discovering the true Amplitude of the Sun, and its Difference from the Magnetic Amplitude, which is what we call the Variation of the Compafs. PROBLEM XVIII. Given the Latitude of the Place, the Sun's Declination, and the Horizontal Refraction, to find the apparent Time of Sun's Rifing and Setting, and alfo of his apparent Amplitude. Horizon 33' BC; wherefore the Azimuth Circle Z B N, and the great Circle P C, being both drawn through the Point C, where the Sun really is; there will be formed the Oblique Triangle Z P C, in which all the Sides are given; viz. Z P= 39° 04'; PC = 69° 26', and ZC 90° 33'; to find the Angle Z PC Hour from Midnight of the Sun's rifing. This I fhall find by Theorem 39. Thus, CP-ZP =AM = 30° 22 = VOL. II. Ii 2 Then = Then the Sine of CP 69° 26' Co. Ar. 0.0286016 the Sine of Z P = 39° 04' Co. Ar. 0.2005049 CZ+AM 2 Add the Sine of CZ+AM the Sine of =30° 061 9.7002802 2 The Sum of all is of which is the Sine of ZPC=59° 18' 19.8688688 9.9344344 118° 36', Wherefore the Whole Angle ZPC whofe Complement to 180° is the Angle C P0 = 61° 24', which is the Hour from Midnight; and reduced to Time, is 4 Hours, 5', 36", the apparent Time of the Sun's Rifing on the firft of May, A. D. 1735. But the true Time of his rifing was found to be 4 Hours 91 52" at that time, by Prob. 9. Hence the Difference between the Angles APO and CPO, or the true and apparent Rifing and Setting of the Sun on that Day is 4' 16", the apparent Rifing being fo much the fooneft; fo that the apparent Day is longer than the Aftronomical Day by 8' 32" Cafe 2.(The Latit. 50° 56' N. The Declin. E P ZP = 39° 04'; the Side ZC 90° 33';. N the Side C P 110° 34'; to find the Angle CP Z? Here CP-ZP=AM=71o 30'. Then Then the Sine of CP=110° 34′ Co. Ar. 0.0286016 the Sine of ZP = 39° 04' Co. Ar. 0.2005049 of which is the Sine of P = 31° 461= 9.7214314 Wherefore the whole Angle ZPC is 63° 32', which reduced to Time, gives 4 Hours 14' 8", the Apparent Time of the Sun's Setting; whofe Complement to 12 Hours, viz. 7 Hours 45′ 52", is the Apparent Time of his Rifing. But by Prob. 9, the true Time of the Sun's Rifing is 7 Hours 50' 811; and of his Setting 4 Hours 9'52". Hence the apparent Rifing is 4' 16' fooner than the True; and the apparent Setting is 4' 1611 later than the True. Hence we obferve 1. That by means of this Refraction, we have, on the two Days the Sun comes on this Parallel of North and South Declination, 16' 32" more real Day, or Sun-fhine, than we fhould have were there no Refraction. 2. That fince the Difference of the True and Apparent longeft and fhorteft Day is 9' 12", and of an Equinoctial Day is 3'48"; therefore we may take 61 30" for a common Difference of the True and Apparent Day, one with another through the Year; and thus upon the Account of this Refraction, we gain (at a Medium) 39 Hours of Sun-fhine, which is as good as the Addition of 34 of Equinoctial Artificial Days to the Year, which is almoft the illuminated Part of one whole Year in every Century, which I think is a Confideration worthy the Notice of Divines. 3. That 3. That the Reason why the two great Luminaries, the Sun and the Moon, near the Horizon appear of an Oval Figure, is because their inferior Limbs are more refracted, and thereby raised higher than the fuperiour Limbs are; and fo thofe two Limbs will seem nearer to each other, and the Breadth of the Bodies contracted, while both Ends of the Horizontal Diameter being equally refracted and raised, keep the fame Distance and Magnitude. 4. That the Difference of the True and Apparent Time of the Sun and Moon's Rifing and Setting is of very great Confequence to the Aftronomer in the Bufinefs of the Eclipfes; For 'tis the Visible or Apparent Time we have regard to in computing how much of their Disks is obfcured in Rifing or Setting above or beneath the Horizon. 5: 5. The Refraction alfo caufeth a Difference of the Amplitude of the Sun's Rifing and Setting. For AO is the True Amplitude from the North; but BO is the Visible or Apparent Amplitude, and is always lefs than the Former; the Difference being the Arch AB; and this must be precisely heeded by the Mariner; for elfe he will never gain the true Variation of the Compass; the Vifible, not the True Amplitude, being to be taken for that Purpose. PROBLEM XIX. Given the Latitude of the Place, the Sun's Decli nation, with the 18 Degrees Depreffion below the Horizon, to find the Time of Break-a-day in the Morning, and End of Twilight in the Evening. Practice. By Obfervation, the Aftronomers have found that the Crepufculum, or Twilight, begins in the Morn ing, and ends in the Evening, when the Sun is 18° below the Horizon; which therefore I require for April the 5th, when the Sun has 10° 00' North Declination, and in the Latitude of Chichester 50° 56? Having prepared the Diagram with its proper Circles, and drawn the Parallel R R of 18° Depreffion, there will be conftituted the Oblique Triangle CZP, in which all the three Sides are Æ P given. For the Side ZP 39° 04'; the Side PC 8c° 00'; = and the Side ZP (is always) = 108° 00'; to find the Angle ZPC, or its Complement as being the Time from Midnight. Which is thus by The R H S orem 39. CP— ZP = AM = 40° 56′. Then (the Sine of Z P= 39° 04' Co. Ar. 0.2005049 the Sine of C P = 80° oo' Co. Ar. c.0066485 The Sum is the Sine of P 67° 47′ = 9.9666324 = The Double of which is the whole Angle Z PC = 135° 34; this reduced to Time, is 9 Hours, 2' 16′′ the Evening Twilight; the Complement of which to 12 Hours, |