Refraction from Slr Ifaac Newton's Table, and the Remainder will give the true Altitudes of the Pole Star; and then by Trigonometry, or the Table in my former Book, p. 101, 102, corrected, find how much the Pole Star was then higher or lower than the Pole itself, (its Distance from that Pole being this Year, 1749, 20, 5', 6",) which Quantity add or fubftract as Occafion requires, and you will have the true Elevation of the Pole or Latitude of the Place. This leffer Degree of Accuracy in the Time, will be fufficient for the prefent Purpose, by reafon of the very flow diurnal Motion of the Pole Star

5. The fame first clear Night, take the greatest or meridian Altitude of as many of the more elevated bright Stars as you well can, at leaft of fix. The Mean of thofe Altitudes, when they are corrected by Sir Isaac Newton's Table_of_Refraction already mentioned, and when their Declinations, North or South, are allowed for, from p. 70 of my laft Book, or from Vol. II. p. 516-519, of Mr. Hodgson's, will give the Elevation of the Equator, and, its Complement, the Elevation of the Pole, or Latitude of the Place, without any regard to the Time of the Night, when thofe Obfervations are made.

6. The true Latitude being thus found, the next clear Night take the Altitude of as many of the brighter fixed Stars as you can, near the prime Vertical, Eaft or Weft, at the least of Six; noting the Times by the Pendulum or Watch, as already. adjusted to the Time, tho' imperfectly. Then from each of thofe Altitudes, firft diminished by the Table of Refraction, compute, by the two Rules of Trigonometry in p. 96-99 of my laft Book, the exact Times to the Meridian of your Place, to Minutes and Seconds, when thofe Obfervations were feverally made, and correct your Watch and Clock

accord

accordingly, which will now, and not till now, give you the juft Time at your Meridian, with the greateft Accuracy.

7. And now the Shadow of a Plummet Line, or an erect ftraight Line, at Twelve o' Clock, apparent Time, will give you a true Meridian, for finding the Variation of your two magnetick Needles, to be fet down accordingly. I need not add, that great Care must be taken, that neither any Loadstone nor Iron be near thefe Needles at the Time of the Obfervations.

8. You have nothing now to do but to make Ufe of your Refracting and Reflecting Telescopes, and by them to obferve, and that with the greatest Nicety you can, two or three Eclipfes or Conjunctions of Jupiter's Planets, especially those of the first and fecond, which are noted in the Table at the End of my laft Book; and to fet them down with their Times as obferved accordingly. The Conjunctions to be taken, both at equal Diftances from Jupiter, and at the crofs Hair in a Meridian, which, when compared with the fame Eclipfes and Conjunctions to be observed at Oxford, and at Southwick, by Mr. Blifs and Mr. Lynn, (as also several of them at Lyndon, by Mr. Barker,) will afterward give the Ditference of the Longitudes of the Places of Obfervation; and, at length, how much they are East or Weft of the Meridian of the Obfervatory at Greenwich.

Shortly after this Mr. Whifton had feveral Difcourses, with Mr. Barker of Lyndon, and other ingenious Perfons, about the best Method of afcertaining the Longitude of Places by Land, and on the Coafts; when it was difputed, whether a Trigonometrical Method of Survey, would not be more exact than what had hitherto been made ufe of, I mean the Eclipfes of Jupiter's Planets; feeing fuch Longitudes cannot be determined, by this latter

Way,

2

9

Way, more exactly, than to an entire Minute in Time, or, in our Latitude, to nine Miles, but commonly to no less than ten or twelve. About this Time alfo Mr. Whifton received a Letter from Mr. Lynn, of Southwick, who had been appointed one of his Land-obfervers, dated Nov. 10, 1740, containing a complete Set of his Oblervations of Ju piter's Planets, for the foregoing Month of October... In this Epiftle Mr. Lynn defired Mr. Whifton's Opinion of a peculiar Contrivance of his own, for dif covering the Longitude of different Places at Land, by Obfervations of the fame falling Stars (as they are vulgarly call'd) which appear and difappear almost in an Inftant of Time; which Inftant, if it be compared with the different Inftances of Time, in different Meridians where the fame is feen, will give the Difference of those Meridians with greatExactness. As Mr. Whiston and his Friends were debating of these Matters, Nov. 12, it came into his Mind, that we might have much better Marks, than thofe propofed by Mr. Lynn, for Distances not too great; and these are Shells or Balls of Fire: which, if thrown up exactly at a known Point of Time, in a known Meridian, and obferved 100 Miles every Way at a like known Time, in other Meridians, would afcertain the Difference of all fuch Meridians, which we call their respective Longitudes,

This Method was immediately approved by Mr. Lynn, and all others to whom it was propofed. It was in Part practifed, by Mr. Whifton's Direction, and recommended to publick Ufe about 26 Years ágo, as may be seen in his and Mr. Ditton's New Method for the Discovery of the Longitnde, first publifhed A. D. 1714, where are feveral Calculations and Tables for the proper Execution of it: It has likewise been tried by Mr. Whifton's Order lately, and will be fo again, with great Care, and, it is to be hoped, with very good Effect, fhortly. For it

is plain, that because every fuch Signal may be given at a determinate Time, as fuppofe 20" beforeTen at Night, that the Ball may be at the greatest Altitude juft at Ten, and becaufe 'tis not very difficult to find other Meridians within 15" or a quarter of a Minute, this Method by Signals will fhew the Longitudes of Places four times as exactly as they can be found by Jupiter's Planets, or, in our Latitude, to two or three Miles; which is abundantly fufficient for the Purposes of Navigation. Mr.Whiston has furnished us with fome ufeful Obfervations on this Head, which are here adjoined. No

1. Such Balls of Fire, thrown up along our Coasts, may be easily seen acrofs the Sea, as far as Dunkirk and Oftend in Flanders; as Calais in France, and all along the Promontories and Islands of that Kingdom which extend into the British Channel. They may still more easily be feen from the Isle of Man into the Northern Coasts of England, the Southern of Scotland, the Northern of Ireland, and the Northern of Wales, and will connect the Longitudes of thefe Places together. They may be also seen from the Western Coast of Wales, all along into the Eastern Coafts of Ireland, and thereby connect the Longitudes of England and Ireland all the Way. And if the Balls be thrown up from the Isle of Skie, the Light will be well feen in the neighbouring Western Islands, as well as in the Northern Parts of Scotland. Laftly, if they be thrown up near Faro Head, and Dunsby Head, and Buchan Neffe, in the North of Scotland, they will be eafily feen in the Iles of Orkney and Sherland themselves; which are the remoteft Parts of thefe Kingdoms, and fo will connect them, as to their Longitude, for ever here. after.

2. Wherever thefe Balls are thrown up with this haft Intention, they ought to be continued for three or four Nights together; and the Latitude of each

Place

Place fhould be afcertained alfo. Nay, indeed, if fuch Latitude be but taken with fufficient Accuracy at every County Town (or what is equivalent thereto) through Great Britain and Ireland, this will be abundantly fufficient for a new and actual Survey of thefe Kingdoms, and will afford the moft perfect Materials for a new Set of most compleat Maps of them; far preferable to any that have been heretofore made thereof.

3. This Method includes the other Method of a trigonometrical Survey allo. Since the Distances between each Station of fuch a Mortar may be always as near as poffible the fame, i. e. fixty geographical Miles; or may make together a Square equal to 122,400 Yards nearly: And every Spectator, who obferves the Bearing of the Shell from his own Place or Meridian, has four Triangles, whofe Angles are all given, and the remote Sides of each 122,400 Yards given alfo: It is therefore most easy from each of thofe four Triangles, to find the distinct Point in that Square where the Spectator himself ftands; the Mean of which Distances will be exceeding near to his own Pofition: And tho' any Spectator fhould chance to be in the fame Meridian or Parallel with two of the Stations of the Mortar, yet will he have ftill three fuch Triangles whereby to difcover that Distance in all Pofitions.

I have already acquainted the Reader, That Mr. Whiston had fent Mr. Renshaw and Mr. Birkbeck to make Obfervations round the Coafts, for fettling the Longitude and Latitude thereof, &c. The Expences of which Expedition amounted to more than the Subfcription afore-mentioned, which he had received from his Royal Highness the Duke, and fome other Noble and Honourable Perfons, the munificent Promoters of his Scheme. Not long after their Departure, the Parliament paffed an Act for appropriating a Sum of Money, to be disburfed