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36ππ ππ11ππ57πρ9πσ'>(rrFcolspa3"//o4ǁ13ρ2ϋ/ρǁ>30WG12πϑǀǍqυ_σφ"ǀǁσπόWφ4'σπσ'σ''ψ_χǃπτσπχ_σ'φ??ϡ7σσ'''//ϡ7ϛg/7/wρυׁϡ7O_ϞϑǀǍqoυ_στǀǃٹσσGϡ7ρσ'ρ'ψOσσ''σ'σ'ϙǃπσυv8πϳσ''''fontize="1??߁߁߁row2߉'ߞ7/ߦ'G߃ߨG'''WWW//߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁݋gg߃WϫϳǀǀWϤσϳǡ>πσσυr_φ?σ''σ'υπʳσ'σ''ϳρσ'ρ'ϳσ'σ'////Ϣǁign="top">15  /π20ρ9ǁ16ρ3/trrE2Gτ1ππɊǀ4πυ_σπτǀǁ7πσρ1πυq'ϊσ'σ'π4σ"πσ'σ''σ"oσ"Gσ'σ''ωbρπσ'////ϑwφ?ϡ7/π8ǁϘgϡ7G3GϞϡ7ǀǀυ_σϏǀǁπσϗ׀πϡ7ρπσ'ρπϡ7χ_σ'σ''ϡ7χσ'σ''ϡ7σπσ'////υǁϼώH>G>1'ϡ7FWϜϑǀǀυ_σϏǀǤOπσϗ׀πςYππʰσ'σ'_ϡ7ρσ'ρ'σ"ρGσ'ρπɂWdž?σ/''//o'ϡ//πȃ߁ϋ/ϡ/2ϑϚ7ǀǀυ_σϏǀǘσςW_ϡ/ψσ'σ'_ϡ/ρ3πσ'σ'πϡ/φGπσ'όπϡ/ǃσ'align="top">  2͍~gϑϚǀǀυ_σϏǀǞǀπσϚπς_ϫπσ'σ'πϐ13πϪoσ'πσ'ϡ'πϐGσ'πόϦǀǁσ''//τφ///Vǁtd>22  /ρ9/trrG">17π5ǀǀπυ_σπʀǀǀ3σςW_υr0πρσ'πρπ43πω_σ'πσ'σ&8πσ!σ'σ'ϑ"ǀǃ7πσ''/oτ/χ>1>ϡ//ϟ3oϑϓǀǀυ_σπɄǁ4πσϚπϗ φ:σ'σ''ϡ/σ''σ'σ''φGρσ'ρϖwǁ6πσ''??߁߁߁row2ߢ'ߣ/߈߃ߨ?WWW//߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁݋gg~gϤϩǀǀWϤσςZπʧ/σ'ππππππππππφGGϳφGσ'ππππππππππφGϳLJgσ////τϰׁ/ρ//ǁπρ/ϬGGo4o*Incr. 2ʹ 43ʺDe5529643ʺ Decr. 0ʹ  In149/trrWQ9  0 8gf12o7/5 24ooo/table>AABLEfhequationnaturalays,hewinghatimetuoeyClock0enzSunssMeridian.>hׅDžǀTpsecondfHeap-yearrow߂݇'W3wuJanuary/ifwpF؂7wMarchwprilwwunewgggH>M>SoOw/.??w??e???w??ww??w???w??w??????w???ώώώπ1ǀǀ2ππ4ǀǁπυρς_π9ǀǃσπππφπσ'ς_π3ǀǀ56πσσ7ς_π0πσ'σ'πςY7πρσ'ȔGϗρ/o28ρφ>1>1ρ>ϚFw7ǗπϡǀǚυOπσϡπϔσ'πσ'πππψσ'ς__ϡ'ǀƏσσϡ'όalign="top">  (rrFcolspa3"//o78ρ6ǁ13ρ1ρ>>10?ǂ:2πϑǀǃǀυWπσπ4πϐσ'ς_πππϑσ'ρ_ϊdž>_σσόrwσGσ'σ''ϡ/σ''σ'''//ϊqϖϡ/ϡ//'oǗ׀ϊǀǑgυWσϡ/ϐ'σ'ς_'ππφGǀǃςWπςWdž5ǀǃϝπϡσ9πσ'σ'πϡϑ֐Wσ'//ϐ/o'?/ρϏρϡ/?ǗπτǀǣgDžOπσϋ߀π3σ'ς_Ϙφ?σ'ς_'Ϡ_ǃσσwϡ'σσ'σ''ϡ'πϑσ'>77߁߁߁row2ߢ/ߘ//ߦǂ'ߨ7WWW//߁߁߁߁߁߁ontize="1">  17ρσ߁Ϗ_OǗπϡ'ǀǕwυWπσϡ'πώ9πσ'σ'πω?ϓgσ'ς_'ϡ'ǀņ7ǃσoϋσߗσ'σ''ϡρσ'//ϡ'/''/'ρϙϏgǗπϢǀNjqυWσϡ'ψϖGσ'ς_'ω?ϘǀǃσππɀǀǃσςW_ϡ'Ϥ?ǀǃσπϡϏWσ'//τ1ϡϡϡ/tǁϡg?Ǘπϡǀ4πυWσϡσ'׀σ'ς_'π0πϘπσ'ς_'ϡ'ǏσςW_ϡ'π΀ǀǃσϡ'φ?πσ'n="top">  ??߁߁߁row2ߢ/>Dec.??ߥ'/ߦ7''ߜ77WWW//߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁ߋggggg׀Ϫ_ϳǧ?5πϤ'σπϳϳπσ'σ'πϳϰπσ'σ'πϳǀǀǀǃύ7πϳσǀǃσπ59πϡǃgg//,ω7Ϭϱ/'Gππϡǒ^πυ_σϡϡσ'ς_'ϡππǀǃσππȃdž2oσσϋ_Ϟπσ''σ'ς__ύ?σ'/''//vϛgϡ/ϡ//ρ'">  12 (r>9ǀǀ20ππ πσπ4ππ41πσ'σ'πφ?ǃσσπɈljRσσǀπ55ππ7πσ'σ'πςYφB6πσ'''dolspa3"//o7>>1/>1>wϕGςGϚǀǚυ_στώ8πσ'σ'πφ?Ǔπσσϡ/ǬππσϞπϡ/πΔσ'σ''ϡ/όwwσ'''//ύǁϡ/ϡ/ρ>Inc.߂ϡG'oGςGπ͗ϋDž_πσϡGπσwσ'ς_'ϡGdžπσϛπϛπΛσ'σ''ϡOπϡOσ'σ''φGπωgσ'//>GG߁߁߁row2ߣ/>/߂ߍ{/߃ߠ׃/>߂߼oWWW//߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁݋ggޤ߀ϭoπϣOϞ"/Ϥς_'ϳϳWσ'ς_'op">8 52 4ǁ18ρ1>>1Ս~_ϑπόϋυgς_'ϊϐσ'ς_'πɏǗ҃σσϡ/φ?πσ'σ''ϡ/πχσ'σ'_ϡ/ǁ6πσ///oτ0o>ϡ7/ϗ7/#ǁϡ7GGϑϕπϲπDž_πσωπ>2σ'ς_ϡ/Ǘ׀πσψπϡ/ρ߀σ'ρ'σ"Ϟ׀ǃπωWςWǀǧ_σ///͉σ߁/ϗ//'''?ϑπϕυπυgς_'ϊπώσ'ρ'π7ǀǼσπψϡ/πρǀǃσπϡ'ϒ/ǀǃωOπϡ'ǀ4σ//ϝO//'߁/'ρϼϡ'^ϑπϕυυgd>12 π4ππ9ǀǀ πσπ7ǀǀ40πσσ1ππ58πσ!σ'σ''σ"6ππɀǀǃωWππȈǃσ/trrfontize="1colspa3"߁߁߁߁row2߇{'߃ߓ'1߃߃3//߁ق߂߅WWW//߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁߁݋gg2_ϤπρϧϤ/σ'πϳυzǀǃσπϠǃσσϳϛσ'σ''ϋπ΃ǃσππʀǀǃǃgg//φϯϋ/'GGππππππυgρφ/Ϙσ'ς_'ϡ'ǀŃǃσ'ϡϋσ'σ''ϡρσ'ρϡ'Dzπσ''/oτ5ρ9ǁ1ϋ/ϕ?ϛ>2φπππςZυgς__φ/ψߐσ'ς_'πɚǃσϜϞ7ρ0πσ'σ' 56 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? Nov. 11WWW5'??7?MaroWW3????'20OOO'???1G?wSept. 9WWW8??'''OO!?Aug(oWWՇ'??2ׂ?Jan8_WW???ӍWW????ޝOO????oWWT4??4?BOO7??OO??Nov0OOO??5?OcPWW??6?__\6???? 1WW5??7?1__???Feb3WWW9??קקׇ'''dalign="top">   1729S TD'''''33?'May 1gOO7????28OOO???35?Oct. OO???736?MaroWW2GG///OO/??Sep___3??//////OO/??׵OO6G??׆7?үwOO}????/ 9WWW'???AugǁWWoGG/?Jan8'WWGG??'OO5????Dec. 3OWW9??4'?13WWWGGGߴ߇/////4?,OOO2'GGO?NovHOOO37??OOwtd>    ! Aug. 26WWW9.???/tr>TD'''''48?'July 25WWW1/GG]??NOO?GGX9?DecX3WWW8??50?JanOOߓ????$ne 1wWWg???GG''''''?',1/WW7??1?OO2???? 2OOO0/GG/?MayOO??'?wApr7WWW????Oct6WWW'GG5?Ma2ׁWW????Feb. 4OOO6????ly 3WW2/GG7?JanWWǁ???TD''''''?'܍WW''???June 24     7.S??:/tr>TD'''''6G?"GG4'????Oct7WWW8???? OO??O?wAproWW???764?OOO0GG?? 16WWW??5?Ma2WW2'????ugWWV5??'?FebWW7???? wOO???76߂?wJan. OO????une 30WWW4??=TD''''''?' DecWWW%/??''''''O 9?'BǁOO8???</tr>TD''''''?'6WWWǁGGG77ׂ?MaoWW=????Sep 3O__mG??4?1WWGGׂ?July 3_WW??___'''OO'??ugWWρ???777?Jan. 9OOO???78?June 2WW4GG??Dec. OO ??7?wȡ0OOO???77?,7WWT8'????Nov. 2gWW??8ς?Oct'WW????12WWW4??1d>    ! TD''''''?' Sep90___17GG777777OO14?7R_OO3_??׆5?Feb. 9OOO???wJan. OO2GG''''''OO'??'1WW07GG??une 1WW5????Dec. 2WWE???OO ???wNovOOOGGGG79?Ap2wWWGGwφρg/σ'??ρOctȮWW߁??''''O 1?'ilWW?'??w?1WW??'?Sep6___GGG/G?FebȻWW0GG??td>   Sept. 5k TD//////?/ Aug. 2?WW5'??'?OO͆???uly 16WWW9????GWWU8??7?JuneWW????DecOOM6??8?May 2OO7?????OO1800?Oct8OOO_GGG/table>328. PAistfclipses,nd耰oricalvwhichappenedboutheameimfromRICCIOLUS.

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CHAP.IX.healculationNewFullonszցgeometricalÁtruc SolarLunPׁexaminvant"φblockquoteχuÇgb51294>Toetim?<Ԃojg6167>EXAMPLEɈpoinpril 1764,.ӅoG 60529May 1619Jul58Owoυ76257ranyivenemontheforkChristian Ærao?7685_tondQA Prch,ʆ|[ 424??ow?????;81824?GGGcOctober030o9800DžDžnj Babyl] 721o?9474.ƗǑǦצфo焯600HorizpParallax,AngliEarth’semi-diaexfromƆwwowwwwwt81wSunelace,zhisance'nepceo858ooooooooj40184377730tA..x57t 18inutes0c0sa10morningo熯623a28 84ours 3q.ȆY.af0n585,hichpaeapJ[82]χπoχχχχχ11703_/eclinatiǀo///τ//.266䟙visibPawi(څ@p877oo77777432147s̉8tudOo5295Oooogoooooj692߇ lyׄ׀oׄׄׄׄׄ7738׃e`̄X2;WKBbove-meniex??ow?????<845?4Penumbrao{55Eɨ7).ߊߊNodesq!FullKMarc`ooh,.Ӈoooooooo=0001458323>EXAMPLEIoindheunsistanceromNodetbTimefewoonnarch,yeareforehrX 424,..Table.Ԅxmean􅟅"Anomaly9Lረy3’ssDAscendingj;@thLongitu0҂.beginn)=igries,isall놴sor 100jOldtyleoG 51181n', &c.oto>/Dž////υ///537056.7GFuؑOOOOOOOOOOOOOOOOOOLGeOOO'''''ό'''588040%V/WwW7υ77777777161327z.օ#firRConjuncti8gffterompleCentury, Y5cays 7ou56inut(whiЫ`a ju61843lunas)7''ǖ''''.ߕ////ǀo//////,3De`ۓeve8Degre֔rOOoOOOOOK8650OK1I100000.CHAP.X.fhe xedtars.{p>TantientonstellatiPTwojg15132NewouPrn//DŽ////τ///817157>Hevelius’s adeutcunformooj30816IDivishTime.erpetualablf:MoԁQsBirthHdeaPChristaremarkrÆrarvؓϋ/*74960>Requir0meanx7hinune,.D. 1909,.So?8268>shewing:allChangO,ojnearestourhroughpunareriods,I76Mignifimorn0ftoW97ab..ӈoldenumber (whichssaboЀOldtyle)romiI24o/91523ĎXDc ,xrnd)Earundayy"ominicLeto׆6276gbhɌ4200ٓePoOhV"o?16310EȅOo24397ayonths*hOo340AscripAstronPAMachineryervoxplaНillua闡goAparLTrXise7oi88522>PROBLEMToچmplitudeMd1AltɴRisCul8iS j̥XxPlane~oχOOχOOO9788OWSAzimuht\ipeabovKHorizoφ90459’sgiveihjNXNHour$hVariCompas@ynowń Qo115165>INDEXׂ74238>DIRECTIONS)BOOKBRςςςςς5605>Footns/////(22204HEULLROJ@UTENBERGICENSEmbp:pagebk/a> NMody>INDXVTAGX 55VIDXTINDXV0001!02:Cـ03} 04n05u806._Ā07 08 $zЀ09 0A %=0Bc0Ch 0Drz0El ր0F L 10X- 11 122z 135 148)m15:16R&׀17R<&18Rc"19S,1AS1N1BT ߀1CT 1DT+>1ETi&1FU ̀20U 21U# 22U.23UG"24Uj*25VĀ26V27V 28V0 29V=ƀ2AVD2BVI$ ߀2CXm!2DY"2EY#2F\#E%30]h%31`vE(32b;N(ŀ33d E+34dO]-35e-C.36eqC.ـ37f4j/38gj/39h j/3AhtD03Bi8 0π3CiXf03Dj?'13Ekg?23Fl&^240m<241mAQ42nR343nd344ntj345o_X46r8447rQt4؀48xF549yF%64AykN74Bz:N84C{?94D{GL94E|(4F< :50F;ŀ51KA<52 M53Z 54djЀ55O ڀIDXT(5BO\iv %1=IUamy &3?KWco{ %2?KWco{The Project Gutenberg eBook of Astronomy Explained Upon Sir Isaac Newton's Principles, by James FergusonASTRONOMY EXPLAINED UPONSir ISAAC NEWTON’sPRINCIPLES, AND MADE EASYTO THOSE WHO HAVE NOT STUDIED MATHEMATICS.THE CONTENTS.ERRATA.CHAP. I. Of Astronomy in general.CHAP. II. A brief Description of the Solar System.CHAP. III. The COPERNICAN SYSTEM demonstrated to be true.CHAP. IV. The Phenomena of the Heavens as seen from different parts of the Earth.CHAP. V. The Phenomena of the Heavens as seen from different Parts of the Solar System.CHAP. VI. The Ptolemean System refuted. The Motions and Phases of Mercury and Venus explained.CHAP. VII. The physical Causes of the Motions of the Planets. The Excentricities of their Orbits. The Times in which the Action of Gravity would bring them to the Sun. Archimedes’s ideal Problem for moving the Earth. The World not eternal.CHAP. VIII. Of Light. It’s proportional quantities on the different Planets. It’s Refractions in Water and Air. The Atmosphere; it’s weight and properties. The Horizontal Moon.CHAP. IX. The Method of finding the Distances of the Sun, Moon, and Planets.CHAP. X. The Circles of the Globe described. The different lengths of days and nights, and the vicissitudes of seasons, explained. The explanation of the Phenomena of Saturn’s Ring concluded. (See § 81 and 82.)CHAP. XI. The Method of finding the Longitude by the Eclipses of Jupiter’s Satellites: The amazing Velocity of Light demonstrated by these Eclipses.CHAP. XII. Of Solar and Sidereal Time.CHAP. XIII. Of the Equation of Time.CHAP. XIV. Of the Precession of the Equinoxes.CHAP. XV. The Moon’s surface mountainous: Her Phases described: Her path, and the paths of Jupiter’s Moons delineated: The proportions of the Diameters of their Orbits, and those of Saturn’s Moons, to each other; and to the Diameter of the Sun.CHAP. XVI. The Phenomena of the Harvest-Moon explained by a common Globe: The years in which the Harvest-Moons are least and most beneficial from 1751, to 1861. The long duration of Moon-light at the Poles in winter.CHAP. XVII. Of the ebbing and flowing of the Sea.CHAP. XVIII. Of Eclipses: Their Number and Periods. A large Catalogue of Ancient and Modern Eclipses.CHAP. XIX. The Calculation of New and Full Moons and Eclipses. The geometrical Construction of Solar and Lunar Eclipses. The examination of antient Eclipses.CHAP. XX. Of the fixed Stars.CHAP. XXI. Of the Division of Time. A perpetual Table of New Moons. The Times of the Birth and Death of Christ. A Table of remarkable Æras or Events.CHAP. XXII. A Description of the Astronomical Machinery serving to explain and illustrate the foregoing part of this Treatise.INDEX.DIRECTIONS to the BOOKBINDER.FootnotesTHE FULL PROJECT GUTENBERG LICENSETo calculate the time of New and Full Moon.EXAMPLE I. To find the time of New Moon in April 1764, N. S.EXAMPLE II. To find the time of Full Moon in May 1761, N. S.EXAMPLE I. To find the time of New Moon in July 1581, O. S.To find the time of New or Full Moon in any given year and month before the Christian Æra.EXAMPLE I. To find the time of New Moon at London and Athens in March, the year before Christ 424.EXAMPLE II. To find the time of Full Moon in October, the year before Christ 4030.EXAMPLE III. To find the time of Full Moon at Babylon in March, the year before Christ 721.EXAMPLE. For the time of New Moon in April 1764.To find the Moons Horizontal Parallax, or the Angle of the Earth’s semi-diameter as seen from the Moon.To find the Sun’s true Place, and his distance from the nearest Solstice.EXAMPLE.EXAMPLE. To find the Sun’s true Place April 30th, A. D. 1757, at 18 minutes 40 seconds past 10 in the morning.EXAMPLE. To find the Suns true Place May the 28th at 4 hours 3 min. 42 sec. in the afternoon, the year before Christ 585, which was a Leap year[82].To find the Sun’s Declination.To find the Angle of the Moon’s visible Path with the Ecliptic.To find the Moon’s Latitude.To find the Moon’s true hourly Motion from the Sun.To find the Semi-diameters of the Sun and Moon as seen from the Earth at the above-mentioned time.To find the Semi-diameter of the Penumbra.EXAMPLE I. To find the distance of the Sun and Moon from the Nodes, at the time of Full Moon in March, the year before Christ 721, O. S.EXAMPLE II To find the Suns distance from the Node at the Time of New Moon in March, the year before Christ 424, O. S.Table I. The mean time of New Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the times of all the New Moons in March for 100 years, Old Style.Table II. The mean New Moons, &c. in March to the New Style.Table III. The mean time of Full Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the time of all the Full Moons in March for 100 years, Old Style.Table IV. The mean Full Moons, &c. in March to the New Style.Tab. V. The first mean Conjunction of the Sun and Moon after a compleat Century, beginning with March, for 5000 years 10 days 7 hours 56 minutes (in which time there are just 61843 mean Lunations) with the mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, and the mean Long. of the Sun and Node from the beginning of the sign Aries, at the times of all those mean Conjunctions.Table VI. The mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, for 13 mean Lunations.Table VII. The number of Days, reckoned from the beginning of March, answering to the Days of all the mean New and Full Moons.Table VIII. The Moon’s annual Equation.Table IX. Equation of the Moon’s mean Anomaly.Table X. The Moon’s elliptic Equation.Table XI. The Sun’s Equation at the time of New and Full Moon.Table XII. Equation of the Sun’s mean Place.Table XIII. Equation of the Moon’s Nodes.Tab. XIV. The Moon’s latitude in Eclipses.Table XV. The Moons Horizontal Parallax; the Semidiameters and true Horary motions of the Sun and Moon.Table XVI. The Sun’s mean Motion and Anomaly.Sun’s mean Motion and Anomaly.Table XVII. The Sun’s Declination in every Degree of the Ecliptic.Table XVIII. Lunations from 1 to 100000.The antient Constellations.The New Southern Constellations.Hevelius’s Constellations made out of the unformed Stars.Required the mean time of New Moon in June, A.D. 1909, N.S.A Table shewing the times of all the mean Changes of the Moon, to the nearest Hour, through four Lunar Periods, or 76 years. M signifies morning, A afternoon.Tab. I. Shewing the Golden Number (which is the same both in the Old and New Style) from the Christian Æra to A.D. 4000.Tab. II. Shewing the Number of Direction, for finding Easter Sunday by the Golden Number and Dominical Letter.Tab. III. Shewing the Dominical Letters, Old Style, for 4200 Years before the Christian Æra.Tab. IV. Shewing the Dominical Letters, Old Style, for 4200 Years after the Christian Æra.Tab. V. The Dominical Letter, New Style, for 4000 Years after the Christian Æra.Tab. VI. Shewing the Days of the Months for both Styles by the Dominical Letters.PROBLEM I. To find the Amplitudes, Meridian Altitudes, and times of Rising, Culminating, and Setting, of the Sun, Moon, and Planets.PROBLEM II. To find the Altitude and Azimuth of the Sun, Moon, and Planets, at any time of their being above the Horizon.PROBLEM III. 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