Page [unnumbered] A New METHOD For Discovering the LONGITUDE BOTH AT SEA and LAND, Humbly Proposed to the Consideration of the PUBLICK. BY William Whiston, M.A. sometime Professor of the Mathematicks in the University of Cam|bridg. and

M.A. sometime Professor of the Mathematicks in the University of and Humphry Ditton, Master of the New Ma|thematick School in Christ 's Hospital, Lon|don. LONDON: Printed for JOHN PHILLIPS, at the Black Bull in Cornhill. 1714.

Page [unnumbered] TO The Right Honourable THOMAS Earl of Pembroke and Montgomery.

Earl of and The Right Reverend Father in God PHILIP Lord Bishop of Hereford.

Lord Bishop of The Right Reverend Father in God GEORGE Lord Bishop of Bristol.

Lord Bishop of The Right Honourable THOMAS Lord TREVOR, Lord Chief Justice of the Common Pleas.

Lord Lord Chief Justice of the Common Pleas. The Admirals of the Red, White and Blue Squadrons.

The First Commissioner of the Admi|ralty.

The First Commissioner of the Navy.

The First Commissioner of Trade.

The Master of Trinity-House.

The Hon. Sir THOMAS HANMER, Bart. Speaker of the Honourable House of Commons.

Bart. Speaker of the Honourable House of Commons. The Hon. General STANHOPE.

The Hon. FRANCIS ROBERTS, Esq

Esq Page [unnumbered] ISAAC NEWTON, President of the Royal Society.

President of the Royal Society. WILLIAM LOWNDS, Esq

Esq WILLIAM CLAYTON, Esq

Esq Mr. JOHN FLAMSTEED, Astronomer Royal.

Astronomer Royal. Dr. EDMUND HALLEY, Savilian Pro|fessor of Geometry.

Savilian Pro|fessor of Geometry. Mr. JOHN KEILL, Savilian Professor of Astronomy.

Savilian Professor of Astronomy. Mr. SANDERSON, Lucasian Pro|fessor of the Mathematicks.

Lucasian Pro|fessor of the Mathematicks. Mr. ROGER COTES, Plumian Profes|sor of Astronomy. Commissioners appointed by Act of Par|liament for the Discovery of the LONGITUDE. This New Method for that Discove|ry is with all due Submission humbly Dedicated by The Authors.

THE INTRODUCTION.

BEfore we come to give an Account of this our New Me|thod for the Discovery of the Longitude, both by Sea and Land, which we here take leave humbly to propose to the Consideration of the Publick, we think it reasonable to premise somewhat by way of In|troduction: To give some Account of the Nature of the Problem before us; to speak a little of the Methods hitherto try'd, and the Reasons of their ill Success; and to add a brief Historical Narration, from what Occasions and by what Steps this Page 6 our Method was first discover'd, and has arriv'd at its present Degree of Maturity.

As to the Problem it self, the In|vention of the Longitude; it is plain|ly this: To discover in some mea|sure a like sure way of frequently knowing, how far we are distant, on the Earth Spherical Surface, in Degrees, from any known Meridian, Eastward or Westward; as we can easily know, almost at any time, how far we are distant, in Degrees, on the same Surface, from the middle Circle or Equator, Northward or Southward. Now in this Case it must be noted, that as the Diurnal Motion does naturally imply fixed Poles, and a fixed Equator; which infer a different Meridian Altitude of those Poles, and of that Equator, and by consequence of all the hea|venly Bodies, in different Latitudes; which different Altitude may in clear Weather be easily observ'd by proper Page 7 Instruments, and thereby that Lati|tude may be readily discovered; so does not the same Diurnal Motion at all imply any Phaenomena, whence the Longitude may be discover'd to us: Because the same Parallel still bears, through its whole Circumfe|rence, the same Relation to those Poles and that Equator, without any Difference. The Diurnal Motion therefore, which affords an obvious Foundation for the Invention of the Latitude of every Place on the Earth, affords us no such Foundation for the Invention of the Longitude of the same Places. Nor is it therefore an easy Problem, either astronomical or practical to discover the same.

As to the Methods hitherto tryed, they are either Celestial, or Terre|strial; and may be reduc'd to these Seven, Four that are Celestial, and Three that are Terrestrial.

(1) The Eclipses of the Moon.

(2) The Eclipses of the Sun.

Page 8

(4) The Motion of the Moon.

(5) The Variation of the Needle.

(6) Clocks, or Watches.

(7) The Log Line or Dead Rec|koning.

First, The Eclipses of the Moon are useful for the Longitude. For its Immersions into the Earths Shadow, its nearest Distances to that Center, and its Emersions therefrom, are all at distinct and known Points of ab|solute time. So that where and when they can be nicely observ'd; and the Difference of the apparent times at every Meridian noted; the respective Longitudes of those Pla|ces may be thereby found in time; and by allowing 15 Degrees of the Equator to an Hour, may be found in Degrees also.

Secondly, in the same manner may the Eclipses of the Sun be made use of; especially as now improv'd by our great Astronomer Mr. FlamsteedsPage 9Construction of them; and as they will, we hope, be farther improv'd by Mr. Whistons actual Exhibition of them, in his Instrument, just ready for Pub|lication. Which Method, by the Difference of the apparent time of any Part of the Eclipse in different Places, gives the Difference of Me|ridians, or of Longitude in the like manner as before.

Thirdly, The Eclipses of Jupiters Satellits afford another like Method for the Discovery of the Longitude; and that on the same Foundation with those of the Moon.

Fourthly, the Motion of the Moon, with its Distance from the Sun, or rather its Appulse to and Occultation of those fixed Stars that ly along its Course, is another re|markable Method for this purpose; and is of the same Nature with the Eclipses of the Sun as to this matter.

These Four may justly be called Celestial, or Astronomical Methods of Page 10 discovering the Longitude, because they make use of the Celestial Bo|dies, or of the Stars in order to that End. The Three Terrestrial Me|thods are as follows.

5ly, The Variation of the Needle from the North is now, especially since Dr. Halleys noble Observations and Map thereto relating, become one Method for the Discovery of the Lon|gitude; particularly in those Parts, where that Variation is best known, and the North and South Position of its Lines are most remarkable. For by crossing the Meridians there, you also cross the Curves of equal Va|riation, and discover in some measure your Longitude thereby.

Sixthly, The Use of Clocks or Watches at Sea is another Method; and was attempted by the famous Hugenius. And indeed if they could be exactly kept to an even motion, and so shew the Hour at any one certain place at Land; the Com|parison Page 11 of the Time known by that Clock or Watch, with the apparent time at the Ship known by the Sun or Stars, or another Clock or Watch regulated by them, would discover the Longitude from the Place to which that first Clock or Watch was adjusted, in time, and so, as be|fore, in Degrees also.

Seventhly, The Log-line and Dead Reckning, when all fails, is the last Remedy in this case; and from thence the Seamen guess, as well as they can, by the Angle and length of their Course, what Longitude and Latitude they are in: And when by Observation they find their Er|ror in Latitude, they conclude up|on a proportionable one in Longi|tude also. And so for want of a sure Guide, either Celestial or Ter|restial, they are forc'd to depend on this; which yet is, as well as the rest, very uncertain and inac|curate.

Page 12 For to come to the Reasons of the small Success of these several Methods.

As to the two first, the Eclipses of the Sun and Moon; to say nothing here of the slowness of the Moon's Motion, which renders any great de|gree of exactness impossible; or of the difficulty of Calculation and Con|struction, especially in the Sun's E|clipses; and of Observations in both: The single rareness of these Eclipses, which is not seldom made still rarer by cloudy Weather, renders them of very little use in Navigation.

As to the third Method, by the Eclipses of Jupiter's Planets; this must be own'd of much greater use: Since the quickness of their Motion, espe|cially as to the innermost, makes the Moment of their Immersion into, or Emersion from Jupiter's Shadow ve|ry distinct and nice; and their fre|quency, which is almost one for every Day, renders them fit for the constant uses of Navigation. Nor Page 13 have we hitherto had any other Me|thod so useful at Land as this. Yet are there great Difficulties belonging to this Method; especially at Sea. The best Tables of their Motions are hitherto too imperfect to be at all times depended on, as to the exact absolute Time of their Celebration: And they require Telescopes of such a length as have not hitherto been manageable at Sea, in that state of Tos|sing and Agitation, which Ships there are subject to: Which difficulties, added to the impossibility of seeing these Eclipses for about three Months every Year, when Jupiter is near the Sun, renders this Method at present of small use in Navigation.

Nor can the fourth Method, or the distance of the Moon from the Sun, with its Appulse to, or Occultation of those fixed Stars, which lye along its course, give us the Longitude to suffi|cient exactness. For, to say nothing here of the slowness of the Moon's Page 14 Motion, the want of the utmost accu|racy of even the place of some of these fixed Stars themselves, and of the Sun it self; or of the necessity of the use of smaller Telescopes, even in this Case, as well as of the trouble of the Calculation and Construction, which are lesser Difficulties here also; 'Tis plain the Theory of the Moon, espe|cially in some positions, is not exact enough hitherto for our purpose; as not serving for this Longitude nearer than to two or three Degrees: where|as the Seamen want it within one Degree, or less. Tho' indeed it must be allow'd, that if the Moon's The|ory could be once so far perfected, that its place might be with certain|ty calculated nearer than to two Mi|nutes of a Degree, this would be a very useful Method in order to the Discovery of the Longitude at Sea. Which Improvement therefore of it's Theory is a thing highly desireable in Astronomy.

Page 15 We come now to the Terrestrial Methods, and to those difficulties which render them also incapable of discovering the Longitude, with that certainty, and to that degree of ex|actness, which the purposes of Na|vigation require. Thus the Curve lines of the Variation of the Nee|dle, which is the first Terrestrial Me|thod, are of small use, because the Laws of that Variation are not yet brought to a sufficient certainty, not|withstanding the most useful endea|vours of Dr. Halley in that Matter: The Neighbourhood of Iron Mines, of Iron, or of Loadstones themselves, does sometimes disturb the general Rules, and deceive the Observers of that Variation: The Position of those Curves, too far Eastward and West|ward, in a great part of the World, renders this Variation useless as to any general Discovery of the Longitude: and even there where the Position of these Curves is the most advanta|geous, Page 16 as it is about the Cape of Good Hope, and a considerable way on both sides of it, yet is the distance of those Curves for the difference of one De|gree of Variation, about 100 Geo|graphical Miles, i. e. near two Degrees of a great Circle; and so this Method is incapable of shewing the Longitude very nicely in any Case whatsoever.

Thus the second Terrestrial Me|thod, by Clocks or Watches, tho' the easiest to understand and practice of all others, has been so long in vain attempted at Sea, that we see little Hopes of its great usefulness there. Watches are so influenc'd by heat and cold, moisture and drought; and their small Springs, Wheels, and Pe|vets are so incapable of that degree of exactness, which is here requir'd, that we believe all wise Men give up their Hopes from them in this Matter. Clocks, govern'd by long Pendulum's, go much truer: But then the diffe|rence of Gravity in different Latitudes, Page 17 the lengthening of the Pendulum-rod by heat, and shortening it by cold; together with the different moisture of the Air, and the tossings of the Ship, all put together, are circum|stances so unpromising, that we be|lieve Wise Men are almost out of hope of Success from this Method also.

And as for the Log-Line, and Dead-Reckoning, which is the third Terrestri|al Method, they were the known defi|ciencies of this common way, as al|ter'd by Storms, and Currents, and the Inaccuracies of the way it self, and of even the Latitude, as commonly taken; together with the too frequent and enduring cloudy Weather, when they can take no Latitude at all; which have occasion'd the Seamen to desire some other Assistance for the Discovery before us.

We now come to our last Business, viz. to give the World a short History of our own Proposal; from what oc|casions, Page 18 and by what steps this our Method was first discover'd, and has arriv'd at its present degree of Matu|rity. As to which matter, the Rea|der is to know, that somewhat above a Year ago, Mr. Whiston and Mr. Dit|ton, with some other common Friends, spent part of an Afternoon and the Evening together. Mr. Ditton took an occasion, among other common discourse, to observe to Mr. Whiston, that

'The nature of Sounds would afford a method, true at least in Theory, for the discovery of the Longitude';

The difference be|tween the apparent time, where the Sound is made, and where it is heard; abating on|ly the time for its diffusion, which was now well known; is the difference of the Lon|gitude of those two Places in time.

Whiston

Page 19 viz. when the French Fleet was engag'd with Ours, off Beachy-head in Sussex; [which was A.D. 1690.] and himself was at Cambridge; and that he had been inform'd, that in one of the Dutch Wars, the sound of the like Explosions had been heard in|to the very middle of England, at a much greater distance. Upon this, Mr. Whiston, when they part|ed, told Mr. Ditton, that he took the thing to be so considerable, that tho it had been discoursed of in mix'd Company, after an unguard|ed manner, yet he look'd on it as fit to be conceal'd; since no body could tell, what Improvements might on farther Consideration be built upon such a Foundation.' 'That as to the Propagation of Sounds, he remembred to have himself plainlyheard the Explosion of great Guns about 90 or 100 Miles,when theFleet was engag'd with Ours, offin[which was1690.] and himself was atand that he had been inform'd, that in one of theWars, the sound of the like Explosions had been heard in|to the very middle ofat a much greater distance. Upon this, Mr.when they part|ed, told Mr.that he took the thing to be so considerable, that tho it had been discoursed of in mix'd Company, after an unguard|ed manner, yet he look'd on it as fit to be conceal'd; since no body could tell, what Improvements might on farther Consideration be built upon such a Foundation.'

Ditton

Whiston

Ditton,

Ditton

Ditton

Ditton

Whiston

viz.

July

Whiston

Ditton,

Ditton

Isaac Newton,

Halley,

Guar|dian,

July

Englishman,

December

Isaac Newton,

Clarke

James

Halley

Oxford,

Cotes

Cambridge.

sinceMr.immediately own'd the truth of the Proposition, and added,Which Advice Mr.follow'd; and ac|cordingly desir'd and obtain'd the Silence of those, that had then heard,what had pass'd. This Proposition about Sounds, and their distant Pro|pagation, with respect to the Longi|tude, did upon this so fix it self in Mr.'s Mind, and did occa|sion such Improvements there, that in less than two Days time he brought a small Paper to Mr.contain|ing a Scheme, how that Theory of Mr.'s about Sounds might be reduc'd to Practice, and be actually apply'd to the discovery of the Lon|gitude at Sea; which was then not much unlike the former branch of the following Essay, only more im|perfect: Which Scheme Mr.ap|prov'd of. Soon after this Mr.imparted this Discovery to a very good Friend, belonging to the Admi|ralty, in order to gain farther light as to its practicableness at Sea; and that proper Questions might by him be ask'd of Seafaring Men re|lating thereto, without any Suspici|on;which could not well be avoid|ed if we our selves had ask'd them; especially since the Notion was then got abroad, that we had a Project about the Longitude to propose to the World. The result of this En|quiry was, that those Sea-men our Friend enquir'd of, did not remem|ber to have heard Sounds at Sea any whit near so far as the before|mention'd Examples shew'd they had been heard at Land; which difficulty put some stop to our Progress for a little while. However, at last, after farther enquiry, the final result was this, That tho' Sounds were not ordi|narily either at Sea or Land heard very far, yet that was not at Sea, more than at Land, any certain Argument, that they could not spread so far; because Sounds had been heard a full Degree at least, or 60 Geo|graphical Miles over Sea, even with|out any extraordinary Contrivance,either at the sounding Body, or the Ear; both which were yet, for cer|tain, capable of great improvements, in order to the enlargement of that distance. So that the Objection start|ed against the spreading of Sounds at Sea seem'd to be in a manner over, and we at liberty to prosecute our Design, as before, of discovering the Longitude by means of it. About this time Mr.discover'd and propos'd a great Improvement of his own to this Method;That the Guns, which were to make the Explosions in the former Case, might also carry Shells, full of Powder, or such other combustible Matter, as would take fire at the utmost Alti|tude; and thereby certainly and ex|actly exhibit the point of the Azi|muth, and the Distance of the sounding Body; and so join the use of the Eye and Ear together for the same purpose. Tho' at the first he mustown he suspected, that the Apparent Diameter of that Light or Fire would in great distances be so small, as not to be there visible. In this very junc|ture a day of extraordinary Fire|works happen'd [it was the Thanks|giving day for the Peace,7th, 1713.] the Contemplation of which, did much revive and encourage this Notion: and the certain Account he soon had, that those Fire-works, nay, the small Stars, into which the Rock|ets commonly resolv'd themselves, were plainly visible no less than 20 Miles, put an end to his doubts im|mediately; and made him very se|cure, that such large Shells as might be fir'd at a vastly greater height, would for certain be visible for about 100 Miles; which he look'd on as nearly the limit of Sounds also, as to any purposes of Longitude. This Improvement of Mr.'s, which was also then for the main the samewith the second Branch now contain'd in this Paper, was also approv'd of by Mr.and agreed to as fit to be a part of the former Design for the Discovery of the Longitude at Sea. Mr.did farther add, for Im|provement, a sure Method of Tri|gonometrical Calculation, to ascer|tain from the Observations the ho|rary Difference of Meridians (and by consequence the Difference of Lon|gitude in Degrees) between the Ship's Place, and that of Explosion; with|out computing the Time of the Sound's propagation: but since this Method is somewhat more operose than that, which is propos'd hereafter, he chooses to omit it. He did also first observe that great Use of our Method at Land, in the Surveying of Countries, for the Perfection of Geography; which was also readily taken notice of by Sirand afterward by Dr.andthat both of their own accord, upon our first communication of our Me|thod to them. For when Matters were brought to so hopeful a Posture, and necessary Tables were preparing for the actual Practice of the whole Method, we began to think of in|timating to the Publick, that we had a new Discovery, as to the Longi|tude, to propose to the World. Which we soon did, by our Letter inserted in the Paper call'd theof14. and repeated by another in the same Author's Paper call'd theof10. following. Having before commu|nicated the matter to the illustrious Siras we did afterward to those great Men, Dr.Rector of St.'s, Dr.ofand Mr.ofHow far we profited by this Communication, and what their Opinions were con|cerning our Method, we need notsay: because we do not give Account here of every occasional Improve|ment, either of our own or others; and because we now publish the in|tire Method, as it stands at present, to the whole World, for every one's open Judgment, and the farther Im|provements of the skilful. Only so far their Opinions and Declarations appear to have been on our side, that upon hearing what they and we had to say, the Committee of the House of Commons, which was appointed to inquire into this matter, came unanimously to a Resolution in our Favour; and the Legislature have thereupon thought fit to pass an Act, appointing a noble Reward for such as shall discover a better Method than has been hitherto us'd for the finding the Longitude. Which Reward, whether we have any just Claim to, in whole or in part, we do hereby intirely submit to the Sagacity andJustice of those eminent Persons, whom the Legislature has been pleas'd to intrust with the Tryal, Experiment, Judgment, and Determination of all such Proposals.

We conclude all with our hearty Wishes as Men, that this our Design may tend to the common Benefit of Mankind: as Britains, that it may tend particularly to the Honour and Ad|vantage of this our Native Country; and as Christians, that it may tend to the Propagation of our Holy Re|ligion, in its original Purity, through|out the World.

London, July 7. 1714. William Whiston, Humphry Ditton.

LEMMATA, or Preparatory Propositions.

I. ALL Sounds are propagated almost evenly; and are ob|serv'd to move 14 Mea|sur'd, or 12 Geographical Miles in one Minute of Time: i. e. one Geo|graphical Mile or Minute of a De|gree in five Seconds. This is well known from the last and most accurate Observations* a|bout Page 29 the Velocity of Sounds, which are those of Mr. Dereham. Only a small Addition of Velocity is to be made, when a strong Wind carries the Sound with it, and Substraction when it opposes it.

II. The Sound of a great Gun may be heard by the Ear, duly as|sisted, if the Wind be favourable, or still, both by Sea and Land, at the least 100 measur'd, or 85 geogra|phical Miles. In the open Sea also, the Point of the Compass may be nearly determin'd whence it comes. This is very probable, as to the Distance, from many known Experi|ments*; wherein the Ear, even un|assisted, has heard such Sounds much farther. And if the Sound were in|creas'd by a sounding Board, which might prevent its diffusion upwards, Page 30 and so spread it farther Horizontally on all sides; and if the Ear were assisted by a hollow Tube of Metal, of the shape of a Bell or Tunnel, apply'd thereto, this Proposition would soon be more indisputable. Nor is there any great Difficulty, as to the Point of the Compass, whence the Sound comes at Sea, where nothing can reflect or echo the same in any other than the true Angle.

III. The Distance of the sounding Body, where the Sounds are of the same Strength, and Tenor, and Cir|cumstances, may, within some La|titude, be determin'd by the Ear, duly assisted, and frequently exercis'd in such Observations; even at very considerable Distances from the sounding Body. This appears from the obvious difference of the same Sounds at very Page 31 different Distances at present; which is in a duplicate Proportion of those Distances: and from the great Im|provements, Experiments made on purpose would probably afford us therein. N.B. In order to determine ac|curately the Distance of a given Sound, there must be distinct Trials made, in an open Place, both by Sea and Land, in clear and in foggy Weather, with the Wind in all Po|sitions, and of all Degrees of Strength; and this at several Distances of the Hearers: but till that is done, we must leave this matter to the Ear alone.

IV. A strong Wind carries Sound along with it in a Circle; where the Sounding Body is a Point in its Axis: and is more or less remote from its Center, according as the Wind is greater or less. Page 32 This appears by the Demonstration following. Let the Proportion of the Velocity of the Wind, to the Velocity of the Motion of the Air that causes the Sound, be as AB to AD. [illustration] Let the two equal Circles GDHE, GCHF, be described upon the Cen|ters A and B; and let any Line, as KL, be drawn Parallel to DF. KI will therefore be always equal to Page 33 Let the two equal Circles GDHE, GCHF, be described upon the Cen|ters A and B; and let any Line, as KL, be drawn Parallel to DF. KI will therefore be always equal toML. or to the Velocity of the Wind, and according to its direction: as AM = AK = BL = BI will be equal to the Velocity of the Motion of the Air that causes the sound, and according to its direction; or from the Center to the Circumference of that Circle which includes the sound. Whence the Diago|nals BK, BM will be the distance or mea|sure of the Equal sounds; and the points K. M will be in the Circumference of that Circle GDHE of which the sound|ing body B is a point in its Axis. Q.E.D. Corollary (1.) Because the Lines AB and AK, and the Angle BAK are given; the distance of equal sounds BK is also given by plain Trigonometry. As the same line may be found Geometrically also, by applying its length to a scale of equal parts. Page 34 Coroll. (2.) Two equal Circles, sliding one upon the other, according the direction of the Axis FD is the rea|diest way of solving this Problem, for the use of Seamen; as being so very easy in Practice.

V. The Interval of apparent time, in two places, where a Sound is excited, and where it is received; besides that which is due to the real propagation of the Sound it self; is the Diffe|rence of their Meridians, or of their Longitude in Time. Thus if a Sound, excited just at 12 a clock at one place, comes to another after the very same Time that is due to the Sounds propagation, as at the distance of 14 measured Miles, one mi|nute after 12. At the distance of 28 such Miles, two minutes after 12. &c. 'tis evident the places are under the Page 35 same Meridian, and have no diffe|rence of Longitude. But if it be heard sooner or later than those times, the Difference is what answers to the Temporary difference of their Meri|dians, or of Longitude, Westward or Eastward: and so is a sure indica|tion of the same. As is very obvious on a little consideration; and as we shall shew presently by example.

VI. An Ordinary Great Gun is easily able to cast a Projectil about a Mile and a quarter, or 6440 English feet, in perpendicular height. This appears by that known * The|orem in the Art of Gunnery, which demonstrates, that the utmost Alti|tude is always equal to half the utmost Random of the same Gun and Powder: Page 36 which utmost Random, of ordinary Great Guns, with a very small charge of Powder, is known to be about two Miles and a half, or 12880 Feet. N.B. That it appears by the same way that the largest Great Guns, with their largest charge of Powder, are able to cast a Projectil twice, nay thrice, and even four times the beforemen|tioned height. But because the charges and trouble are in such cases much grea|ter; and it is uncertain whether the advantages will be proportionably aug|mented, we choose to speak moderate|ly, especially before tryal; and to propose nothing here but what is for certain cheap, practicable, and advan|tagious; and leave those more surpri|zing heights, to the consideration of the publick afterward: Only with this observation, that the Altitude will ever be as the Squares of the Velocity, with which the Projectil is thrown.

Page 37 VII. The time of the Ascent or Descent of such a Projectil; without the con|sideration of the resistance of the Air; (which in the case of lead bul|lets, iron shels, or the like dense bo|dies is but very small, and in Wood not very great;) is 20″ or ⅓ of a Minute: and is always the same in the same height. This appears from the known Velo|city of descending or ascending bo|dies*, which fall or rise 16▪1 English Feet in one second of time; and by con|sequence 6440 Feet in 20″. those lines of descent or ascent being known to be ever as the Squares of the Times.

VIII. Gunpowder may be discharged, or combustible matter set on Fire at that utmost height. Page 38 This all that deal in Rockets, Bombs, and Mortars do very well know. It being the great business of their art to proportion the Match or Fusee to any particular time when it shall give Fire; which may as well be always adjusted to 20″ as to any other number. Nor indeed is it impossible to contrive all so, that the very beginning of the de|scent shall be immediately instrumen|tal in that matter, and thereby render the experiment more exact and infal|lible.

IX. Fire or Light 6440 Feet high, will be visible, in the night time, when the Air is tolerably clear about 100 measured, or 85 Geographical Miles: i. e. one whole degree, and 25 minutes of a great Circle, from the place where it is, even upon the surface of the Sea. Page 39 This is easily deduced from the Ta|bles of Tangents and Secants, applyed to our Earth; as will appear presently. Only it may be noted that the Refra|ction of Light out of the somewhat thinner Air above, into the somewhat thicker Air beneath, increases this di|stance a little; as also that an Eye upon the Mast of a Ship will see such Fire or Light 10 Miles farther than one on a Level with the Surface of the Sea; as will appear presently also. N.B. That the Distances this Fire or Light can be seen, abating the con|sideration of the Atmosphere, are near|ly in a subduplicate proportion of the Altitudes; and so at four times the height here mentioned, to which yet we have observed Projectils may be thrown, this distance will be nearly twice as large; i. e. about 200 measu|red, or 170 Geographical Miles; e|ven Page 40 without the allowance for refracti|on, or for the elevation of Mountains, whereon such Guns may be plac'd: both which when allowed for will im|ply, that 'tis possible, if the light be strong enough, to extend this distance to between 200 and 300 Geographical Miles, or minutes of a great Circle. A vast extent this! and capable of affording proportionably vast advan|tages to Mankind, upon the present foundation!

X The Angle such fire or light is seen above the Horrizon will very exactly discover its distance; as will an easy observation its Azimuth. The former branch is evident from the nature of a Sphere, with the usual Tables of Tangents and Secants: and may thus be computed by plain Tri|gonometry. Supposing the eye of Page 41 the Spectator placed at the surface of the Sea; and not considering the very small difference by the refra|ction. Let A represent the Earth's Center, BD the length of the Secant of 1°. [illustration] Page 42 Page 43 2′ 5. above the Radius; or 6440 feet. ED the Tangent of the same Angle. CB the length of the Secant above the Radius, at any lesser Angle, as BAF. and CF the Tangent of that last Angle. 'Tis evident that the Angle DFC is the elevation of the fire or light above the horizon at any given Point F. and that in the plain Trian|gle DCF the Angle DCF is given, equal to a right Angle, and to the An|gle FAB. FCB is its complement; and equal to the sum of the remote Angles CFD, and CDF. The inclu|ding sides also CF and CD are given; the former being the Tangent of the given Angle FAB, and the latter the difference of the Secant of the same Angle from the Secant of 1°. 25. So that by the known Rule of plain Trigonometry, as the sum of the sides, CF + CD, is to their difference,CF − CD, or CD − CF: So is the Tangent of the Semisum of the Angles, ½ CFD + ½ CDF = ½ FCB, to the Tangent of their Semidifference. Which Semidifference substracted at remoter and added at nearer distances to that Semisum; gives the Angle sought CFD. Q.E.I. According to this Rule the follow|ing Table is made to every Minute, or Geographical Mile; for the ease of all that may use this Method, and may desire some exactness therein. Miles distance. Angle above the Horizon. 1 46—25 2 27—42 3 19—16 4 14—40 5 11—50 6 10—20 7 9—0 8 7—55 9 6—50 10 5—55 11 5—20 12 4—54 Page 44 Angle above the Horizon. 13 4—30 14 4—8 15 3—52 16 3—37 17 3—23 18 3—11 19 3—0 20 2—50 21 2—41 22 2—33 23 2—25 24 2—18 25 2—12 26 2—6 27 2—1 28 1—55 29 1—50 30 1—46 31 1—41 32 1—37 33 1—33 34 1—28 35 1—24 36 1—20 37 1—17 38 1—14 39 1—12 40 1—10 41 1—7 42 1—4 43 1—1 44 0—59 45 0—57 46 0—55 47 0—53 48 0—51 49 0—49 50 0—47 51 0—45 52 0—43 53 0—41 54 0—39 55 0—38 56 0—36 57 0—34 58 0—32 59 0—31 60 0—30 61 0—28 62 0—26 63 0—25 64 0—24 65 0—23 66 0—21 67 0—20 68 0—19 69 0—18 70 0—17 71 0—15 72 0—14 Page 45 Angle above the Horizon. 73 0—13 74 0—12 75 0—11 76 0—9 77 0—8 78 0—7 79 0—6 80 0—5 81 0—4 82 0—3 83 0—2 84 0—1 85 0—0 N.B. It appears by this Table that the distance will never be less exact in this Method than is the Observati|on of the Altitude; since one Mile here never corresponds to less than one Minute; but that generally the di|stance is much more exact than the Observation: Since one Mile com|monly corresponds to considerably more than one minute; nay at very near distances to more than one whole degree; as is evident by inspection. As for the observation of the Azimuth, 'tis too easie to need any demonstra|tion. Page 46N.B. If the Eye be elevated above the surface of the Sea, it will see the fire or light farther; according to the fol|lowing Table. Miles distant. Elevation in feet. 1 1 2 4 3 8 4 15 5 23 6 34 7 45 8 57 9 71 10 88 11 107 12 128

XI. If the fire or light can be rendred compleatly visible during the intire time of the ascent or descent, as in the ordinary Sky-rockets, its Distance may be exactly determin'd also from the time it appears above the Hori|zon, by the use of the following Tables, even without the knowledge of the Angle of Elevation. Page 47A Table of the number of feet that Bodies fall or rise, as far as 20″ of time. ″ feet. 1 16▪1 2 64▪4 3 145 4 259 5 402 6 580 7 789 8 1030 9 1294 10 1610 11 1948 12 2318 13 2721 14 3156 15 3622 16 4122 17 4653 11 5216 19 5812 20 6440 A Table of the Excess of the Secants in Feet, above the Earths Semidia|meter, as far as 1°. 2′ 5. ′ feet. 1 1 2 4 3 8 4 15 5 23 6 34 7 45 8 57 9 71 10 88 11 107 12 128 13 151 14 174 15 199 16 227 17 256 18 288 19 321 20 357 21 393 22 430 23 470 24 512 25 556 26 601 27 647 28 695 Page 48 feet. 29 745 30 798 31 853 32 909 33 968 34 1026 35 1088 36 1151 37 1216 38 1283 39 1352 40 1422 41 1493 42 1569 43 1642 44 1720 45 1800 46 1882 47 1963 48 2047 49 2134 50 2222 51 2312 52 2404 53 2497 54 2592 55 2688 56 2787 57 2887 58 2991 59 3093 60 3198 61 3305 62 3415 63 3526 64 3639 65 3755 66 3870 67 3988 68 4118 69 4229 70 4353 71 4479 72 4608 73 4735 74 4866 75 4998 76 5132 77 5269 78 5407 79 5546 80 5687 81 5830 82 5974 83 6121 84 6271 85 6422 Page 49N.B. The Rule for Practice is this: Observe the Number of the Seconds of Time that you see the Fire or Light, either ascending or descen|ding, in the former Table; with its corresponding Number of Feet. Take this Number of Feet out of the entire Number 6440, and keep the Remain|der. For where that Remainder is found in the latter Table, you will find the true Distance over against it, e. g. Suppose the Light or Fire is ob|serv'd to take up 12″. or a fifth Part of a Minute, in its visible Ascent or De|scent. The corresponding Number of Feet in the former Table is 2318, which deducted from 6440, leaves 4122, for the Difference: Which Number in the latter Table corres|ponds to somewhat above 68′. and shews that the real Distance sought, is somewhat above 68 Minutes, or geographical Miles. The Demon|stration is easy from the former Page 50 Scheme. For DB − DC = CB, and so DA − DC = CA. or the Difference of the Secant of 1°. 25′. and of any Part of it visible in ano|ther Horizon, as at F, is equal to the Secant of that Angle DAF, or of the Arch BF, which is the Distance required. Only if the Bottom of the Atmosphere be too thick to permit the Light or Fire to be seen to any certain Altitude, allow|ance must be made for the same, in the use of these Tables.

XII. When a Sound and a Light are made at the same Place, ei|ther at the same time, or at any gi|ven Interval; the Distance of such Sound and Light from the Auditor or Spectator may be exactly determin'd. For if they are made at the very same time, the Difference of the Ve|locity of Light, which is, physically speaking, instantaneous, and of Sound, Page 51 which goes 12 geographical Miles in a Minute, will, with great Exactness, determine that Distance. And if there be a given Interval between them, it is easily allow'd for.

XIII. If the Longitude or Lati|tude of one Place be known, and the Distance and Position of another be also known; the Longitude and La|titude of this other Place is known also. This is too obvious to need a De|monstration; and may be easily shew'd on a Map, with a Pair of Compasses, apply'd to the Scale of that Map.

XIV. If the Longitude or Lati|tude of one Place be known, and its Distance from another be known also, and the Longitude of that o|ther Place be otherwise known, its Latitude is thereby known. And if Page 52 its Latitude be otherwise known, its Longitude is thereby known also. This is also too obvious to need a Demonstration; and may be shewed on a Map, as well as the foregoing.

XV. Hulls of Ships, without Sails or Rigging, may be fixed at Sea in all ordinary Cases, by Anchors; and in extraordinary Cases, where the Ocean is vastly deep, by Weights let down from the Hulls quite through the upper Currents into the still Waters below, as near as possible to the Bottom. This Matter belongs to Tryal and Experimenrs, and is not to be here particularly demonstrated. Only we may observe, that the lower Parts of the Waters in the Ocean are commonly found to be free from the Currents and Motions of the higher Parts; and that the Method by which those very Cur|rents are discovered, is no other than Page 53 by thus letting down the Lead far below them; which, tho' it touch not the Bottom, yet makes the Boat out of which the Lead is thrown, in the Words of an Eye-Witness, *ride as firmly as if it were fastened by the stron|gest Cable and Anchor to the Bottom. N.B. If any Current or strong Wind does, in some measure, carry away such an Hull, with any ordinary Lead, or Weights, care is to be ta|ken that the Cord or Chain be up|ward as small, and make as little Re|sistance to the flowing Water as po|ssible; and that the same Cord or Chain with its Weights or Leads be|low, be as large and cumbersome, and make as great Resistance to the still Water below, as possible: that so the Motion of the Hull may be in|sensible. Note also that in case there appear still some Motion in the Hull, the Mariners are nicely to observe its Velocity and Direction; and at con|venient Page 54 Seasons to bring it back again, as near as possible, to its original Station. N.B. These Hulls may be fixed in proper Places as to Latitude, by the known Methods of observing the Latitude; and as to Longitude, by Eclipses of the Sun, or Moon, or of Jupiter's Planets, or by the Moon's Appulse to fixed Stars; or rather by an actual Mensuration of Distances on the Surface of the Sea by Trigo|nometry, just as Monsieur Picard and Cassini measur'd the Length of a Degree of a great Circle on the Land; while the Light to be thrown up from the Ships will afford the same Advan|tage that any elevated Mark does at Land, and while the vastly greater Length of a Basis or measur'd Line on the Shore, the vastly greater Distances of the Ships; and the much greater Evenness of the Surface of the Sea than of the Land, do give us hopes of more Exactness in this Way of Mensuration than in any other. Page 55N.B. By the same Method, if done with sufficient Accuracy, we may also hope to discover the Quan|tity of a Degree in all sorts of great Circles, and perhaps more exactly than even Monsieur Picard or Cassini have been able to do: because we may hereby actually measure a much lar|ger Portion of such great Circles than they could. Which Advan|tage of this Method is in itself very considerable also.

XVI. If the Altitude of the Sun, at the best Advantage, can be ta|ken within four Minutes of a Degree at Sea or Land; the time is thereby determined to about half a Minute: if to two Minutes of a Degree, the time is determin'd to about a quarter of a Minute, even in our Latitude; while nearer the Equator the like Limits determin the time still more exactly. Page 56 This the Astronomers well know: and any that observe in common Quadrants how an Hour, in the mid|dle between Noon and either Mor|ning or Evening, contains usually about 7 or 8 Degrees of Altitude; while no less than 15 Degrees makes an Hour upon the Equator, will easi|ly agree to this Proposition.

XVII. The best time for the exact Discovery of the Hour at Sea, and of adjusting all Watches or Move|ments to shew the same afterwards, is that of the rising and setting of the Sun; that is, in case Allowance be made for the Horizontal Refraction of his Rays; but not otherwise. For if the time while the whole Body of the Sun is rising or setting, which may be very nicely observ'd at Sea, be added at Night to, and substracted in the Morning from, the Time that any Table of its rising Page 57 and setting, or a particular Trigono|metrical Calculation, does determine; the Sum in the first, and Difference in the second Case will give the true Time when the Sun's Center will ap|pear to be in the very Horizon. And this because the Sun's Horizontal Re|fraction is observ'd to be very nearly equal to his apparent Diameter. N.B. The Exact time of the Sun's rising and setting, at all Declinations, and in all Latitudes, is found by the following Rule of Trigonometry. Out of half the Sum of the Com|plement of the Sun's Declination, and of the Complement of the Latitude of the Place, and of an Arch of 90°. deduct severally the two former Sides, to gain two Differences. Then say, As the Rectangle of the Sines of thofe two former Sides: to the square of the Radius:: so is the Rectangle of the Sines of those two Differences: to the Square of the Sine of half the Angle at the Pole, included between Page 58 the same two Sides, which Angle is the Measure of the Time. For Example. Suppose an Hull of a Ship was fix'd in the Latitude of London, and there were occasion to compute exactly the Time of the ri|sing and setting of the Sun, for the longest Day of the Year. The Cal|culation is thus. Compl. of Declin. 66° 31′ Compl. Lat. 38 30 Quadrant. 90 00 Sum 195 01. Half 97° 30′ 30″ Deduct. 66 31 00 First Differ. 30 59 30 Deduct from the former Half 38 30 00 Second Differ. 59 00 30 Log sin. 66°. 31′. 00″. 9.9624527. A Log. sin. 38. 30. 00 9.7941496. B A + B 19.7566023. C Log. rad. square 20.0000000. D Log. sin. First diff. 9.7117341. E Page 59 9.9331794. F E + F 19.6449135. G D + G 39.6449135. D + G − C 19.8883112. ½ = 9.9441556. or (61°. 33′. 44″. Its double 123°. 7′. 28″. or (8h. 12′. 30″. Note also that the Amplitude can|not be exactly taken even at Sea, without the like Allowance for Re|fraction. And the Difference of Am|plitude, when the first Edge of the Sun touches, and the last leaves the Horizon, is to be added or sub|stracted in this Case, to that when it appears to be half set; in order to ob|tain the Sun's true Amplitude: as well as we added or substracted the Diffe|rence of time before, for the exact Ad|justment of the true Moment of its rising and setting. Page 60The Solution of the Problem. Let a great Gun, with a Shell that will take Fire at its utmost Altitude, be discharg'd perpendicularly 6440 Feet high above the Surface of the Sea, e|very Night exactly at 12 a-Clock, at all convenient Distances and Situations, and from known Places. This Dis|charge will, by the Distance and Point of the Compass of its Sound, nearly give the Longitude and Latitude to all Places or Ships within the hearing thereof: And it will, by the same Di|stance and Azimuth of its Light or Fire, exactly give the same Longitude and Latitude to all Places or Ships within the Sight thereof; according to the foregoing Lemmata. Q.EI. For Example: Let us suppose an Hull fixed in a known place, 30 De|grees more Westward than the Me|ridian of London; and that every Mid|night its Great Gun is discharged, as before; and that a Ship sailing by at Page 61 54′ 40″ after Eleven, sees the Fire or Light 30′ above the Horizon; i. e. by a foregoing Table, at 60 Minutes, or Geographical Miles distance. It was therefore 12 a Clock at the Hull, when it was only 11 h. 55′ at the Ship. So that the difference of time is 5′ and the difference of Longitude upon the E|quator 1° 15′ and the Ships Longitude from the Meridian of London is here|by known to be 31° 15′ Westward. Suppose also that the Weather be such that only the sound can be heard, and that it proves to be so weak as to be justly esteem'd 60 Geographi|cal Miles, or one Degree of a great Circle, distant. This Distance an|swers to 5′ of time, for the interval of the Propagation of the Sound: which therefore, if it be heard just at 12 a Clock at the Ship, will imply that when the Explosion was made it was at the Ship only 55′ past eleven, the same moment that it was full 12 at the Hull; and that therefore the Page 62 difference of Meridians is the same as before, viz. 5′ in time, or 1° 15′ up|on the Equator, Westward. Suppose farther, that the Light be seen at the same time that the Sound is heard; with no other than the small difference of the slowness of the Sound, in comparison of the instan|taneous motion of the Light; and that the difference of time between the most elevated appearance of the Light and the hearing of the Sound; (which may be easily and exactly ob|serv'd by any tolerable movement whatsoever, or by a Pendulum, that vibrates half Seconds:) be found to be 4′ 40″ or, which is all one, that the intire difference of the Explosion made, and of the Sound heard, be 5′ in time. This difference will imply the distance of the Ship from the Ex|plosion to be 60 Geographical Miles. And if the sound is heard at the Ship 54′ 40″▪ after Eleven, the difference of Longitude upon the Equator will Page 63 still be 1° 15′ and the real Longitude from London will be 31° 15′ Westward, as before. If the Azimuth of the Fire or Light be also observ'd, take with your Com|passes from your Scale the true distance, 60 Minutes, or Miles, and set it from the place of the Hull, on the true Angle, in any large Map or Sea-Chart. This will determine the very Point where the Ship is, both for Longitude and La|titude. The same thing may be done for the Sound, in case the Point of the Compass be observ'd also. If the Latitude of the Ship be known, take the known distance, ei|ther by the means of the Light or Fire seen, or, if the Weather be too Fog|gy for that, of the Sound heard; and let it cross the known parallel of La|titude in the Chart; and this will de|termine the Longitude. The like is to be done for the Latitude, were the Longitude first known. But that not being the usual case, it needs not be Page 64 farther insisted on. Nor need we shew how all this may be done by Calculation also: since those that un|derstand any thing of Navigation can|not be to seek therein. N.B. In case some parts of the Ocean prove so very deep and rough that no Hulls can be fixed in them, the way to recover the Longitude, which may be by this means interrup|ted, is rightly proposed by Sir Isaac Newton himself, in his Paper delivered in to the Committee of the House of Commons, viz. to sail obliquely from the last Hull into the Parallel of the next, and so along the same; till up|on approaching to that next Hull the Longitude be anew recover'd, and the Voyage be continued as before. Nor is this Interruption of any conse|quence; because it cannot happen but in places where there is no Dan|ger; and where Seamen are under no concern for the knowledge of the Longitude.

OBSERVATIONS.

PROBLEM. To find the LONGITUDE both at Sea and Land.

(1.) IF in all proper Roads of Ships such a great Gun be plac'd and discharg'd, exactly every Mid|night, whether on Shoars, or Islands, or in Hulls, at the Distances of a|bout 600 Geographical Miles or 10 Degrees, All Ships that sail with|in any tolerable Distance may com|monly every Week or Ten Days thereby correct their Reckoning, and know their Longitude, as well as Latitude, even when the Heavens are not clear enough to make Cele|stial Observations for either.

(2.) The Ordinary Watches, Movements, or Log-Lines in Ships, when thus Corrected and Adjusted, once in a Week or Ten Days, will Page 66 well enough shew the Longitude du|ring every one of those short Distan|ces between the Hulls; and so will render the knowledge thereof still more universal.

(3.) If one such Row of Hulls be any where found too defective, a double Row may there be laid, Pair by Pair, in the same [or equidistant] Meridians; with proper Distincti|ons in the Sounds, or the Light, to prevent mistaking one Row for the other. Nor will there, in this Case, be room for almost any Uncertainty, since even in Cloudy Weather, as much as the Wind carries away the Sound of any one, so much will it usually bring the Sound of ano|ther.

(4.) If it be any where necessary, Masts may be Erected upon Hollow Empty Vessels, with White Spheres at their Tops; and these Vessels may be fix'd in proper Places, at Page 67 equal Distances between the Hulls, for the more sure guiding the Ships in Places of Danger. And since from the Top of any Mast that is 88 Feet High, the Top of another as high may be discovered at the Di|stance of 20 Miles, there will hard|ly be occasion for more of these Ves|sels any where than one every 120 Miles: Nor will these Masts and Vessels be any Annual Charges at all.

(5.) Besides the great Guns, and their solemn Explosions, In proper Places, at several Havens, where there is any Danger at the Entrance of Ships, as well as at other conveni|ent Promontories jetting out into the Sea, a Rocket may be thrown up from the Top of a Neighbouring Steeple, or Hill, or the like most elevated Place every Midnight, for the Seamens better Direction and Security.

Page 68 (6.) Signals of all Sorts may be given by this Method, by mutual Agreement. As suppose in Storms we would know which way, and how strong the Wind is at the near|est Explosion, &c. Ships may thus give Signals of Distress to the Hulls, or to one another. The News of great Events may be also this way carried very soon over the Sea; especially, if any Ships were plac'd within Sight and Hearing of each others Signals, as a Fleet may sail in Times of Peace, &c. In short, no one knows how far this Method of Communication by these Kinds of Signals may be improv'd; and how great a Convenience may hence arise to the several Parts of the Globe, especially in the Way of Trade and Commerce; and even for the Propagation of Knowledge both Divine and Human through|out the World.

Page 69 (7.) If in any clear Night a suffi|cient Number of such Explosions were made at proper Distances in any Country, and convey'd in or|der from one to another; so that the Second Gun were fired when the Light of the First was seen, or other|wise; with the Observation of the exact apparent Times when they were made, when the Light was seen, what Angle, or how long that Light was above the Horizon, and what Azimuth it had; both the Longitude and Latitude, as well as the Distance and Position of all these Places, might by this means be rea|dily determin'd at Land; especially if the Experiments were repeated several times, and were compar'd one with another. And by the same Observations every where, the Lon|gitude and Latitude, Distance and Position, of all other Neighbour|ing Page 70 Places from those, and so from another, might be readily deter|min'd also.

N.B. This Method of Survey is no hard Thing in Practice, even to those that know little of the Ma|thematicks: For any Right Angle, set by a Plummet or Level, with Two Pins or Points, for the Eye and for the Object, does by the Propor|tion of its Sides give the Angle above the Horizon; by the Angle its Horizontal Side makes with the Meridian, it gives the Azimuth; and by the Interval of Time be|tween the Light and Sound, it gives the Distance of every Place from that of Explosion, according to the Figure following. Page 71

[illustration]

North

South;

Eastward.

•

Great-Britain

Ireland,

Where AB represents the Horizon|tal Side of the Norma or Square, and BC the Perpendicular Side; whose Proportion once given, as suppose 80 to 35, the Discovery of the Angle of Elevation CAB is most easy, as here 23° 38′ Where also NS. represents the Meridian Line lying fromtoand the Angle SAB, suppose of 32 Degrees, 15 Minutes, represents the Azimuth,We need not add that a Plummet of 98 In|cheslong will vibrate half Seconds, for the Interval of Time between the Light seen and the Sound heard. Nor is there, we think, any way yet discover'd of surveying Countries and Kingdoms that can compare with this, either for Expedition, Cer|tainty or Cheapness. A Specimen of which we hope soon to give the World in an Actual Survey ofandand their Coasts hereby; if the Publick please to give us Encouragement and Assi|stance therein.

(8.) The way of casting a Shell 6440 Feet high is very easy: for the same Force or Charge of Gun-pow|der that will cast any Shell 12880 Feet for its utmost Random, at the Elevation of 45 Degrees, will cer|tainly cast the same Shell perpendi|cularly upward 6440 Feet, as we have already observ'd. And since the time of this entire perpendicu|lar Projection, or Ascent and Descent Page 73 together, is 40″, or some very small Matter more; on Account of the Resistance of the Air; We have ano|ther sure Way of Adjusting the same Projection to that Height; viz. by observing what Quantity of Powder will cast the Shell high enough to stay very little above 40″ in the Air, before it falls to the Ground.

(9.) This Method of firing Pow|der, or other combustible Matter, at, or very near the utmost Height of 6440 Feet, may be well enough put in practice, even tho' some conside|rable Error should be committed in the adjusting the Fusee to give Fire in 20″. Since the Mistake of even a Fifth Part, or Four entire Seconds, in that Case, would produce but an Error of the 25th Part of the whole Altitude: and the Mistake of a Tenth Part, or Two Seconds, would occasion an Alteration of no more than the Hundredth Part thereof. Page 74 This is evident, because this Time belongs to the highest Part of the Projectils Motion, which is the slowest: And because the Lines describ'd by all Ascending and De|scending Bodies are still in a Dupli|cate Proportion of the Times of such their Ascent and Descent.

(10.) If one or more Rows of such Hulls were laid in the same or Equidistant Meridians, Southward or otherways, Ships might with greater Safety than formerly go to discover those Parts of the Globe which are hitherto undiscover'd. Nor can we at present guess what Advantages may thereby accrue to the Parts of the World already dis|covered.

(11.) Every one of these Hulls may be Places of Observation as to the Variation of the Needle, to the Currents, to the Soil, the Fowls, the Fishes, and other Phaenomena of the Page 75 several Places where they are fixed; and an excellent Means of keeping up a mutual Correspondence be|tween the several Parts of the Globe, for all useful Purposes what|soever.

(12.) As this Method ought to be put in Practice by the Consent of all Trading Nations; so ought every one of the Hulls employ'd therein to have a legal Protection from them all; And it ought to be a great Crime with every one of them, if any other Ships either injure them, or endeavour to imitate their Explo|sions, for the Amusement and De|ception of any.

(13.) Since the Charges of the Powder for each Gun will be very small; since the Shells and their Contents come to no great Price neither; since the Persons employ'd in the Hulls may be in part taken out of such Places where they are Page 76 maintain'd at the Publick Charge already; and so will require only some Additional Rewards, or Future Privileges for such their Service; And since the Land-Explosions, which will be much the most nu|merous, will be withal much the cheapest; It will appear, upon the Whole, that the Annual or Constant Expences of this Method will be comparatively very small and incon|siderable: especially if they are, as they ought to be, equally distributed among the several Trading Nations of the World.

Page 77 The Advantages of this Me|thod. (1.) THIS Method requires no Depth of Astronomy, no Nicety in Instruments, and but seldom any Celestial Observations at all, either as to the Latitude, or the Hour at the Ship; and so is to even the common Sailors the most Practi|cable.

(2.) It does generally determine the very Place of the Ship, both as to Longitude and Latitude at once, and so is the most Compendious.

and at once, and so is the (3.) It does generally determine the very Place to a few Miles, at the farthest; and so is the most Accurate.

(4.) It affords Help even in Clou|dy and Foggy Weather, when no Celestial Observations can be made, and the Latitude it self cannot be otherwise found, and so is the most General.

it self cannot be otherwise found, and so is the Page 78 most secure.

(6.) It will commonly afford a double way of Observation at the same time, by the Eye and by the Ear, which will confirm or correct one another; and so is the most certain.

(7.) The more inaccurate Branch, by the Sound, is not only more uni|versal than the other; but is also much more exact than any Method formerly discover'd: So that in the very worst Circumstances this way is certainly the very best.

(8.) It is the most undoubted and exact where there is the greatest Want and Danger: And if it should at all be deficient, it is there only where there is no Danger, and hard|ly any occasion for knowing the Longitude, as has been shew'd alrea|dy. So that on all Accounts it is plainly the most Useful and Advan|tageous.

APPENDIX.

IT is farther humbly propos'd to the Learned, Whether it may not be proper for all Nations, up|on this Occasion, to agree upon one first Meridian, or beginning of Lon|gitude, for the common Benefit of Geography? And whether it may not be proper, in that Case, to fix it to the Pike of Tenariff, as the most noted Place already; and as the Place whence the Highest and most generally useful Explosion must in this Method be made every Mid|night continually for the Discovery of the Longitude it self?