiments and Obfervations for many Years.
The Experimental School and Obfervatory of Edinburgh, built by the Subfcription of the Nobility and Gentry of that Kingdom, has been rendered famous by Af * Laurin, The Royal Academy of Sciences de- puted in T747 the King's Aftronomer* LeMonier, to obferve there an «nnulary Eclipfe of the Sun.
XVI.
The Royal Obfervatory of Parts y the moft fumptuous Monument that ever was confecrated to Aftronomy, was built under the Diredion of the great Colbert, immortal ProteSor of the Arts and Sciences. It is near 200 Feet in Front, 140 from North to South, and 100 in Heighti the Vaults are near eighty Feet deep ; there are alfo feveral others in Paris, and in other Parts of Frjtnce, as that of M. Lemonier at the C^- pucbines of St, Honore, that of Af. Delijle at the Hotel de Cluny, that of M. La Caille at the College of Majarin, that of the Palace of Luxem^ hurgb, that of M de Pouchy in Rue des Pojles, and that of M. Pingre it St, Genevieve j the Obfervatory of Marfeilles which F, Pezenas has ren- dered famous, that of Lyons where F. Beraud made Experiments and Obfervations for a long Time, that of Rowen and Touloufe from which M. Bowin and M. Dulange, M. d^ Auguier fend annually to the Academy a great Nimiber of ufef^and curious Experiments and Obfervations; that of Strajburgb wher Af. Brakenafer has made fome.
XVII.
The Senate of the Republic of Nuremberg, ereded an Obfervatory in 1678, and put it under the Diredion of Geo, Cbrifiopber Eimmart, Phil, IVurzelban built another in 1692, defcribed in his Book Uraniet Ncrica Bafts, The Adminiftrators of the Unive^fity of Leyden, eftab- liflied in 16909 an Experimental School sind Obfervatory. Frederick I, King of PruJJia, having founded in 1 700, an Academy of Sciences at
*,
.PHYSICAL WORLD. XXHI
Birlin, built an Experimental School, with an Obfcrvatory. The pre- 9^ ^^^ fent King of Pruffia^ added a fupcrb Edifice, where the Academy aftu- "* '^*^' ally holds its Aflfemblies. The Inftitution of Bologna a famous Academy, P^l««ly eftabliihed in 1 709, by the Count of MarftgU^ with the Permiflion of J^j' JlJ'j. Clement XI. has a fine Experimental School and Obfervatory, which Manfredi and Zanotti have rendered famous. There are four Experi- mental Schools, with Obfervatories, at Rome ^ that of BUncbini, that of the Convent oi Ara Cali, that of the Convent of Minerva, and that of Trinite du Mont. There is alfo one at Genoa, founded by the Mar- quis of Salvagi; one at Florence, which Ximenet has rendered famous ; cist zt Milan, ereded in the College of Brera, in 1713. The Supe- riors of the Univerfity of Altorf, in the Territory of Nuremberg, ered- of Akort ed an Experimental School, arid an Obfervatorv, and furnifiied it with >" 1714* all the neceffary Implements. In 1 714, the Landgrave of Hejfe, Cbarlet I. Heir of the States and Talents of the celebrated Landgrave we have al- ready fpoke of, built a new Experimental School and Obfervatory, and put It under the Diredion of Zumback: In 1722, the King of Portugal^ OfUQion^ JobnV, ereded an Experimental School and Obfervatory, in his Palace *° ■7«». at Lijhon ; there is alfo one in the College of St. Antony. The Expe- rimental School and Obfervatory at Peterjbourg, is one of the moft mag- f^^*^?^ nificent in Europe, it is fituated in the Middle of the fuperb Edifice of ,y^."* the Imperial Academy of Peterjbourg, it Is compofed of three Flights of of Utrecht Halls, adapted, for making Experiments and Obfervations, and is 150 "*■'*** Feet high. In 1726, the Magiftrates of the Republic of Utrecbt, built an Experimental School, and an Obfervatory, in which the famous Mujcbembroek made his Experiments and Obfervations. In 1739, the King: of Sweden trt&jtAont at Upfal, and put it under the DireSion ofUpfiJ of Wargentin. In 1740, the Prince of HeJfe Darmfiad, ereSed ano- "* *739- ther at Giejfen, near Marborougb. There are two Experimental Schools and Obfervatorics, at Vienna, where P. Hell^ and F, Liganig, diftinguifli of Vienna; themfelves aftually. There is one at Tyrnaw in Hungary ; one in A- knd, at JVilna, &c. &c. Of Wibui.
Such are the renowned Eftablifhments to which we are indebted for our Knowledge of the Syftem of the World, and 'the Improvements it receives every Day ; but there are a great many Branches, which require fuch long Operations, and fo great a Space of Time, that Pofterity will always have new Obfervations and Difcoveries to make. Multum igerunt qui ante nos fuerunt,fed non peregerunt, multum adbuc re flat Ope- ris multumque reftabit ; nee ulli nato pofl mille Sacula pracludetur Occafio aliquid adbuc adjiciendi. (Sxnec. Epif. 64.)
XVIII.
Thofe great Exahiples of all the civilized Nations of the World,. have at length brought the Noblemen and. Gentlemen of this Country,,,
XXIV SYSTEM OF THE
to a true Senfe of the Importance of procuring to their Childrtflf thofc Means of Inftrudiont which may prevent their regretting in a more advanced Age, the mif-fpent Time of their Youth ; which is the only Period of Life in which they can apply themfelves with Succefs^ to the Study of Nature : In this happy Age, when the Mind begins to think, ' and the Heart has no Paffions voilent enough to trouble it. Shortly} 4he Faflions and Pleafures of their Age will engrofs their Time» and when the Fire of Youth is abated, and they have paid to the Tunralt of the World the Tribute of their Age and Rank, Ambition will gain the Afcendant. ' And though in a more advanced Age, which will not however be more ripe* they ihould apply themfelves to the Study of the Sciences, their Minds having loft that Flexibility which they had in their youthful Days, it is only by the Dint of Study, they can attain what they might acquire before with the greateft Eafe. Publick To improve therefore the Dawn of their Reafon, to fecure them from
€ftibUfli*ain Ignorance, fo common among People of Condition, which expofes them die City of daily to be fcandaloufly impofed upon, to accuftom them early to the DobliD for Habit of thinking and afiing on rational Principles, a School ha« been Yourb^ln^ eftablifhed on the moft approved Plan, where, after having fpent fome evry Bnnch Time in learning Elementary Mathem aticks, they are initiated ^^tMadw *" ^^^ Miftcries of Sublime Geometry, and of the Infnitesimal raaticks pw CALCULATION; from thofe abftraft Truths, they are led to the Dif- fuant to the covery of the Phenomena of Nature, they are taught how to difoeni of ^^^N^ their Caufes, and meafure their Effeds ; from thence they are con* bicmen and duded as far as the Heavens, thofe inunenfe Globes which roll over our Gentlemen Heads with fo much Majefty, Variety and Harmony, letting themfelves of tbefing- ^^ approached ; they are taught how to obferve their Motions, and io- domofire- veftigate the Laws according to which this material World, and all o?Feb^i* Things in it, are fo wifely framed, maintained and preferved. zytfs! "^'^ To relax their Minds after thofe Speculations, they are brought bade to Earth, where, free from all Spirit of Syftem and Refearch of Caufes, they are taught how to contemplate the Wonders of Nature in detai]. But as it prefents an immenfe Field, whoTe whole Extent the greateft Genius cannot compafs, and the Inquiries the moft valuable, and the only worthy of a true Citizen are thofe by which the Good of Society is promoted, they are confined particularly to the Study of what may contribute to the Perfeftion of ufeful Arts, fuch as Agriculture and Commerce, that thus initiated in the true Principles of the dif- ferent Branches of Knowledge fui table to their Rank, having completed their Studies in this School, far from being obliged to forget what they have learned, as hitherto has been the Cafe, thev may be enabled to purfue with Succefs, fuch Inquiries as are beft adapted to their Genius.
r
r^"' ^ — "^fir
PHYSICAL WORLD. XXY
PregTifs of tb€ DifcvoerUt relative to the Syflem of tbe VTortd.
L
X H E firft Views which Philofophcr* had of the Syftcm of the World, rf ' PhTbS^ were no better than thofe of the v ulgar, being the immediate Sugeeftions ^*g a •^ of Senfe; but they correded them; thus the firft Syfttm fuppofed theofWworl4 Earth to be an extended Plane^ and the Center round which the Heaven- ly Bodies revohred.
The BaAjhnians from examining the Appearances of Sence were the of the B^bf- firft who difcovered the Earth to be round, and the Sun to be the Cen- loaiut, and ter of the UniYerfe (m) in thefe Points they were followed by Pvtbagoras and «'/y'*«8** his School
TIL The true Syflem of the World being difcoirered, it may appear fur-
Sizing that the Notion of the Earth's ^ing the Center of the Celeilial otions (hottld generally prevail: for.tho' on « fuperficial Survey it feems to be recommended by its Simplicity, and to fquare exaCtly with the Ap- Ethtu ihte pearances of S^ence, yet on Examination it is found entirely infufEcient to btve bcca. explain the Phenomena, and to account for the Heavenly Motions : This "^^ conftrained Ptolemy and his followers to incumber and embarrafs the Hea-|^e£artli Tens with a Number of Circles and Epicycles equally arduous to be con- to be tt reft 4 ceived and employed, for nothing fo difficult as to fubftitute Error in thel^^"^"^ - room of Truth* i-toiomy.
Probably the Influence of Arifiotle^ Authority^ whofe Writings in Ptoh^ inf% Time were held in the higheft Efteem, and confidered as the Standard of Troth, lead this Philofopher into Error : But why did not Ariftotle de- clare in favour of the true Syftem, which he knew, fmce he en- deavoured to overthrow it: this Reflexion is fufficiently mortifying to the Pride of tbe Human Underftanding, whatever was the Caufe, thus much is certainy that the Ptdomaic Syftem generally prevailed to the Time of O- pomieusk
IV.
This great Man revived the ancient Syftem of the Saiyhnlanx, and of Co^eraicdi] Pffb^orof which he confirmed by fo many Arguments aiod Difcoveries revive« che that Error could no longer maintain its Ground againft the Fvidence of J^'^^ jf^;| Demonftration ; thus the Sun was reinftated hvCoperhicus in the Center of thnoru. * the World, or to fpeak more exa£tly, in the Center of our Planetary Sj&eau
(n) NawTov b his Botfk ps Systkmatk Mvitdi fttiribvtei ihli Opiaida to Noma Poapilius, tad iayi, (Pa^ 1 .) it wm to reprereot the Sua io the Ceater of tbe Celeftiri Oihict that Noma caufod t rouid Temple to be built ia hQoOw of Tefti, the Goddefc of Fire « the Middle ^ vhkh s petpetml Fire wst preferred.
1
XXVI SYSTEM OF THE
V.
Syftem of ^^^ Copcmican Syftem eafily accounts for all the Celcftial Phenomena^ TithoBraheand tho' Obfervation and Argument are equally favourable to it, yet 7/Vitf- Brabe an eminent Philofopher of that Age refufed his aflent to th^ Evi- dence of thefe Difcoveries, whether deluded by an ill- formed Experiment* (b) or carried away by the Vanity of making a new Syftem, he compofcd one which fteers a middle Courfe between ihofc of Phlomy and Copernicus \ he fuppofed the Earth to be at reft and the other Planets which move round the Sun, to revolve with him round the Earth, in the Space of 24 Hours ; thus retaining the moft exceptionable Part of Ptolomy's Syf- tem, viz. the inconceivable Rapidity with which tht primum Mobile is fuppofed to revolve, from whence we may learn into what dangerous Errors the mif- application of Genius may lead us. . .
The Difco- Tho^ Tycbo erred in the Manner he made the Celeftial Bodies move, \«"«» ^^^ yet he contributed very much to the Progrefs of the Difcoveries relative to Syft«n of* *^^ Syftem of the World, by the Accuracy and long Series of his Obfcrva- the World, tions. He determined the Pofition of a vaft Number of Stars to a Degree of hI!^T*^df exaSnefs unknown before ; he difcovered the Refraction of the Atmofphere, ^ ^ °' by which the Celeftial Phenomena are fo much influenced ; he was the fird who proved from the Parallax of the Comets, that they afcend above tho Moon ; he was the firft who obferved what is called the MoorCs variation \ and in fine, it is from his Obfervations on the Motions of the Planets, that Kepler who refided with him, near Prague, during the laft Years of his Life, deduced his admirable Theory of the Motions of the Heavenly Bo- dies.
yi. How mvch Copernicus undoubtedly rendered important Servicts to Human Reafon remaiDcd to by rc-eftablifliing the true Syftem of the World : It was already a great ]rd i^«r^o^ P^***^ gained that Human Vanity condefcended ta place the Eirth in the Num- peroicBt. her of the fimpte Planets; but much ftill remained to be difcovered : neither the Forms of the Planetary OrbitSj^ nor the Laws by which their Motions are regulated, were known \ for thefe important Difcoveries we are in- debted to Kepler.
(b) It WIS objedled to Coperaictts, that the Motion of the Earth would produce EftA* which did not take Place ; that, for Example, if the EartK moved, a Stone dropped from die Top of a Tower, ought not to &11 at the Foot of it, becauCe the Earth moved during the Tidi •f the Stone*s defcent^ that notwithftandiog it falls at the Foot of the Tower. Coriivicoi replied, that the Situation of the Earth with rel)>e£l to Bodies that fait on its Surface wai tbe fame as that of a Ship in Motion, with refpefk to Bodies that are made to fall in \i\^ afTerted, that. a Stone let hW from the Top of the Mad of a Veflel in Motion, woold fiUl i* the Foot of it. This Experhnent which is now inconteflible was then ill-made, and wm CheGn^ «r the Pretext which made Trcho reluf^ his ai&nt to (he PifcQveries of CopenucQi.
r
PHYSICAL WORLD. XXVII
This eminent Philofophcr found out, that the Notion which generally pre- ^
bailed before his time, that the Planets revolved in circular Orbits, was cf-ofKe^eV Toncous; and he difcovered, by the means of Ticho's Obfervations, that tbc el pticiif the Planets move in ElHpfes, the Sun refidtng in one of the Foci : and ihat ^^^ oibiti. ihty move over the different Parts of their Orbit, with different Velocities, fo ^][i^'**Jf that the Area defcribed by a Planet, that is, the Space included between theiheftrcmitad firaight lines drawn from the Sun to any two Places of the Planet, is always ^« '«»«•• proportional to the time which the Planet employs to pafs from one to the other. '
Some years afterwards, comparing the Times of the Revolutions of the j^^j^^^ different Planets about the Sun, with their different Diftances from him, he which Tub- found that the Planets which are placed the far theft froni the Sun to move fift» between iloweft, and examining whether this Proportion was that of their Difttnces,j|^"^*^ he difcovered after many Trials, in the Year i6i 8, that the Times ofthe diftta* their Revolutions were as the Square Roots of the Cubes of their mean ^^ Diftances from the Sun.
vn.
Kepler not only difcovered thefe two Laws, which retain his Name, and which regulate the Motions of all the Planets, and the Curve they defcribe^ but had alfo fome Notion of the Force which makes them defcrtbe thia Curve; in the Preface to his Commentaries on the Planet Mars, we difcover the firft Hints of the attradive Power ; he even goes fo fiir as to fay, that the Flux and Reflux of the Sea, arifes from the gravitv of the Waters towards the Moon: but he did not d^luce from thb Principle what might be expeded from his Genius and indefatigable Induffay. For in his Epitome of Aftrono* niy(c) he propofes a phyfical Account of the planetary Motions from quite different Principles; and m this fame Book of the Planet Mars, he fuppofes in tiie Planets a iriendly and a hoftile Hemifphere, that the Sun attrafis the one jindrepek the other, the friendly Hemifphere being turned to the Sun in the nianets defcent to its Perhihelium, and the Hoftile in its Recefs.
VIIL.
The Attradion of the Celeftial Bodies was fugeefted much more clearly ly M* Hook, in his Treatife on the Motion of the Earth, printed m the Year 1674, twdve Years before the Principia appeared. Tbe/e are bis Wordsf Page 27» ^^ I fliall explain hereafter a Syftem of the World, diffierent in ma* M ny Particulars from any yet known, anfwering in all Things to the com* «< roon Rules (^Mechanical Motions. This depends on the diree following tf Sufpofitions, ^
(c) Sse Gxtfoiy, Bosk i^ h|« #>;
XXVIII SYSTEM OF THE
''*S!!r ^*^ ^^ ^^^^ ^^^ cddlial Bodies, whatever, have an Attradton, orgravitatti^ ^rnuH*!^ " Power towards their own Centers, whereby they attrad, not oiJy their irsai^A* ** o^n Parts and keep them from flying from them, as we may obferve th« '* Earth to do, but that they do alfo attrad all the other celeftial Bodies that ** are within the Sphere ot their ASivity ; and conrequently not only the '' Sun and the Moon have an Influence upon the Body and Motion of the- ** Earth, and the Earth on the Sun and Moon, but alfo* that Mercury, Ve« ** nus, Mars, Jupiter aud Saturn, by their attradive Powers, have a confi* ^* derable Influence upon the Motion of the Earth, as in the fame Manner '' the correfponding attradive Power of the Earth hath a coniiderable inflo-^ ** ence upon the Motion of the Planets/'
'' ad That all Bodies whatever that are put into adired and (imple Motion,^ ** will fo continue to move forward in a ftreight Line, till they are by fome ^* other effedual Power defleded and turned into a Motion, defcribing a Cir«^ ** cle, an Ellipfe, or (bme other more compounded Curve Line."^
** ^d That thefe attra&ive Powers are fo much the more powerful in ope^ << rating, by how much the nearer the Body wrought upon is to their own *« Center."
** Thefe feveral Degrees I have not yet experimentally verified, but it is. ** a Notion which if fully profecuted as it ought to be, will mightily affift the ** Allronomer to reduce all the celeftial Motions to a certain Rule, which i «< doubt will never be done true without it. He th^tt underftands the Na-- " tureof the circular Pendulum and circular Motion, will eafily underftand << the whole Ground of this Principle, and know where to find Diredions << in Nature for the true ftating thereof. This I only hint at prefent to fuck <* as have a Capacity and Opportunity of profecutiog this Enquiry, &c/*
IX.
We are not to ima^ne, that this Hint thrown out cafually by Hpoi, de» trads from the Glory of Niwton, who even took Care to make Mention oC it in his Book tU S^tmati mundi (d)» the Example of H«oi and KepUr makea us perceive the wide Difference between having a Notion of the Truth, aixf being able to eftablifli it by irrefragable Demodlration; it alfo fliews us how little the greateft Sagacity can penetrate into the Laws and G^nftitution o£ Nature^ without the Aid and Diredion of Geome^y.
X.
Scrtate ao- Kephff w^o made (iich important Difcoveries» whilft he fbltow^ thu qn«
tkttsoflUperring Guide, affords us a convincing Proof of the Errors into which the
ler. brighteft Genius mav be feduced, by indulging the pleafing Vanity of in*
venting Syftems j who could believe, for Inftancci.uuit fuch aMu couldt
MflA4itioa tf 1)31.
' P H YSICAL WORLD. XXtt
idopt the wild Fancies and whimfical Reveries of the Pythagoreans, eon- €erning Numbers: yet he thought that the Number and intenral of the pri* mary rlanets bore fome Relation to the five regular Solids of Elementary Ge- ometry (e), imagining that a Cube infcribed in the Sphere of Saturn would touch the Orb of Jupiter with its fiJt Planes, and that the other four Kgular Solids, in like Manner, fitted the Intervals that are betwixt the Spheres of the other Planets: afterwards on difcovering that this Hypothefis did not iquare with- the Diflances of the Planets, he fancied that the celeftial Moti- M38 are performed in Proportions correfponding with thofe^ according to which a Cord is divided in order to produce the Tones which compofe the Odave in Mufic (0 ;
Kepter having fcnt to Ticho a Copy of the Work, in which he attempted' to eftablifh thofe Revcries.Ticho recommended to him, in his An- Wife cmw- fwer(g), to relinquifli all Speculations deduced from firft Principles, all ^^'%^^J^ ibning a Priori, and rather fiudy to efbbHfh hisRefearches on the fure and *^ firfld Ground of Obfervation.
The great Hugbens himfelf (h) beHeved that the fturth Satellite of Saturn, ^'»««fica which retains his Name, making up with our Moon and the f6ur Satellites of HMhce^ Jupiter fix fecundary Planets, the Numbenof the Planets was complete, and It was labour loft to attempt to difcover any more,, becaufc the principle Planets are alfo fix in Number, and the Number Six is a perfeS rlumber^ as being equal to the Sum of its aliquot Parts, i> % and 3.
XL
It was by never deviating from the moft profound Geometry, that NeW'^ Un dffcovered the Proportion in which Gravity ads, and that in his Hands ihe Principle of which Kepler and Hook had only fome faint Notion, became the Source of the moft admirable and unhoped for Difcoveries. . AdYanisgcc
One of theCaofet which prevented Kepler from applying the Principle ^f^lIpUr •F Attradion to explain the Phoenomcna of Nature wirh Succefs, was hisin hit time* fenorance of the true Laws of Motion. Newton had tho Advantage over**»«»*»«®nf®f Kepler of profiting of the Laws ofMotion, eftabliftied by Hughens, which £221^ n1" he has carried to fo great a Height in his Mathematical Principles of Natu-derftood. stdPhilofopby.
xn, . The Maihemalfcal Principle of Natural- Phifefophy confift of three ^^^gjjj^ Books, befides the Definitions, the Laws of Motion and their Corollaries ; tlie fi^ Book-is compoted of fourteen Sedions^ the fecond contuns nine,
(^) M]rfteriiiin Cofinogi^iciBB* • (f). MyOvivn CoTmogniphiaini^
(g) Uti fnfpeofit fpeGaUuiooilms ^ priori ^eTcei^MtiNi tmiirem pettw «d «lbf«rvitiOfk€t ^^M finml oUcrcbtt confidenndM idjiccrcai «(it U Kepler who fpeaks) oou» in fcauidtm< «iitMQcm os](fteru cefmognphsd
XXX SYSTEM OV THE
and the third, the Application of the two firft to the Exjrfication of the Phoenomena of theSyftemof the World.
XIII
The Princtp'm commence with eight Definitions 9 Newton (hews in the ^fiuiiom. t^Q fir (I ho^ the^iwtn///; of Matter and tbe ^antity of Motion fliould be meafurcd ; he defines in the third, the Fis intertt^e, or refitting Force,whKh all Matter is endued with ; he explains in the fourth what is to be undcrftood by a^ive Force ; he defines in the fifth 4be centripetal Force, and lays down •in the fixth, fevenih and eighth the Manner of meafuring its abfolute ^anhtj/f its motrix ^antity, ^nd itr accelarative ^antity ; atlerwardsheclUblilhcs the three following Laws of Motion.
XIV.
rtwiofmoift. That a Body always per reveres of iifelf, in its State of Reft, or ot •sioji. uniform Motion in a ftraipht Line.
ad. That the change of Morion, is proportional to the Force imprcff"*
and is produced in the ftraight Line in which that Force a&s.
3d. That Adion and Readion are always equal with oppofite Di«
regions.
XV. t^e'^afcai! Netvton having explained ihofe Laws, and deduced from them fcvenl oa coottin* Corollaries, commences his firft Book with eleven Lemmas, which com- the princi- pofe the firft Seftion, he unfolds in thofe eleven Lemma; his Method of ^MRml^^' Prime and ultimate Ratio f ; this Method is the Foundation of infinilcfljnttl geometry Geometry, and by its Affiftance, this Geometry is rendered as certain 11
that of the Ancients, the other 13 The thirteen other Sedions of the firft Book of the Princlpia, are employ lofiriont'^on^*' in demonftrating general Propofitions on the Motion of bodies, Abftrac- £e im!tion ^tng from the Species of thefe Bodies and of the Medium in which tbef
^fbodiet. move.
It is In this firft Book that Newton unfolds all his Theorv of the graviu* tion of the celeftial Bodies, but does not confine himfelf to examine tbe Queftions relative to it j he has rendered his Solutions general^ and has givett a great Number of Applications of thole Solutions.
XVI.
h^tftf In the fecond Book, N^ton treaU of the Motion of Bodies in refilbS cfae motioiior Mediums.
bodiei io re- fhi, fecond Book which contains a very profound Theory of Fluids, mm diral "** ^^ ^^^ Motion of Bodies which are immeiied in them^ feenois to have beefl to deftined to over throw the S vfliem of Vortices,though it is only m the Scholi-
^J^***^^;^ urn of the laft PropoCtion^that Newton openly attacks Dejcgrtitp and ffVV^ ^Di^m^^ ^ celeftial Motions are sot produced by Vorticei.
r
PHYSICAL WORLD. XXXI
XVIL
^ In fine, the third Book, of the Principia treats of the Sy aem of the World ; ™j2,^Jf In this Book, Newton applies the Propcfltions of the X^o firft : inihcr^ftem .this Application we (hall endeavour to follow ^(rw/on, and point out theofthtwwUL. Connexion of his Principles, and (hew how naturally they unravel the Me« chanifm of the Univerfe.
xvin. The Term, Attraftion, I" employ in the Senfe inVhich Newton has defined Whtt iV it, underftanding by it nothing more than that Force, by which Bodies tend^^^*>y^^* towards a Center, without pretending to aflTign the Caufe of this Tendency. ^ *"^^'
Principal Phenomena of the SyJIem of tbe World.
X HE Knowledge of the Difpofition and Motions of the Celeftlal Bo- dies muft precede a juft Enquiry into their Caufes. It will not therefore appear unneceflary to prepare our Readers by a fuccinddefcription of our planetary Syflem for our Account of the manner ^^ti;/0/i demonfirates thepowers which govern the Celeflial Motions and produce their mutual Inffuences. This De- fcriptionmuft neceffarily comprise fome Truths, difcovercd bythatilluflrious Philofopber^ the Manner he attained them with be defcribed in the Sequel.
The celeftlal: Bodies that compofe our plknetary Syftcm, are divided into of "the celt ' Primary Planets^ that is, thofe which revolve round the Sun, as their Gf»/^r '*** *>«*»«• and Secondary Planet i^ othcrwife, called Satellitety which revolve round their 2^y['^ rcfpeaive Primaries as Centers: There are fix Primary Planets whofc into priod- Names and Charadera are as follows,^ i«i •^ <ccoa
i# JL£ ^rypltnet*.
9 Mercury^ <^, '
^ Fenuff Kamei tod
^ Tbe Earthy, •?!j:'^"'
o iWtfr/, fiJptJpMaet*.
3. Jupiter^,
1) Saturn*.
In eniimcratihg tBe Primary Planets, wc follow the Order of their Dif-^^^J[7 tances from the Sun, commencing with thofe which are neareft te him. thtt iitve
The Earth, Jupiter, and Saturn, are the only Planets which have been^«**»^«^. difcovered to be attended by Secondaries : TheEafthhas only one Satellite, ^^J^^^° namely, the Moon ; Jupiter, has four, and Saturn five, exclufive of his Ring, ftiai bodies of fo that our Planetary Syftem is compofed of eighteen celeftial Bodies, in»<»or pUneu. eluding the Sun and the Ring of Saturn. * , . ' SecooTdi-
^''' vifioa of the
The Primary Planets are divided into fuperior and inferior Planets, the pUaeu into iflferior Phntti are thofe which are nearer the Sun than the Earth is j thcfe^^^VJ*^ '■*•
XXXn S V S T E M OF THE
^
which tre are Merciiry and Venus ; the Orbit (a) of Venus includes that of Mefcnfy ^^''^'iLj' *"^ •^'^ ^^* ^""» *"^ ^^^ Orbit of the Earth is exterior to thofc of Mcrcuqr what 't^T ^nd of Ve nus^ and inclofesthem and the Sunalfo. tmiofe- This Order is difcovered, by Venus aiid Mercury fometimes appearing to "•"'• be interpofed between the Sun and us, which could never happen unlcfs how chi« or-^hefe Planets revolved nearer the Sun than the Earth, and it is very percciv* ier hat beett able that Venus recedes farther from the Sun than Mercury ^oes, andam- difcovcrcd. fgquently its Orbit includes that of Mercury.
which trt *^^^ fupcrior Planets are thofe which are inoVe diftaift from the Sun than theVuperior ^^^ Earth 18, thefe are three in Number, Mars^ Jupiter %xA Saturn \ we pitiMu and know that the Or'bitsof thefe Planets indole the Orbit of the Earth, be* Trrli *****' caufe the Earth is fometimes interpofed between thciti and the Sun. ^et".**" The Orbit of Mars incWes that of the fearth, the Orbit cS Jupiter thst of Mars, and the Orbit <rf Saturn that of Jupiter f^ fo that of the three fu- perior Planets Saturn is the remoteft from the Earth, and Mars is the neareft. hdw ft hat This Arntingement b difcovered by thofe Planets which are nearer the beeo difco- Earth (b) fometimes coming between the Eye and the Remoter, and intcrr vcred, ccpting ihem from our View.
IV.
AU tfaePlanets are opaque Bodies ; thb apoears of Venus and Mercury,
Th« plaoett becaufe when they pafs between us and the oun, they refemble black Spots
-flre opi^ae traverfing his Body, aud aflTiime all thofe various Appearances which are
*^^ called Phafcs) that is, the Quantity of their Illumination depends on their
Pofition in refped to the Sun and us.
For the fame Reafon, fmce Mars has Pbafes we Infer his Opapity, and the fame Conduiion is extended to Jupiter and Saturn, becaufe their Sate- lites do not appear illuminated while their Primaries are between them* and the Sun which proves that that Hemifphere of thofe Planets whidi is tunn The plaaeti ^ ^^om the Sun is opaque : Laftly, we know that the Planets are fphcri' w«rphcrical cal Bodies, becaufe, whatever be their Pofition, in refped of us, their Sur« face always appears to be terminated b]^ a Curve.
We conclude that the Earth is fpherical, becaufe in Eclipfes her Siaddw, always appears to be bounded by a Curve, and when a Ship faib out of fight, it gradually difappears, firft the Hulk, next the Sails, and laftly the Maft, finking to the Eye and vaniihing, and moreover, \\ the Earth was an extend* cd Plane, Navigation would luive difcover«I its Limits and Bbandaries the contrary of which is proved by manv Voyagers, fuch as Drake, ForbiA# and Lord Anfon, who have failed rouno the World.
(a) Ori>it b tlieCwfewUdia^aactdtlMiw itimltiaf riwd (he Bodf which Aim It ai a Center.
(b) Wolf *« ElcmMs «f AOrgmar*
PHYSICAL WO R LT). XXXIII
V.
All that vre know therefore concerning the primary Planets, proves that J***'^,'*^^ they are opaque, folid and fpherical Bodies. tUof'thc
The Sun appears to be a Body of a Nature entirely different from the Pla- famcMtorc, nets ; we know not whether the Parts of which it is compofed be folid or ^
.fluid ; all that we Can dtfcover is, that thofe Parts emit light & heat, and burn ue that the when condenfed and aflembied in fufiicient Quantity ; hence we may probabl; tli« 6«o iira •conclude, that the Sun is a Globe of Firerefembling teire(lrialFire,*fince thc«^*^*^^** Effeds produced by this<and the folar Rays, are exskQly the fame.
VI.
All the celedial Bodies compleat their Revolutions round the Sun in Ellip- in ^htt ^ fes (c)y more or lefs excentic, the Sun refiding in the common Focus of all curve thece their Orbits j hence the Planets in their Revolutions fometimes approach J*^"|J^^^t' nearer, and fometimes recede farther from the Sun ; a right Line pafling bout the fun. through the Sun and terminating in the two Points of the Orbit of a Planet, ^^^ {, ^^ . which are neareft and remoteft from the Sun, is called the Line of the Apfides^ line of the the Point of the Orbit which is neftreft the .Sun is called the PeriUlium \ 'pfi^J" ^^ itnd the Point of the Orbit which is remoteft from the Sun is called the |[^ pj^eli Apbeliunt. vin.
The primary Planets in their Revolutions round theSon, carry alfo their i^ ^htc di- Satellites, which at the fame Time revolve round them as their Centers. itAionthe All fhcfe Revolutions are performed in a direaion from Weft to Eaft (d),Pj,"^' ''" There appear from Time to Time Stars that move in all DircQions, and r ' -with aftonifliing Rapidity, when ibey are (ufficiently near to be vifible, ihtkj^ ^®* are called Comets.
Wehave notyetcolle8ed Obfervations fufficienttadetermjne their Num- ber, all that we know concerning them, and *tis but lately that the Dif- Icovery has been made; is that they are Planets revolving round the Sun like '^* f **"**' the other Bodies of our Sy ftem, and that they dcfcribe Ellipfes fo very cxcen- "* ^ "*^* trie as to be vifible only while they are roovieg -over a very fnuU Part ot * their Orbit.
vn. All the Plaiiets'in their Revobtionsrouvd the 'Sun, dbCsrve the <wo Laws Theplmets M>f K^er. •o'^ ^^^*
ObferTfttions evince, that the Comets obferve the firft bf thfefeLaws,^^^[''J[l5j^p *jian*e!yi that whi*h makes the celeilral Bodies --(e) defcfibe eqcral Areas in e-kr
(0 A Species bf Curve, which is (he fame "with what Is commonly called an Oval, the foci are ' the points in which Gardeners ia, their pegs in order to trace this curve of which they make t ' frequent nfe.
(d) The SpeAator is fuppofed to be placed on the Earth.
(e) By (he Word Area, in general is underftood ^ Stkrface, here it (ignifies the Space sfi- ciadcd between tv/b Uaf » dr'awo irom tb« Ceoier co iwo foists wtier e the Pi«D9t i« fbiuzdi
XXXWr SYSTEM OF THE
qual Times ; and in the fcqoel it wifl be flmwir, diat all the Obfemtions that have hitherto been niadc, concerning their Motions, render it highly proba- ble that they arc regulated by the fecond Law, that is, that ihar pcnodic (i^ Times are in the fefquiplicatc ratio of thdr mean Diftances.
VIII. .
f^fpMiht Admitting thefc two Laws of Krplrr, confirmed by all aflronoroical Ob-
T*^* /^ fcrvations, from them we may derive fcveral convincing Proofs of the Mo-
• •^ tion of the Earth, a Pobl which had been fo long conteftcd ; for fuppofing
the Earth to be the Center of the Ccleftial Motions, thefc two Laws afc
' not obferved ; the Planets do not defcribc Areas proportional to the 1 im«
around the Earth, and the periodic Times of the Sun and «]f Moon, tor
inftance, round this Planet, arc not as the Square Roots of the Cubes Gttnw
mean Diftances from the Earth ; for the periodic Time of the Sun aroundiDc
Earth, being nearly thirteen Times greater than that of the Moon, il$ i^"-
tance from the Earth would be, according to Kepler's Rule, bctwcenfavc
and fix Times greater than that of the Moon, but ObfenrationsdemonlWK,
that this Diftance is about four- hundred Times greater, therefore, admitn^
the Laws of Kepler, the Earth is not the Center of the celcftwl i^*-
volutions. ^ , , p.,,fg
The centripetal Force(g) which Newton has demonftrated.to.be the UJ^
of the Revolutions of the Planets renders the Carve they defcribe »«^"° r"
Center concave (h) towards it, fince this Force is exerted in drawing tne
off from the tangent (i) ; now the Orbits of Mercury and Venu^ m opj
Parts, arc convex to the Earth ; of confequence, the inferior Planets
not revolve round the Earth. . ^
The fame may eafily be proved of the fuperior Planets j forthetc
♦hofc Areas trc proport'tonal to the Times, that is, they art greater Or lefs, « ^^ ^*"** which they are defcribed are longer or Ihorter. , , ^^^
(f ) Periodical Time, is the Time that a Planet employs in corapleating ita Revolution m iW ' An Example, of Sefqaiplicate Rauo wilf render it more intelligible than a Defini"<»» ^^ then the mean Diftance of Mercury from the Son, to be 4, that of Venus 9, ^ P* ^^ Time of Mercvy 40 Days, and let the periodical Time of Venns be required, ^^^'^^^^^^^ firft Numberi 4 and p, there wUl refult 64 And 7 2p ; afterwards extraaing the ^'^f^Tt^ tbefe two Numbers, there will be found 8 for that of the firft, and ay for that of the ^^^^^ | by th« Rule of three you will hive 8 : 2 7 : : 40 : 1 3 $> That is the Square-Root of the ^^^y mean Diftance of Mercury from the Sun, is .to the Square Root of the Cub^ •f the mean p» ' Venns from the Sun, as the periodic Time of Mercury round the Sun is to the periodic ** . ^,t of Venus roun<|. the Siip,which is found to be 135,. accordipg to the Suppofitions w<iic been made, and this is what is called Sefquiplicate Ratio. . ^ , ^^
(g) The Word Cemthfetal Force carries its Definition along with it* /®^ *' ^ ■o more than that Force which makes a Body tend to a Center. ^^.
(h) The two Sides of the Cryftal of a Watch may ferve to expUia ihofe ^. j^. CAVE and Convex^ the Side exterior to the Watch is convex, and that wbicb i' Side of the Dial-plate is concave. (i) A Tangent is t right LiM which touches % Corvti without cutting it.
PHYSICAL WORLD, XXXV
Ametimei observed to heJire^(k), {omttimti JlMtionarf, and afterwards retrograde i all thofe Irregularities are only apparent and would vanilh if the ^rth was the Center around which the heavenly Bodies revolved^ for none of thefe Appearances would be obferved by a Spedator placed in the Sun, fince they refult only from the Motion of the )£arth in its Orbit combined with the Motion of thofe planets in their refpeflive Orbits ; from hence wc may fee the Reafon why the Sun and the Moon are the only heavenly Bodies that appear always dired; tor as the Sun defcribes noOrbrt^ its Motion can* not be combined with that of the Earth, and as the Earth is the Center of the Moon's Motion, tons (he fliould always appear direft; as would all the Planets to a Spedator placed in the Sun.
When Copernicus firft propofed his Syftem, an Objc6Hon was raifed againft it, taken from the Planet Venus by fome who alledged, that if that Objeftioft Planet revolved round the Sun ihe (houid appear to have Phafcs as the Moon, "*«*f «® c» to which Copernicus anfwered, if your Eyes were fufficiently acute youJ^^J.^^^^ would adually obferve fuch Phafes, and that perhaps in Time fome Art maypiaaetveaae be difcovered fo to improve and enlarge the vifual Powers, as to render thofe Phafes perceivable: This Prcdiaion of Copernicus was firft verified byjlj^i^"^^^ Galileo, and every Dtfcovery that has been made fince on the Motion ohioa the heavenly Bodies has confirmed it.
IX-
The Planes (I) of the Orbits of all the Planets interfeA in right Lines pafling through the center of the Sun, fo that a Spedator placed in the Center of the^"^' f ^ Sun would be in the Planes of aU thofe Orbits. Ort>iu imer
The Right Line, which is the common Sedion of the Plane of each Or- feet bit, with the Plane of the Elcliptic, that is, the Plane in which the Earth v^hat h nm moves, is called the Une of the nodes of that Orbit, and the extreme Points^crftood by of this Seaion, are called the Nodes of that Orbit. Jj^ j|^^«^«e
The Quantities of the Inclination of the Planes of tlve different Orb!ts,the m^ with the Plane o{ the Ecliptic, are as follows, the Plane of the Orbit of^' ^ orbit Saturn is inclined to the Plane of the Ecliptic in an Angle of 2<i f, that of. ^ . Jupiter Id t« that ^f Mars in an angle fome what lefs than id, that of Venus o/tbc'oT fome what more than ^^ \, and that of Mercury about ^d. bits to the
^ Ecliptic
The Orbits of the primary Planets being Ellipfea, having the Sun in one of their Foci, all thefe Orbits are confequently ezcentric, and are more or lefsfo,according to theDiftance between their Centers and the Point where the Sun is placed.
(k) A Plinet it fatd to be DimtCT when it appears to move tccordiag to the Order of the Signs, -that is, froai Aries to Tanros, from Tavrvs to Gemini, &c. which is alfo faid to move ja conTeqnentia, it is ftatiooary when it appears to correfpond for fome Time to the fame Poiou of the Heavens, and in £ne it is RiTJkooaADa when it appears to move contrary to the Order of the Signs, which is alfo faid to move in Anteccdentia, that is, from Gemini to Taums,^ from Tanms to Aries, &c.
(I) Tkf phuie «f the Orbit of a Fiaiist if the fwfiice oa which it isfiippoicd fm990.
XXXVl yrSTEM OF THE'
•xccotricitf Theeicentrictty of aU tboTe Orbits have been oKtiiired, indhDve ban
ILr^tt l«mi^^"'^ ^' foHows, in dccimtl Parts of the fcmidiimrter of the Earth's orbit,
ditmcicn fuppofed to be (kTidei) iiilo 100,0^^ Parts,
•fiht ttrth That of Sanim^ $4207 Patts*
That of Jupiter, 25058
Thtt of Mars, 141 15
That of the Harib, 469a
Th*t of Vtnos, 500
And in fine, that of Mercury, 8149 Psrt$.
The excentricity oi the Planets mcafured in decimal Parts of the femidi*
o*MhV'X' ameter ot their Orbits, fuppofed to bt divided into 100,000 Parts, sie
nc(» io femias fotloWS,
.'itrntifrtoi rhut of Saturn, 5683 Psiti.
urn^iftit »j-,^^^^^f Jupiter, 4822
That of Mars, 9263
That of the Earth, 5700
That of Venus, 694
Thst of Mercury, 21000 Fwls Whence it appears that the Excenlrictty of Mercnry is aknoft infenfiUc.
XL
Proportion The Planets are of different Maenitodes; of the Earth alone we know the »r ihf (liftahfolute Diameter, becaufe this Planet is the only one whofaCircumfierencc j^**^*^^^,^ admits of adual Menfuration, but the relative Magnitudes of the Diame- *ters of the other Planets have becndifcoyered, and the Diameter of the Sua being taken for a common Mcafure, and fuppofed to be dividcdinto 1000 Parts: That of Saturn is 137
That of Topiter 181
That of Mars 6
That of the Earth 7
That of Venus 12
That of Mercury 4
Hence we fee that Mercury is the leaftof all the PlaoeCs» for Spheres are as the Cubes of their Diameters.
xn. ^ The Pknets are phced at different Diftancaa from the Siob taking the ^ ^il^, Diftance of the Earth from the Sun for a common Meafuro, and fuppofinff firfDthcfaott divided inta ioo/KX> Parts^ the mean Diftnacea of the Pfanela are as follows.
That of Mercury is 38710
That of Venus 7333
That of the Earth loooo
That of Mars 1 5 2369
That of Jupiter jaoi loi
In fine^ that of Salona. 9$38po
PHYSICAL WORLD. XXXVII
The mean Diftancesof tjic Pun and the Planets from the Earth, have al- Dj^^^y^,^ fo been computed in Semidlametcrs of the Earth; the mean Diftances of thcti^ pUoct^ Son, Mercury and Venus from the Earth are nearly equal> and amount to^rom tbt aaooo Semidiametcrs of the Earth, thai of Mars 1533500, that of Jupiter*'"** 1 15000, and that of Saturn 21 0000.
XIII.
The Times of the Revolutions of the Planets round the Sun, are lefs in Periodic Proportion of their Proximity, thus Mercury the neareft revolves in 87 Days,**"** ^^ ^^ Venus next in Order revolves in 224, the Earth in 565, Mars in 686, Jupi-'tJ^^****^ terio 4332, and Saiurn the remotcil from the Sun in 10759, the whole in round Nuspbers.
XIV.
The Plancis, befides their Motion of Tranflation round the Sun, have a-Rotitlop of Bother Motion Qf Rotation round their Axis, called their Dt urnal RevolutionJht phatu
We only know, the diurnal Revolution of the Sun and of four Planets, Mctot em namely of the Earth, Mars, Jupiter and Venus ; this Revolution has beenP??^*^ ^? difcovered by Means of the Spots obferved on their Difcs, (m) and which *'*'^**'^*' " facceiEvely appear and vanifli 5 Mars, Jupiter and Venus having Spots on Inwhtcplt their Surface, by the riegular Return and fucccffive Difappearance of the fame "".• '*»'»• ^ Spots it has been foi^nd, that thefe Planets turn round their Axes,and in what^*^^" Time they qompteat their Rotation; thus it has been obferved, that Marsceived makes his Rotation in 23!^. aook and Jupiter in 9!^. ^Gm,
Aftronomers are not agreed about the Time m which Venus revolves loceititnde round its Axis ; moft fuppofe the Time of rotation to be abput 23 h. But J^'jljj"*?*'*' Sign. Btanchini who obferved the Motions of this Planet with particular iahe'iSLr Attention, thinks fl)e employs 24 Days in turning round; but a? he was ti<» of ve compelled to remove his Inftniments durine the Time he was obferving,**** ao Houfe having intercepted Venus from his View ; and as he loft an Hour m this Operation, 'tis probable that th^ Spot he w:as oblerving during this Interval changed its Appearance; however this be bis authority in Aftrono- intcal Matters deferves we Ihould fufpend our Judgment till more accurate Obfervations have diicided the Point.
M. de la Hire obferved with a Telefcope 16 Feet long. Mountains in Venus higher than thpfe of the Moon.
The extraordinary brightnefs of Mercury arifing from his proximity toTheroteti6n . the Sun, prevcnta our difcovcring by Pbfervation i\s Rotatiqp; ^nd Satqfn^^^'^'y is too remote to have his Spots obferved. urn**cwinot
In the Year 17 15 Cqffini obferved with a Telefcope 118 Feet long ;bcdifcovcr three Belts in Saturn refembling thofe obferved in Jupiter, but probably*^ !*y^ t}ioie Obiervatioas could not be purfued with accuracy fuiScient to con-^b/^'^ cUide the Rsotation of Saturn abput its JUis»
(«) By the Difk of •Pkoet U ttiderftood Uut Part of its forface whidi ii vifible (0 w, .
XXXVIIl SYSTEM OF TftE
bat tailogy As McrcarjT and Saturn are fubjed to the fame Laws that dired the tToScfSte Courfes of the other Planets, and aj far as has been difcovered appear tfMt cbofe to be Bodies of the fame Nature, Analogy authorizes us to conclude plcjMtf re- that they alio revolve, round their Axes ; and perhaps future Aftronomers AflrAjti^ may be able to obferve this Motion, and to determine its Period,
XV.
There appear from Time to Time Spdts upon the Sun, which have ferved to difcover that it has a rotatory Motion about its Axis. How the ro It was long after the Difcovery of thofe Spots^ before Aftronoiliers couM ^*«<«^^ obferve any, fufficiently durable and permanent, to'enable them to determine iu^iithu the Time of his Revolution. Keill in the 5th Lefture of his AArondmy» been difco relateSrthat feme Spots have been obferved to pafs from the Wefiern Limb ^^^ of the Sun to the Eaftern Margent in 13 Days and half, and after 1 3 Daft and half to re-appear in the Weftem Verge of his Diflt, from whence he in- fers that the Sun revolves 'round its Axis in the Space of about 27 Days from Weft to Eaft, that is in the fame Diredion of the Planers ; by means of . thofe Spots it has been difcovered,^ that the Axis round which the Sun it- vo Ives, is tnc'ined to the plane of the Ecliptic in an Angle of yd.
Jaquier^ in his G)mmintary on 'Newton^ has made feme Refledions on thefe Spots that deferve to be remarked; as no Obfervations prove the ' Times of their Occultation to be equal, but on the contraty, all the Ob- servations he eould colled, provethem to be unequal ; and, that the Time . during which they are concealed, has been alwavs longer than that, during which they have been vifible, from hencd he concluded (as atfo tP*f Art. 41 1, of his Aftronomy) that thofe Spots are not inherent to the Sua, but removed from his Surface to fome diftance.
The Solar Spots were firft difcovered in Germany ^ in the Year 161 1, bf
^Jobn FabriciUfy (n) who from thence concluded, the diurnal Revolution of
the Sun. They were afterwards obferved by Scbeiner^ (o) who publifted
the Refult 6f his Obfervations. The fame Difcovery was made by Galih
in Italy.
JScbeifur obferved mdre than fifty Spots on the Surface of the Sun; tbij may ferve to account for a Phenomenon^ related by many Hiftorians, tbit the Sun, fometimes for the Space of a whole Year, has appeared very Pale, as this Effed would natutally follow from a Number of Spots fufE- *ciently large and permanent, to obfcure a confiderable Portion of hii Surface.
(n) Wolf. Elemeau Aftroiioimat Cip. 1.
(o) Scheiner htving infenncd hit Sapcrior thtt he bid difcovered Spett in the Sun, he gft««lf replied, <« thtt it impoffible, 1 hav« retd Arittotk two or thi«e tiioei «ve£« aad htvc f^i ^ V At leaft ncaiioB ©f it. »»
P H Y S I C A L W O R L D. XXX»
It U no longer doubted that the Earth turns round her Axis in 23h 56m which compore our agronomical Day; Aom this Rotation arife the changes of Day and Nighty which all the Climates of the Earth enjoy.
XVL thedM*
This Motion of the Celeftial Bodies about their Centers alters their Fi-o^^«f<>- guresy for it is known that Bodies revolving in Circles, acquire a ForceJJ^J^ ^. which is fo much the greater, the Time of their Revolution being thetb«plaiictai. fame as the Circle which they defcribe is greater. This Force is called ^^fi'^^" . Centrifugal Force \ that is, the Force which repels tbem from the Center ;'J^!^^J^^" wherefore, from their diurnal Rotation, the Parts of the Planets acquire a u,, j j^ Centrifugal Force, fo much greater as they are nearer the Equators of thefeccntriptuL Planets: ((ince the Equator is the greateft Circle of the Sphere,) and fo force. much lefs as they are nearer the Poles (p) ; fuppofing therefore the Heaven- ly Bodies in their State of Reft, to have been perfect Spheres, their Rota- tion about their Axes muft have elevated their equatorial and depreflfed their polar Regions, and of Confequence changed their fpherical Figures into that of Oblate Spheroids, flat towards the Poles.
The Theory thus leads us to conclude, that all the Planets, in Confe- J^^**^^^*^^ quence of their Rotation, Ihould be flat towards the Poles, but this is only in which the fenfible in Jupiter and the Earth. In the Sequel it will appear, that theel«vttion of Proportion of the Axes (q), in the Sun, is aflignable from Theory, but is|jLre5!|*Ji'. too incondderable to be obferved.
The Meafures of Degrees of the Meridian, taken at the Polar Circle in France, and at the Equator, fix the Proportion of the Axes of the Earth to he as 173 to 174. By the Help of Telefcopcs the oblate Figure of Ju- piter has been perceived And the Difproportion of his Diameters. is much greater than that of the Earth, becaufe this Planet is a great deal bigger, and revolves with greater Rapidity about its Axis than.the. Earth ; the Propor- tion of the Axes of Jupiter is efteemed to be as 13 to 14. obferTttloa
XVII. pr»v«th*t
As the Spots of Venus, Mars and Jupiter are variable, and frequently ^^^^^^^ change their Appearance, it is probable that thefe Planets, like our Earth, ler, Venus* are furrounded by denfe Atmofpheres, the Alterations in which, produce thefe •nd the Sua -. Phenomena in refpeft of the Sun, as his Spots are not inherent on his Difk, J^Jj^"^-. and as they frequently appear and difappear, it is manifeft that he is furround-i^^Qiofpbercs s cd by a grofs Atmofphere, contiguous to.his Body, in which thefe Spots arc fucceffively generated and didplved.
(p) The Poles tre the Points tboat which the Body revolves, and the Equator, th« Circle eqoi diftant from thofe Pointo dividing the Sphere into iwt> equal Parts.
(q) Axis or Diameter, in general, ia a Line which paiTes through the Center, and is tenni- Bated at the Ciicumterence, In the prcfent Cafe, the Axes are two Lines which pafs through tb» QcaUtf 0D»«f wbtch is terowMtcd at the Polf s, iod the other at the £qaaior».
XL SYSTEMOFTHE
xvni.
What has hitherto been fet forth was known before the Time of Newfon^
bot no one thought before htm, that it was poffible to difcover the Quan-
titles of Matter in the Planets, their Denfittes, and the different Weighu
of one and the fame Body futceflively transterred to the Surtaces of the dif-
tmiCm^ik^ftrtni Planets. How Newton attained to thofe aftonifhing Difcoveries will
§m^ !•»«' be explained in the Sequel ; at prefent it fuffices to fay, that he found out
^^^'•'*Mhat the Maffes of the Sun, Jupiter, Saturn, and the Earth, that is the
ft«#fiJ* C^iiantities of Matter thofe Bodies contain, are to one another, as i t^f
ifi^^ lyfTii. foppofing (r) the Parallax of the Sun to be lo' 3' ; that their >cnrities are as too, 94, 67, and 400; 6c that the \^ eights of the Tame Body, ^w^tirU* p''C*^d fuccefllively on the Surfaces of the Sun Jupiter, Saturn, and the Earth, ^ tht *«w?woiild be as 10000,943, 529, and 435 ; in determining thofe Proportions, ^^••^•^*' AVw/tf/i has foppolcd the Semidiameter&of the Sun, Jupiter, Saturn, and the wCff»^« Rarth,tobeas 10000,997, 791, and 109.it will be (hewn hereafter whynci. ffs^pMU'^ ther the Denfity, nor the C^antity of Matter of Mercur), Venus, sod Mt€ '^t«»»j**Mars, or the Weights of Bodies at their refpcSivc Surfaces, are known.
^f$f$4 tft ibtf VI V
It follows from all thofe Proportions that Saturn is fiearly 500 Times lefs pft>f0ft,iiM than the Sun, and contains 3000 Times lefs Matter, that Jupiter is 1000 omU > uik« Times lefs than the Sun, and contains 1033 Times lefs Matter. Com- •mirfit(Tc«arp3^^j with thc Sun the Earth is only as a Point, being 100,0000 Times lefs; IndoAbc* and In fine, that the Sun is ii6Times greater, than all the Planets togeher.
, $M« XX.
Corfiparing the Planets with ohe another^ we 'find that Mercury sod Mars are the only Planets lefs than the Earth ; that Jupiter is not only the biggeft of all the Planets, but is bigger than alt the Planets together, sod that this Planet is two thoufand Times bigger than the Earth.
XXI
The Earth befides her annual and diurnal Motion, has alfo a third Mo- '^*/^^tion, by which her Axis recedes frohi its Rarallelifm, (fj& alter a certain Time
iqiihioxei. is direded to different Points of the Heavens, from this Motion arifes whtt
. is called tbe Preceffion of the Eqnint>xes that is, the R^greflion ot the equi-
' ItftToo*it u "<^^al Points, or thofe Points in which the lereftrial Equator cuts thc
' perfbinied Fcliptic. The eqiiinodial Points mbve contrary to tbe Order of the Signs,
tnd iowhfttand their'Motion is fo very flow, that they do not compiear a Revolution
J^JJ^Vilj^S^in lefs than 25920 Years, they recede a Degree in 73 Yeais, and thetn-
iti annual ' nual Quantity is about, 50''.
qtuotity
(r) The parallax of the 6un, is the Aftgle, 'andcr which the SemidkRifeter of the Eattb itftea fHmithe fiun, ind in general £hd pataltaz of cny celeftial Body, with refpeft to the £iitb, i9 the Angle vhder which the i'efniditimetcr of the Earth wonld be fecn from that Body.
(0 A tine is faid to be psYattel wten it alwayi prefemttlw ftme pofitkir with itfttA^t^ . P«k( fvppofcd fixed*
PHYSICAL WORLD. XLI.
Ahif/Mi firand, is will ftpfear in the Sequel, the Ciufe of this Motion in Ike Attrtdion of the Sun anrf Moon oti the Elevation of the eqoetorial Partb of the Esrth.
The Preceffion of the Eqainoxes hai caufed a Diftiodion of the Yetr Tropicd into the tropieai and fydinaL The rropical Year is the Interval of Time y*y- elapM hetween two fucceffive vernal Or autummri Equinoxes, in two annual ,^'* Revolutions of the Earth. This Year is fomewhat (horter than the fydereal Year, or the Time intervening the Earth's Departure from any Pofot of her Orbit, and her Return to the fame*
XXIN
It remains to defcribe the iecondary Planets, which exclufive of the Ring ThefeeoMk of Saturn, are lo in Number ; namely, the 5 SateHires of Saturn, the 4 '^ P>*««**- of Jupiter, and the Moon, the only Satellite attending the Earth.
Obfervation proves that ihefe Satellites in revohring round their Primaries. J^ <*• oMerve the Uws of Kepler. ^'J^ ^
The Satellites of Jupiter have been but lately difcovered : The Difcovery Kepler, bafore the Invention of Telefcopes was impoffible. Galliko difcovered the l^'^coverjof four Satellites of Jupiter, which in Honour of his Patron, he termed the ^\^^^^ Medicean Stars. Thefe are of the greateft Utility in Geography and Aftro- *
nomy.
Hugben/'w^s the firft who difcovered one of Saturn's Satellites ; it ftill re- AadoMoft tains his Name, and is the fourth* Afterwalds Cajlm difcovered the four ^^ ^*^* others^
XZIII.
Takine the Semidiameter of Jupiter as a common Meafure, his 4 Satd- Diftta^of lites revoltc at the foHowirtg Diftancet ; the firft at the Diftance of 5 Semi- ^*|"'?*~ diameters, the fecond of 9, the third of 14, and the fourth of 25, ne^d- ^^ '^^u ing Fradions. Thefe Determinations have been deduced by Cgjtni from his pbact. OUervalions of their Eclipfes.
Their periodic Times round Jupiter are fo much the longer as they are TkaiirfcrloA remoter from this Planet. The firft revolves in 42 Hours, the fecond in bmjmitt^ 85, the third in 171, and the fourth in 400, negleding the Minutes,
The diurnal Rotations, Diameters, Bulks, Malfes, Denfities, and attrafitve Forces of thefe Satellites, have not as yet been difcovered ; and the beftTele^ Icopes reprefent them fo vaftly fmall, that there is no Hopes of ever attaiii- tng Certainty m thefe points ; the fame is the Cafe with regard to the SateN lites of Saturn : Thefe are placed fliU* further beyond the reach of our Rdearches.
XXIV.
Taking the Diameter of Saturn's Ring^ for a common Meafure, the {JJf*^^
Dift'ances of the Satellites of Saturn commencing v?ith the innermoft, ^re of* uvan in the following Proportions. from fetora.
XLII. SYSTEM OF THE
Ic their p€ri The firft 18 cxpreflcd by i , the fecood by 2, the tbiid by $, the fearth by ^uJlSl 8, aod the fifth by 24, negleding Fraaioos ; and their periodic Tifliea, la* plaiitc cording to Cajini, are 45^ 65^ 109^, 382^ and 1903* refpefibtdy.
The Mooos of Saturn, all revolve b the Plane of the Equator qt thit
Planet, except the fifth, which recedes from it about 15 or 16 Degrees.
Several Philofophers, and among them Hugbens^ have fufpcded^ tbain
•f flwh^ Tekfcopes were once brought to perfedion, a fizth Satellite of Situra te|
MDccrniAga tween the fourth and fifth would be difcovered, the Diftance between tbofe
filth fuel- two Satellites being two great in Proportion to that which feparates the
Urn*'' ^'others ; but there would then occur, thia other Difficult v, that this SateUitf,
, ' which would be the fifth, notwithftanding muft be lels than any of i^
four interior Mooos, fince with our mofl perfed 1 elefcopcs it cannot be
perceived.
The Orbits of the Satellites of Jupiter, and of Saturn, are awrly con- centric to thofe Planets. Ohfervfttioo Maraldi has obferved Spots on the Moons of Jupiter, but no Coniequm- ^f MaraMi ^cs could as yet be derived from this Obfervation, which if properly poniiw SefueTlUci ^ accurately repeated, might condud us to the Knowledge of feversl> •r Jupiter, terefting Particulars refpeding the Motions of the Satellites.
XXV.
Of the Hog Saturn, exdufive of his five Moons, is alio furrounded by a Riflgi ^ oCSttafn. where adhering to his Body; for through the Interval which fepaniesw idhw t^ Body from the Ring, we can view the fixed Stars : The EHameter of thi the hody of Ring is to the Diameter of Saturn as 9 to 4, according to Hughent^ tbit» n'lifttwie ^^^^^ ^*^*" ^^^ Double of the Diameter of Saturn ; the Diftance of the B»7 ^omthcb«! of Saturn from his Ring, is nearly equal to his Semidiameter ; lb that W 4y of Uic Breadth of the Ring is nearly equal to the Diftance lietweeo its ioteiwr 1 1 dr*' tter ^'"^^ ^"^ ^^^ Globe of Saturn. Its Thicknefs is very inconfiderable, wf ltibf«adtL' ^^^^ it ttiins its Edge to the Eye, it is no longer yifible, but only appesr»» lt» thick- a black Line extended acrofs the Globe of Saturn. Thus this Ring under- J*^/ goes Phafcs according to the Pofiiion of Saturn in his Orbit, which prows
ptqoeVidJi it to be an opaque Body ; and which like the other Bodies that compo'e^'^ fabjca to planeury Syftem, ftiines only by refleding the Light it receives from tht Fh**«. Sun.
. We cannot difcover whether the Ring of Saturn has any Motion of R^JJ*
tion^ as no Changes in its Afptd are obferved to authorife us to coocluoe
this Rotation. * r *
The Plane of this Ring always forms with the Plane of the Eclip^.'^
an Angle of 23^ i, hence its Axis remains always parallel to itfelf ^
» its Revolution round the Sun. .
Of the dif- The Difcovery of the Ring of Saturn, the only Phenomenon of the K«»
cofer|r of obferved in the Heavens is due to Hugbens. Before his Time, AftronointfJ
o"io'iMcoo obferved Phafea in Saturn, for they confounded Saturn with his Ring; but tbofc
^''^Vitbe Phafcs were fo different from thofe of the other Planets as to be utterly '^^*
PHYSICAL WORLD. XLIU
pKctUe* In Hevilius mty be Teen the Nimet he gives to ihofe AppeArances ^ He- of Seturn, and how far (t) he wu frorti afligning the true Caure. '^'^
Hngbftu compariM the different Appearances of Saturn^ found they were produced bf a Ring furrounding his Body ; and this Soppoilition is fo confor- — bic with all Teldcopic DifcoTerics, as to be now generally received*
Gffimry defcribing the Notion of HalUj^ that the terreftrial Globe is g^^** ^ only an AJTemblage of Shells concentric to an internal Nucleus, propofes a cer^agSlt Conje£bjre concerning this Riog» that it is formed of feverid concentric rii«. Shells detached from the Body of that Planet, whofe Diameter was former* ly equal to the Sum of its adual Diameter, and the Breadth of the Ring.
Another Cbojefiure has alfo been propoGed, that the Ring of Saturn is on- i^^ ^^^\, ly an Aflemblage of Moons, which from the immcnfe Diflance appear toiiteiorjnpi be contiguous ; but thofe Conje£hires are not grounded en any Obfervation. <*' ^^ ^*'
By the Shadows of the Satellites of Jupiter and Saturn projeded on Sfi^^rieVTbo their Prinuries, it has been difcovered, that they are fpberical Bodies, dlf t.
XXVI.
The Earth has only one Satellite, namely the Moon ; but her Proximity of themota has enabled us to puflb our Enquiries coocerniq; this Satellite much further than about the others.
The Moon performs its Revolution round the Earth in an Ellipfe, the Whtt carve Earth being placed in one of the Foci i The Form and Pofition of this El- ^^^^^ lipTe 'li continually changing ; thefe Variations are caufied by the Adion of the ^^'tl^ Sun, as will appear in the Sequel.
The Moon in her Revolution round the Earth obferves the firft of the two Laws of Kepler^ and recedes from it onl v by the Adion of the Sun upon her $ ihe oompleats her Revolution round the Earth from Weft to Eaft in 27 d. J^JJJ"^'* 7 h. 43 m. which is* called its perMical Montb.
The Difc of the Moon is (ometimes totally, and at other times partially^ illuminated by the Sun. The illuminated Part is greater, or lefs, according to its Pofition with rerped to the Sun and the Earth ; thefe are called her Her phtfet. Pbajei. She aflumes ail thofe various Phafes during the Time of her /jnodic ^J^]^"^'^ Revolution,' or the Interval between two fucceffive Conjun^om with the Son. This fynodic Month of- the Moon confifis of 29 Days i nearly.
The Phafes of the Moon prove that ihe is an opaque Body, Ihining only Tbt 1
by reBeaing the Ught of the Sun. , !iS"ffl!
We know that the Moon is a fpberical Body, becaufe (he always ap^ cti bod/T'* pears to be bounded by a Curve.
The Earth enlightens the Moon during her Nights, as the Moon does the The etrth Earth during ours ; and it is by the refleded Light of the Earth that we fee ^^^^^ the Mppn, when ihe is not illuftrated by the Sun. dsrinf het*
nights. (I) HarelMt !a ofrarcnlo de Sttvroi Nttirt fiicie diftiogniflief the different Afpe€fct of Satorn hj tbe NeoBet of MoMrphericiini, TrirphericniDf Spherico-tsfatniDi eUipti-CQt&fttvtBy fphert* ^ecn^idstviii, sad febdiTidet them sgua into other Pbsfct.
XUV. SYSTEM OF THE
bfT^IS ^ '** SiirfiKe of the Earth it about 14 tiittcs gr«Mer thrn flat of the '* '^^ Moon, the Eirth faen from the Moon would appear 14 times Wighier, tud
rcfloft 14 timet more rays to the Moon, than the Mom doet to ut, fap-
pofiflg both equally capable of refle£bng Light. lacGMtiom The Plane of the lunar Orbit forms with the Plane of the Ediptii^ la •fthcoMt Angk of about 5<^* •fdicvoo. .j^ ^^ ^^^ ^ ^1^ Q,.^ ^^^j^ ^^ ^^^^ defcribet ronad (he
Earth, it called ibe Line 0/ the Apfides (0) •/ the Mqqh.
The Moon accompanies the Earth in her annual Rcfolutioo renad du Sun.
If the Orbit of the Moon had no other Motion but that by which it ii
carried round the Sun along with the Earth, the Axis of this Orbit wooU
always renflain parallel to itfelf ; and Moon being in her Ap9gee^ aad ia her
Perigee^ would he always at the fame Diftances from the Ewrth, and wcoU
always corrcfpond to the fame Points of the Heavem ; but the Line of the
Timeof the Apiides of the Moon rcYolves wiih an angular Motion round the Earth, sc-
7fXl£ ^rding to the Order of the Sigm ; and the Apogee and Perigee of the Mtx»
of Uic tp do not return to the fame Points ia lefs than 9 Years, which is the Tiiaesf
£dct. the Revolution of the Line of the Apfidcs of the Moon.
Xcv«lation The Orbit of the Moon inierfe£b the Orbit of the Earth in two Pointty
^f^"^^ which are called her Nodes ; tbefe Points are not always the fame, but cbsnp
" perpetually by a retrogreffivf Motion that is contrary to the Order of the
Timeof itt Signs,, and this Motion is fuch, that in the fpace of 19 Years the Nodei
rcTolatiMi. perform a whole Revolution, after which they return to the fame Poiots sr
the Orbit of the Earth, or of the Ecliptic. tl'^Ua y^^ Excentricity of the Orbit of the Moon changes alfo continaslln \n^^ this Excentricity fometimes increafes, fometimes diminiihes, fo that theDif* ference of the greateft and lead Excentricity exceeds half the leaft.
It will be explained in the Sequel how Newten difcovered the Caufe of lu
tbofe Inequalities of the Moon.
roBiITrtr ^^ ^y uniform Motion that the Moon haa, is its Motion of Rrtstioi
uis. abput her Axis ; this Motion is performed exadly in the fame Time as itt
Revolution about the Earth, hence its Days coofift of 27 of our Days, 7^
In wlist 43*'
time it it This equality of the lunar Day and the periodic Month makes the Mooi
pcrfcnncd. ajways prefent to us nearly the fame Difc.
The uniform Motion of the Moon about its Axis> combined with the la- equality of lis Motion round the Earth, produces the apparent Ofcillttioo LibrttioQ ^f of the Moon abckut her Axis, foroeticnes Eaftward, and at other tiaMi Weir ^e. mo^ii. ward, and this is what is called ker Liiraiien ; by thb Motion ib^ pftfeD"
{u\ Tht luKt of the Apfidet of the Moob is the Use whk& ptflet Uiroagh the Afot^^ Perigee *, apogee it ^he Point of the Orbit the Remote^ from the Berth, tad the Perigee h the Peint of the Orbit the neareft to the Earth \ and io geifefal^ the Ap6de« of aoj Orbil vt^ f oiotf the ReoMteft froxDt aad ae«reft to> the ceatral Potjit.
PHYSICAL WORLD. XLV
to M fomeiiiMt PWi which w«rt coooeftM, nni conoeah others thit wtre ▼ifible.
Thit Librtiion of the Moon srifes from her Motion in tn Elliptic Orbir^ Iti c««l«. lor if ihe revolved in t cirovlar Orbit, hftving the Eftrtb for its Center, Mid turned about her Axis in the Time of her periodic Motion round the Earth, ifae would in all Pofitiom turn the fame D.fc ezafily towards |he Eartb.
We are ignorant of the Form of the Surfiice of the Moon, which is on lh» other Side of her Difc with Refped to us. Some PhiloTophers have eves attempted to explain its Libration, by affigning a conical Figure to that Part of its Surface, which is concealed from us, ai^ who- deny W Rotation round her Axis.
The SurfsRce of the Moon is <ull of Eminences and Cavitiea, for which wt$km ihe fttk&s on every Side the Light of the Sun, for if her Surface w«s even and poliflied like a Mirror^ flic would only refled to us the (mage of the SuQ. ^.
The mean Diftance of the Moon from the Earth is nearly 60 i Semi- thll™^ diaroeten of the Earth. from tl#
The Diameter of the Moon is to the Diameter of the Earth, as 100 to !?^^* 365^ its Ma& is to the Mafs of the Earth, as i 10 39, 788 and its Denfity itl mtSr*' is to the DenHcy of the Earth, as 1 1 to 9. Its den6tr.
And laftly, a' Body which woqld weigh 3 Pounds at the Surface of the Whatbodiet Earth, transferred to the Surface of the Moon would weigh one Pound. y'^t!^ on
All thefe Proportions are known in the Moon and not in the other Satel- '^' ^'^*^* litcs, becaofe this Planet fupplies a peculiar Element, namely her Adion on the Sea, which Newtm knew how tomeafure aixl to employ for determining bcr Mafs, the Method he purfued in this Enquiry will be unfolded in the Se- quel
Theory ef the Primary Ptantts.
I.
In accounting for the celeilial Motions, the firft Phenomenon that occurs to be explained is the perpetual Circulation of the Planeu round the Center of their Revoltuions.
By the firft Law of Nature every Body in Motion perfeveres in that rec- ticlioear Courfe in which it commenced, therefore that a Planet may be defleSed from the ftraight Line it tends to defcribe inceflantly, it is Neceflsry that a Force diflPerent from that which makes it tend to defcribe this Araight Line flioold inceflantly A3 on it in order to bend its Courfe mto a Curve, in the fame Manner as when a Stone is whirled round in a Sting. The Sling inceflantly reftrMns the Stone from flying off* in the Diredion of the Tangent to the Circle it defcribes. Hew tke
To explain this Phenomenon, the Ancients invented their folid Orbs f^f '«?* p^* end DifiarUi Voriiees, but butb one and the other of tboifc Expircati^ns Ind o^fcV
XLVL SYSTEM OF THE
tet expUiD were mere Hypothefes devoid of Proof, and though DefcarUs tkpUmtioii tion^o"the ^^ ^^^^ Philofophical, it was no lefs FiSiitious and Imagiaary.
pUoeti in II.
their orbrtt. NewtoH begins with prorag in the firft Proitofition ^a), that the Areas defcribed by a Body revQlting round an imtrtoveaWc Center to which it it tripui^***" continuaHy urged/ are pnoportional to tlie Times, and Teciprocilly iti the fore- xvhich Second, that if a Body revolving round a Center dcfcribcs about it Areas liirjtrj tnc proportional to the Times, that Body is aSuatcd by a Force diredcd frot^'flying *®. ^^^^ Center. Since therefore according to Kepkr^s Difcoverics, the Pla- cff bythe ncts defcribe round the Sun Areas proportional to the Times, they are ac* tangent. tuated by a centri()etal Force, urging them towards the Sun, and retaining them in their Orbjts.
Newton has alfo (hewn (Cor. i . Prop. 2.) that if the Force aOing on a Body, urges it to difierent Points, it would accelerate or retard the Dc(crit>rion df the Areas, which would confequently be no longer proportional to the Times : Therefore if the Areas be proportional to the Hmes, the revolving Body is not only aduated by a centripetal Force, direfied to the central ^ody, but this r orce makes it tend to one and the fame Point.
HI. As the Revolutions of the Planets in their Orbits prove the Exiftance of ^ centripetal Force drawing them froni the Tangent, fo by their not dcfccnding in a ftraight Line towards the Center o\ their Revolution, we may conclude that they are ad;ed upon by another Force diiFerent from the Aodthepro Centripetal. Newton has examined (b) in what Time eKh Planet would jeaile force Jefcend from its prcfcnt Diftance to the Sun if they were aSuated by no them "rem ^^^'^^ Porce but the Sun's Aftion, & he has found (P.36) that the different Pla- ftUing to nets would employ in their Defcfenr, the Half of the periodic Time of the the center Revolution round the Sun of a Body placed at Half their prefent DiftanceS, and confequently thefe Times wbuld be to their periodic Times, as i to 4\/2. Thus, Venus for Example would take about 40 Days to defcend to the Sun, for 40 : 224 : : i : ^^/^ nearly; Jupiter would employ two Years and a Month in his Defcent, and the Earth and the Moon fixty-iix Days and nine- teen Hours, &rc. fince then the Planets do not defcend to the Sun, (bme Force mufl: neceflarily counterad the Porce which make them tend to the Sun, and this Force is called the Proje^ik P$rce,
IV. Of the cen- The EflFort exerted by the Planets iri Confequence of this Force to re- force^oftbe ^^^ ^^^^ the Center of their Motion, is what is called their Centrifugal pltaett. Fffrce^ hence in the Planets, the centrifugal Force is that Part of the projec- tile Force, which removes then! dirediy from the Center of their Revolu- Mon.
(a) When the Propoiiciont are qaoted without qvotiog the Bdok, they are the Propbfitiont of the firft Book.
(b) Dt fyftcmate mondi, ptgc 3 1 . cditioa 1 ;^3 1 .
PHYSICAL WOULD. XLVIL
.'V.
The projeQite Force has the Tame DrreAion in all the Planets, for they all revolve round the Sun from Weft to Eaft.
Snppofing the Medium in which the Planets move to be void of all Re* Mance, the Confervation of the projeAile Motion in the Planets, is %c^ « counted for from the Inerria of Matter, and the firft Law of Motion, but its Phyfical Caufe, and the Reaion of its Diredion are as jet unknown*
VI. Kewtoadlf
' After having proved that the Planets are retained in their Orbits by a covert the Force direded lo the Sun, Nfivhn demonftrates (Prop. 4,) that the centri- Jj^.'^pJi^JI* petal Forces of Bodies revolving in Circles are to one another as the Squares to the Saa of the Arcs of thofe Circles defcribed in equal Times, divided by their 50 1>« >a tha Rays, from whence be deduces (cor. 6) that if the periodic Times of Bo- JJ^ J^^5 "J^JJ dies revolv'uig in Circles be in the fefqutplicate Ratio of their Rays, the cen- of their dif tripetal Force which urges them to the Center of thofe Circles, is in the tancei from inverfe Raib of the Squares of thofe fame Rays, that is of the Diftance of Jjj/'^^ ihofe Bodies from the Center : But by the fecond Law of Kepler, which all die timet tad the P|anets obferve, their periodic Times are in the felquiplicate Ratio of diftmoet. their Diftaaces from their Center ; confequently, the Force which urges fei^fiJi^J^ the Planets towards the Sun. decreafes as the Square of their Diftance of thair or- from the Sun increafes, fuppofing them to revolve in Circles concentric to bjtt Mag the San. "'^»^-
yriu * The firft and moft natural Notion that we form concerning the Orbits of the Planets, is that they perform their Revolutions in concentric Circles ; B«fcraiU|i- but the Difference in their apparent Diameters, and more accuracy in the i^tJjJJ!^^ Obfervations^ have long (ince made known that their Orbits cannot be con- that the pi«* centric to the Sun ; their Courfes therefore, before Kepferh Time, were ex- ««• revolt plained by czcentric Circles, which anfwered pretty well to the Obfervations g^J^^cw OP the Motions of the Suit and the Planets, except Mercury and Mars. trie cirdci.
From confidering the Courfe of this hft Planet, Kepler fufpeaed that the But Kepler Orbits of the Planets might poffiUy beEllipfes, having the Sun placed in one JU'tJl^ of the Foci, and this Curve agrees fo exadly with all the Phenomena, that ^oWt in ci it is now univerfally acknowledged by Aftrdnomers, that the Planets revolve Hp^* round the Sun in elliptic Orbits, having the Sun in one of the Foci,
VIII. Affumtng this Difcovery, Newton examines what is the Law of centripe- tal Force, required fo make the Planets defcribe an Ellipfe, and he found {P»op. ti.) that this Force muft follow the inverfe Ratio of the Pianet'a Diftance from the Focus of this Ellipfe. But having found before (cor. 6. Prop. 4.) that if the periodic Times of Bodies revolving in Circles be in the fefquiplicate Ratio of their Rays, the centripetal Forces would be in the in^ verfe Ratio of thofe fame Diftances ) he bad no more to do to invincibly
XLVIIL SYSTEM OFTHE
prove that the centripetal Force which dire£b the celeftial Bodiea in their Coorfet, follows the inverfe Ratio of the Square of the Diflaooet| but to examine if the periodic Tiaies follow the fame ProportioD in EUipfet m m
tb*t tfi eliip But Ntwhn demonftrates (Prop* 15.) that the periodic Times in EUtpAv iMChcpcrio gre in the fefquiplicate Ratio of their great Axes \ that is, that tfaofe TtMoo^ «r!o'thc* ^^^ in. the fame Proportion in Ellipfes^ and Grcles whole DiaoKters are equal IkiMpropor to the great Axes of thofe Eltipfes.
tjpa M ia This Curve which the Planets defcribe in their Revolution is endued with Coai^'iieot ^^^* Property, that if fmall Arcs defcribed in equal Times be taken, the lytbtceotrt Space bounded by the Line drawn from one of the Extremities of this Arc, prtti force aiK] by the Taqgcnt drawn from the other Extremity increafes in the fame uioi'^the ^^^^ ^* ^^^ Square of the Diftance from the Focus decreaies; from piwtf in whence it follows, that the attradive Power which is proportional to this their orbitt. Spscc^ follows alfo thb fame Proportion*
tbt fijosreL . **•
of the diT Newtmt^ not content with examining the Law that makes the Plaoela de» taoce. (cribe Elites; he eliciuired further weather in confequence of this Law: Tkm tmiri ^1^ mif^t not defcfibe other Qirves, and he found (Cor. i* Prop, ty) dial ptui Sm^ this Law would only make them delcribe a conic Se£bon, the Center of tfae b«^ ID this Forpe being placed in the Focus, let the projedile Force be whal it wouU. the^tMU Other Laws, by which Bodies tnigbt defcribe conic Sediims, would maka can only de them defcribe them about Points difrartent from the Focus. Newt§m (bund, ^be conic fc^ example, (Prop. 10.) that if the Force be as the Diflance from the Center^ H^M^ it will make the Body defcribe a conic Sedion, whofe Center wouU be the ^acad in Center of Forces, tlms Newton has difcovered not only the Law which the oMof tiM centripetal Force obferves in our planetary Syftem, bnt he hu alio Iliewn ^^' thai no other Law could fubfill in our WorU in iu prefent Sute.
Maana^ of Newtm alterwafda examines (Prop. 17.) the Curve e Body wouUdeicribe doecmAoiof with a centripetal Force decreaftng in the inverfe Ratio of the Square of the iTplmtfuo Di&BBCt, fuppefing the Body let go from a gi^ Poi^r, with « Difec< p^Qf the . tion and Vieloqity i^nned at Pleafure.
Uw of cen, 7*0 foWe th|s Problem^ he feA out with the Remark he had made^ (Pr^p^
for^^tobe i^*) that the.Velfxjiiesof Bodies defcribing conic SetQiona» are in eaoh P^
giveo. of thofe Curves, as the Square-Roois ,of the principal Parameten, divided
by the Perpeadiculars, let fall from the Foci 00 the Taii§eots to tkofe
Points.
This Propofition is not only very interefting, coniidered merely as a geo^ metrical Probleoi, but alfo of great ufe in Aftronomy; for finding by Obfervation the Velocity and DireSioft of a Planet in any Part of its Orbit, by th<: Afllilance of this Propofition, the Remainder of its Orbit is found out, and the Petermination of the Orbits of Comets, naay in a great Meafiira i^ be deduced from this Propofition.
PHYSICAL WORLD. XLIX
XI.
It is eafy to conceive that in coniequence of other Laws of centripetal l^^^ Force different from that of the Square of the Diftances Bodies would ^^'^^^^ defcfibe other Curves, that there are ibme Laws by which notwithftan- of other ding the pn^eiEHle Force, they would defccnd to the Sun, and others by Uwtofcen which notwithftanding the centripetal Force, they would recede in infini-J3dbL*d«^ turn in theHeavexily Spaces; others would make them defcribe Spirals, ^Cf^nbed. and Nnuten in die 4ad Proportion, mveftigates what are the Curves de-: fcribed in all Sorts of Hypotliefis of centripetal Forces.
XII.
It evidently appears from all that has been faid tliat the perpetual Circula- f^e perpe- tion of the Planets in their Orbits depends on the Proportion between thetwi clrcuk- centripetal and the projedtile Force, and thofe who afk why the Phnet$|;^° ^^ }^^ arriving at their Perihelia, reafcend to their Apbelia, are igncNrant of this^^j.^or^t9 Proportion ; for in the higher Apfis the centripetal Force exceeds the Cen-refnits from trifiigal Force, fince in defccndihg the Body approaches the Centre, and int**«Pf^ft»- thc lower Apfis on the Contrary, the centriAigal Force fiirpailes in itsJJJ^^^"^^ turn the centripetal Force, fince in reafcending the Body recedes from thet«i and pro. Centre : A certain Combination between the centripetal Force and the cen- j«^i'« ^'ce- trifugal Force was therefore requifit, that they might alternately prevail and caufe the Body to defcend to the lower, and reafcend to the higher Apfis per- petually.
Another Objedion was alledged with regard to the Continuation of die Heavenly Motions, derived from the Refiftance they (hould undergo in the Medium in which they move. This Obje^on Newton has amwered in ^^^ ^^^^ (Prop. 16. B. 7.) where he (hews that the Refiftance of Mediums dimmifhaminwhich in the Ratio of thcif Weight and their Dcnfity ; but he proved in the Scho- «»»« hwvrn- Ihnn of (Pftyofiiion 22. B. 2.) that at the Height of two hundred Miles a-Jji^^^'^^^^ bove the Surface of the Earth, the Air .is more rarified than at the SurfiM», of Ju reiiii, in the Ratio of 30 to 0,0000000000003998 or nearly as 7 5000000000000 ancc. to I, ftiom whence he concludes (Prop. 10. B. 3.) iupponng the Refiftance of the Medium in which Jupiter moves to be of this Denfity, this Planet defcribing five of its Semidiameters in 30 days, would from the Refiftance of this Medium, in loooooo years fcarcely k>fe looooooth Part of its Mo- tion ; from hence we fee that the Medium in which the-Planets move may be fo rare and fubtilc, that its Refiftance may be regarded as Void ; and the Proportibnality conftantly obfervcd, between the Areas and the Times, is a conrincmg Proof that tfris Rdiftance is aihially infenfible.
XIII.
As we have ftiewn that the Proportionality of the Times and of the A- reas which the Planets deicribe around the Sun, proves that tliey tend to the Sun as to their Centre, and that the Ratio fubfifting betwQpn their periodic Times and their Diftances, fliews that this Force decreafes in the invenc
L SYSTEMOFTHE
Ratio of the Square of the Diftances. If the Planets which peribrm their Revolutions round the Sun be furrounded by others which revolve round them, and obferving the fame Proportions in their Revolutions, we may con« elude that thefe Satdlites are ureed by a centripetal Force direded to their Primaries, and that this Force decreaies as that of the Sun in the duplicate Ratio of the Diftance.
We can difcover only three Planets attended with Satellites, Jupiter, the Earth, and Saturn; we know that the Satellites of thofe three Planets de- fcribe around them Areas proportional to the Tunes, and omfequently aie urged by a Force tending to thofe Planets.
Thecompa- XIV.
rifoii of the Jupiter and Saturn having each feveral Satellites whofe periodic Times Snwf and ^^' Diftances are known, it is eafy to difcover whether the Times of their dUUocM of Jlcvolution about their Planet, are to their Diftance in the Proportion difco- thefsteHiteaveredby KifUr; and Obrervations evince that the Satellites of Jupiter and of Stturn Saturn obfcrve alfo this fecond Law of Kfpltr in revolving round tiicirPri- pVovM tiwt "paries, and of confequence the centripetal Force of Jupiter and of Saturn the centri-decreafe in the Ratio of the Square of the Diftances of Bodies from the petal force Centre of thofe Planets.
of thofe pit- yy^
uTWi'in*^'^ As the Earth is attended only by one Satellite, namely the Moon, itap- vcrfcratioof pears at firft View difficult to determine the Proportion in which the Force the Tquate a<£ls tliat maRes tlie Moon revolve in her Orbit round the Earth, asindiis
tlJt^ **'^' ^^^'^ ^^ ^^^ ^° '^^"^ ^f Comparifon.
How^New. Nswhn has found the Means of fupplying this Defedl; his Method is as ton difcove- foUows : All Bodics which fidl on the Sur&ce of the Earth, defcribe accord- *<^^ ^V ^***ing to the Progreffion difcovered by Galliko^ Spaces which are as the Squares foJce of "the o^*e Times of their Defcent. We know the mean Diftance of the Moon Earth hi- from the Earth which in round Numbers is about 60 Semidiameters of the low. the Earth j and all Bodies near the Surface of the Earth are confidered as cqui- fame piopor- j-^^^^ ^^^ ^^ Centre ; therefore if the fame Force produces the Defcent of heavy Bodies, and tlie Revolution of the Moon in her Orbit ; and if this Force decreafes in the Ratio of the Square of the Diftance, its Action on Bodies near the Surface of the Earth ftiould be 3600 Times greater than what it exerts on the Moon, fince the Moon is 60 Times remoter from the Centre of the Earth ; we know the Moon's Orbit, becaufe we know it prefent the Meafure of the Earth, we know that the Moon defcribes this Orbit in 27 Days, 7 Hours, 43 Minutes, hence we know the Arc (he de- fcribes in one Minute ; nowby(Cor. gProp. 4.) the Arc defcribcd in a gi- ven Time by a Body revolving unifbnnly in a Circle with a given centripe- tal Force, is a mean Proportional between the Diameter of this Circle anJ x\it right Linedefcribed in the Body's defcent during that Time.
j
PMYSICaLWORLD. LI
It is true that the Moon does not revolve round the Earth in an cxaft Circle, but we may fuppofe it fuch in the prefent Cafe without any fcnfiblc Error, and in this Hypothefis, the Line exprefling the Quantity of the Moon's defcent in one Minute, produced by the centripetal Force, is found tobeneariy ic Feet.
But the Moon according to the Progrefiion difcovered by Gallileoy at her pnefent Diftance would defcribe a Space 3600 Times lefs in a Second than in a Minute, and Bodies near the Surface of the Earth defcribe, according to the Experiments of Pendulums, for which we are indebted to Hu^hens^ about 15 feet in a Second, that is, 3600 Times more Space than the Moon defcribes in the fame Time ; therefore the Force caufing their Defcent ads . 3600 Times more powerfully on them than it does on the Moon ; but tliis is cxa^y the inverfe Proportion of die Squares of their Diftances*
By this Example we fee the Advantage of knowing the Meafure of the Earth ; for in order to compare the Verlc Sine which exprefles the Quantity of the Moon's defcent towards the Earth, with the cotemporary Space dc-(\,re of"^ fcribed by Bodies falling by the Force of Gravity near the Earth, we muft Birth* wm know the abfolute Diftance of the Moon from the Earth, reduced into Feet, ncccfrtry for as alfo the Length of the Pendulum vibrating Seconds j for in this Cafe it is?!***°s *!• not fuiEcient to know the Ratio of Quantities, but their abfolute Magni- *^^*'3r* tudes»
Xvf» Jupiter, Saturn, and our l£arth therefore attra& Bodies, in the famegQthorifetut Proportion that the Sun attrads thofe Planets, and Indudtion authorifes us to conclude, to conclude that Gravity follows the fame Proportion in Mars, Venus, and^!>«^ nkUJi Mercury ; for by all that we can difcover of thefe three Planets, they appear J*^",mepro! to be Bodies of tlie fame Nature with the Earth, Jupiter, and Saturn ; from portion in ipvhence we may conclude, with the higheft Probability, that they are cn^ «be pi*"<^« dued with the attra<ftive Force, and that this Force decreafes as the Square ^'^J.^j^yj*^^^ of theDiilances.
xvli. It being proved bv Obfervation and Induftion that all the Planets arc en- From dued with the aittra«ive Power decrealing as tlie Square of the Diftances j J**^^'^* ^.^ and by the fecond Law of Motion, A^on is always equal to Re-adkion, ciude/Sie** wc (hould conclude witli Newton^ (Prop. 5. B. 3.) that all the Planets gra-mututi as- Titate to one another, and that as the Sun attradls the Planets, he is rcci- trtaion of procally attnufted by them ; for as the Earth, Jupiter, and Saturn ad onj"^^^**^" their Satellites in the inverfe Ratio of the Square of the Diftances, there is '^ no Reafbn why this Adlion is not exerted at all Diftances in the fame Pro* portion ; thus the Planets ftiould attract each other mutually, and the £f- fe&s ot this mutual Attn^Aion are fenfibly perceived in the Conjundion of Jupiter and Saturn,
LII SYSTEMOFTHfi
XVIII.
As Analogy enduces us to believe that the fecondary Planets ai« in all Refpeds Bodies of the fame Nature with the primary Hanets, it is highly prob^le that they aie alfo endued with tlie attnuStive row^, and confe- quently attraft their Primaries in the fame Manner they are attnKSled by them, and that they mutually atttad each other. This is further coniirmed l^ the Attra<aion of the Moon exerted on the Earth, the EffeSls of which are vi- fible in the Tides and the Preceffion of the Equinoxes, as will appear in the Sequel : We may therefore conclude that the attra<ftive Power belongs to all the Heavenly Bodies, and that it aAs in all our planetary £yftem in the ihverfe Ratio of the Square of the Diftahces.
XIX.
But what is the Caufe which makes One Body revolve round another ? for Wtiat caufejj^ftance, -tlie Earth and the Moon attrading each other with Forces decrea- Wiy?evoUcf*^g^^ the duplicate Ratio of their Diftances, why Ihould not the Earth round ano-rcvolve round the Moon, infteadof caufing tlie Moon to revolve round the thcr. Earth ; the Law which regulates Attraftion does not therefore depend on
the Diftance alone, it muft depeod alfo on fome other Element, in order to
account for this Determination, for the Diftance alone is infui&cient, iince it
is the fame for one «nd the other Globe.
This canftf Erom examining the Bodies that compofe our planetary Syftem, it is natuml
appears tube to conclude that this Law is that of their Mafles ; the Sun, round whom all
the mafa of^^ Heavenly Bodies turn, appears much bigger than any of them 5 Sa-
^e^ centra ^^^^^ ^^^ Jupiter are much bigger thah their Satellites, and our Earth is
much bigger than the Moon whidi revolves round it.
But as the Bulk and Mafs are two different things, to be certain that the led*"^ ^"^bJ Gravity of the Celeftial Bodies follows the Law of their Maffes, it is necef- roaflfes*l>fthef^ to determine thofe Mafles. planets ne- But how Can the Mafles of the different Planets be determined ? this
ceflary to jVh^^^;^ haS ftlCWn.
aetermme _.__
point. rp^ ^^^ ^^ p^^^ J ^j^^^ condu&d him to this Difcovery.
Since the Attradrion of all the Celeftial Bodies on the Bodies which fur-
vioad that round them follows the inverfe Ratio of the Square of the Diftances it is
N^i'Jf^'^«^^y probable that the Parts of which they are compof«d attrad'each
. this dVcovc-^*^^ i" *^ ^^^^^ Proportion. .
ry. The total attiaaive Force of a Planet is compofed of the attradive Forces
of its Parts ; for fuppofmg feveral fmall Planets to unite and compofe a big
• one, the Force of this big Planet will be compofed of die Sum of the For-
ces of all thofe fmall planets ; and Netvtort has proved in (Prop 74
75 and 76,) that if the Parts of which a Sphere is compofed, attrad each
other mutually in tlie inverfe Ratio of the Square of the Diftances, thefc
t>HYSICALWOftLD. LUI
entire Spheres will attract Bodies which are exterior to theiH, at whatever Diftance they are placed in this fame inverfe Ratio of the Square of Diflan- oes I and of all the Laws of Attradtion examined by NewUn^ he has found only two, namely, tliat in the inverfe Ratio of the Square of the DUlan- ces, and that in the Ratio of th« Ample Diftances, according to wliicli Spheres attra& external Bodies in the fame Ratio in which their Parts mu* tually attract each other j from whence we fee the force of the Reafoning "which made NiWton conclude that fince it is proved on one Hand from Theory, (Cor. 3. Prop. 74.) that when the Parts of a Sphere attradl each o- ther with Forces decreafmg in the duplicate Ratio of the Diftances, the en- tire Sphere attrafts external Bodies in the fame Ratio, and on the other, Obfervations evince that the Celeftial Bodies attraft external Bodies in this Ratio, it is obvious that the Parts of which tlie Heavenly Bodies are com- pofed, attradl each other in this fame Ratio.
Newtcn examines (in Prop. 8. B. 3.) what the lame Body would weigh at the Surfaces of the different Planets, and he found by means of (Cor. „ ^ . c 2. Prop. 4.) in which he had demonftrated, that the Weights of equal Bo- "eiKht of dies revolving in Circles, are as the Diameters of tliofe Circles, divided the ftmebo- by the Squares of their periodic Times, therefore the periodic Times of ^>' "P^" ^^^ Venus round the Sun, ot the Satellites of Jupiter round this Planet, of thei^''^^."^ Satellities of Saturn round Saturn, and of the Moon round the Earth, andthcftmedif- the Diftances of thofe Bodies from the Centres about which they revolve ^"!^c from being known, fuppofing alfo that they defcribe Circles, which may be fup-^^**'^**^** pofed in the prefent Cafe, he difcovers how much the fame Body would weigh transferred fuccelfively on the Surfaces of Jupiter, Saturn and of the Earth.
Having thus found the Weights of the fame Body on the Surface of the different Planets at the fame Diftance from their Centres, NewUn dedu- An<* prove* CCS the (^lantities of Matter they contain, for Attradtion depending on the q^j^atittw of Mafs and the Diftance, at equal Diftances the attractive Forces are as thcmittcr are Quantities of Matter in the attracting Bodies; therefore the Mafles of theP'^P<'^^'«»*l different Planets are as tlie Weights of the fame Body at equal Diftances ^^Jg^[' from their Centres.
XXI.
We may difcover after the fame Manner the Denfity of the Sun and of thof^ Planets which have Satellites, that is, the Proportion of tlicir Bulks F««n and M^^, for Newtoriy (Prop. 72.) has proved, that the Weights of e- J^«°^«^« qual Bodies, at the Surfaces of unequal homogeneous Sphere ;, arc as their^denfi- the Diameters of thofe Spheres; therefore if thoie Spheres were heteroge-ti«t. neous and equal, tlie Weights of Bodies at their Surfaces would be as their .Denfity, fuppofing the Law of Attraftion to depend only of the Diftance,
LIV SYSTEMOFTHE
and the Mais of die attrading Body; tfaerdbre the Weights of Bodies the Surfaces <^ unequal and heterogeneous Spheres, are in the compound Ratio of their Denfities and Diameters ; coi^uently the Dcnfities are as the Weights of the Bodies divided bv their Diameters^
XXIf.*
Tkcrimikft From hence we find, that the fmaller Planets are denfer and placed near- and deoTcftcr the Sun, for where all the Proportions of our Syftem were laid down, Mu^ JJ^we faw that the Eartli, which is lets and nearer the Sun than Jupiter and fta. Saturn, is more denfe than thofe Planets.
ZXIII.
Newton deduces from thence, the Reaibn of the Arrangement of tlic Cdeftial Bodies of our planetary Syftem, which is ad^^ted to the Denfitj of their Matter, in order that each might receive a Degree of Heat more or tefs according to its Denfity and Diftsmce ; for £]q>erience fhews us that The rf«ronthe denfcT any Body is, the more difficultly does it receive Heat ; fixim aflifaed bjy^hcnce Niwton concludcs that the Matter of which Mercury is compofed NewtoB. Qxoxild be feven Times denfer than the Earth, in order that Vegetation might take place ; for Illumination, to which, ceteris paribus. Heat is proportional, is inveifely as the Square of the Diftance^ but we know the Proportion of the Diftances of the Earth and Mercury from the Sun, and from this Pro- portion we difcover that Mercury is feven Times more illuminated, and confequently feven Times m(H% heated than the Earth ; and Newton dif- coverod, fiom his Experiments on the Thermometer, that the Heat of our Summer Sun^^ feven Times augmented, would make Water boil ; ttiere- fore if the Earth was placed at the Diftance of Mercury fix>m the Sun, our Ocean would be diiTipated into Vapour; removed to the Diftance of Sa* turn finom the Sun, the Ocean would be perpetually frozen, and in both Cafes all V^etation would ceafe, and Plants and Animals would perifti.
XXIV.
Tke dtnfi- It cafily appears, that the Mafles and Denfities of fuch Planets only as hUnrtl **2"^ attended by Satellites can be difcovered, fince to arrive at this Difcove- ^hich htTery we muft compare tlie periodic Times of the Bodies revolving round thofe fatciiitea on. Planets, the Moon alone is to be excepted, of wliich mention will be made
moon cz~ a a v .
ccpttd. Having determined the MaflTes of the Planets, we find that thofe Bodies
Why tbertm which have lefs Mafs, revolve round thofe which have a greater, and the "^^jjj^^lj.' greater Mafs a Body has the greater is, ceteris paribus, its attradivc Force; till rtrolalthus all the Planets revolve round the Sun, becaulc the Sun has a much greater Mafs than any of the Planets, for the MafTes of the Sun, Jupiter, and Saturn are refpedtively as i, i loo and .3000 ; fmce therefore the Mai- (t% of thefe Planets exceed thofe of any other in our Syftem, it follows tint the Sun (hould be the Centte ot the Motions of our planetary Syftem.
1
rr
PHYSICALWORI^D. LV
xrvi.
If AttraAion be plt>pc»tionaI to the Mafles, the Alteration caufe4 by the T^ •!<««• Adkmof Jupiter on the Orbit of Saturn in their Coniundticn, ^"^^J^^JJ^J*^ much to exceed that produce4 in the Orbit of Jupiter bv the Adion of &i. mutvdjj * turn, fince the Mafe of Jupiter is much greater than tnat of Saturn, an^F^^'^ >a this Obfavation evinces ; the Alteration in the Orbit of Jupiter in its Con-^^J^*^ junction with Saturn, though fenfible i$ Qoi^derabljr leis than wha^t is ob- ntk»Tf thti? ferved in tbe Orbit of Saturn. malTn,
xxyii.
But if the Effe<a rf Attraftion, or the Space defcribcd by the attraded Body, depends on the Mafs of the attracting Body, why (hould it not alfo depend on the Mafs of the attraft^d Pody ? This Point furcly deferves to be examined.
Experiment proves that all Bodies near the Surface of the Earth, when the Rcfiftancc of the Air is removed, defcend with equal Velocities ; for in the Air-pump, after exhaufting the Air, Gold and Feathers fall to the Bot- tom in the fame Time.
Newton has confirmed this Experiment by another, in which the fmallefl Di£Ference becomes obvious to our Senfes. He relates (Prop. 14. B. s. and Prop. 6. B. 3.) that he compofed feveral Pendulums of Materials en- tii^y dmcrent 5 for inlfance of Water, Wood, Gold, Glafs, &c. and ha^ ving fufpended them by Threads of equal Length, for a ^nfiderable Time their Ofcilhtions were Synchronal.
XXVIII.
It admits therefore of no Doubt, that the attraftive Force of our Earth ^t^rtAioa is proportioned to the Mafles of the Bodies it attracts, and at equal Difbn- •„ proportki* ces it depends folely on their Mafles, that is on their Quantities of Matter ; nil to the hence if the tcrrcftrial Bodies were transferred to the Orbit of the Moon, ™*^** '*'***" it havu^ been proved ;lready that the fame Force z&s on the Moon andf^'£^*°beii^ on thofe Bodies, and that it decreafes as the Square of the Diftances. The had to the Diftances being fuppofed equal, it follows, that fuppofing the Moon de-*?™* <>J n>«- prived of her projedile Force, tliofe Bodies and the Moon would fall in^j'^^jnj * the fame Time to the Surface of the Earth, and would defcribe equal Spa- bodies. ces'in equal Times, the Refifbmce of the Air being taken away.
The feme Thing is proved of j 11 the Planets having Satellites, for in- (lance, of Jupiter and Saturn 5 if the Satellites of Jupiter, for example, were all placed at the fame Difbnce from the Centre of this Planet, and deprived of their projcftile Force, they would defcend towards it and reach its Surface in the fame Time; this follows from the Proportion be- tween the Diflances of the Satellites and their periodic Times.
LVI SYSTEMOFTHE
XXX.
From the Proportion between the periodic Times and Diftancei of the primanr Planets from the Sun, h may be proved in like Mvuier, that the Sun a^s on each of them proportionally to its Mafs, for at equal Diftanccs their periodic Times would be equal, in which Cafe, fuppofmg their pro- jefiilc Force deftroyed, they would all reach the Sun at Ae iamc Time-, therefore the Sun attrads each Planet in the dired Ratio of its Mafs.
XXXI.
This Truth is further confirmed by the Regularity of the Orbits whidj the Satellites of Jupiter defcribe round this Planet, for NexuUn has proved i[ Cor.3. Prop. 65. ) that when a Syftcm of Bodies move in Circles or regu- lar Elfipfcs, thcfe Bodies cannot be a£ted upon by any fenfible Farce but the attrad^ive Force which makes them defcribe thofe Curves ; now the S>i tellites of Jupiter defcribe round that Planet circular Orbits, fcnfiUyr^- lar and concentric to Jupiter, the Diftances of thefe Moons and of Jupi- ter from the Sun fhould be confidcred as equal, the Difference of tlidr Diftanccs bearing no Proportion to the entire Diftancc ; therefore if any 0* the Satellites of Jupiter, or Jupiter himfelf, were more attrafied by the Sun in Proportion to its Mafs than any other Satellite, then this ftnwg- cr Attradlion of the Sun would dillurb the Orbit pf this Satellite j aw Ncivtcn fays, (Prop. 6. B. 3.) that if this Aftion of the Sun on oncot the. Satellites of Jupiter was greater or lefs in Proportion to its Mais than that which it exerts on Jupiter in Proportion to his, only one thoufandth part of its total Gravity, the Diftance of the Centre of the Orbit of this Sa- tellite from the Sun would be greater or lefs than the Diftance of the Cen- tre of Jupiter from the Sun, by the two thoufandth part of its whdc Dif- tance, that is by a fifth Part of the Diftance of the outermoft Satellite of Jupiter from Jupiter, which would render its Orbit fenfibly excentric; fmce then thofe Orbits arc fenfibly concentric to Jupiter, the acceleratitig Gra- vities of the Sun on Jupiter and on its Satellites, are proportional to their Quantities of Matter.
The fame Reafoning may be applied to Saturn and its Satellites, wbofe Orbits arc fenfibly concentric to Saturn.
Experience and Obfervation therefore leads us to conclude, that the At- traftion of the Celeftial Bodies is proportional to the Maflos, as well in the Aitrtaionattraaing Body, as in the Body attracted ; tliat it is the Mafs which dcter- fiilwiyi re- mines a Body to revolve round another, that every Body may be confidtf- ciproc . ^ indifferently, either as attrafting or attr^ded ; in fine, that Attraffion is always mutual and reciprocal between two Bodies, and that it is the Pro- portion between their Mafles which decides when this double AttniSBon mall or ftiall not be fenfible.
PHYSICAL WORLtf. tVlt
llivre is afiother Property of Attradiofi^ by which it aQs ^udtly 6n Attnfttai Bodieswhethtr atReftorinMotion, oiid produces e<}ual Accelerations in ^y*^*°^* equai Ttmes, from whence it fellows that m AQion ts continued afid unt- mtiDudix form. Wbidi fufficiently appears f#on(i the Manner gravity accelerares whether the falting Bodies, ahd from the Motion of tht Planets, which as we have ^^'** ^5 «< fliewn before^ Are only greater ProjedHes regulated t^ the fame Laws. mociM."^
ixxin.
Since the Proportion fubfiflii^ between the Ma^ of Bodtte which at- >MI« of tra£k each other determines how much one apprxMches towards the other, *^A^^'"-^' it is evident that the S6n having a much greater Mafs than the Planets, [hcpiunt their Aflioo on him ihonld be infcnrible. Hovfrever the Adi6ri of the oa Uu faa Planets upoll the Sun, tho^ too tnconfiderable to be fenfible, p^ciduces its Ef- fe& ; and on Examination we find that the center round which each Planet revotves is not the center of tM Sun, but the Point which is the common center of Oravity of the Siin and Planet whofe revolution is conddered. Thus the Mafs of theSm being (o that of Jupiter sis x to ^^^ and the diftance of Jupiter firom the Sun being to the Sun's femi diameter in a Ratio fomewhat greater^ it follows tb«t the common Center of Oravity of Jupiter and the Sao ia not far diftant from the Surface of the Sun.
By fhe fame way of reafoning we find that the common Center of Gra- vity of Saturd and thaSoif h\lt within the SorfiMre of the Sun, and making the fame Calculation for all the Planets, Nittiton fays (Prop. 1 2!, B, 3.) that if the Eartfi and all the Planets were pfaced on the fame Side of the Sun, the common Centes of Gravity of the Sun and all the Planets would fcarce be one of his Diameters diftant from his Center. For thor* we cannot deter- mine the MaBes of Mercury, Vends and Mars, yet as thefePlariets are ftill lefs than Saturn and Jupiter^ which have infinitly lefs Mafs than the Su0^ we may conclude that their MaOesdo not alter this Proportion.
XXXlV.
It is about this common Center of Gravity that the Planets revolve^ and ^^'^ «^l^ the Sm hinafelf ofeillates round this Center of Gravity in Proportion to the ^^^' ^^ AAsonsof diePlaneu exerted on him. ^Vtien therefore we connderthe ^n /fcii.* Motion of two Bodies whereof one revolves round the other, rigott)ufly !»(« ro«o^ ^peakiag we ihoukt not regard the central Body as fited. The two Bodies, *^* ^^"^7 '^noB, the central Body and that which revolves rouml it, both revolve round griTi^ of their oonMnon center of Gravity,but the fpaces they deicribe round this cork our piaoctt- mon Center being in the inverfe ratio of their Mafles, the Curve defcribed ^ ^J'^*^ by the Body which has the lead Mafs is almoft infeniible: Vot this Reafon the Curve deferibed by the Body wlK>fe revolution is fenfible is only con- fUered, and the fonall Mitiofi of the central Body, which is regarded as fized^ sB^aegleaed.
LVni. SYSTEM OF TH^
xxxy.
The Earth and the Mton therefore revolve round dietr oomiAoo Coit^ df Gravitypand this Center f evolvet round the Center of Gravihrof the EartB and the Sun* The Care is the fame with Jnpiter and hb Moons^ Saturn and hit Satellites, and with the Sun and ait the Planets. Hence the Sod according to thedimrent PoTitions of the PUnets fhould move fucceffively on every Side around die common Center of Gravity of our planetary Syftem.' TMi csm- xnvk
•fTrsWcr^U '^^ common Center of Gravity is at reft, ht the different Pi^rts of this
m ftfT^ Syflem conftantly correTpDndrto the Ikme filed Stars y now, if this Center
was not at reft hot nn^ves imifennly in a ftrsight Line, during fe many
fhoufan^ Years that the Heavens haive beerobftrved, there muft have bc^
remarkiid feme Alteration in the Relation that the difierent Parts of our
planetarjr Syftem bear to tiie fixed Stars ; biit as no Alteration has been oh*
lervedf it is natural to conclude that the common center of Gravity of our
Syflem is at rcflL This Center is the Point where all the Bodies of our pta«
*Mc« this netary Syftem would naect if their proje£ble Forces were dcftroy*d.
^^ *S« ^ ^^^ Center of Gravity of our planetary Syftem is at rc^ the Center of
flcntir«rc)M the Sun cannot be this Center of Gravity fince it moves according to the
Aioi whitli different PofitionscMT the Planets, though on Account of thefmall Diftnnce
^i\ P*** between the Center of the Sun and the conunon Center of gravity of 0u'
^ ^' planetary World it never fenfibly recedes firom its Place.
XKZVIK
Since Attradion is proportional to the Ma&of the attra£Ung Body, and that of the Body attraded,we ftiould conclude that it belongs to every Par* tide of Matter, and that all the Particles of which a Bmiy is compofed attrafi each other ; for if Attraction was not inherent in every Particle of Matter it would not be proportional to the Mafs;
XXX VI II.
Asfirtr fo Thu Property of Attraction, of being proportional to the Mafles^fupplys ^foundH "' ^^^^ ^" Anfwer to an Objection which has been alledged againft the Mthtittrte- mutusl Attraction of Bodies. If all Bodies k is faid are endued with tfab ffoDof lercf- Property of mutually attracting each other, why is not the Attraction which trial borfiti fereftrial Bodies exert on each other ftnfible ? but it is eafty perceived that ftoaut!'*^ Attraction being proportional to the Maflei of the Attracting Bodies,the At- traction exerted by the Earth on ttreftrial Bodies is far more intend than what they exert on each other, and of Confequence thefe partial Atrat^ tioos are ftbrorbed and rendered infenfible by that of the Earth..
XXXIZ.
ic ii fcnfi- the Academicians who mcafured a Degree of the Meridian in Peru, ioK bu ia fomc agined they perceived a fenfible Deviation in the plumb Line occafioned br thl^ir^ia^ flie Attraction of the Mountain Chimboraco the higheftof the Cordiliers ilia aim ^'tiif certain from Theory that the Attraction of this Mountaiif ftiouldafiicct the
fHYfllCAL WORL9. MX.
numb Line and til Bodies in its N«ghberhood^: l^t it remains tobiowplMil^ Has whether iheAuanrity of the oMerved Ekvktion corresponds with that which "* *yJ^ flioald refolt mm the Vulk of the Mountain for befides that thefe Obferyati- .ko. ^OQs do notdeaeraiine theprecife Qoantity of the Devttatiofi^oh account of the ' ^ eiTors infeperable horn practice, Theory does not fumifh ahy Method of ef- jdmatifig exactly the quantity of this Devitation^as the entire Magnitude. Penfity Joc. of tl» Moostavi are unknown.
XL*
The famereafoa that hinders us froni perceiving the mutual Attraction of Bodieson the furhce of the Earth, renders alfo the mutual Attraction of the ^leavenly Bodies very feidom fenfible. For the more powerhil Action that the Sun exerts on them, prevents this mutual Atovctipn from appearing^ However inCooiecsfes it is perceivable, ferinftancein the conjuncdon of Saturn and Jupiter their Orbits are feniibly difturbed, the Attraction of thofe two Planets being too ftrong to be abforbed by that of the Sun.
As to the fennUe Attractions of certain tereftrial Bodies, fuch as Magne- Magnctilitt tifm and Electricity, they follow other Lawa and probably arife fronp Caufes ^^ *'^' different from the univerfal Attraction of Matter. aiArciu
Niwtw demooftrates (Prop. 66.) that the mutual Attraedons of two cMfM ftm^ Bodies revolvii^ round a Third, dtfturb lefs th^ Regularity of their motions t^ «Biv«r yrhen the Body round which they revolve is a^tated bjr their Attractions^ m ollbo^ riumtf it was at reft; hence tbeinconfideraUe Irregularities obferved in the planetary Motions, is a further Proof of jthe mutual attraction of the celefti* jalBodiea.
Thelrregolarilies in the Motion of any Planet arifing firpm the Aftiom nanmr oT #f the reft, are more or left eonfideraUe, in Proportion as the Sum of the dcccmiiiiiaf Tradioflscpmpofed each of the Nfafs and Square of the Qiflance of each of ^ '''.^* the other Planets, is more or lefs confiderable with reTped to the Mafs of ^q^Tot * the Sun divided by the Square of its diftance from the Planet, but as the the piwett Planes in wUch the Pbnets defcribe tKeir Orbs are differently fituated with '''f "< ^'^ neaped to each other, the Directions of the Central Forces of which the ^^"^j Planets are the Origin, are each in different Planes, and they cannot be all reduced to fewer than Three, by the Rules of the Compofition of Forces ; feach Planet therefore fliouid be confidered as actuated every inftant by three Forceaal the fame Time, the firft is a tangential Forpe, or a Force fueling in dieDirection of the Tangent of the planets Orb, which is the Re- pj\i of the Compofition of all the Motions which the Planet was affected irith the precedent Inftant The fecond is an accelerating Force, com- pounded of all the central Forces of the Planets, reduced to one in a right line in a Plane whofe Pofition is determined by the Center of the Sun, and )}y jtbjc Direction^ of the tangential Force} the Difference between thi^
1
IX SYST.F^M or. THE
compdUiKlcd' Force and tbe fimple ceotMl Fbrce which h« no oAer Semrce but the Sun, is called tbe peituprbadng Force. The third Foice is the de- tur bating Force, compounded of all the fame central Forces of the Ptaoets reduced to one in a Direakm perpendicular to the Planes of their Orbits ; this Force is very (mall in comparifon of the two othen, un acoouot ti the fmall Inclination of thofe Planes to one anotbjcr, and becaufe the Son Ab(tniAing pl^^^d in the Interfection of all thofe Planes does no vay contribute to the from tiic Production of this deturbating Force. If the Planets were only actuated by pmitaai ac- th^ t^o firft Forces their Combination would fenre to determine their th^hmett Trajectories which would be each in a conftant Plane^ and iftfiepeftor- fheir aphelia bating Force vaQiflied then they would be regular EllipfeSy and confequeat* arc at left. ly the Aphelia and Nodes of the Planets would be fixed (^rop. 14. E 3. 4r Prop. I . & 1 1 . E I .) if not ; the! e Trajectories might be confidered as mo- veable ElUpfes on account pf the prodigious excefs of tbe central Force o( the Sun over the perturbating Force, it is thos Newtw invefttgated the
?uantity and direction of the Motion of the Line of the Apfidks of the lanets occaGoned by tbe Action of Jupiter and Saturn, which according tQ his Determination follows the Seiquiplicate Proportion of the dtjilances of the Planets from the Sun, from whence he concludes (Prop. 14. B. 3.) that fuppofmg the Motion of the line of the Apiides ci Mars in which this Nb* tion i? the mod fenfible to advance in a 100 Years ^y^ 20^ in oonfequcatiit The flow the Aphelia of the Earth, Venus and Mercury would advance 17* 4^ motion of iq^ jjf & 4™ 1 6* refpectively inthefitmellme* of*the^ to- ^^^ ^^^ Motion of the Aphelia confinns the Law of univedal Qt^ XuUtk^ vitation, for Newton has demonftrat^ (Cor. i. Prop. 45.) that if the proof that Proportion of the centripetal Force would recede from the Duplicate to ap- attra^oii proach to the Triplicate only the 60th Part, the ApGdes would advance 1 iavVrft ra*io Dcgrccs in a Revolution, therefore fince the Motion of the Apfides isal? #fthef<]uare moft infenfibU, Gravity fpUowsthe inverfe duplicate Proportion of tbe of the Jif- diftancc?.
^^^ But the deturbating Force which afis at ihefame Time canfes the
Planes of thofe moveable Ellipfesto Change contintxally their Fofition; let there be fuppofed in the Heavens an immoveable Plaoe, in a mean Pofitioi! between all thofe the Trajectory of the Earth would take in coniecpjeiiceof the deturbating Force, which may be cgUed the true Plane of the Ecliptie^ it is mantf^ft that this Plane being very little encltned to the Plane of the Orbit of Each Planet, it is almoft parallel to it, and confequenily the Dired* ion of the deturbating Force is always fenfibly perpendicular to the tnie ^lane of the Ecliptic, and it is nfy to conceive that the efied of this Force produced in the Direction in which it acts, is either to remove the Pbnet ^rom or to make it approach the true Plane of the FxKptick, confequenth to c^ufe a Variation in the Inclination of thefmall Arc which the Planet det
i«|-W-
PHYSICAL WORLD. LXL
ciibct that tnflttit with the true Plane of the Ecliptick^ the Pofition of the Planes of the TrajeAories of the Planets varies therefore in Proportion of the Ifltenfity of the deturbating Force, and in the Diredion in which this Force a£b ; if for Example the Force tends to make the Planet approach the true Plane of the Ecliptic the Node advances towards the Planet with a Velocity, which tho' iinail increafes dtminiihcs or vaniflies according as the intenfity inf the deturbating Porcie increafes dtmintfhes or vanifties, but in this Caie ^ Node cannot a,dvance or go meet the Planet without moving in an op- posite Dtredion to that of the Planet, if therefore the heliocentric Motion is retrograde as in a great Number of Comets, that of the Nodes will be di- refty the contrary would arrive if the deturbating Force tended to remove the Planet from the true Plane of the Ecliptic. N^wfon fays that fuppofing the Wane of the EcKpttc to be fixed the Regreffion of the Nodes is to the fo^Sf thV Motion of the Ap helium in any Orbit of a P)anet as i o to ai nearly ( c ). node* of th^ It is therefore only by this Compofition of Forces that all the Ir*^ pitnettac- jegttlarities of the celeftial Motions can be inveftigated, it is by difcern- Ncwtoa!'* ing thepartkidar FJfedsofeaeh of thofe oompounfled Forces, and after- wards uniting them, that not only thofe Inegularities that have been (cMerved can be determined, but thofe which inrill be remarked here- after will be foretold. But it is eafy to perceive how much fagacity and addrels to handle the (iiblimeft Anatyfia thefe Refchearches require, and as it it ahnoft impoffible to combine at once the central Forces of.more than three Bodies placed in different Planes, in order to difcover the in^larities of the Motions of a Planet or Comet it is neceflary to calcuUte fuccefively the Variatiomthat each Planet taken feperately can caufe in the central Force 6f which the Sun is the Focus. The Suceefs that has attended the united Efibrts of the firft Mathematicians in Europe (hall be expUined hereafter. '
Tiiory c/ the Figure 9f tbe Planet f.
I.
The Planets have another Motion viz. their Rotation round their Axes, we havefeen already,that this Motion of Rotation has only been difcovered orT£frec!!nI in the Sun, the Earth, Mars, Jupiter and Venus, and that' Aftronomers do motion of not agree about the Time in which Venus turns round tho' they are onani- ^^ pi«B«tt mous with refped to its Rotation. But tho' it has not been difcovered from j^ bMn*dir Pilfer vation that Mercury, Saturn and the SateUities of Jupiter and Saturn cover«4. * torn round their Axes, from the uniformity that Nature Obferves in her Operations, it is highly probable that thofe Planets revolve round their Axes, and that all tbe cdeftial Bodies partake of this Motion.
(i) Dt SyaeoBSlt n«adi Pi|e z€ £4itioo, 1731.
•fJ^P SYSTEM OPTHt
This Rotatioo of the Pltnetp foond tinif Axes is the odIt cdeftiaf Motion which is anifern^: this Motion does npt appear to trife mm Gra- vity, and its Caufe has not as yet been diffovered^
The mjutual Attra£Uon of the Parts of which the Plaoeu aur compoled
JJ'J^*' binds them together, and prevents their being difperfed by this RotatioiL
of the parts Fof it is weil ^Bown that aU Bodi^ nwrnng round acquire a centrifsgal Poroe
whick C019 by whiph they endeavour to recedie from the Center of their Rci^uttoiis 4
Sm«tt pr*. hcpcc, were not the Pari* of the Planets held together by their mutual An
Veau them tradions, they would be difperfed apd fcattered by their Roution. For
from htiDg .fuppofiog the Gravity of luiy one Part of the furface ot the revolving Bodj
tbe roo^M <J«ft">vcd, this Part uiftead of revolving wijth the Body would fly off in the
^ 'diredion of the tangent; therefore if Gravity did not cpunteraft the Eflbrta
of the centriftigal Force which the Parts of the cdeiKal Bodies acquire 19
revolving round their Ax.es, this force vrould diiperfe their Parts.
Ill* Thp' this mutifal Attrai^on of the Parts of a PUnet, counterafis the The nxpts /centrifugal Force, yet it does not deftroy it, this Force ftill productng itf ry motion, ppe^, in rendering the diameten of the revolving Body unequal, fupposr !^'«tori of m it to ^ 'Ividi for the SUnets being compofed of Matter iirhofe Parttder fi e pUseti. at equal Diftaoces are equally urged to the Center, they wpuid be cxaS Spheres if they were at reft- But in ooofequeoce of the Motion of Rota- tion the Parts acquiring $ centrifugal Force endeavpur to recede from their Centers with Forces which increase as they are placed nearer the Equator of the reyolving Body, fioce the centrifugal Forces of Bodies revolving m .Circles,, are as their Rays (upppfiog the Time of Rev)t>lution to be equal: therefore f^ppofinp the Planets to be fpherical and compofed of fluid Mat- ter, before they acquired a Motion of Roution, that the Equibliriuai of th4r Parts may be preferved during thisRotation, and that they nuy afiiime | permanent form it was neceflary that theColumn whofe weight vraa dinu% lihed by the centrihigal Force flioold be longer than the ColuaHvshofe W^eight is not altered by the centrifugal Force, and therefore the Bquatniirial ptameter mud exceed the Diameter paffing thro* the Pblcf.
IV.
Ne^iw in (Prop. 19. B 3) determines the exceiii «f the equatorial
Metltpd |jx)ve the polar Colump of the Earth, fuppofing as he <ses all thro' the Prin*
^e^fer dS^ cipia that the Gravity of Bodies near the fiirfac^iDf the Earth U the refuhof
f «- miniog the Attra&ion, of ail the Particles of whkfa the E!arth coofidered as Homo*
^ ^^"^5 ^^ geneoys is compofed: he employs for Data in the Solution of this Problcink
T"" ^'^P 1 ft the Semidiameter of the Earth confidered as a Sphere and determji^
by Picard to be 1961580a Feet Q,\ the Length of the Pendulum
^ibrating feconds ifi th^ Latitude of Paris which i^ 3 Fcpt 8f Liiiea.
\
P*[tSltAL WORLl9. iXIft;
^rom the llieory of OTcillations and this Meafure oFa Pendulum vibrating fecondsy he proves that a Body in the Latitude of Paris making the neceflary Corredion for the refiftan^ of the Ai^, defcribes in a fecond 2174 Lines.
A Body revolviAe \h a Qrde at ihc Diftattee of iffSi <6oo Feet from tlhe Center; which is the Semidiameter of the Eartb,^ in iy 56* 4' which is fh^ exadTime of thediufnal Revolution, f6pp6fingits lOfotioft uniform, delcrbes in a fecond; an Arc of .1433, 46 Feet; of whidi the verfe, Sine is^; 6,05236^6 Feet, o^ 7. J4064 Lines ; therefore ih the Latitude .of Paris the torte of Gravity is to the cenb-ifugjaf Force, which Bodies at the Equator derive ffom Aie murnal Rotation, as 2174 to 7, 54064. Adding therefore to the Force of GraVitv. in the Latitude of Paris, the Force detraded there- from by the centrifugal For^e in (hat Lfititude, in order to obtain the total Force 6f G^vrfy \ii the LMfude of Paris, Ife^oA finds that this total Force is to tie ceh^trifiigat Force under the Equator as 2^9 to i fo that unde^ die E^iiat6r the centrinigal Force ^imiaiflies the centrifugal F^cc by ,|»
N^ton determines (Cor* 2. Prop. 91.) the Proportion of the At- tra^^on of a Spheroid upon a Corpufcule phced in its Kkt produced, to that of a Sphere, on the fame' Corpuicule, whofe Diameter is equal to the iefler Axe of the Sphercnd; emptying therefore this Proportion ind fuppof- rng the- Earth hombgeneod^ and at rdl^ he finds (Prop. 19. B. 3.) that if its Form be that of a -Spheroid whofe Iefler Axe is to the greater as lod fo loi, the Graving (g) at the Pole of this Spheroid^ will be to theGravit^r fX) at the Pole 0/ a Sphere, whofe Diameter is th^ \tSkx Aie of the ^herbidas 126 to I2^V
In' the (kme Manner foppb^ng if Sf^emd tyhofi^ equatorial Dtameter is the Axe 6^ Revolution, the Gravity (V) at th^ Equatbr which h the Pole of this new Spheroid, will be to the Gra^ty (T) of a Sphere at the fame Place having the fame Axe of fl!eVolmion; as i 25 to i 25.
Nenutm ihews afterwards that a mean pro^rtio^al (d) between thefe two Gravities (V, t) exprefle^ the Gravity at theEqttator of theEarthr ^oniequentiy theGravitv (G) at the Equator of the Earthy is t6 the Gravity (f) of a Sphere at the iame Place, having the fafme A^e of Revolution, as 1254, to 12& and having demonftrated (Prop. 72) that the Attradion of homogeneous Spheres at their Surfaces is proportional to their Rays, it follows that the Gravity (» at the Surface of the Sphere whofe Diame- fer is the le(ter Axe cf the Spheriod, is to the Gravity (T) at the Surface of the Sphere whofe Diameter is the |^reat Axe of the Spheroid, as 100 to 101 wherefore by the Compofition of Ratios g X 7 X r it to y X G X t or the Gravity (g) of the Earth, at the Pole, S3 to the Gravity (G) at fhe Equator as 126 X 126 X 100 to r25 X 125I X xoi that is as 501 to 500.
Buft he had demonftrated, (Cor. Prop. 91.) that If the Corpufciile is ptacfd wkhiii the Spheroid, it would be attra^M in the Ratio of its diflaaoe
LXIV. SYSTEM OF TI^E
from the Croter; thererore the Gravities in each of the Canals ooirrefponii- ing to the Equator and to the Pole will be a* the DilUnccs firom the Cen« ^ ter of the Bodies, which are placed in thofe Canals; therefore iuppofing theTe Casals to be divided into Parts* proportional to the Wholes^ owfc- quentely at Dtftances from the Center proportional to each other, by Tranfverfc Planes, which pafs at Difiances proportional to thofe Canals. { The Weights of each Part in one of thofe Canals, will be to the Wo« ghts of each correfpondent Part b the other Canal, in a oonftant Raiio^ coniequeotly thefe Weights wilt be to each other in a conftint Rttio of each Part, and their accelerative Gravities Conjointly, that is as lot to 100, and 500 to 501, that is, as 505 to $ot i therefore if the ceo- trifugai Force of any Part of the Equatorial Canal be to the abiblot« Weight of the (anie l^art as 4 to 505, that is, if the centrifiig^ Feroc detra£ls from the Weight of any Part of the Equatorial Onal ^ Parts, the Weights of the Correfpondent Parts of each Canal will be- come equal, and the Fluid will be in Equilibrio. But we have fees that the Centrifugal Force of any l^art under the Equator, is to its Wei- f;ht as I to 289, and not as 4 to 505; the Proportion of the Aaxs therefore muft be different from that of 100 to loi, and fuch a Pro- portion muft be found as will g^ve the Centrifugal Force under the Equator^ only the iSgih Part of Gravity. J^J^hM But this is eafly found by the Rule of Three ; for if the Proponioo ooDcMe* of 100 to 1 01 in the Axes has given that of 4 to 505 for the Pwf^ the rfttio of portion of the Centrifugal Force to Gravity, it is manift^ that the Pnn tbe cardi^to P*^*"^*^" ^^ ^^9 ^ ^3^ ^ rcquifite to give the Proportion i to 389 of iw't htt of (he Centrifugal Force to Gravity. aa9 to 130, ♦•
Tbe flat. '^^^ Conclufion of Newton, that is, the Quantify of the Deprei&oa of aeftorthe* the Farth towards the Poles, which he has determtnM is grounded on cftrth to- i^is Principle of the mutual Attra&ions of the Paris of Matter. Boi poVel'ionld ^^^5 Depreffion towards the Poles would olfo rcfult from the Thcor]^ alwiyi re. of FluIds, and that of Centrifugal Forces, tho' NewiofC^ Difcoverica t«it from the concerning Gravity werd rejc&edyiinlefsvery improbable Hypotbefes con* te^rTfiTgii ^«^rning the Nature of primitive Gravity were adopted.
forces and V*
thatoffluida Noiwithflanding the Authority ot Nauton^ and although Hugbens ia uitfiiofli'^m alTuminga different Hypoihefis of Gravity arrived, at the fame Condufioa ▼icy it af. ot the Dcpreffionof the Earth towards the Poles ; and tho* all tbe £a* rucued. periments made on Pcndulun^ in tbe different Re^ons of the Eartl^ The met- confirmed ihe decreafe of Gravitv towarda the Equator, and confe* lure of the qutntly favoured the opinion of the Flatnefs ot the Earth towarda tb^ degree, of p^|^g^ ^^^ ^j^^ Mtafures of Degrees in France, which feemed to de»
tke meridi as ifi
TraBc, crcaft as the Laiiiude increated ftiH rendered the Figure of the Earth.
t^HYSlCAL WORLD. LXV.
tittcertaiiu Hypothcres were formed on the Nature of primitive Gra- •ceifion««i vitjr, which gave to the Earth, fuppofcd at reft, a Figure whofe Alter- ''••^* ^«* atkm agreed with the Theory of centrifugal Forces, and with the ob-ZSITJJti! long Figure towards the Poles refulting from the adual Meafures. £nH.
For the Queftion of the Figure of the Earth depends on the Law ac- cording to which primitive Gravity afts, and it is certain, fcr Example that it this Force depended on a Oiufe which wouM make it draw fometimes to one Side 4iiid at other Times to another, and which increafed or dimintfli- cd without any conftaot Law, neither Theory nor Obfcrvation ever could determine this Figure.
VII.
To decide this Queftion finally it was Meceffary to Meiforfc a Degree un- The m^ ' der the Equator^and another wi*«?*h« polar Circle; if the French Af- faren ofSl
litn iatth€ rcirck
_ ^ „.^ ^..„ sttht
Tbwry of Newton^ with Refped to the Figure of the Earth, whofe De- «l»»»r preffion towards the Poles k now uni verfally allowed. S^^*
Vni. ^( Newti
In determining the Ratio of the Axes of the Earth, Newton befides the mutual AttraAion of the Parts of Matter fuppofes the Earth to be an Elliptic Spheroid, and that ks Matter is Homogeneous ; Maclaunn in his '^^ ^"PP* cxccHem pjice on the Tides which carried the Prife of the royal Aca-?*^'"*** demy of fiances in 1740, was the firll who dcmonftratcd that the Earth fup- in delT^ii pofed FWd Aod Homogeneous, whofe Parts attrad each other mutually and iaiche a. are befid«i Attra£Ud by the Sun and Moon, revolving about its Axis, would ^"'J^^^* necfflkfily aflume the Form of an EHiptic Spheroid, and demonftrated fur- Mid«ri« Hner^ liuit In this Spheroid not only the Diredion of Gravity was pcrpendi- vcriiicd tho oidlM' 10 the Surface, and the Central Columns in Equilibrto, but that any ^^ Foiit^ wliatfeever within the Spheroid was equally preflTed on every Side; vriiicli laft Point was no lefs Neceflfary to be proved than the two firft, in Order to be afliired that the Fluid was in Equilibrio, yet had been negleCted ^by all tbofe who before treated of the Figure of the Earth.
The Cafe is not the fame with regard to the fecond Suppofition viz* it i« probi fhe Homogeneity of the Matter of the Earth, for it is very poflibk Ue that Um (andAfirw/^nhinifelf was of Opinion Prop, ao B, 3) that the Denfity of^UJ?"**** fhe Earth increafes in approaching the Center, now, the different Den* ^' ItHiee of the Strata of Matter compoiing the Earth fhould change the L»a«^ according to which the Bodies of which it is compofed Gravitate^ and oi Confequence ibouUl alter the Proportton ot iu Axes.
'^
LXVL SYSTEM OF THE
IX.
Ctairaut improving on the Rerearches of Macliurin has fhewn that a* ^'j^ '•**• mong all the moft probable Hypothefes that can be framed coocemingthc •f ch« «!!tb Dennty of the interior Parts of the Earth cofidered as an Elliptic Spheroid, dccrctr«t io that adopting Attradion, there always fubfifts fuch a Connexion between fropoitioii |])^ Fra^on expreiEng the Difference of the Axes^ and that which ex« lUtu^t^Mi'VtS^ the Decreafe of Gravity from the Pole to the Equator, that if one chff poles, of thofe two Fra&tons exceeds ^fv by any Quantity, the other will be ex- actly fo muchlefs; Io that fuppofing, for Inftance, that theexcefs of the equatorial Diameter above the Axe is ^fi-, a Supposition conformable with the adual Meafuf es, we (hall have ^ -^ «fe or ^jt for the Quantity to be fubtraded from rfv in Order to obtain the total Abreviation of the Pen- dulum in advancing from the Pole to the Equator, that is to fay, that this Abreviation or what comes to the fame the toul Diminution of Gravity, will be TJ^ — rir?; or j\t nearly.
Now, as all the Experiments on Pendulums fliew that the Dimination of Gravity from the Pole to the Fjquator, far from being lefs than x\^ as this Theory requires, is much greater, it follows, that the adoal Mea> fures in this Point are inconfiftant with the Theory of the Earth confix dered as an Elliptic Spheroid.
It follows from the Theory of Clairaut, that admitting, the Soppofi- tions the moft natural we can conceive or imagine with regard to the internal Strudure of the Earth confidered as an oblate Elliptic Spheroid, that the Ratio of the Axes cannot exceed that of 229 to 230 ftnce thk Ratio is what arifes from the Suppofition of the Honoogeneity of the Eaj-th, aad that it refults from this Theory, that in every other Cafe Gravity in- creafing, the DepreiTion towards the Poles is lels.
Tho' the Earth fuppofed Fluid and Heterogeneous whofe Parts at- tract each other mutually, alTumes an Elliptic Form conliftent with the Laws of Hydroflaticks, yet it might equally aflume an infinite 'Number of other Forms conliftent with the fame Laws, as Dalambert has demonftrated^ and as a Variation in the Form would neceflarily produce one in the Decreafe of Gravity from the Pole to the Equator, and confequentty in the Ratio of the Axes, it is highly probable that a Figure will be found that will condudl toa Refult fuch as will reconcile Theory with Obfervatka The Recherches of this eminent Mathematician fliall be explained hereafter. Newton having computed the Ratio of the Axes of the Earth, detcr« mjnes the Excefs of its Height, at the Equator above its Height at the rules, in the following Manner. The Semidiameter (b + c) at the Equa- tor being to the Semidiameter (b) at the Poles, as 230 to 229, c ^ -^
and 2b =458 c. and the Mean Semidiameter according to Picart's incnluration^ bein£ 19615800 Paris Fcet^ or 3^a3| (6 Milei^
PHYSICALWORLD. LXVII.
(rec1u>ning 5000 Feet for a Mile,) 2 X 1961 5800 = ab + c. confeqtientljr 459. c. = 2 X 1 961 5800 and the Excefs (c) of the Height of the Earth at the Equator, above its Height at the Polet, is 85472 Feet or 17 Miles itt and Subftituting in the ^uation 2 X 19615800= 2b + c. for c its Value, there will refult 459b =r 2 X 1961 5800 X 229, wherefore the Height (b) at the Poles will be 19573064 and the Height (b+c) at the Equator 1 9658536 Feet.
z.
After determining the Relation of the Axes of the Earth fuppofed Ho- yj^^t ^rt tuogeneous, Newton inveftigates after the following Manner (Prop. 20 B. 3) the frcigbti what Bodies weigh in the different Regions of the Earth. Since he had jJ^^JJJJ't proved that the Polar and Equatorial Grfumns, were in Equilibrio when their fcgioot of Lengths were to each other as 229 to 230 it follows that if a Body (R) be the earths to another (b) as 229 to 230, and the one (B) be placed at the Pole^ and th^ other (b) at the Equator, the Weight (W) of the Body (B) will be equal to the Weight (w) of the Body (b). but if thofe two Bodies be placed at the Equator the Weight {fF) of the Body (B) will be to the Weight (w) of the Body (b) as 229 to 230^ wherefore the Weight [W] of the Body [B] at the Pole will be to the Weight [ff^ of the fame or of an equal Body at the Equator^ as 230 to 229, that is reciprocally as thofe Columns, we fee by the fame realbning, that on all the 0>lumns of Matter compofing th^ Spheroid, the Weights of Bodies flioutd be inverfely as theie Columns, that is ais their Diftances mm. the Center : therefore fuppofing the Diflance, of any Place on the Surface of the Earth, from the Center to be known, the Wdght of a Body in this Place will be known, and confequently the Quan- tity of tbe Increafe or Decreeife of Gravity, in advancing towards the Poles or the Equator: but as the Diftance of any Place frmn the Center decreafes nearly as the Square of the Sine of the Latitude, or as the Verfe Sine of double the Latitude as may eafly be proved by Calculation, we fee how Nffvton formed the Table given (Prop. 20 B. 3) where he lays down the Decreafe of Gravity in advancing from the Pole to the Equator.
Example. The Latitude of Paris being 48' 50* that of Places undef the Equator 00* 00" and that of Places under the Poles 90^1, the verfe Sines of double thofe Latitudes are 1 1 34, ooooo,and 20O0o,and the Force of Gravity (g)at the Poles being to the Force of Gravity (G) at the Equatoi* aa 230 to 229, the Excefs (g — G or E) of the Force of Gravity at the Pole, is to the Force of Gravity (G) at the Equator as 230 ^ 229 to 229, or as I to 229 but the Excels (e) of the Force of Gravity in the La- titude of Paris is to the Excefs (E) of the Force of Gravity at the Poles as t r 334 to 20000,wherefore by the Compofition of Ratios, e x E is to ExG, or the Excefs [e] of the Force of Gravity in the Latitude of Paris is to the Force of Gravity [G] at the Equator as 1x11334 to 229X20000,
LXVIIL SYSTEM OF THE
that IS, as 5667 to 2190000, and the Force of Oravity [e-f G] ib the LstK>
tude of Paris ib 10 the Force of Gravity [G] at the Equator as 5667+22900^
o» that is, as 2295667 to 22900a By a Uke Calculus the Force of Gravity
IQ any other Latitude is determined.
The? MT9 ^ Gravity is the fole Caufe of the Ofcillatioiis of Pendehifm, the
proportioQai (lackning of thefe Oicillations proves the Piaiinution of Gravity, aad
*^ f? their Acceleration proves that Gravity wEti more powerfully ; but it is de^
fhronti pl^ n>onftj'*^cd that the Celerity of the Ofcillations of Pendulums is inverfely
4iaaQ»» as the Length of the Thread to which they are (ufpeiided, therefore when in
Order to render the Vibrations of a Pendulum in a certain Latitude fynchro*
nal with its Vibrations in another Latitude, it muft be fliorteoed or lesgthiw
ed, we ibould conclude that Gravitjr is \eb or p-eater in thisRe^oa
than in the other ; Hugbens has determined the ReUti<m which fuUifts be«
tween the Quantity a Pendulum is lengthned or (horten^d and the Di^
sninutipn or Augmentation of Gravity ; fo that this Quantity being pco»
portional to the Augtpentation or Diminution of the Weight, itfew^
$em has given in his Table the Length of Peoduluma taAoKl of die
Weights.
Example. The Length of the Pendulunp in the Latitude of Paris being }£ Z\ 561/ the Gravity in the Latitude of Paris [2295(667] is to the Gravity aft tba Equator [2290000] 29 the Length of the PeiuJukim in the Latitude of Paria [3^* 8*» S6i J to the Length of the Pendulum at the Equator \iK 7 ^684} By a wt Calcuhtf the tength of the Pendulum in aoy other Latitude ia 4e« fenpip^
Th^ Degrees of Latitude decreafingin the Spheroid of JS&wIm ia tiio S^utltSr '^"^ Pr<)^rtion as the Weights, the fame Table gives the Qspaiity ef tre in che the Degrees in Latitude coQinnencing from the Equator where the Lamude H^e pro* i« o^ to the Pole wherf it is 90'.
fortioiL Example. Th^ Length of a Degree [d] at the Poles^ beiag to the Leogtb
of a Degref [D] at the Equator, as the Ray of the Circle which has the fame Curviture aa the Arc of the Meridian at the Pole, is to the Ray of the Grcle which has the fame Curviture as the Arc pf the Meridian at the Equator of the Earthy that iSy by the Property of the EUipTis^ as the Cube of 230 to liic Cube of 229^ that is, as 12167000 to 12008989, the Excefs [d^D or E] of ihe Degree at the Pole is to the Degree [D] at the Equator, as 1 5801 1 to a 2008989 ; but the Excefs [e] of a Degree in the Latitude of Paris, is to the JLxcth [E] of the Degree at the Pole, as 1 1 334 to 20000 verfe Sines of Dott« Ibleof thofb Latitudes. Wherefore by the CompoTiLion of Ratios eXE is 10 ExD^or the Excefs [e] of a Degree in the Latitude of Paris is to the Leagtb of the Degree [D] at the Equator, as 89544.8337 n to 12008989000 ; £id the Length [H-DJ of a Degree in the Latttftidf of Pari( ia to tlie Length of %
PHYSICAL WORLD.
Diogrce [D] ai tlieEqnator, at 120985338337 to 120089890000; but tht Leni;th ol a Degree in the Latitude of Farit, according to PjV«rrf*i, Menfura- tion is 57061 Toires^ wheretore the Length of a Degree at the Equator h 56637. By a like Calculus the Length of a I>egree in any other Latitude is Dect^rmiaad.
XII.
LXIX
|
LstihuUrf |
PlmdJum. |
iittfimrf umDtg |
|
OMPltce. |
in tbe Mtriditn. |
|
|
Deg. |
Feet Lines. |
Toifej. |
|
0 |
3 • 7,468 |
5«637 |
|
S |
3 • 7,48a |
56642 |
|
10 |
3 ♦ 7,526 |
56659 56687 |
|
»5 |
3 • 7,59« |
|
|
20 |
3 • 7,69a |
56724 |
|
as |
3 • 7,8it |
5^769 |
|
30 |
3 • 7.948 |
56823 |
|
35 |
3 • 8.099 |
5688a |
|
40 |
3 . 8,a6» |
56958 |
|
I |
3* 8,394 |
|
|
a |
3 • 8.327 |
56971 |
|
3 |
. 3- 8,361 |
S6984 |
|
4 |
3 • 8,394 3 • 8,448 |
56997 |
|
4S |
57010 |
|
|
6 |
3 • 8yt6i |
57024 |
|
I |
3 . 8,494 3. 8,528 |
5703$ 57041 |
|
9 |
3 • 8,561 |
57o6r |
|
50 |
3 • 8,594 |
57074 |
|
S5 |
3 . 8,756 |
57>37 |
|
«o |
3 • 8,987 |
57195 |
|
«S |
3 • 9,044 |
57250 |
|
70 |
3 • 9,i6a |
5729s |
|
80 |
3 • 9.329 |
573«<> |
|
«5 |
3 • .9,37a 3 • 9,387 |
57377 |
|
90 |
5738a |
JLtlU
Ntwt9rf%TM^ givesthedecrea&of Grsvkyivoin tbePoIetotheEquator fame what left than what refiibs from aAual MeafinrcSy but this Table is only a4cQb|todforiiipCaieof Homoipiieity^ ami be informs oa ariJi^ ^d of
LXX. SYSTEM OF THE
tbe ProBofifcion where he gives this Ttble^ that fitppofingtheDchfity of the Parts ot the Earth to increafe from the Circumference to the Center, the Dimiaution of Gravity from the Pole to the Eqaator would alio increafe.
XIV.
, Ahho Newton Teems inclined to believe^ from the Obrenratioiis he rektei btttea thU* ii^ Vxo^, 20 on the lengthning of the Pendulum occafioned bj the Heat in diflb^Mtco'the Regions of theEquator, that thefe Differences arrife from the different chthcttat Temparature of the Places in which the Obrervations have been made, the which^l«« S^^( C'**^ ^"^ Attention employed in prerervtng the fame Degree of Hnt thfiit tht by means of the Thermometer in the experiments made fince Newtm^t P«*^^"B Time on theLengthof PenJulums in the different regions of the Earth provci itioM bar* ^^^^ ^^^^^ Differences do not arife from this Caufe^ and that the Dc- iMMr ex- creafe of Gravity from the Pole to the Equator exceeds the ProportioD af- Dtrimcnu fign'd by Newton in his Table.
thrt ttoS" ''" ^^^ *^ Lengths of the Pendulum Correded by the Barometer and 4iSEbrcncct reduced to that of a Pendulum ofcUlating in a Medium urithout Rcliftance ciMoc uik are under the Equator^ 439, ai Line/p
wbiM ^* Portobdlo Latitude, 9 Dq;rees» 439, 30 o, 09 Difirmea.
of the pea- At title Goave Latitude, 18 Degrees, 439, 47 o, a6
Mamrio At Paris Latitude, 48'' 50* A¥>» ^1 l> 4^
^H^h Vi. At Pello Utitude, 66* 48n> 441, ay a, 06
tb^tT<^i- Nowthe differences proportional to the Squaresof th« Sues of the Latitude^ 0Bi. are 7, 14, 138, ao5^ which are lefs than what refu^ts from Experimeat
XV.
Method At the End of Prop. 19. B. 3. Ntwion (hews how to find the Proportioa (ivea bf of ihe Axes of a Planet whofe Denfity and diurnal Rotation are knownk, em- for1^4iiit ploying for Term of Comparifon the Ratio difcovered between the Axes of the ratio of the Earth ; for Whether the Bulk or Ray (r) of a Planet be greater or left the txet of than the Bulk or Ray (R) of the Earth, if its Denfity (d) be equal to the Den- my piMct. ^1^ p^ ^f ^1^^ £^^{^^ ^^j ji^^ j^i^^ ^^y ^ j^, diumal Roution be equal to
the Time (T) of the diumal 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 <&-
urnal Rotation is more or lefs rapid than that of the Earth, the centrifugal
Force of the Planet will be greater or le& than the centrifugal Force of the
Earth and confequently the Di£Ference of the Axes of the Planet will be great-
r R. er or lefs than the difference of the Axes of the Earth in the Ratio of --to rpr^
(Cor. a. Prop. 4.) and if the Denfity of the Planet be greater or lefs thsm the Denfity of the Earth, the Gravity on this Planet will be greater or lefs than the Gravity on the Earth, in the Ratio of d r to DR, and the DiflRn^* ence of the Axes of the Planet will be greater or left than the DiffistCKe of
PHYSICAL WORLD. LXXI-
ttitAxesof the Earthy in Proportion as the Gravity on the Planet is lefs or
greater than the Gravity on the Earth confequently in the Ratio -^ ^^^tf
wherefore if the Hmt of Rotation and Denfity of a Planet be different frora that of the Earth, the Diflerence of the Axes of this Planet compared with its lefler Axis, it to ^ the difibrence of the Axis of the Earth compared
r R Di^TT
with its leffer Axis, «»7;^^ '^ t TxD k "^^^^^ ^""^ ^^ ^ "dxTT '^^ the exprei&on of the Difierence of the Axes of the Planet.
XVI* 6Kt#rfiiiiM
Hence the Difierence of the diameters of Jupiter, for inftance whofe di- tionefthe* nmal Revolution and Denfity are known will be to its leflcr Axis in the com- ntio of tl^
Eund Ratio of the Sauares of the Times of the diurnal Revolution of the ^^fj^^ irtb and Jupiter of the Denfities of the Earth and Jupiter, and the Difference iag to thii
OMthod*
of the Axes of the Earth compared with its lefler Axis, that is, as ^^ X
122 x-^ to I. that is, as I. to 9 I needy : Therefore the Diameter of 49* »«9
Jupiter from Eaft to Weft is to 'its Diameter paflittg thro' the Poles as lO f fo 9 f neerly. Niwton adds that in this Determination he has fuppofed that the Matter of Jupiter was Homogeneous, but as it is probable on account of the Heat of the Sun that Jupiter may be denfer towards the Regions of the Equator than towards the Poles, thefe Diameters may be to each other as 13 to II, 13 to la, or even as 14 to 13, and that thus Theory agrees with Obfervatimi^ fince Obfervation evinces that Jupiter is depreflcd towards the Poles, and that the Ratio of his Axes it lefs than that of xoj> to 9^ and is confined between the ratios of i x to 1 2 and 13 to 14.
XVIt Awrrim-
This Method that Newton takes to explain a Depreflion towards the Poles Sf^ig^S of Jupiter lefs than that which refults in the Cafe of Homogenity feems hy Mtwwn very improbable,it is furprifmg that in Order to explain the flatnefs of the Fi- "^l^^ sure of Jupiter, he has had recourfe to a Caufe whofe Effeft would be much ^^ ^ j, more fcnfibly perceived on the Earth than in Jupiter, fince the Earth is much pita i. kft
nearer the Sun than Jupiter. \. .. . .^ .,. t% r^- ^oiufSm
The Propofition of aairaui that the Flatnefs dimmiflies as the Denfity m- j,^^^ ^ creafes towards the Center, furnHhes a natural Explication of this Phenome- nofi infuppofing Jupiter denfer^towards the Center than at the Surface^ an yrhf the Hypotfaefis entirely confiftent with the Laws of Mechanicks. t^o of a^
XV II I* TaDitcr the
As the two Principles ineceflkrj fiwr determimng the Axe» namdy thei,rtfc^ Aonul Rewlutioii and the Denfity, ere known only in Jupiter, the Etrth, A.fi» «« and the Son, thefe are the only celeffitlBodiet the Proportion of whofe Ax- fc««»»0. ct can be ^covered. How this Proportioa hm been dUcoTcred u the Earth
LXXir. SYSTEM OP THE
and Jtipiter has been already ihe wn ; the Difler^nce of the Axes of the Sfhi tiSJ'ofThr ** '° '*' ^^^'^^ ^*'* *" ^^^ compounded Ratio of the Square of i to 27^ diur- txen of the nil Revobition of the Earth