Idea Longitudinis: Being, a brief DEFINITION Of the best known AXIOMS For finding the Longitude. OR, A more Rational Discovery thereof, than hath been heretofore Published.  
By Edward Harrison, Lt.  
LONDON, Printed for the Author, and sold by Mr. Sellers, at the Hermitage; R. Mount, at the Postern, on Tower-Hill; and P. Lea, at the Atlas and Hercules in Cheapside, at the Corner of Friday-street, 1696.   

To the Right Honourable, the Commissioners for Executing the Office of Lord High Admiral of England, &c  
My Lords,  
IT is a saying in the Navy, He that knows not how to obey Command, is not worthy to bear Command; and another saying I have often heard in the Navy. It is hard for an Officer to know when he goes too fast or too slow, that is, whether he is too severe in the Execution of his Duty, or too dull or slow; in which Cases, it is sometimes difficult to please our Superiors, because of their different Humours: As it is the Duty of a Subject to be True and Loyal to his Prince, so it is the Duty of Servants, to be Faithful, Humble, and Submissive to their Masters. I thought it my Duty, my Lords, Humbly to present you with this small Treatise, not only as a Servant, but that whereas some part of it may happen to fall under your Construction, more particularly the Chapter concerning Magnetic Variation, which I Humbly Commend to your Joint Care and Consideration, for the Improvement and Encouragement of Navigation, and Amendment of Faults in the Navy, if I may presume to say there is any Faults there; an Elegant Style cannot Reasonably be expected from Sea breeding: I am not willing to seem tedious, if in my Discourse in this Book, you find some small Faults; I hope your Wisdom will be pleased to Pardon, and Excuse them.  
I am, my Lords, Your most Humble, and Obedient Servant, EDWARD HARRISON.   

PREFACE To the Reader.  
AFter Columbus returned from his Discovery of the Land now called America, he happened into Company with some Spaniards, who had the Vanity to tell him, that he had done nothing, but what they could do as well as he; Yes, Gentlemen, said he, now I have shown you the way; he called for a Hen's Egg, and desired them to make it stand on one end, (without leaning,) on a smooth and flat Table, they all tried, but none of them could make it so to stand; he tried after them, and made it stand, etc. so could they also, when he had showed them the way: I doubt not but in a short time, there will be many Pretenders to the Longitude, and to understand it better than I; be pleased to remember that I showed the way (or can if I please.) Mistake me not; think not that I am designed in this small Treatise, to Teach the whole Art of Longitude; Art Mathematic is very Copious, part of which is Art Longitude, Ingenious and Compendious, requiring much larger Volumes than this is; I say, I can (if I will,) God willing, show you the true Principles, the right Radix, and Basis, whereon this Fabric may be built; one Man might carry a Stone, to St. Pauls-Church in London, and lay it on the Foundation, give Directions for Building the same, but he alone could never have perfected, (as now it almost is,) that Stately and Glorious Edifice; I may begin my work to Day, but what Encouragement I may meet with in carrying it on, I know not; or if it may please God that I may live to see this Art brought to such Perfection, as to be fit for Seamens Practice; some Years ago, I presented a few Lines concerning this Art, to a Nobleman, or Person of Quality, which Lines he little understood, and less regarded; which one of my Friend's understanding, well compared to casting Pearl before 〈◊〉 I have been informed of one who pretended to find the Longitude, and requiring a Gratuity, was sent to Mr.— to have his Approbation; I think they might as well a sent him to a been Robbed; I Discoursed this Art with some Fellows of the R. S. whom I found too much aiming at their peculiar Advantage; therefore I resolved to appear on the Public Stage, in Print, Nevertheless, the Description is a little Veiled, though it is what I thought convenient to Publish; As for my Style, I understand not how to Express my Sentences, in Topical Syllogisms, or Sophistical Rhetoric; if you meet with a plain Method, downright Reasoning, and matter of Purpose, it is what I aim at; I know my Method differs much from other Writers, I write the Truth to the best of my Knowledge, and value not Carpels; and in spite of Envy, I presume to declare, That I believe there are but few Mariners in England, that understand how to keep an Account of a Ships way on the Sea, as well as I have done, or may do; and if I know more than others, it is by Divine Authority, by Industry and Experience, by an Inborn Idea, and Instinct in Nature; it was ordained for me by God Almighty, from my Mother's Womb. My Knowledge in the Mathematics is but little, therefore I dare not compare myself to the Learned Dr. Wallis, and many others, who have writ large Volumes of Geometry, Algebra, and Cubick Aequations. Brother Tar, there have been in England, many Pretenders to the Longitude, and some have writ concerning it: If thou hast this small Treatise by thee, thou mayst find more in it fit for thy purpose and Perusal, then in any former Book of this Nature; there have been many Persons, when they have attained some Knowledge in Cosmography, and Accidentally thinking on some of the ways contained in this Book, believe they have found the Longitude, and trouble their Brains to little purpose. Therefore, this Book is very convenient to ease their Brains, from such Burdens; because it contains all the most noted ways, and Fundamental Principles, whereby the most Learned of this Age, have endeavoured to find the Longitude; and whereas you may think that this Book doth not wholly inform you of any Practical Method, for finding the Longitude; yet it is hoped that the said Science will become Practicable, in few Years, (and already is to the Ingenious, but not to the Ignorant.) Till than I advise you, duly to consider the Fifth Chapter in this Book, concerning Magnetic Variation, which if you understand well, you have gained a Science, that for Seamen's Practice, is little Inferior to the Longitude: How the World may esteem of this Book, I cannot tell, but I hope it will be as a Safeguard, or means to save many a Ship, from being Wrecked Ashore, and save many a Seaman's Life. Some Blockheads are apt to say, the Longitude cannot be found; no, no, it cannot Accidentally, as a Sow does a T— d in the Streets, but by Care, Diligence, and Industry, it may be found, without which, it cannot be understood. Though we have been at the Dutch for Hydrographical and Geographical Draughts; let us not go the to French to learn their Use. But why do I reflect, I expect no Thanks for my Pains, but to be reflected on again, as Harrison's Whimsies, or the like; I pray forsooth, how many such Whimsical Inventions can my Countrymen boast of, that they have not borrowed? I have often heard them boast of Drake and Candish Sailing the World about, but not a word of the Portugueses that showed the way. If any Envious Person pretend I have borrowed most of my Book, may he be obliged to Quote the Authors, where I have not; I advise some Mathematic Bookseller, for his and the Public Good, to Re-print Mr. Street's Astr. Car. with its Appendix and Calendar, and to Add a New and more Easy Theory of the Moon's motion, by Mr. Halley or Mr. Newton; Tables of Jupiter's Satellites, and a Catalogue of fixed Stars, and their true places, by Mr. Flamstead, if they are to be had; if not, to borrow from Mr. Cassini, and Hevelius. Some of the ordinary Mathematicians may hate to be outdone by a Tarpolin, if they have aught to say against him, it's because his Practice and Experience may prove him to be a more Competent Artist in Navigation then themselves: If I have Committed some Blunders, the Name of Tar, and the Novelty of the Subject, may Excuse me to the Judicious.  
Your Friend and Servant, Edward Harrison.   

THE CONTENTS.  

Chap. I. COncerning a first Meridian. pag. 1.  
Chap. II. A Definition of Longitude.  
Chap. III. A Definition of Time, and Aequation of Natural Days.  
Chap. IU. Of Automatas or Horological Self-movers.  
Chap. V. Of or Concerning Longitude by Magnetic Variation.  
Chap. VI Longitude by the Moon's motion, by her Conjunctions or Eclipses, and Apulses to fixed Stars, of her Illumination by the Sun.  
Chap. VII. Longitude by Jupiter's Satellites.  
Chap. VIII. Conclusion.    

Idea Longitudinis: BEING A brief Definition of the best known Axioms, for finding the LONGITUDE, etc.  

CHAP. I. Concerning a First Meridian.  
DIvers were the Opinions of the Ancients, about the middle and Centre of this World; before Christianity, the European Heathens esteemed those places as the Centre of this World, where their Gods were chiefly Worshipped; as at Delphos, for Apollo's Oracle, at Ephesus, for Diana's Temple, etc. The Primitive Christians, believed Jerusalem to be the middle of the World; Ptolemy who lived Anno Christi 138. begun his Longitude at the most Western parts, (as he thought) at the Fortunate Islands, now called the Canaries. Lactantius was of Opinion, that the Earth was a Plain, and not a round Body, and would not believe there was any such thing as Antipodes, which is now received and embraced for a certain approved Truth. Since the Earth's Globular Form hath been discovered, there have been many disagreeing Opinions about a first Meridian; Geographers beginning at St. Michael's at Gratioso, at Pico; Some begin at the Lizard of England, others at London, some at Paris: A Spanish Merchant willing to prefer an Island to this Honour, writes, (viz.) Nullum inveni inter Auctores, quos legebam concordiam; aliis Hesperides Insulae pro primario meridiano placebant; quibusdam Corni Insula, pluribus fortunatae Insulae, non nullis Palma Insula, aliis alia atque alia loca, etc. And a little further proposeth an Island he calleth Abroxos, it lies towards the Coast of Brasile; ought he not, think you, to have been complained of to the Pope, for not knowing his Duty to St. Peter's Church in Rome. The Reason why many begin their first Meridian from the Isles Azores, is because it is said thereabouts, the Compass hath no Variation, (concerning which, I shall say more when I come to write of Longitude by Magnetic Variation.) Methinks they take up too much breadth for a first Meridian, for suppose I were to draw a large Draught of the Azores, or of the City of London, where must I place my first Meridian? a Meridian-Line, in a Sea-Chart, or Map, is no bigger than other Lines, save only so as to distinguish it from the rest; besides, Astronomers and Astrologers, pretend to observe and Calculate, to Seconds of Time, and Motion; therefore our first Meridian ought to be supposed to be a small narrow Line, or Circle. I could Baffle and Impose on the World as our Predecessors have, false Arguments for other places, from whence they might account their first Meridian. God forbid I should be so wicked, Honour and Glory, and beginning of Good, belongs to God; a first Meridian may be represented, and if the Heads of our Church and State, think it good, let there be made a Figure, representing a first Meridian, and Erected over St. Paul's Church in London, with this Inscription, Glory be to God, good Will towards Men, this presents our first Meridian, etc. this may be an Ornament to our Church; may it be Sacrilege for any of the King of England's Subjects, to account any other Meridian a first Merid. save that which passeth right over St. Pauls-Church in London, cutting the Equinoctial at right Angles, and passing through both its Poles. I hope this Advice may put a Period to Cavilling about a first Meridian; indeed I may except against wicked Captious, Atheistical Humours; for there was never any thing by the Wit of Man so well devised, or so sure established, which in continuance of time hath not been corrupted. It is always Midday or Noon, in some part of the World. Every Meridian is divided into four Parts, or four times Ninety Degrees, and subdivided etc. They be Innumerable, but you may reduce them to what number you please, as to 21600, or half so many, or more, or less, as is most convenient for your purpose; they are all equidistant at the Equinoctial, and in every lesser Circle, Parallel to the Equinoctial, but Incline nearer together until they intersect one another in the Poles: I allow but one first Meridian, beginning at St. Pauls-Church in London, or if occasion require, you may begin at any other part of the same Meridian.   

CHAP II. A Definition of Longitude.  
Circle's of Longitude on the Earth, have their beginning at any part of our first Meridian, pass round the Earth, and terminate where they begun, may be imagined to be infinite in number, but may be reduced to what number you think most convenient for your purpose: There is but one great Circle, the Equinoctial; all Circles parallel to it, are lesser and lesser Circles, as they decline towards the Poles; each divided into 360°, and subdivided, etc. and may be accounted either Easterly, or Westerly, as the Practitioner pleaseth; it is our design to measure the Arches of these Circles, by Astronomical Observations, or otherwise, thereby to know our difference of Longitude from our first Meridian, when we are either to the Eastward or Westward of the same.  
Longitude in the Heavens is accounted on one great Circle, the Ecliptic, (you may if you please, also Account it on lesser Circles, parallel to the Ecliptic, but that is needless and not usual,) which hath its beginning at the first point of Aries, or where the Sun will be this Year 1696, March the 9th Day, 3 h. 21′ 20″ P. M. it cuts the Equinoctial in two opposite points, in the beginning of ♈ and ♎ it's greatest Obliquity from the Equinoctial, (in these our Days,) is 23° 29′, it ends where it begins. The Theory of the Planets, and Stellary Motions, are accounted on the Arches of this great Circle, because in their Revolution they respect the Ecliptic Poles, as their Centre, (and the Sun also) and not the Equinoctial Poles, (except the Earth only, in her Diurnal Motion.)  
sidereal Longitude is accouted from the first Star of Aries, on the Ecliptic also; it begins where the Ecliptic is cut by a great Circle, that passeth through the 1 ⚹ of ♈ and the Ecliptic Poles; the difr. Long. between the 1 point of ♈, and the 1 ⚹ of ♈ is this Year the 9th Day of March, 28° 52′ 9″ which difr. is the praecession of the Aequinox.   

CHAP. III. A Definition of Time and Equation of Natural Days.  
Atque in se sua per Vestigia, Volvitur annus.  Virg. 
OLD Style, or Julian Year, is our English Account, contains 365 d. 6 h. of Astronomical years, there are divers kinds, but I shall only mention two, the Solar, or mean Tropical Year, is 365d d 5 h 49′ 1″ the Sidereal Year is 365d d 6 h 8′ 30″ the natural Day in most parts of Europe, is divided into 24h the Suns (or Earth) mean motion in the Ecliptic in 24h is 59′ 8″ the longest natural Day is 361° 1′ 15″ the shortest is 360° 57′ 10″ the difr. in one Day is but little, but in a Month's time is considerable; each difference adjusted is called Aequation of natural Days; the shortest natural Day, will be this Year the 18th Day of June, when the Sun is in 7° of Cancer, or thereabouts, for then the ☉ and ♁ are in their Apogaeon (or Auge, Apoge, Aphelion, Absis, have all one Signification in Astronomy,) the 17th Day of December, they will be in their Perigaeon, or Perihelion, or nearest distance; this Inequality of Natural Days, seems to me, to be the cause why our Summer half Year is (now in our times,) almost Eight Days longer, than our Winter half Year; as also it is the cause of the Impossibility of any Clock, or Watch. (though they move very regularly,) always to show the true time of the Day; Mr. Parker in his Almanac, teacheth us when to Add or Subtract the Time aequated to or from the mean time, to accord with the Apparent Time: In most Books of Astronomy, there are Tables for our purpose, Vide Astr. Ang. lib. 3. p. 84 and 85. Canon's Aequationum Dierum Naturalium; & Canon's Equationis dierum Naturalium, duabus praecedentibus Composit. & nostro huic Seculo citra errorem sensibilom subservien. And Ph. trans. N. 214. pa. 248. Tabulas aequationis Dierum, cum Solis loco adeund. etc. All which Tables you must well understand, before you can attain to Practical Longitude, (except Magnetic Variation,) it may seem necessary here, that I show how to find the time of the Day or Night by Observation; there are many ways Published in several Mathematic Books, but I shall reduce them to one, (for I think Mr. Molineuxes Sciotericum Telescopium, will do us little or no service) right way, and commend you to Colson's Calendar, see his Astronomical Problems, Prob. 9 and 10. instead of Hours and Minutes, work by Degrees and Minutes; and whereas I said that 360° 59′ 8″ was equal to 24 Hours; you may work only by 360° for when you observe in the Night, it is supposed you take the Sun's right Ascension exactly true, at that very Time and Place of your Observation, allowing for the Sun's Diurnal difference of R. A. also allowing for your difference of Longitude, from our first Meridian, else all your trouble may prove good for nothing. As yet I have never seen any Universal Ring-Dial, or other Sundial, that showed the true Time of the Day, (except about Noon) our Dialists thinking the Sun's Refraction not worth their notice, but those that pretend to find the Longitude, must duly consider Refractions and Parallaxes.  
It seemeth not proper in this Chapter, but I think it convenient to add something concerning Instruments; common Practice, and Experience teacheth, that a Forestaff is a useful Instrument, both for backward and forward Observations; I have also had Experience of it myself. and for forward Observations, I like it not (and for backward Davis' Quadrant is better;) for in its use, there happen several Errors, hard to Correct; as the Excentricity of the Eye, and end of the Staff; a true Horrizon cannot be found by it in the Night, but only guessed at; besides the height of the Eye above the Water, and the great difficulty of seeing two Objects at once, that is the Sun or Star, and the Horizon; for if the Star be high, whilst you are a looking for it at one end of the Vane, you lose the Horrizon, at the other end of the Vane, or a looking for one, you lose the sight of the other; therefore to avoid such Errors, for taking Altitudes in the Night, I commend you to a Quadrant, with a Pendulum from its Centre; see the Figure of it in Moxon's Tutor to Astr. Prob. 13. p. 48. This Instrument may seem very troublesome at first, for want of Use and Custom; use a weight of at least two or three Pound, with a small Wire, or Catts-Gut; for taking small Heights, or Distances, you may use an Almicanter Staff, for ordinary Uses; but if your Observation requires greater exactness, Vide Tichonis Brahe, Astronomiae Instauratae Mechanica, or John Hevelii Machinae Caelestis pars prior, etc. instead of Instruments that resolve Mathematical Questions, as Sectors upon Quadrants, Analemmas, etc. Stick close to the Doctrine of plain and Spherical Triangles, and to Logarithmical Tables; but on better Consideration, the Quadrant in Moxons Tutor to Astr. aforesaid, is not very fitting for Sea Uses, without some Alterations, therefore I have contrived a Quadrant something like the former, with weights that Commands it, so that it will always continue in the same position you direct it to; It may be contrived to hang like a pair of Scales or Ballance, having an Axis in its Centre, of Gravity, on which it is equally poised (without the weight) to turn round, having a Swifle and Ring to hang or hook to any convenient place in the Ship, or those that please may have a Stand purposely for it; there must be a small Line, or slippery Cord or Cords fastened somewhat slack, from Corner to Corner, on the Circumference of the Quadrant, on which Cords hang the weights of 20 or 30 Pound, or more or less, as you find most convenient for the Substance or Radius of the Quadrant; from the said weights, or rather from that part that slides on the Cords, may come two Indices, one to point to the Altitude on one side of the Quadrant, and the other, to the Comp. Altitude, if the Quadrant be reversed on the other side; and those that please may also have either Pendulum or Indices, from the Centre of the Quadrant, to point either to the Degrees of Altitude, or Comp. Altitude: It is easily managed in blowing Wether at Sea, or Ashore, and the Price not above 20 Shilling, I hope, for a Common one; I am a little Proud of the Invention, however I forbear to Applaud it too much, and to Print the Figure of it, till I have made further Experience of it.   

CHAP. IU. Of Automatas, or Horological Self-Movers.  
MR. Blundeville. from Gemma Frisius, writes of a ready way (as he calls it, (to find out the Longitude of any place, by some true Horology, or Watch; to that purpose, Mr. Rook writes, viz: Ad momenta temporis accuratissime notanda (quod in hujusmodi Observationibus est palmarium) perutile erit Oscillatorium, ab Ingeniosissimo & candidissimo Hugenio feliciter excogitatum. There have been some Experiments made at Sea for finding the Longitude by Pendulum Watches, as you may read in the Ph. trans. N. 1. pa. 13. I know several Seamen will buy this Book, that are not able to furnish themselves with a Sett of Ph. Transactions, therefore it may be convenient to Insert the following Narrative.  

A Narrative concerning the Success of Pendulum Watches at Sea, for the Longitudes.  
The Relation lately made by Major Holmes, concerning the Success of Pendulum Watches at Sea, (two whereof were Committed to his Care and Observation in his last Voyage to Guiney, by some of our Eminent Virtuosos, and grand Promoters of Navigation,) is as followeth. The said Major having left that Coast, and being come to the Isle of St. Thomas, under the Line, accompanied with four Vessels, having there adjusted his Watches, put to Sea, sailed Westward, seven or eight Hundred Leagues, without changing his Course; after which, finding the Wind favourable, he Steered towards the Coast of afric, North North East, but having Sailed upon that Line, a matter of two or three Hundred Leagues, the Masters of the other Ships, under his Conduct, apprehending that they should want Water, before they could reach that Coast, did propose to him, to steer their Course to Barbadoes, to supply themselves with Water there. Whereupon the said Major, having called the Master and Pilots together, and caused them to produce their Journals and Calculations, it was found that those Pilots did differ in their Reckonings, from that of the Major; one of them Eighty Leagues, another about an Hundred, and the third more; but the Major Judging by his Pendulum Watches, that they were only some thirty Leagues distant from the Isle of Fuego, which is one of the Isles of Cape Verd, and that they might reach it next Day, and having a great Confidence in the said Watches, resolved to Steer their Course thither, and having given Order so to do, they got the very next Day about Noon a sight of the Isle of Fuego, finding themselves to Sail directly upon it, and so arrived at it that Afternoon, as he had said. These Watches having been first invented by the Excellent Monsieur Christian Hugens of Zuilchem, and fitted to go to Sea, by the Right Honourable, the Earl of Kincardin, both Fellows of the Royal Society, are now brought by a New Addition, to a wonderful Perfection; the said Monsieur Hugens, having been informed of the success of the Experiment, made by Major Holmes, wrote to a Friend at Paris, a Letter to this effect.  
Major Holmes at his return, hath made a Relation concerning the usefulness of Pendulums, which surpasseth my Expectation; I did not imagine that the Watches of this first Structure, would succeed so well, and I had reserved my main Hopes for the New ones: but seeing those have already served so successfully, and that the other are yet more Just and Exact, I have the more Reason to believe, that the Invention of Longitudes, will come to its Perfection. In the mean time, I shall tell you, that the States did receive my Proposition, when I desired of them a Patent for these New Watches, and the recompense set apart for the Invention, in case of Success; and that without any difficulty, they have granted my Request, commanding me to bring one of these Watches into their Assembly, to explicate unto them, the Invention, and Application thereof to the Longitudes, which I have done to their Contentment. I have this Week Published, that these Watches shall be exposed to Sale, together, with an Information, necessary to use them at Sea; and thus I have broken the Ice. The same Objection that hath been made in your Parts, against the Exactness of these Pendulums, hath also been made here, to Wit, that though they should agree together, they might fail both of them, by Reason that the Air at one time might be thicker, then at another. But I have answered, that this difference, if there be any, will not at all be perceived in the Penduls, seeing that the continual Observations made in Winter, from Day to Day, until Summer, have showed me, that they have always agreed with the Sun, (I doubt the Truth.) As to the Printing the Figure of my New Watch, I shall defer that yet a while; but it shall in time appear, with all the Demonstrations thereof, together with a Treatise of Pendulums, written by me some Days since, which is of a very subtle Speculation.  
I have read of a Glass Globe, that a King of Persia had, in which he could see all the Celestial Motions; of the same kind with our Clocks and Watches, though perhaps more Elaborate and Subtle, was that Sphere Invented by Archimedes', which did represent the Heavenly Motions, the Diurnal and Anual Course of the Sun, the Changes and Aspects of the Moon. etc. This is frequently Celebrated in the writings of the Ancients.  
Jupiter in parvo cum cerneret aethera Vitro,  
Risit, & ad Superos talia dict a dedit;  
Huccine mortalis progressa potentia curae▪  
Jam meus in fragili luditur orbe labour.  
Jurapoli, rerumque fidem, legesque Deorum,  
Ecce Syracusius transtulit arte Senex.  
Inclusus Vaaiis famulatur Spiritus astris,  
Et Vivum certts motibus urget opus.  
Percurrit proprium mentitus Signifer annum;  
Et simulata novo Cynthia mense redit.  
Jamque suum Volvens audax instria mundum,  
Gaudet & humanâ sidera ment regit.  
Quid falso insontem tonitru Salmonea miror?  
Aemula naturae parva reperta manus.  
I have heard from Dutch Seamen several Stories of a wonderful Sphere or Clock at Strasburgh in Germany, which as they say, hath or had a regular and perpetual Motion, and showed the Celestial Motions, etc. Mr. Newton in his Idea of Geography and Navigation, pag. 90 and 91. writeth concerning Automatas, or unerring Clocks, and saith, that the nearer you advance within the Arctic or Antarctic Circles towards either of the Poles, the Motion is so much slower than at London; but in his Preface to the Reader▪ saith, This Paragraph, ought thus to be Corrected, that the further you advance towards either Pole, their Motion is swisaer, and the further they are carried towards the Equator, their Motion is retarded, etc. The cause wherefore these Instruments may move swifter nigh the Poles, then near the Equinoctial, cannot proceed from the Oval Form of the Earth, as some think; the cause of their swifter Motion nigher the Poles, in my Opinion is cold Wether, and Frosts; I believe that in England, in Frosty Wether, our Clocks move swifter than in Summer, for in Frosty Wether, Springs may contract a little, and grow stiffer, consequently have more force to make a swifter Motion; and in Hot Wether they may extend, and be a little more pliable, therefore the Motion may not prove altogether so swift as in Frosts: There are other Causes also, that may hinder the regularity of their Motions; see Ph. tr. N. 47. p. 951. and 976. Some may desire to know my Reasons for Springs, contracting in Frosty Wether, take a piece of Cold Iron or Steel, one or two Foot long, about ½ or ¾ of an Inch Square, heat it red hot, keep heating and well Hammering it hot an Hour or two, when you have done, measure its length exactly before it be Cold, lay it aside in the Air, where the Frost may thing it a Winter's Night, and if you measure it in the Morning, you will find it considerably shorter. Experience teacheth, that there are few Watches that have a regular Motion; for it seems impossible, that the Springs in all their parts, should be so exactly Hammered, as to draw always equally, and by what I can learn from Watch-makers, a ballsnce Watch that requireth winding up every 24 Hours, keepeth time more exact, than one that goeth a Week, before it need winding up. About Seven Years ago, my curiosity carried me to Gresham College, when the Assembly was seated, the Precedent told me, they had caused several Experiments to be made with these Instruments, and thought fitting not to commend them for Common Practice at Sea, for fear that the Errors that might happen in their use, should prove greater than the Errors in the common Practice of Navigation; but now let us handle our Subject a little more closely, and suppose that three or four of the said Watches being good work, well made, and carried to Sea in one Ship under the Command of Ingenious Men, may prove very useful towards the keeping a true Account of a Ships way on the Sea, not for finding the Longitude from our first Meridian, but to help to find your difference of Longitude every 24 Hours, or every two or three Days, as often as you observe the Latitude; provided they be not too much tampered with, keeping the Indices always moving, but never move them with your Fingers, except extraordinary occasion require it; desire not that they should always show you the true time of the Day, (you may if you please, keep one for that purpose besides,) but learn by continuance of time, to find the Motion of each Watch in a Year, or in a Month, or Day, and Hour, and having the true Theory of each Watch's Motion, with their equalities and inequalities, you may by Calculation, find at what time of the Day or Night the Indices of each Watch, (for I suppose, they may not all move just alike,) will point to such or such an Hour, Degree, or Minute, in any Meridian; keep them from being hurt by any Violent Motion, as falls, or knocking near them; keep them from Winds, from too moist Airs, and stinking Fumes; such as are when Salt Water Casks are emptied on Deck, or in a Ships Well, where Men have been Stifled; keep them very clean from Salt Water, or any Rust or Filth; let there be a place in the Ship, properly appointed for them, to hang in Equilibrio. I find in the Ph. trans. N. 47. p. 937. Instructions concerning the use of Pendulum Watches, for finding the Longitude at Sea, together with a Method of a Journal for such Watches, etc. Brother Tar, if these Automatas could speak, (as the Welsh Man thought,) they would tell thee, they hate Novices; and if thou art so, they may not bite thee, but they may happen to break thy Head, or do the some other Mischief; or in a more plain meaning, I dare not approve of their use for the difference of Longitudes, except only in an East or West Course, or in Case of some unknown Currents, use thy discretion. The Watches that are now esteemed most useful, have a Pendulum Spring to regulate the Motion of the balance; those that desire to know more of these Automatas and Mechanical Motions, may read Bishop Wilkin's his Mathematical Magic. Water-Glasses, 24 Hour Sand-Glasses, and such like Self-movers, are of no use in this Science, though I have mentioned them for Vulgar Satisfaction only; but of what use Mercurii or Quicksilver may prove in keeping time true by the regularity of its Motion in Glasses, I cannot yet inform you.    

CHAP. V. Of or concerning Longitude, by Magnetic Variation.  
THE Variation of the Compass (by which I mean the deflection of the Needle, from the true Meridian,) is of that great concernment in the Art of Navigation, that the neglect thereof does little less than render useless, one of the noblest Inventions Mankind ever attained to; I desire the Ingenious Seamen, that the Knowledge of Magnetic Variation, may be always in his great Esteem; for without it, Navigation cannot be perfect. It is my Opinion, that many Ships have been put by their designed Ports, and more Ships lost for want of knowing the Variation, then hath been lost for want of the Longitude; how many Ships in Sailing from the South-f●re-land, to the Maese, hath been put to the Northward of the Maese, for want of minding the Variation? for the like cause, some Ships have miss the Island Barbadoes, and met with other dismal Accidents. Mr. Edward Wright, an able Mathematician in his time, in the latter end of his Correction of Errors in Navigation, did write concerning the Haven finding Art, by the Variation of the Mariners Compass, but alas he knew nothing of the Variation of the Variation, or as I call it, of the Increase and Decrease of the Variation in the same place; therefore that part of his Book proved very Erroneous, by supposing that the Variation at any place, never Altered, now we know better.  
There are many of Opinion at this present time, that the Longitude may be found by the Variation of the Magnetical Horizontal Needle; I doubt the possibility thereof, from our first Meridian, for many parts of the World will afford us no Practicable proportions for the difference of Variation between them, according to their distance in Longitude; nor can the quantity of the Earth's Atraction, be easily determined in all places, besides the quantity of each Polar Atraction, for there are four, at least two, of them lie in the bowels of the Earth, and not in the Air, as Mr. Pond saith; it is probable that these Magnetic Poles have a Motion from North to South, but whether they move altogether with one Motion, or with several; whether equally, or unequally; whether Circular or Libratory; if Circular, about what Centre? If Libratory, after what manner, are Secrets as yet unknown to Mankind; That which I call the more proper North Magnetic Pole, Predominates at London; and the Period of its motion, as some say, is about 370 Years; and others write, that the Period of the Motion of the American Pole, is about 700 Years; some think the Magnetical Inclinatory Needle, always points directly to one of these Poles, which I dare affirm to be an untruth, and can prove it by Practice, Experience, and Infallible Demonstrations. The mean Motion of the Variation here at London, is about eight Minutes, or somewhat more in one Year; it is my Opinion, that most places in the World, have not altogether so swift an Alteration of the Variation, as at London; but in many other places it is a little slower, especially near the Equinoctial; for the nearer one of these Poles is to any place, there increase or decrease of the Variation may be swiftest. As the Sun in the Tropics, differs his declination but slowly, so the Horrizontal Needle, is in its slowest Motion, when it hath the greatest Variation East or West, at London; and whereas some places have above 22 or 30 Degrees Variation North-Westerly, I doubt those places will not have above 22 Deg. Variation, North-Easterly, in one Revolution of the said Poles. That all Magnetical Needles well touched, have the same direction exactly, as Mr. Sellers hath proved by many Experiments, see Ph. tr. N. 26. p. 478 but if badly touched, they may vary sometimes one or two Degrees from the true Magnetical Meridian, as often happens at Sea, as our Mariners say, that the Compass in the upper or lower beetackle, sometimes varies near half a point from each other; I have often taken notice of their expressions, and tried to find the cause; and when I found no Iron near them, (or the like Obstructions,) that might draw me off the Compasses, I have found that one, and sometimes both, had a a weak touch, or Old and Rusty, and good for nothing, except to throw overboard, etc. Five Hundred such Compasses, I believe, at this present writing, may be found belonging to the Navy, etc. A true Knowledge of the Variation is very requisite in keeping a Sea reckoning; it troubles me to think what Ignorant Persons are Masters of Ships; it is scarce two Years since, in my company, some Masters of Ships, complained of a wrong Course steered by their Comodores, who in the Night by a fair Wind, were carried too near the Borlings, even so near, that some of them were obliged, (as I was informed) to go between the Borlings and the Main. This Error happened for want of good understanding Masters in the Comodores Ships, they knew not the Variation, else forgot to allow for it; for though the true Course from the Lizard to Cape Finister be S. S. W. the Course to be Steered by Mariners Compass, at present, is S. S. W. ½ W. and S. W. by S. It is scarce one Year ago, (to this present writing,) since a Master of a— Rate Ship told his Captain, that he observed 14 or 15 Deg. Variation about 6 Leagues off of Malhago by the Stars, (there is about 6 Deg.) If I may compare a Man to a block, that same Man knew little more how to find the Variation by the North Star, or any other Star, than a Buggilug or Bracket on that Ships Quarter; I doubt whether or no, he ever saw an Azimuth Compass. When you would observe the North Star, to find the Variation in the Night, consider its distance East or West from the Pole; a Nocturnal may be of good use in this Case. England does not know how many losses hath happened for want of a better Knowledge in the Variation of the Compass through only a Pilot of a Ship: suppoie between the Bunt-Head and the K. K. or Gunfleet, if he understands not the Variation, he may in my Opinion, as well deserve a Rope, as a Branch. But the Extra. Pilots will blame me for mentioning Variation or Course in Pilot Water, where the Strength and Course of Tides and depths of Water, is of much more Consequence. My Lord's Commissioners of the Admiralty, etc. You have been pleased to give us a Form to keep our Journals at Sea; there is in my Opinion two Columns wanting in that Form, that Column for Longitude. If you please, my Lords, let it be accounted from our first Meridian; may there be added one Column called Meridian Distance by plain Chart, and accounted from the last Land seen; and another for the Variation of the Compass. I have belonged this War to Six several Rates in the Navy, and never saw an Azimuth Compass Aboard any of them; my Judgement tells me, that every Ship of War, requires at least three such like Instruments, to observe the Variation, though they ride only at an Anchor, at the North, or in the Downs; the Commissioners of the Navy have taken Care to provide such Instruments, and I believe the Masters of Men of War, may have them for ask for, (for the Boatswains Indent for them.) I believe they are ashamed, (or aught to be;) for some of them knows not what to do with them; the Instruments if well used, may be a means to help to save a Ship, and Ships Companies lives; they are good to be used for the Instruction of Ships Company and Youth, there is Education in the Navy, (little enough,) that is good: Navigation seems to decay, or decline; I wish it be not a Crime, for some Gentlemen in the Navy, to understand it. Now I will say something to my Honourable Company Masters; little do they know, how many Ships have been lost for want of a better Knowledge of the Variation; I believe I could name some, (and several in great danger by report,) but dare not fear of the Law: Captain William Wildey understood the Variation very well in my Opinion, I believe it was almost as good to him as the Longitude between St. Helena, and any part of the East-Indies. When I was in East-India, I understood what Variation there was in most Adjacent Parts so well, that I have offered in Discourse in Company, to go in a Ship that set Sail from any part of the Coast of India, bound any way, two three or four Hundred Leagues, I would keep no Account of her way for a Week or ten Days time, and any fair Day when I could have Reasonable Observations, I would a told them the place where the Ship was, as well as they that kept the most exact Reckoning, (almost as well, if you please) provided they had not seen the Land since I saw it; and this I must have done by the Lattitude and Variation observed, October the 30th, 1688. in the Offing at Cape Bona Esperance, the Cape bearing from us about North, distant 6 or 7 Leagues; the mean Variation by three Azimuth Compasses, and Nine Observations, was 10° N. Westerly; the same Year, November the 16th, Variation at St. Helena, 1° 4′ N. Westerly, the difference is 8° 56′ the the Meridian distance, by plain Chart, is 20°, difference of Longitude is 21° 54′, in Sailing directly between the two aforesaid places we raised or laid (Sea Terms,) the Variation somewhat gradually, therefore having the difference of Longitude, and the difference of the Variation given between the two said places, it may be supposed that the difference of Longitude between the places, may be found by Observation of the Variation; I answer yes, it may be nearly guessed at, and I know how to make proportions for finding the difference of Longitude by the Variation, not only between the two aforesaid places, but in many other places. But it is a Method I do not approve of, and advise the Industrious Seamen not to use it, (except in Cases of great Necessity,) but rather to learn by former Journals, or from some Experienced Artist, what Variation is at such places where you are bound to, and all along your Voyage as near as you can, notwithstanding the Variation of the Variation: I believe the difference of the Variation between any two places in East-India, may be always near the same; and not only there, but in most other parts of the World (near the Isles Azores excepted,) that are not above 20 or 30 Degrees distant asunder; this I recommend as a Secret, worthy Observation. But there are several places that will not allow of any proportions like the former; as the Downs, the Channel of England, and several Degrees Westerly, from Vshant; there is but little difference in the Variation: The Variation also altars apace in Sailing N. or S. under the same Meridian, not always gradually, but in some places faster than in others. It is found by Experience and Practice, that the Morning Variations are the greatest, as I have found sometimes near 30 Minutes; and my Opinion is, that this difference happeneth not from the Oval Form, or Eliptical Motion of the Earth, but that the Sun's Refraction is considerably greatest in a Morning; if the Sun's greatest Refraction be but 34′ as our Astronomers affirm; how came it to pass, that some Englishmen and Hollanders, that Wintered in Green-land, and Nova Zembla, saw the Sun five Days sooner then was expected, according to the Latitude of the place; but to prevent the former difference or Error, subtract the Sun's Refraction from the observed Altitude, allowing the Refraction, when the Sun is in the Horizon, to be a few Minutes more in a Morning; then in the Evening; I cannot at present Certify you how many Minutes the difference is, because I have lost my former Amplitudal Observations. It is a Fault in our East-India Commanders, that they have not used to Subtract the Sun's Refraction, etc. (they commonly take the Sun's Declination from the preceding Noon, which is also a great Fault.) Vide Astr. Ang. page 94. Tabula Refractionum Triplex. But near the Poles it is probable, the Sun's Refraction is greater, then near the Equinoctial: If the Variation of the Compass were better known, and Tables of the Variation, for all the most noted parts in the World, as Headlands, Capes, Islands, etc. The Tables Calculated to a certain Year, because of the Increase and Decrease of the Variation, and the difference of the Variation, between those places; then the Knowledge thereof: would be almost as good as the Longitude known, (some few places excepted,) and if there be 10 or 20 Years difference, in laying or setting down the Variation in some places, it matters not, provided the Year be set down, when the Variation was so much at such places, and whether Increasing or Decreasing, as for Example; suppose in the Year 1708, one should happen to be 10 or 12 Leagues South, off of C. B. Esperance, and find the Variation 12° 28′ as I told you before, the difference of the Variation between the said Cape and St. Helena, is 8° 56′ by which Rule, when you are at the said Cape, you may know what the Variation is at St. Helena, viz. 3° 32′ both N. Westerly, increasing; the like Examples may be considered of most other places in the World, that are not above 20 or 30° distant asunder, (except about the Azores.) I present you with another Method, viz. When we have such or such Variation at London, thereby to know what Variation there is in any other part of the World; for if at this present writing, I know exactly what Variation there was in all parts of the World, I believe it would be no hard matter then by knowing the Variation at London, to find what Variation there was in other parts, in future Ages. This Method I recommend to the Consideration of the Ingenious, as also to see, if they can find the Lattitude and Longitude of each Magnetic Pole; but some People with think, I have writ nothing to the purpose, if I do not tell them wherefore there is little or no Variation about the Azores; the quantity of the Earth's Attraction, is but little in some places, two Degrees or three, may be the most, and in most places at Sea, the more solid parts of the Earth, have no Attractive quality, for then the Needle is without the Command of the more Magnetic Vigour of the Earth, as for Example, in the Year 1688, about 8 or 10 Leagues at Sea, in the Offing at C. B. Esperance, when we had about Ten Deg. Variation. I was told by Experienced Artists, that there was not above 7½ or 8 Deg. at most Variation Ashore, or in the Harbour at the Cape, which is a very quick Alteration, for any where thereabouts, above Ten Leagues off at Sea, in Sailing on any point of the Compass, 10 Leagues, you will not alter your Variation above 12 or 14 Minutes at most: The like Experiment hath been proved on the Coast of India, and in the Meriterranean. Therefore it is evident, that Promontories, Capes, and Headlands, draw the Compass a little, and that only when you are near them, within 10 or 12 Leagues; besides the Earth's quality of hindering it from pointing to its Poles; there are four Poles (at least) which have a Sympathetical Virtue, with the Magnetical Needle, to which it naturally inclines; two of them that are furthest within the Earth's Orb, I call its more proper Poles, and the other two in the Cortex of the Earth, the Magnetical Poles; these four Poles draw the Needle, some one way, and some another, so that they hold it amongst them, each requires a share; but that Pole Predominates most, to which it is nearest: The Isles of Azores I account lies almost between the two proper Poles, which two Poles always (for aught I know,) bear N. and S. from those Islands, for there it is without the Attraction of the Magnetic Poles; but I believe there is some Variation at the Azores, and will be more in time. If the Magnetic Needle were very high up in the Air, it would have no respect to the Earth, or to any Poles but its own, or Centre; this is my Opinion. The cause of the quick Alteration, and great Variation, at Newfoundland, and some other places; I would also tell you my Opinion, but I am afraid of seeming tedious, with Tautologies.  
In using Azimuth Compasses, take care the Chart Librate well in the Box, and that the point of the Brass Needle, on which the Chart Librates, be as exact as may be, in its proper place or Centre of the Box; trust not to one Observation, when you can have the Medium of 5 or 6 or more, nor to one Amplitude, when you may have the mean of 3 or 4 Azimuths; mind to subtract the Sun's Refraction, etc. Suffer no great Guns, or other Iron, too near your Compasses; those are best that have the quickest Motion, you may try the points of the Needle, by seeing what Iron they will take up, but be very careful, and use it not often, for you may spoil the Needle. With a Needle and round Loadstone, may be perfom'd many Natural and pleasant Conclusions; but to think, that such a Terrula, (as they call it,) hath or represents the like Magnetic Force or Power, in all Species as the Earth, is a weak and ridiculous Opinion; whereas it may be thought in these parts of Europe, there is no occasion for carrying Azimuth Compasses to Sea, because it may be supposed most Masters, knows what Variation there is in most Adjacent places; it is a mistake, for the Major part, nay ⅔ of them, I believe, knows little or nothing concerning it, as I could prove by manifest Examples; If I were to declare what I know, and sometimes been an Eye witness to; but Truth ought not to be spoke at all times; besides, I am not willing to disoblidge some Persons, that might think I reflect too much on them; those Masters that have understood something of the Variation, often forget it, for want of Azimuth Compasses, or for not being obliged to give an Account thereof: I have known some Masters of Ships, that knew, (by hear say from others,) that in such places, there was about half a Point West Variation: I have asked them how they accounted it from what point of the Compass, (pretending myself Ignorant,) they have answered, I might Account it from N. or S. E. or W. or from any point, it was always Westerly; neither do they know how to estimate the Variation in their Reckonings; but it may be objected, how can the Masters be so Ignorant, that go and come well from Port to Port; I answer Thickie, West-Country-Man, lock zure, Life and Soul Man, can carry a Ship to Newfoundland zure, and near a word a Book zure; this is by long Experience and Custom, not by Art; I have seen the Blind lead the Blind a Begging; I knew two Blind Men in Cochin, that would go very readily to any House in that Town, and I have sent one of them an Errand two Miles into the Country, but they were both born Blind; therefore by long Experience and Custom, they naturally know most Adjacent places. As to Masters or Pilots, their carrying Ships in and out of Harbours, and for the Coasting part, (when they can see the Land,) I have nothing to say against them: And if a mischance happens, you will rarely find any of them without a lying Excuse to salve their Ignorance. But it may be said, the Masters make Observations, and keep a Reckoning, yes, so they do, and a very bad one oftentimes. I will acquaint you how they do, that knows not how to allow for the Variation, as they ought; it is likely they can tell, whether they have Sailed between the South and the East, or S. and W. or N. and E. or N. or W. having wrought their Days Work by Log and difference. Lattitude and Departure, they find what dist. the Ship hath run by Log. so having that dist. and diff. Lattitude by Observation, they can find, (as they think,) the Departure, without allowing for Variation; and this kind of Reckoning, is the cause of so many great Mistakes, in their Easting and Westing; for the Log. is but a false supposition, to find the distance run, as hath been Experienced in one Fleet, where some have had 70 Miles on the board, some 80, and others about 90, the same 24 Hours, and all the while, not above a League asunder. Now I will acquaint you with the best known Common Method, for keeping an Account of a Ships way on the Sea. Be as curious as possibly you can, in observing the Sun's Meridian Altitude, or for want thereof, some known Stars to find the Lattitude by; if you observe with Davis' Quadrant, see your Vanes very carefully and exactly placed, especially the Shade Vane; when the Horizon is very clear, observe somewhat close, when hazy a little more open; these cautions I give, that you may observe every Day alike, and thereby the better to Judge of your true difference of Latitude by Observation, then work your Days work, and find what Course the Ship hath made, as near as possibly you can find it, by allowing for Lee-way Variation, etc. (or lying by, or any other Impediments, as Tides or Currents, or a great Sea,) and having the true diff. Latitude by Observation, and the Course given, you may easily find the distance run, and departure by the common Method, and difference of Longitude by Mercator, etc. It is my Opinion, that the use of the Log. is good to help to find the Ships Course, though there are some able Artists that use no Log. but now to our purpose again, as for Mr. Bond's Longitude found, (as he called it) he limits his Hypothesis to the City of London, affirming himself (as he had a great deal of Reason,) that the same Calculus is not sufficient for other places, whereby it appears, that his Rule is far short, of the so much desired general one. The following digression may please some Capacities: Famianus Strada, in the Vein of Lucretius, writes, viz.  
Magnesi genus est lapidis mirabile, cui si  
Corpora ferri plura Stylosve admoveris, inde  
Non modo vim motumque trahent, quo semper ad Ursam,  
Quae lucet vicina Polo severtere tentent.  
Verum etiam, etc.  
Outinam haec ratio scribendi prodeat usu;  
Cautior & citior properaret Epistola, nullas  
Latronum verita Insidias, fluviosque morantes,  
Ipse suis princeps manibus sibi conficeret rem,  
Nos soboles Scribarum emersi ex aequare nigro  
Cousecraremus Calamum Magnetis ad Oras.  
But this Invention is altogether Imaginary, having no foundation on any real Experiment. The Royal Society in London, have a great Loadstone found in Devonshire, that will move a Needle, at 9 Foot distance: Some Persons may happen to Read this Chapter, that understand not Navigation, and think that most Ships are lost for want of understanding the Longitude, or the Variation; I say, I believe such Accidents may have happened, but very rarely; for most Ships have been lost by many other Accidents, as Storms, or the like; Example, our great Loss by Storms lately in the straits of Giblaterra, and the late Hurricane at Barbadoes, in which Ships I believe, were some as able Seamen, and Experienced Artists in Navigation, as the World did afford. The finding the Lattitude by the Inclination of the Inclinatory Needle, is at present thrown out of Doors, as of little or no account, as well it may, if we will be such Novices, as to confine the Inclinatory Needle in a narrow Cycloid, as commonly it is, by which means, it becomes useless at Sea, and not manageable; therefore it ought to be contrived, to hang in Equilibiro, so that it may have a free Circular Motion, any way on its Centre of Gravity, and then it will much easier show the Inclination, and Variation also, if need require it; and if the Theory of its Inclination were known, (all the World over) we might also find the Latitude by it.  
The following words were forgot at the end of the 4th Chapter, viz. Our Countryman Mr. Watson, who made an Ingenious Clock (for our late Queen) which showeth the Celestial Motions; and Monsieur Didiers Celestial Globe, showing the apparent Motions from East to West, and from West to East, of the Sun, Moon, and fixed Stars, see Ph. Tr, N. 136. p. 895. I think a Globe may be projected, and made like the later, that may show Latitude, Longitude, Sun or Stars, Horary distance from the Meridian, and Variation, etc. But it would be too costly for ordinary Uses, and nothing hinder its Truth or equal Motion, more than the different Temperatures of Air and Wether, though we may attribute something to the goodness of the Springs and Oils.   

CHAP. VI Longitude by the Moon's Motion, by her Conjunctions or Eclipses, and Apulses to fixed Stars; of her Illumination by the Sun.  
THE Question is yet unresolved, which time ought to be called the true Conjunction or Opposition, whether when the Sun and Moon are in one Line perpendicular to the Ecliptic, or perpendicular to the Orb of the Moon, or when they are equally distant from the Nodes. Mr. Shakerley's Tabulae Britannicae, precept, 15. pag. 67.  
Let us Correct this Learned Mistake, and agree with most Astronomers, that it is always New Moon, when the Sun and Moon have both one Longitude, from the first point of Aries. The mean motion of the Moon, in one Natural Day is 13° 10′ 35″ her mean motion from the Sun in one Day, is 12° 11′ 27″ but in her motions, she hath many inequalities, for which purpose, Tables of her motions may be required; I refer you to Astronomia Carolina, Astronomia, Harmonicae, Astronomica Instaurata, Tabulae Britannicae, Astronomia Anglicana, Cursus Mathematicus, Rudolphus' Tables, not forgetting Mr. Newton's, and Sir Ionas Moor's Tables; yet amongst them all, the Theory of the Moon's motion, remains In perfect, and not easy to Calculate; many able Mathematicians have writ concerning finding the Longitude, by the Moon's motion: Mr. Norwood writ something, but it was never Published; I have been informed, his Method was by the Moon's motion; concerning which, he writ a large Tract of her motion, and contrived an Instrument for taking her distance from fixed Stars. Mr. Streets way is unknown to me, but we suppose his way by the Moon's motion also, by his contriving an Instrument, for taking Angles by Reflection; I have seen the Instrument, but he could not bring it to perfection, which I gather from those who have had some Cognizance thereof; see his Appendix to Astr. Car. I have seen a Pamphlet writ by John Herne, wherein his Method for finding the Moons Southing, is very Erroneous, as also, almost all the rest of it; you may believe the like of Theakers Book, and Wooden Tools; these I mention, that Seamen be not deluded by such Foolish Tools and Pamphlets. There is a late Author saith, viz. find the true Moment of time, in which the Moon comes to the Meridian, and thereby the Longitude of any place may be found after this manner, etc. in answer thereto, Sir, I assure you, the Longitude is not to be found after your manner, nor by any of your Methods, till better Taught. I presume I know better than yourself, what belongs to Meridian Altitudes, especially at Sea; and if you please to learn from me, that when the Sun hath South Declination, 20° or 23°; and in North Lattitude, 50 or 60° it is too difficult a matter to find Noon or Midday, by any usual Sea Instrument, within two or three Minutes of time; our observers commonly begin to observe a little before the Bell strikes Seven, and in the aforesaid Latitudes, it is common to observe till a quarter of an Hour past 12 a Clock, before they can perceive the Sun falling (as they call it,) but when the Sun is within twelve Degrees of your Zenith, then be very quick to attend, or else you may lose your Observation; the like of the Moon, or any Star; any other time of the Day is more easy and true to be found at Sea, than Noon. An Old Experienced Navigator pretended to know, how to South the Moon by the North Star, on the Meridian; I asked him how often he hath seen the Moon and North Star on his Meridian, both at one time, as also how we must do in South Latitude, to North the Moon; and if it were possible to find the time of Moons Southing or Northing, it is to no purpose, to expect the Longitude thereby, considering we can have but one Observation in 24 Hours, besides the Error of accounting her motion in our first Meridian; there is no Calculation as yet so exact in any Almanac or Ephemeris, that tells us the true time of the Moons Southing, in any Meridian without Error. Mr. Newton writes, that from the Error of one Minute of an Hour in the Moon's motion from the Sun ariseth an Error of 7° 12′ in the Longitude of the place propounded, and in the motion of the same Moon, from any fixed Star, riseth an Error of 6° 48′ and moreover (he saith,) it is evident, that if the Errors of both places be not of the same Denomination, and lesser than one Minute of time; the Error of Longitude cannot be less than then 13° etc. The Moons mean motion being but 13° 10′ 35″ is little in proportion to 360° therefore the two Objections are very considerable; however, as I am a Favourer of the Longitude, by the Moon's motion, I will undertake to solve one Objection, and propose how the other may be solved; then as to the first, I answer, that I know how to find the true time (when we can have Reasonable Observations) of the Day or Night, to one or two seconds of time; and if I Err 4 or 5 seconds, it matters not, others may observe as true as I, if they be careful; in the Practic part of Navigation, it very often happens, that one Error Corrects another, as for Example: Suppose we Err 4 or 5 Minutes in the Lattitude, 2 or 3 Minutes in the Suns R. A. (or Dec. in the Day time,) 3 or 4 Min. in the Stars R. A. and about as many in its Altitude; it is ten to one odds, but these Errors, (if not much greater,) will so help to Correct one another, that you will come very near the true time of the Day or Night; and what Blockhead will trust to one Observation, when he can have the mean of 6 or 8 Observations; I account him an Ignorant Observer, that Errs above 10 or 12 seconds of Time, Day or Night; trust not to Mr. Seller's, Colson's, Norwood's, Newton's Tables of the Suns R. A. for for they are of no use in this case. In observing the time of the Night, be very careful to find the Suns R. A. true, for want of good Tables of the Sun's place, and R. Asc. Tables of the Sun's place and Declination may serve, with a little more trouble, for Example, Anno 1696, March the 19th, at 3h A.M. 30° to the Westward of our first Meridian; I desire to know the Suns R. Asc. The Tables of the Sun's place and Dec. in most Books of Navigation, wants Correction; Mr. Parkers Ephemeris, for this Year, gives the Sun's place at Noon, in our first Meridian, 9° 44′ ♈ ☉ Dec. 3° 51′ N. but 30° to the Westward, the ☉ place at Noon, will in 9° 49′ ♈ and the ☉ Dec. 3° 53′ N. if you consider the Diurnal difference of the ☉ place and Dec. you will find his place at the time proposed, to be in 9° 27 ♈ ☉ Dec. 3° 44′ N. then having the ☉ present Dec. say, as Rad. to Tang. Comp. 23° 29′ ☉ greatest Declination, so is the Tang. 3° 44′ the present Dec. to the Sine 8° 38′ the ☉ R. A. from ♈ at the time and place proposed; but there is a readier way, having found the ☉ place, Vide, Astr. Car. Tabula Ascensionum Rectarum, and against the ☉ place, is the ☉ R. Ascention, etc. This Example I thought fit to add for Seamens Instructions.  
In answer to the second Objection, that the Theory of the Moon's motion is false; it is not long ago since Mr. Thomas Street lived amongst us, who said (as I have been informed,) that he was capable to perfect the Theory of the Moon's motion, so that her place might be as truly found by Calculation, as any of the rest of the Planets, if he had Encouragement; 'twas ten thousand pities he had not, but such is our English Ingratitude. There are now living in England, two Men, that I believe are capable to perfect the Theory of the Moon's motion, which if either of them will be pleased to undertake, as also to furnish us with large Maps of the fixed Stars, such as Dr. Sprat is pleased to mention, Hist. R. S. p. 190. I may be capable to Practise and Instruct others in the Practic part of Longitude at Sea; or the Ingenious may put it to Practice, without my further Assistance: Tables of the Moon's place, right Ascension, and Declination, would be pleasing Easie, and more Intelligible to our Seamen, if they be truly Calculated for Noon or Midnight, in our first Meridian: But I think I can find as great Objections, as either of the former; it is very difficult to contrive an Instrument (useful at Sea,) for taking the Moons true distance, from fixed Stars, for if you Err but one Minute of motion in the distance, it will produce an Error of about 28′ in Longitude; and if the Stars place which you take your distances from, happen to be one or two Minutes false, the Error will be so much the greater; also Idleness is the root of Ignorance, and many other Evils: Our Mathematic Schoolmasters, that Teach Navigation, most of their Scholars when they come to Sea, are half to begin again; a Seaman hath much Nightwork, as well as Daywork, it is convenient to go to School at Nights, to learn to know the Stars, how to find the time of the Night by Observation, and how to find the Moon's place by Observation, I mean to Practise it, for Examples are best Precepts; many able Mathematicians have writ concerning finding the Longitude by the Moon's Eclipses, concerning which, you may find many Examples in Ph. trans. of the Royal Society, as also in a new System of the Mathematics, by Sir Ionas More, in the Doctrine of the Sphere, to which I refer you. It is more difficult to find the Longitude by an Eclipse of the Sun, then of the Moon; because that of the Moon happeneth at one and the same time, all over the World, but an Eclipse of the Sun appears various in the various parts of the Earth; the duration of a Solar Eclipse, appears longer in some places of the Earth, then in others, therefore the end of a Solar Eclipse, happeneth not at the same Moment of time, all over the World. The Superior Planets suffer no Eclipses, when the Earth comes between them and the Sun; because the Conical Shadow of the Earth cannot reach them.  
Anno 1688, October the 14th 12° 40′ Mer. dist. West. (plain Chart) from the Mauritius, I observed the Sun Eclipsed, at the end of the Eclipse the ☉ alt 27° 35′ ☉ Dec. 12° 3′ S. Lat. 31° 6′ S. will give the Hour of the Day, 10h 33′ 48″ A. M. In our first Meridian, the end of the Eclipse, happened by some Calculations, at 7h 15′ A. M. the difference is 3h 18′ 48″ converted into Degrees and Minutes, gives 49° 41′ Longitude East, from our first Meridian. The Penumbra of the Moons Disk, signifies little or nothing; Astronomers make more ado about it then needs. Brother Tar, have a care of peeping on an Eclipse of the Sun through a Telescope, for endangering the Eyesight, as I knew one Captain Norgrave did: I will tell thee the best way I know for observing Eclipses of Sun or Moon, take a Looking-Glass, set it before thee, so that thou mayest see the Sun or Moon by Reflection on the Glass, then with a Perspective, or two or three Foot Telescope, look on the Looking-glass for the Sun, etc. or you may have smoked or red Glasses, to save the Eyesight. That the Longitude may be found by the Moons Eclipsing any of the rest of the Planets, or any known fixed Stars, is as certain, as by Eclipses of the Sun or Moon: If Mr. Halley was capable to observe the transit of the Sun and Mercury, as appears by these words, viz. Schema Solis ad ingressum Mercurii St. Helena, Anno 1677, Octob. 28th, 9h 26′ 40″ P. M. surely with ordinary Telescopes, we may be capable to observe, when a Star begins to Culminate and limerge in (or near) the Moons Disk. Of or concerning Longitude by the Moons Approach and Apulses to fixed Stars, this some think will be the most Practicable way for Seamen, (yet mentioned) when the Theory of the Moon's motion is better known. Mr. F. hath ingeniously written to this purpose, in his Doctrine of the Sphere, Annexed to Sir Ionas Moor System Mathematics, to which I advise you. It is said, that the Moon moveth swifter at New and Full, then at Quarters. To find the Moon's place by Observation, the most Ingenious Mathematical way is, by taking her distance from two known fixed Stars; see Mr. Seller's Practical Navigation. The Doctrine of the Sphere, problem 20. but few Seamen understand the Affection and Solution of Spherical Triangles, that way is tedious and troublesome; I know Seamen care not to take so much pains, besides the trouble of finding the Moon's Parallax; and contriving Instruments for taking her exact distances from fixed Stars; the Moon's place may be found Geometrically, by Scale and Compasses; or on large Maps of the fixed Stars; first, knowing her distance from any two known Stars in that Map; but an easier way is, if we could contrive an Instrument to take her difference of Longitude from any fixed Star, at one distance, which I think not impossible, especially when she is near the Meridian, or Nonagesima, and then is the best time of Observing. Illuminatio Lunae per Solem. see Mr. Sellers, his Atlas Coelestis, in the Figure taken from P. Gassendi, Institutio Astronomia, lib. 2 cap. 26. etc. The Moon being a round Body, and receiving its Light from the Sun, it follows, that always one half of it, yea, somewhat more, must be enlightened by him; for seeing that the Sun exceeds the Moon in bigness, and that the bigger Spheres always enlightens above half the less, it does follow, that above one half of the body of the Moon must always be Illuminated. And seeing that the Moon altars her position, and in running about the Earth, doth variously Face the Sun; it must needs be, that according to its various Access to, or Recess of the Sun, less or more of the Illuminated half, will appear to us; which Variations of her appearances, are commonly called her Phases. The Moon is never less Enlightened, then when she is at the Full, or in opposition with the Sun; because when she is Full only, that part towards us is Enlightened; whereas when New or in Conjunction with the Sun, she is wholly Illuminated, that part which is then toward us, being Enlightened by the Earth, and the other part that is turned from us by the Sun. For the Moon doth not only borrow her Light from the Sun, but receives some weak Illustration from the Earth; because the Earth being an Opake Body, must of necessity reflect part of her received Light; and forasmuch as the Earth is bigger than the Moon, consequently more Light must be derived from the Earth to the Moon, then from the Moon to the Earth. This is confirmed by Experience, because this Secondary Light, as Galilaeus calls it, after the first Quarter, quite vanisheth, by reason of the Moons being too far distant, and without the bounds, to which the reflected beams of the Earth reach. Le Grands body of Philosophy, see Fig. 30. part. 5. Chap. 20.  
Now if the difference of the Moon's Phases, or the quantity of her Illumination by the Sun, be mensurable by Instrument, than this Method may happen to prove good for finding the Longitude. In the Ph. tr. N. 29. p 451. is a Description of an Instrument for dividing a Foot into many Thousand parts, and thereby measuring the Diameters of the Planets, to great exactness, etc. Also see Ph. tr. N. 21. p. 373. concerning a way for taking the Diameters of the Planets, and for knowing the Parallax of the Moon, etc. The consideration hereof I humbly recommend to the Ingenious, more especially to the Royal Society of London.  
I had almost forgot; I desire you to take Notice, that one good Map of the fixed Stars, may serve for ever, without Alteration (save that it may decay in time, which bad usage, or a little Alteration, of the Sun's Declination, which is scarce worth our notice in one Hundred Years,) provided that either the Equinoctial, or the Ecliptic Line, (in those Maps) be made to slide upon it, and then it is only sliding them a little every Year, according to the Praecession of the Aequinox; the like aught to be considered in Celestial Globes and Planispheres; also one good Table of the fixed Stars places, may serve for ever, by adding only the Praecession of the Aequinox.   

CHAP. VII. Longitude by Jupiter's Satellites.  
GAlilaeus, in the Year 1610, the 7th of January, at the first Hour of the Night, discovered 4 less Planets about Jupiter, which like so many little Moons are whirled round him. Those of them which are nearest to Jupiter, move more swiftly, than those which are more remote. The Revolutions of those Secondary Planets are thus Calculated; the innermost Satellite, revolves to the Sun in 1d d 18 h 28′ 36″ so precisely, that in 100 Years, the difference is not sensible; The Periods of the Revolutions of the other Three Satellites to Jupiter's Shade, are as follows.  
 d h ′ ″ ‴ Period Secundi. 3 13 17 54 3 Period Tertii. 7 3 59 39 22 Period Quaerti. 16 18 5 6 50  
The Attendants of Jupiter, whenever they enter the Verge of his Shadow, do suffer an Eclipse after the same manner, as the Moon doth, when she dips in the shadow of the Earth, and are totally deprived of Light, as being Opake Bodies, which borrow their Light from the Sun. The 3 first of these in every Revolution, produce 4 Eclipses; the first, when the Satelles enters into the Rim of Jupiter; the second, when the shadow of the Satelles, doth darken the Rim of the said Planet; the third, when the upper part of Jupiter, at his Elongation from us, doth hide the Satellites; and the 4th, when the Satelles dips in the shadow of Jupiter, so as that the first Satelles, within the space of 7 Days, doth effect 16 Eclipses; the second 8, the third, 4; so that all of them together, produce 28 Eclipses; the fourth, after that he hath reached the Nodes, doth make 4 Eclipses in 17 Days; but when near his bounds, he never suffers a defect of his Light, because his Latitude is so large, that he never touches the Rim of Jupiter, or reacheth his shadow. These Eclipses are of great use, in order to the determining of the Longitudes of places. Le Grand's Philosophy. But the Eclipses for our purpose, is only the Immersion or Emersion of the Satellites, in the Verge of Jupiter's Shade. Many there are who prefer this Phaenomenon before others; because the Satellites of Jupiter have no sensible Parallax; and in every position of Jupiter above the Horizon, (in the Night, when Wether permits,) are conveniently to be observed, with a Telescope of 12 or 15 Foot long, a fine danceing Instrument indeed at Sea, especially in a Gale of Wind, (than not manageable,) to look through a Tube of 15 or 18 Foot long, which hath only two Glasses in it; and I have been troubled at Sea, to find an Object with a Perspective of 1 Foot and a half long, which hath only two Glasses in it; therefore at Sea, for the better finding an Object, we commonly use Telescopes with 3 or 4 Glasses in them, of three or four Foot long, (the Telescopes) through which I have often looked for Jupiter, but never could see his Satellites through one of that length; and what must we do for the Longitude, when Jupiter rises and sets Cosmically or Acronically, as in September, this Year: but we will suppose the best, that the Wether should be so fair, and Sea smooth, that we may possibly get Observations two or three times in a Month, indeed it would be a very great help and satisfaction to us, if the Observations proved good. Mr. Colson, an able Mathematic Teacher, told me, he had near one Hundred Observation by him, made at Sea, with a Telescope of 6 Foot long, which he contrived with a convenient apparatus, for managing it. I have one 5 Foot long, in which I have seen the Satellites; keep your Glasses very clean, especially the Object Glass, from Mists or Dews. I desire to know what we shall do for Tables of Jupiter's Satellites, for Years to come, (always for four Years at least,) Mr. Parker in his Ephemeris, hath inserted a Catalogue of the Eclipses of Jupiter's Satellites visible, under the Meridian of the Observatory, (I suppose he means the King's Observatory in Greenwich-Park,) or near it in the Year 1696. But what must they do for such Tables every Year, that are in the West and East-Indies; a late Author in his Book Printed Anno 1695, hath inserted two Years Tables for the time past, viz. 1693 and 1694. borrowed perhaps out of some old Ephemeris; it is well he said something of the time past, its likely he knew little or nothing of what was to come; yet some of our able Astronomers revile and reflect on our Seamens Ignorance, because the Seamen, (as they say,) cannot find the Longitude, Indeed I think our Seamen have most cause to rail at our Mathematicians, that have done nothing, (as I know of,) to any purpose, for the Encouragement or Improvement of Navigation, for almost 20 Years past, (except a Tide Table,) as I shall prove by Sellers' Practical Navigation, the most useful Book for Seamen yet extant, and the Impression worse now, than it was almost 20 Year ago; compare the Tables of the Sun's place and Declination, in the 7th Edition of the Practical Navigation, with Tables of the Sun's place and Declination in Parkers Ephemeris, for this Year, and you will find considerable difference; and that the Impression was better 18 or 20 Years ago, I prove by Pag. 330, viz. A Table of the Variation of the Sun's Declination, to be applied for Years to come, etc. If the Tables were the same, as in Anno 1680, or thereabouts, we might by the said Table of Variation, have Corrected the Tables of the Sun's Declination, but there is imposed on us, new dates of Years, etc. The aforesaid Book wants Correction very much; there is wanting in it a larger Table of difference of Latitude and departure, such a one as is in Colson's Calendar; the Tables of the Sun's right Ascension, aught to be more large, and Calculated to Degrees and Minutes, to a certain Year, etc. Pardon this Digression, now to our purpose again; since we are unfurnished with fitting Tables of all the said Satellites, I recommend you to the best I know of, viz. See Ph. Trans. N. 214 p. 237. to 256. Monsieur Cassini, his New and Exact Tables for the Eclipses of the first Satellite of Jupiter, reduced to the Julian Style and Meridian of London, etc. But in Calculating the Eclipses of the Satellite by the said Tables, there sometimes happens an Error of 3 or 4 Minutes of time, I believe I know how to Correct that Error, (though it hath baffled the Ingenious,) and would a done it here, if it had no required Figures or Cuts for Demonstration. Saturn hath also five Satellites attending him, but are not accounted so worthy our notice for the Longitude, as the former, therefore I pass them in Silence.  
The Sun, Jupiter, and all the rest, (except the Moon,) of the Planets, have a Circumrotation in their own proper Vortex, as Telescopial Observations testify, by several spots that appear in their Phases. Perchance it may be said, why have not I furnished this Book with regular Tables of the Moon's motion, and of Jupiter's Satellites: It would be a very unreasonable demand to require them from a Man that hath wanted both Books and Instruments, (till now) also conveniences and opportunities, having only a small cabin, sometimes not high enough to stand upright in, nor my length to lie down in; insomuch, that I have been obliged to borrow both Books and Instruments, for the common Practice of Navigation, besides the Circumstances of my Employs, and many other Inconveniencies, that might and did attend such Studies and Observations. I will conclude this Chapter with the following words, which I take, to be the Ingenious Mr. Flamstead's, viz.  
As by Lunar Eclipses, so also by the Eclipses of Jupiter's Satellites, the difference of the observed Moment's of the Occultation or Emersion of a Satellite from his shadow, noted carefully in two distant places, will be the difference of Meridian's, betwixt these two places in time; but I cannot hope that this Method shall prove of much use to the Ingenious Seamen, because the Observations require long Telescopes, which in a Ship will hardly be manageable; nor can we expect to find the difference of Meridian's, by one only Observation of a Satellite Eclipse, as we have hopes we may by a Lunar, by reason that as yet, the inequality of their motions, and the time required for the transmission of Light from the Planet to our Earth are unknown; nay, their mean motions are scarce so exactly stated, but that we may Justly suspect them Erroneous; omitting these therefore, the best Method for the discovery of the Longitude, will be in my Opinion, (I am dubious, he is now of another Opinion,) by the Moon's Apulses to, or observed distances from fixed Stars, upon which Accoun I would recommend the Improvement and Correction of her Theory, with the Doctrine and Construction of Apulses, to the Study of the Ingenious Astronomer and Seamen. Humanum est Errare, I had almost forgot, Mr. Newton hath contrived an Instrument for his own use, to see Jupiter's Satellites by reflection, on well polished Mettle; the Instrument is about 15 Inches long, as some say, other 9 or 10 Inches, and call it a reflecting Telescope; I am informed it is of little or no use. I have not seen any of them, therefore can give you no better Description. I also add, To tell some Masters of— of Jupiter's Satellites, is like telling a Story to a Bear; they know better how to manage a Cann of Phlip. The setting and well-manageing a Telescope, is of great Consequence.   

CHAP. VIII. Conclusion.  
OMnia probate, quod bonum est tenete. That which I have written in this Book, I designed for the public good of Mankind; in which I hope I have not offended God. If any Arts or Sciences, Commerce or Trade, be Good and Just in their kind, than what I have writ concerning Longitude, is Good and Just in its kind, that is, if it be not Abused: Though there was an Officer in the Navy, (as I was informed,) who Cursed and Damned the Man that should discover the Longitude; thou Old, Inveterate, Rusty, Musty, Filthy, Cankered, Carnal Devil, for Cursing down upon thy Marrowbones, (if thou hast any,) and ask God Almighty forgiveness for thy Sins, know that it it is not in thy Power to Damn any Man but thyself: God who suffered the Earth to be Inhabited by Angels, for an infinite number of Ages, before he Created Adam, and then expelling them hence for their Wickedness, and turning them to Devils, gave this Globe for a dwelling place to Men; grant that the enormous Crimes of Mortals, may not provoke him to Exterminate our Humane Race, and restore the Devils to their Ancient Habitations, Tur. Spy. Vol. 3. Pag. 359.  
But as for that one Man, (I doubt there is more such,) aforesaid, I believe He did not speak it then out of Ill-will to me, but to some other Person, or rather rashly or unawares; I believe his meaning at that time was, that this ungrateful World did not deserve so great a Blessing, or so worthy a Science. I am thinking what my Country will be pleased to say of me, if they call me ginger, I give very little Credit to Judicial Astrology, nor do I profess any such deceitful lying Arts; if Maggoty, it's an Expression for Fools, and their bolt is soon shot; if Star-Gazer, I answer, a Star-Gazer is better than a Booby; some may Envy me, some Laugh and Scoff at me, (a common Method to solve their own Ignorance,) others Mock and Ridicule me; so our Predecessors did at Columbus, when he came hither to offer them the discovery of the World, and ought not they to have been Recorded for F— s, as (some say,) the Pope was, that Anathematised the Bishop of Scrasburg, for writing of Antipodes. But now I think on't, I have a reserve which they are not like to know yet a while. As I have heard say, the Venetians have offered Rewards; the States of Holland (as I was informed,) some Years ago, took this Science so much into their Consideration, that they offered Ten Thousand Pounds, to any Man that was capable to discover it; Thomas Axe, an Englishman, left a Legacy of One Thousand Pound, (never to be paid I think,) to any Person that should discover the Longitude, within the space of Ten Years after his Decease, if his Wife and Child died Childless in that time; besides, it is to be approved of by the four Professors of Geometry and Astronomy, in Oxford and Cambridge, for the time being, and at least twenty Experienced Masters of Ships, that shall have made several Experiments thereof in long Voyages. Affidavits are to be made before the Twelve Judges of England, etc. He died in the year 1691, and I think took care enough, that the said one Thousand Pound should be Irrecoverable; indeed, I have little better Opinion of either the Venetian or Dutch Gratuities; States may be mistaken in their Policies; God Almighty never ordained that this Science should be well known to the World, by fraudulent means, but if their designs be real, (as you may suppose,) where is the Encouragement? I know not how to recover my Cost and Charges, though I have laid (and shall the rest by and by,) most of the ground work at my Charge; where is the Money to raise and perfect the Work? There is— Pounds wanting, present Pay, towards the Charge of making two wonderful Instruments, for the first making of the Instrument, will be very Chargeable; one of them may prove far more chargeable than the other, and yet when it becomes common, it may be sold at a low Price, I Judge under fifty Shillings; yet before the Instrument can be brought to such Perfection, as to show two or three Examples, may cost several Hundreds of Pounds, and for aught I know, take up most part of a Year, to accomplish them, it is an Instrument that must be truly Cut and Polished, a small matter of a false sweep or stroke may quite spoil it, and make it good for little or nothing; therefore one Hundred of them may happen to be spoiled before we can get the right Art of making them; neither of them will suddenly be fit for Seamens Practice, because the Natural motions that one of them is to show, are at this present writing, I believe, unknown to the World; therefore reasonable time is required to Calculate the Theories of those motions. I will give you a brief Description of one of the Instruments, it is one or two, I know not well which to call it, it is round, its Diameter about 8 or 10 Inches, may be a good size, it is not altogether flat nor Convex, nor Concave, nor Globular, it contains several Circles exactly swept even, to a Hairs breadth, the Areas of each Circle, must have their just proportions, but have no visible point for a Centre, nor are the Circles Cut and raked in its Surface, but aught to appear above it; it hath no strait Lines, save only in its Frame of— which must be divided into 360 Deg. and subdivided, etc. it is Scioptrick, Dioptrick, Catoptrick, P— S.— K. and P.— H— K. and whereas most Secrets seem most wonderful before they are discovered; this Instrument will seem most wonderful, when the best Description is given of it, and when put to common use; to give a true and perfect Description of its secret properties, like the Loadstone, may puzzle the Oxonian Sophist, or Parisian Sorbonist; but this I give for one Aphorism, Natura nil agit frustra; I hope it may answer our designs in the Longitude, nisi Argentum agit frustra; but all is in the Power of God; it is an Emblem of Trinity, Trinity in Unity, and Unity in Trinity. Indeed I have but little more Knowledge of it, then is in the Idea of my Brain, for the Experimental part is most wanting, but the World may believe, that I can produce sound Principles and Evinceing Arguments for my Opinion, else I should not have made it so public; delays are dangerous, Ars longa, Vita brevis; but if it please God, I should be glad to live to see this Art come to such Perfection, as to be fit for Seamens Practice, during the natural Course of my Life. Reader, believe if you please, that he that writ this, could a writ more, and more to the purpose, if he would; I think it enough for five or six Weeks Time and Study, and abundance too much, if for a Gratuity, I may suck my Paw, or only my labour for my Pains; future Ages may be more Competent Judges, but my Mind will be easier when this Book is Published, because therein I have done my Duty, and eased the burden of my Brain. If in this Treatise have seemed to reflect on any Person, it is my Dialect, I desire their Excuse; I Envy no Men: Envy and Ingratitude, is most natural to some, whose Duty it is to understand these things and their Capacities, cannot reach them. If any Person is minded, or can, or will undertake to Correct or Amend what I have writ, I wish them good success; I desire them to own what they borrow, and not to reflect without just cause; it is difficult to write such a Book as this is, (I think it is the first of this nature,) without Faults; it is likely I myself may find some in a Years time, that if I were to write over again, I could amend; I dare affirm, that this Book contains some estimable Expressions and Methods, fit for Seamens Knowledge and Practice, and such as have not been formerly Published; there are some Persons in England, whose Duty it is (being paid for it,) to improve Navigation and Astronomy, and from whom much is expected, and little or nothing of purpose appears.  
It is my Opinion, that the appearances of Comets may be found by Calculations, if any Person capable, think it worthy his trouble. Concerning this Book, the common Vogue will be, viz. but will it do, is it the Longitude, I say? Yes, it is the Longitude begun, and will do with Industry and Encouragement, else not; for it is contrary to Seamens Vulgar sayings, that when the Longitude is found, than there will be abundance of Artists, Navigation will be so easy: No, no, Navigation will not be so easy at present, but much more certain and true. The Learned Bacon said, the Longitude was worth a Kingdom to a Wise Man; but before I conclude, to return to my Instrument, the Description I have given thereof, availeth little, without my further assistance; till then, the Reader if he pleaseth may compare— to Foxes staring on Bunches of ripe Gripes, and cannot get at them; then they are too sour for them: for so my Dream intimateth, when I was among a Crowd of Foxes, awed at my Presence, and after I had looked on them, they vanished, and left me other Objects. The most Ingenious of Humane Inventions, is far less facile than the ordinary performances of Truth and Nature. I love my King, the Church of England, and my Country, and I thank my God, I know myself capable and worthy to serve them, though too much debased for want of Friends in Court. If this meet with its deserved Encouragement, the rest may follow in good time; but I must make haste and conclude, my attendance and dependence being required in our Navy Royal, which Duty, I dare not neglect, for fear of being Excommunicated, or which is as bad, Excluded from Preferment. Quamvis bene merenti.  Nil tam difficile est quod non Solertia Vincat. Te Deum Laudamus. 
FINIS.    

ERRATA.  
PAge 2. l. 9 r. plane. p. 17. l. 8. r. Zulichem. p. 20. l. 6. r. cert is. l. 9 r. Industria. l. 19 r. an Idea. p. 28. l. 3. r. Bond. p. 29 l. 5. r. the increase. p. 30. l. 3. for me, r. one. l. 17. for by, r. with. p. 31. l. 22. r. though. l. 23. r. suppose. p. 36. l. 12. add when Northerly. p. 37. l. 10. r. preceding. p. 59 l. 27. for P. M. r. A. M. add Schema Solis ad Exitum Mercurii, St. Helen, Anno 1677. Octob. 28. 2 h. 4 P. M. p. 55. l. 10. r▪ will be. p. 63. l. 27. r. with. p. 70 l. 2. r. Sun and Stars.