afcertained by taking the Meridian Altitude of the Star, either before or after the Obfervation is made for finding the Time.

NOTE 2. If the Ship's Longitude Eaft of Greenwich in Time be greater than the apparent Time at the Ship, the apparent Time muft be increased by 24 Hours before fubtracting the Longitude; and in this Cafe, the Sun's Right Afcenfion must be taken out of the Ephemeris for the preceding Day of the Month. And if the Ship's Longitude Weft of Greenwich in Time, added to the apparent Time at the Place of the Ship, makes more than 24 Hours, 24 must be subtracted from the Sum, to obtain the apparent Time at Greenwich; and the Sun's Right Afcenfion must be taken out of the Ephemeris for the fubfequent Day of the Month. The Object, whether Sun or Star, whofe Altitude is taken for finding the Time, must be at leaft three or four Points of the Compafs diftant from the Meridian; because, when near to the Meridian, the Alteration in Altitude is too flow for afcertaining the Time with proper Exactness: But the nearer the Object is to the Eaft or Weft the better, provided it be not lefs than 6° high; for the Refraction is fo variable and irregular near to the Horizon, that the Effect of Refraction upon Objects cannot be determined with fufficient Accuracy, when their Altitudes are lefs than 6 Degrees.

Of finding the Longitude at Sea.

MANY Methods for finding the Longitude at Sea by celeftial Obfervations have been propofed, and fome of them fuccessfully practised on Land; but none have been found so convenient at Sea as that of observing the Moon's Distance from the Sun or a fixed Star; both on Account of the Shortnefs of the Moon's periodical Revolution, and confequently her quick Progrefs in her Orbit; and alfo on Account of her being almoft conftantly confpicuous, and thereby capable of being obferved.

The great Difficulty lies in reducing the Obfervations of the Heavenly Bodies made on the Surface of the terraqueous Globe to fimilar Obfervations made from its Centre, which is the only Place where they can appear in their true Situation. The principal Difficulty which we have to furmount in the Calculation is the making of proper Allowances for the Refraction of the Atmosphere, which makes all Objects appear higher than they really are, and for their Parallaxes, particularly that of the Moon, which makes her appear lower than fhe is; confequently our Obfervations of all the Heavenly Bodies, made on the Surface of the Earth or Sea, will be affected by the Refraction; and the Sun and Moon will be affected by their several Parallaxes, unless when they are in the Zenith, the nearer they are to the Horizon, the greater will the Parallax be; because the vifual Ray will pafs through a greater Portion of the

Earth's Atmosphere, and the Object will be fituated more obliquely to the reflecting Surface.

Now as Refraction elevates all the celeftial Objects above their true Altitude, fo Parallax depreffes them below it; more efpecially the Moon, owing to her Proximity to the Earth. The Sun, whofe Parallax is lefs than his Refraction, muft always appear higher than he is; but the Moon, by her Parallax being greater than her Refraction, muft always appear lower than the is. The fixed Stars having no vifible Parallax, and being affected by their Refraction only, must always appear higher than they are obferved; confequently not only the obferved Altitudes, but alfo the Diftance of celeftial Objects will fometimes be much greater, and at other Times much less than their true Diftance, when compared with correfponding Obfervations from the Earth's Centre.

The Reward held out by Government for the determining of the Longitude has induced many to attempt it, especially in the mechanical Line, and though many of them have been vifionary, whimfical Men, totally unacquainted with the Difficulties attending fuch a Difcovery, yet fome, particularly Mr. Harrison, and after him others upon fimilar Principles, have produced Watches or TimeKeepers, that, could they be depended upon in all Situations, and all Temperatures of the Atmofphere, would doubtless ascertain the Longitude of Places. For by that Mode, nothing more is wanted than to find the apparent Time at the Ship, and to correct it by the Equation of Time; the Differenee of this Time fo corrected, and that given by the Watch, turned into Longitude, will be the Difference of Longitude between the Ship's Meridian and that Meridian which the Watch was fet to. But as Watches, though made upon the best Construction, are subject to fome internal Irregularities, and apt to be otherwife affected by Heat and Cold, the Mariner may well be anxious to determine his Longitude at Sea by celeftial Obfervations:

To fhorten the Operations, and to leffen the Difficulties neceffarily attending the Solution of this important Problem, the Commiffioners of Longitude have caused to be published annually a Nautical Almanack, or Ephemeris, containing every Thing that can. well be done to render the Calculations, in finding the Longitude at Sea by celeftial Obfervations, easy to any common Understanding.

To find out eafy Rules for reducing the obferved Distance of the celeftial Bodies to the true Distance, has employed the Attention of Aftronomers for feveral Years, in order to fhorten the Calculations. Some have invented Inftruments, others Lineal Tables; and although they can be looked upon only as Approximations, they fhew the Industry and Ingenuity of their feveral Inventors.

But whatever Methods are taken to reduce the observed to the true Distance, the neceffary Preparations refpecting the Dip of the Horizon, Refraction, Semidiameters and Parallax, muft first be made, in order to reduce the obferved Altitudes and Distance to the

apparent; after this Part of the Bufinefs is performed, the Time faved by fuch Inftruments and Tables will be very inconfiderable.

It is not thought neceffary here to inveftigate the Principles from which the several Rules for reducing the Diitances are deduced, because fuch a Procedure would be inconfiftent with the Plan. It will be fufficient for the prefent to felect two Rules, which feem best calculated to reduce the Distance at Sea; and to fimplify thofe Rules, and render them cafy to Perfons of common Capacity. No other Tables are required in the Process but those which are contained in this Book, and in the Nautical Almanack.

To take the Obfervations neceffary for finding the Longitude at Sea.

The capital Obfervation for this Purpofe is, that of the Distance of the Moon from the Sun, or from fome remarkable Star near to the Zodiac. In order to make fuch Obfervations, the Obferver muft be furnished with a Watch that can be depended upon for keeping Time, within a Minute, for fix Hours; and with a good Hadley's Quadrant, or rather Sextant, which is preferable to a Quadrant. The Inftrument will still be more fit for the Purpofe if it be furnished with a Screw, to move the Index gradually and fteadily; alfo an additional dark Glafs, lighter than the common Screens, to take off the Glare of the Moon's Light, in obferving her Distance from a fixed Star; and a fmall Telescope, magnifying three or four Times, to render the Contact of the Star with the Moon's Limb more difcern→ able: A magnifying Glafs of 1 or 2 Inches Focus will affift the Obferver to read off his Obfervations with greater Eafe and Cer→ tainty.

The Obferver muft, in the first Place, examine his Inftrument with the greatest Care, and adjust it with the utmost Exactnefs; which done, let him proceed to his Obfervations as follows:

If the Distance of the Moon from the Sun is to be observed, turn down one of the Screens, look at the Moon directly through the transparent Part of the Horizon-glafs, and, keeping her there, gently move the Index till the Sun's Image is brought into the filvered Part of that Glafs; bring the neareft Limbs of both Objects into Contact, and let the Quadrant librate a little on the Lunar Ray, whereby the Sun will appear to rife and fall by the Side of the Moon in this Motion the nearest Limbs must be made to touch one another exactly, by moving the Index. When this is effected, the Obfervation is made; and the Divifion coinciding with that on the Vernier Scale, will fhew the Diftance of the nearest Limbs of the Objects.

If the Distance of the Moon from a Star is to be oblerved, when the Moon is very bright, turn down the lighteft Screen, or use a dark Glafs, lighter than the Screens, and defigned for this particular Puipofe; look at the Star directly through the transparent Part of the Horizon-glafs, and, keeping it there, move the Index till the

Moon's Image is brought into the filvered Part of the fame Glafs; make the Quadrant librate gently on the Star's Ray, and the Moon will appear to rife and fall by the Star; move the Index, between the Librations, until the Moon's enlightened Limb is exactly touched by the Star, then the Obfervation is properly made.

The Quadrant is to be held the fame as for a fore Observation, and its Plane must always be made to pass through the two Objects, whofe Distance is to be obferved; for that Purpofe it must be put into various Pofitions, according to the Situation of the Objects, which will foon be rendered eafy by Practice.

At the very Inftant, or at moft within a few Seconds of the Time at which the Obferver gives Notice of completing his Obfervation, fomebody muft obferve the Hour, Minute, and Quarter Minute (if there be no Second Hand) by the Watch used for finding the apparent Time; and at the fame Inftant of the Obferver's giving the aforefaid Notice, or as near to that Time as poffible, two Affiftants muft take the Altitudes of thofe Objects whofe Distance is obferved; all which being done, the Obfervations neceffary for afcertaining the Longitude are completed.

In the Ephemeris is found, the Moon's Diftance from the Sun, and alfo from proper Stars, to every Three Hours of apparent Time, for the Meridian of Greenwich; and to afford the Mariner a greater Number of Opportunities for Obferving, and Means of attaining a greater Degree of Exactnefs, her Diftance is generally fet down from at least one Object on each Side of her. Her Distance from the Sun is found fet down, while it is between 40° and 120°; so that by uling a Sextant, it may be obferved for two or three Days after her firft, and before her laft Quarter; while fhe is between 20° and 40° from the Sun, her Distance is fet down only from a Star on the contrary Side to the Sun; while the is between 40° and 90° from the. Sun, her Diftance is fet down both from the Sun and from a Star on the contrary Side to the Sun; when he is between 90° and 120° from the Sun, her Diftance is fet down both from the Sun, and a Star on the fame Side with the Sun, and alfo from a Star on the contrary Side to the Sun. Laftly, when fhe is above 120° from the Sun, her Distance is fet down from two Stars, one on each Side of her. Her Distance from Objects on the Eaft of her is found in the Ephemeris, in the 8th or 9th Pages of the Month; and her Distance from Objects on the Weft of her is found in the 10th and 11th Pages of the Month.

An Obferver who ufes the Ephemeris, muft obferve the Moon's Distance from fome of thofe Stars only, whofe Distance from her is fet down in the Ephemeris, and the Distances there fet down afford him a ready Means of knowing the Star from which her Distance ought to be obferved; for he has nothing to do but to fet his Index to the Distance computed roughly at the apparent Time, estimated nearly for the Meridian of Greenwich, and look to the Eaft or West of the Moon, according as the Diftance of that Star is found in the

8th or 9th, or in the 10th or 11th Pages of the Month, and having found the Moon upon the Horizon Glafs, he will, by fweeping with his Quadrant to the Right or left, certainly find the Star he wants, if it be above the Horizon and the Air clear, in a Line nearly perpendicular to that joining the Moon's Horns, or, which is the fame, in the Line of the Moon's fhorteft Axis produced.

The Time at Greenwich is estimated nearly by turning the Ship's fuppofed Longitude from Greenwich into Time, and adding it to, or fubtracting it from the apparent Time at the Ship, according as the Ship is Eaft or Welt of Greenwich, and the Distance of the Moon from the Sun or a Star at this Time is found roughly by faying, as 180 (the Minutes in 3 Hours) is to the Difference in Minutes, between this nearly estimated Time and the next preceding Time fet down in the Ephemeris, fo is the Difference in Minutes between the Distances in the Ephemeris for the next preceding and next following Times, to a Number of Minutes, which being added to, or fubtracted from the faid next preceding Distance, according as it is increafing or decreafing, will give the Distance nearly at the Time the Obfervation is intended to be made, and to which the Index of the Quadrant or Sextant must be set.

NOTE. The taking of the Angular Distance may be rendered more eafy and accurate by bringing the Objects nearly into Contact in the common Way, and then fixing the Index tight to a certain Degree and Minute, and waiting until the Objects are nearly in Contact, giving Notice to the Afliftants to get ready with the Altitudes, and when the Objects are exactly in Contact, to call for the Altitudes and the precife Time by the Watch. The Obferver may then prepare for taking another Distance, by fetting his Index three or four Minutes forwards or backwards, according as the Objects are receding from, or approaching to each other; and then proceed to take the Distance, the Altitudes, and the Time by the Watch, as before ; thus may as many Distances be taken as the Obferver thinks proper; but four, at the Distance of three Minutes, or three, at the Diftance of four Minutes upon the Inftrument, will at all Times be fufficient. This Mode of taking the Distance will not only ease the Eye of the Obferver, but also enable him to manage his Inftrument with much greater Facility in every Direction, a vertical one only excepted. If, in taking the Distances, the middle one can be taken at any even Divifion on the Arch, fuch as a Degree, or a Degree 20 or 40 Minutes, that Diftance will be independent of the Nonius Divifion, and confequently free of thofe Errors which frequently arife from the Inequality of that Division in several Parts of the graduated Arch. If the Obfervation be made, as it always ought to be, at the Distance of two Hours before or after Noon, the true Time may be found by the Altitude of the Sun taken at the precife Time of the Dittance; if three Distances are taken, find the Time by the Altitude corresponding with the middle Distance. Thus will any Irregularity in the going of the Watch be prevented from affecting the Result of the Obfervation.

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