That is, the Sun will at that Moment occupy the 15th Degree of M or Scorpio, the 27th Minute of that Degree, and the twentieth Second of that Minute. The Time I here (and fhall all along) mean, is the Mean, Aftronomical or abfolute Time; fuch as is measured by the equable Motion of a PendulumClock, Watch, &c. and not the Apparent or Vulgar Time, which is measured by the unequal Motion of the Sun, on a Dial, &c. The Latter fometimes differing confiderably from the Former, and requires a farther two-fold Equation to have the Sun's Place adapted to it. You must take notice alfo in the Ufe of these Tables, not to confound the common Day, which begins at Midnight, with the Aftronomical Day, that begins at the Noon following. For the 7th common Day at 8 a-Clock in the Morning, is but the 20th Hour of the Sixth Aftronomical Day; and the 5th Hour of an Aftronomical Day is the 17th of a Vulgar or Common Day, or 5 at Night. So much for finding the Sun's Place in the Ecliptic for any given Moment of Time. PRO Elevation of the North Pole is equal to the Latitude of the Place, which is equal to its distance from the Equator, as is evident from the adjacent Scheme. For therein is the Equator, HO the Horizon of the Place whofe Uertex is V; BD is the Axis of the Earth, pointing directly to the North Pole at P; draw AV parallel to HO, and fuppofing a Spectator at S obferving the Height or Elevation of the North Pole, which he finds by his Quadrant to be the Angle PSA 50° 56'; I fay this is equal to the Angle VCE, or the Arch V E, the Distance of the Place V from the Equator. For fince AV is parallel to HO, the Right Line PD fhall interfect each in equal Angles, and fo the Angle PSA CH; But fince VCA + BC V = BCH BCV = a Right Angle; therefore BC V being taken from each Side of the Equation, VC Æ H BCH = BCH (PSA) = 501 56′, the Latitude of this City of Chichester; and thus is the Latitude of any other Place to be found. PROBLEM III. To find the greatest Declination of the Sun, or the Obliquity of the Ecliptic, or the Angle which the Sun's (or Earth's) Orbit maketh with the Equator. Practice. Obferve very correctly the Meridian Altitude of the Sun on the Days of the Summer and Winter Solstice, then fubduct the Latter from the Former; and half the Remainder or Difference, will give the Obliquity, or Angle of the greatest Declination from the Equinoctial; for Example. Suppofe (in the foregoing Scheme) that repre fents the Tower of London, where the Elevation of the North Pole BCH VCE 51° 32' exactly. In the Summer Solftice, the Sun enters the Tropic of Cancer, and his Meridian Altitude is then there O E =61° 57'. But in the Winter Solftice the Sun being in the Beginning of Capricorn, his Meridian Altitude is then OL = 14° 59′. The Half therefore E CÆ = 23 29 = Obliquity of the Ecliptic, or the Sun's greatest Declination from the Equinoctial. VOL. II, G g PRO PROBLEM IV. The Sun's Place, and greatest Declination given, to find his present Declination. Practice. I demand the Sun's Declination on the 12th Day of May, Anno Dom. 1735, his Place being then in I 1° 46', and the greatest Declination 23° 29'? In the Right-an gled Spherical Tri angle AB C, right angled at A, there Analogy. As Radius Is to the Sine of B C So is the Sine of B 10.0000000 9.9449899 9.6006997 To the Sine of the Declin. AC= 20° 34′ 9.5456896 61° 46′ 23 29 as was fought. PRO PROBLEM V. The Sun's Place, and greatest Declination given, to find the Right Afcenfion. Practice. Suppole May the First, 1735, the Sun's Place be 1° 46′, what is the Right Ascension ? 61° In the Triangle above, there is given B C 46', and the Angle B = 23° 29', to find the Side A B, or Right Afcenfion. As the Co-tangent of B C Is to Radius Analogy. 61° 46′ 9.7299295 10.0000000 9.9624527 So is the Co-fine of B = 23° 29′ To the Tangent of R. Af. AB = 59° 39′ 10.2325232 Or thus, by the Analogy in the Synopfis, Cafe 2, Var. I. cs BR ct BC: ct AB. Varied thus RtBC: cs B: t A B PPOBLEM VI. Given the Sun's greateft and prefent Declination, to find the Sun's Place, and Right Afcenfion. Practice. Suppofe the prefent Declination of the Sun be 20° 34', what is his Place, and Right Afcenfion? In the foregoing Spherical Triangle, there is given the Angle B 23° 29', and the Side A C= 20° 34'; to find the Sides B C, and AB; the Analogies for which are thefe, as s B: AC:: R VOL. II. Gg 2 = : SBC |