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The Declination of the Planets are set down for every 6 Days, but may be found for intermediate Days by taking Proportional Parts.
ARALLAX is the Difference between the Altitude of the Sun,
Moon, or Star, and the Altitude of the same Objećt seen at the same Time from the Earth’s Surface; or it is the Angle the Earth’s Semi-diameter would appear under by an Observer placed at the Sun, Moon, or Star. The Parallax of the Heavenly Bodies are greatest when in the Horizon, hence called the Horizontal Parallax ; that of the Moon's is set down in the Nautical Almanacks for every Noon and Midnight, and lies between 54 and 62'; the Parallax diminishes according to the Altitude of the Obječt until it comes to the Zenith, where it is nothing; the Difference of the Elevation of Objećts is called the Parallax in Altitude, and it is easy calculated by saying, as Radius is to the Horizontal Parallax, so is the Co-sine of the Altitude to the Parallax in Altitude: Now, as all Obječts are depressed by their Parallax, so they are elevated above their true Altitudes by Refraction.
To find the apparent Time, and thereby regulate the going of the Watch.
MONG the Methods proposed, that by equal Altitudes of the Sun seems very fit for Pračtice at Sea. At the Time when the Watch stands in need of being regulated, for the Observations intended, let the Sun's Altitude be taken at any convenient Time in the Forenoon, 2, 3, 4, or 5 Hours distant from the Meridian. Set down the Altitude with the corresponding Time exactly (the Index being already set to the Morning Altitude): Note down the Time of the same Altitude in the Asternoon; half the Sum of these two Times, is the apparent Time shewn by the Clock or Watch when the Sun was upon the Meridian of that Place. But it must here be observed, that if the Change of Declination be considerable during the elapsed Time, it must be allowed for, by adding the Difference to, or subtracting it from, the second Altitude, according as it is increasing or decreasing. Lest that an Altitude taken in the Forenoon cannot, by the Interposition of Clouds, have a corresponding one in the Afternoon; it is therefore proper to take several in the Forenoon, in order to secure a correfponding one in the Afternoon. And, if several equal Altitudes can be taken on both Sides of the Meridian, it will be best to find the Noons for each Pair, and the Means of all the Noons thus found for the true one. When there is Reason to believe that the Watch gains or loses considerably, other Sets of Observations may be taken on successive Days, whereby the Daily Variation may be found and allowed for ; by which Means the Artist will have little more to do in finding his Longitude by Observation, than to reduce the observed Distance of the Objećts to the true Distance of their Centers; the Ship’s Time being shewn by the Watch previously regulated.
Find the Ship's Latitude and Longitude by Account, at the Time of Observation, by carrying the Reckoning forward to that Time. * With a Quadrant well adjusted, take the Altitude of the Sun's lower Limb. - . a Take the Difference between the Semi-diameter and Dip of the Horizon, and add it to the observed Altitude, the Sum will be the Sun's apparent Altitude. Take the Difference between the Sun's Refračtion and Parallax in Altitude, and subtract it from the apparent Altitude; the Remainder will be the true Altitude of the Sun's Centre; hence the true Zenith Distance. Turn the Ship's Longitude into Time, and either add to or subtract from the Time per Watch, according as it is East or West; the Sum, or Difference, will be the reduced or supposed Time at the Place of Observation. Take the Sun's Declination out of the Nautical Almanack, and proportion it to the reduced Time: With the Sun's true Declination find the Polar Distance; then, Add together The Zenith Distance, The Co-Latitude, and Polar Distance into oue Sum. .. From half this Sun subtract the Zenith Distance, noting the half Sum and Remainder, then add together . . . The Log. Co-Secant of the Comp. of the Lat. } Rejecting their The Log. Co-Secant of the Polar Distance, Indexes. The Log. Sine of the half Sum, and - The Log. Sine of Difference into one Sum. Half the Sum of these four Logarithms will give the Log. Co-fine of half the Hour Angle; which being doubled and turned into Time, by allowing 15 Degrees for every Hour, &c. or more briefly by the Table, will give the true Time, if the Altitude was taken in the Afternoon; but if in the Forenoon, its Complement to 24 Hours will be the true Time, reckoned from the preceding, or Noon before.
Not E. The Refračtion is found in Table V. of this Book,
the Nautical Almanack,