THE MARINER'S everlasting Almanac Wherein is set down divers Motions of the Moon, with Rules and Tables for finding Her Age every day, and when She cometh to the Meridian, also the time of Her true Rising and Setting, fully examplified and proved. Together with Everlasting Tyde-Tables, containing the true Ebb and Flow throughout the most part of the Seaports and Towns in Europe As also An excellent Table, showing the exact Rising and Setting of the Sun for every five days, with the Degrees proper to the Sun's place. And Lastly, A pleasant Dialogue, containing some Orthographical and Steriographicall Questions, with several other useful things; most necessary for the Good of this NATION, but more especially for the use of our gallant Seamen. Calculated for the Latitude of 57 Degrees 10 minutes. By john Forbes Printer to BON-ACCORD, & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. The second Edition, much Corrected and Enlarged. ABERDEEN, Printed by the Author, Printer to the TOWN and UNIVERSITY, Anno 1683. GOD SAVE KING CHARLES. Long may HE Live, and Reign, with all that RACE: By Whom, we do enjoy much Grace and Peace. Insignia Vrbis abredonie Apelles, stairing long, did look upon The Learning, Policy, and Generous Mind Of that brave CITY, placed 'twixt DEE and DONE; But how to Paint it, he could never find: For still he stood, in judging which of Three, A Court, a College, or, a Burgh, it be. FLOREAT BON-ACCORDIA. TO His worthy, and much respected Good Friend, Captain JOHN TYLER, at Lieth. SIR, HAving heard of your Fame, and of your industrious and vigilant Endeavours into the Mathematical rare Inventions, (even in your younger years,) and especially into that famous and noble Art of Navigation; and that from the mouth of a Credible Person, who was at that time a Teacher of the Mathematics at London: have therefore made bold (though unacquainted) to present You with a second Edition of this Enchiridion, or, small Treatise; to be sheltered under the Protection of Your Patrociny: Whom, (I trust) is able to defend and assist me, in Truth and Verity, against all malevolent and backbiting Opposers; who through their blind ignorance, doth falsely check us of Truths, and some small oversights: as may be seen into the Tyde-Table of Lieth, Printed into an Almanac at Edinburgh, for this present year 1683: set forth by James Paterson Mathematician. Wherefore, expecting your favourable Acceptance, of this small Embryo, which shall ere long encourage me, to publish abroad a larger Treatise, on that excellent Art of Navigation, for the special use of all our Loyal brave Seamen and Mariners, whose painful Labours tend much for the Good of this Ancient KINGDOM. Thus wishing You, and all the Worthy Fraternity of Masters of the Trinitie-house at Lieth, all happiness here in this World, and Eternal Mansions of Joy in the World to come: I ever remain, SIR, Your humble Servant, john Forbes, Printer to BON-ACCORD. An Introduction to the perpetual Tyde-Table, or, Table of Ebbing and Flowing, in the most special Seaports in Europe. THere are divers Motions of the Moon, being 15 in number; accounted by Ricciolus, in his Almagesto Novo Astronomiae▪ lib. 4. cap. 18. But here I intent to treat of those Motions that are most useful for Seamen and Mariners, according as their daily practice doth require. SECTION I. The first Motion of the Moon. The first motion of the Moon, called the diurnal o● daily motion, being the revolution of the Moon from the East to the West, and from thence to the East in 24 hours; or rather almost in 25 hours: so that the Moon in this motion is slowest of all the side●iall Bodies, not following altogether the motion of Primum Mobile in 24 hours: For if the Moon be observed to be in Conjunction with any fixed Star this night the next night following, she shall be found to be distant from the same 13 degrees 10 minutes 35 seconds to which in the Aequator, answereth to 52 min of time This motion, being her proper middle motion i● longitude performed under the Zodiac, because a formerly I have mentioned she performeth 13 degree 10 minutes 35 seconds by her middle motion, which is betwixt the slow and the swift, and passeth through the Zodiac, in 27 days, 7 hours, 43 minutes: and this space of time, is called the periodical month. But because the Sun moveth daily in the Eccliptick, 59 min 8 sec. 20 thirds, towards the East, therefore the Sun's motion being substracted from the middle motion of the Moon in Longitude, there shall remain the distance of the Moon from the Sun, 12 degrees 11 minutes 26 seconds 41 thirds. SECT. II. The Second Motion of the Moon. The Synodical month, or month of Conjunction, being longer than the periodical Month, because the Moon being in Conjunction with the Sun, as admit, in the first of Aries, the Moon having prescribed her motion through the Zodiac in 27 days 7 hours 43 minutes, doth not find the Sun in this point of the Zodiac, because the Sun since the last Conjunction is passed towards the East; therefore that there may be a Conjunction of the Sun with the Moon, she is to pass a whole Sign almost, before she can come to be in Conjunction with the Sun, and this is called, Lunatio vera. But if we have respect to the true motion, the space of the middle Lunation being 29 days 12 hours, the longest 30 days, the shortest 28 day's 23 hours: From hence it followeth, that 12 Synodical months maketh a Lunar year to consist of 354 days, but the Solar year consisting of 365 days 5 hours 4● minutes, maketh the difference 11 days, being called the Epact: which is 〈◊〉 ●●ference betwixt the Solar and Lunar Year. SECT. III. The third Motion of the Moon. The third motion is the motion of the Nods, of the circle of the Moon, contrare to the order of the Signs; for the Orbite of the Moon, is inclined to the plain of the Eccliptick by an Angle of 5 degrees in New and full-Moons, or 5 deg. 18 min. in the quarters, which Latitude of 5 degrees, being the greatest, is called, the Belly of the Dragon, because of the similitude they have with a Dragon or Serpent, as is form by the periphery of the Lunar Eccliptick with the periphery of the Orbite of the Moon, the one being called the North, and the other the South. The points wherein there is no Latitude, or where the Orbite of the way of the Moon cutteth the Eccliptick, being immediately opposed, are called the Nods, whereof the one is called the Northern and ascendent, because to us that are to the North ward, it is always higher, ascending towards our Pole and Zenith, and therefore it is called Caput Draconis or, head of the Dragon, marked thus ☊ The other Node or Intersection, is called Southrens descending, or, the Tail of the Dragon, marked thus ☋ These Nods or points of the intersection, near about which falleth out the Eclipses of the Sun and Moon, are observed to move contrare to the Order of the Signs, the middle motion of the same being 3 minutes 10 seconds 38 thirds at nearest, so that they will absolve their period of motion through the Eccliptick, about 18 years 228 days, 3 hours, 50 minutes. But according to Copernicus in 18 years, 223 days 6 hours, 12 minutes. This motion by some was thought to be equal, but Tycho did find the same unequal, where you are here to observe that your Golden Number, is composed of this motion, being the space of 19 years that the Nods do make their revolution in 19 years, and how to find the same. As also the Epact, whereby we may find the Age of the Moon. SECT. IV. How to find the Golden-Number. AS also, to know at what time the Moon cometh to the Meridian, First, find the Golden-Number, which is had by adding one to the Year of our Lord, ●nd dividing the sum by 19, the remainder that rests over the division shall be the Golden-Number; and ●he Quotient shall show how many revolutions are passed since the head of the Dragon was in the first of Aries. As suppose I desire to know the Golden Num●er for the year 1683, to the which an Unite being added, the sum is 1684: which divided by 19, the remainder is 12 for the Golden-Number, or 12 years' ●re passed since the head of the Dragon was in the first 〈◊〉 Aries, and the most part of that year, the same will remain in Leo, and enters Cancer upon the 29 of October, having performed 88 Revolutions, as in the Quotient is evident. SECT. V. How to find the Epact. HAving found the Golden-Number, the Epact may be easily had for this year, viz. 1683 by multiplying the Golden-Number by 11: (being the difference betwixt the Solar and Lunar year) the product is 132, which divided by 30 the Quotient is 4, and the remainder 12, which is the Epact for this year, 1683: where you are to observe, that the Golden-Number beginneth always the first of january, and the Epact the first of March. SECT. VI How to find the Age of the Moon. TO know the age of the Moon, add to the Epact of that year in which you desire the Moon's age, the months from March inclusive, with the days of the month; and if the sum be less than 30, than the number is the age of the Moon, but if the sum of the addition exceed 30, from the same subtract 30, if the month have 31 days, and if 30, subtract 29, the remainder will be the age of the Moon: the reason of this substraction was to return back the 11 days, which was the difference between the Solar and Lunar year. Example, In the year 1683, I would know the Moon's age the 10 day of August, the month of August being the 6th, and the Epact 12, the days of the month 10: these three E 12 M 6 D 10 added together, the sum is 28, which showeth the 18 of August, to be the 28 day of the Moon. And again, if you require the age of the Moon the 28 day of August, these E 12 M 6 D 28 three numbers being added together, the sum is 46, from which 30 being substracted (because the month hath 31 days) the remainder is 16, so that the 28 of August 1683, is the 16 day of the Moon. This way being frequently used by Seamen, is not so exact as may be required; therefore I would advise Seamen to take notice of the Yearly Almanacs. Having the age of the Moon, we may know at what time she cometh to the Meridian by the precedent Rule, where the first day, or 24 hours after the Conjunction or Change, the Moon is 12 degrees distant from the Sun, in time 48 min. or 3 quar. 3 min. that ●he Moon cometh latter to the Meridian the first day, and so for every day to the Opposition or Full-Moon. Now to know at what time the Moon cometh to the Meridian, accept of this following Table, for this and another use, as shall follow. This following Table containeth five columns, in ●he first and second ye have the Increass and Decreass of the Moon's age, as also, in the third and fourth, ●he hours and minutes that the Moon doth come to the Meridian: for if th● Moon be increasing (a● you may see by the letters je, at the head of th● first column) the hour● and minutes against th● same, is the time of the Moons coming to the Meridian in the afternoon. But if the Moon● be decreasing, (as you may see at the head o● the second column, by the letters De.) Then the hours and minutes showeth the time of the Moons coming to the Meridian in the Morning. The Moon's Age, ❍ Moon coming to Meridian. Moon's Age ☽ In. ☽ De. ☽ Ho. Min. 1 16 0 48 29 2 17 1 36 28 3 18 2 24 27 4 19 3 12 26 5 20 4 00 25 6 21 4 48 24 7 22 5 36 23 8 23 6 24 22 9 24 7 12 21 10 25 8 00 20 11 26 8 48 19 12 27 9 36 18 13 28 10 24 17 14 29 11 12 16 15 30 12 00 15 Example The 5 day and the 20 day of the Moon, I desire to know the Moons coming to the Meridian. I find for both these days 4 hours, showing that the 5 day, the Moon cometh to the Meridian at 4 hours' afternoon, and the 20 day at 4 hours in the morning: the columns of hours and minutes, are had by multiplying the Moon's age by 4, and dividing the product by 5, and if any remain over the division is the numerator of the fraction, and for every Unite account 12 minutes, so you shall have the hours and minutes of the Moon's coming to the Meridian, as in the Table you may find. As for Example, the 7 day of the Moon, I desire to know at what time in the afternoon she cometh to the Meridian, so 7 multiplied by 4 the product is 28, which divyded by 5, the quotient is 5 hours, and 3 remaining over the division giveth 36 minutes, so that the 7 day, the Moon cometh to the Meridian at 5 hours, 36 minutes in the afternoon. Some Examples. Having found by the Rules or Table the Moons coming to the Meridian, if there be any place where a South Moon maketh full-Sea as at the Isle of Wight, I say that the 7 day of the Moon it will be Full-Sea, or high water at that place at 5 hours, 36 minutes. But if the flow be to the Eastward, than you are to subtract 3 quarters of an hour for every point of the Compass, and the remainder shall show you the time of high water at that place. As also, I desire to know the time of full-Sea the 7 day of the Moon at Yarmouth where a South-South East Moon maketh full-Sea: from 5 hou. 36 min. subtract one hou. 30 min. the remainder is 4 hou. 6 min. at which time it will be full-Sea at North-Yarmouth. Again, if at Lieth, where a South-West by South Moon maketh a full-Sea, you are to add 2 hou. 15 min. for 3 points of the Com●ass (because Westward flow) to 5 hou. 36 min. ●he sum shall be 7 hou. 51 min. at which time it will be full-Sea at Lieth. SECT. VII. How to find the rising and setting of the Moon. LAstly, to know at what hour the Moon setteth or riseth for any day of her Age for which purpose this small treatise was intended You may accept of the second use of this Table, in which, first you may know how long the Moon will shine or remain above the Horizon, from the Conjunction or Change to the Full, by knowing the Moon's age in the first column and against the same, in the third and fourth columns you shall have the hours and minutes that the Moon doth shine or remain after the Sun's setting, which being added to the setting of the Sun, giveth the setting of the Moon, Example, I desire to know the 8 day of the Moon at what time she will set, I find in the Table the 8 day of her age, and in the third and fourth 6 ho. 24 min. for so long will she shine after the Sun setteth▪ Then suppose the Sun to set at 5 hours in the afternoon, which being added to 6 hou. 24 min. the sum shall show the time of her setting, at 11 hou. 24 min. at night. For the Moons rising after the opposition or full, look for the Moon's age in the second column and the how. and min answering, being substracted from 12 how. giveth the how. and min. that the Moon riseth before the Sun; which being substracted from the Sun's rising, giveth the time of the Moons rising. For Example, The 17 day of the Moon, I find answering 1 hour, 36 minutes, which being substracted from 12 the remainder is 10 hou. 24 min. that the Moon will rise before the Sun, so that the Moon shineth 10 hou. 24 min. in the morning before the Sun rise, and the Sun ●he same day rising at 7 a clock, 36 min. whereunto ●f I add 12 how. else the substraction cannot be made, ●nd it maketh 19 hou. 36 min: from which 10 hours 24 minutes being substracted, there resis 9 hou. 12 min. ●t which time the Moon riseth before midnight, but ●or saving a substraction, I have added the fifth column, and against the days of the Moon's age you ●ave the compliment of the how. and min. to 12, and ●o one substraction will serve. The reason of this Table was had from Plinius, in his lib. 8. cap. 12, ●nd from others as is mentioned by Ricciolus in his astronomy, lib. 4. cap. 4 Prob. 12. Which Rule although not exact, yet may serve for vulgar use, for ●s the Learned Kepler doth observe concerning this Rule of Plinius, that, Medium inter ejus enormia tenet. A more exact and certain way may be had for the ●ime of rising and setting of the Moon: by knowing ●he place of the Moon in the Ecliptic, which being ●ad for the time you require the Moons rising and ●etting, you are to apply yourself to the last Table of the Suns rising and setting, and there finding the sign and Degree the Moon is into at the time required, ●r when the Moon cometh to the Meridian, by the ●●rst Table, with the Signs and Degrees: then looking ●or the Sun's setting being in the same sign and de●ree, which being substracted from her coming to the Meridian, giveth the time of the Moons rising: and being added giveth the time of her setting, als● which shall be evident by the following Examples for which purpose I have added a second Table showing the Moon's motion in signs, degrees, and minutes, for every day and hour of her Age. Observing the 12 Signs with their marks, and respective months, the first 6 being N. Northern and the last S. Southern: also, there are 12 words in a verse, for the 12 months, each of them beginning with a vowel, except the last, (P.) in Paradise, a consonant being for February, and signifying the 8 day of February that the ☉ Sun will enter ♓ Pisces● ●or the rest add the number of the beginning vowel of each word to 8, the sum shall be the day of the month that the ☉ Sun entereth the respective sign, as E in Evil, being the second vowel, with 8 giveth 10 the day of March the Sun entereth ♈ Aries; as also, O, in Objects being the 4 vowel added to 8 is 12, showing the Sun to enter ♋ Cancer the 12 of june, and so accordingly in all the rest. The six Northern Signs. March, April, May, june, july, August, ♈ Aries ♉ Taurus ♊ Gemini ♋ Cancer ♌ Leo ♍ Virgo, 2 Evil 1 attends 3 its 4 object, 5 unvailed 5 vice, The six Southern Signs. Septem. Octo. Novem. Decem. januar Februar. ♎ Libra ♏ Scorpio ♐ Sagit. ♑ Capri. ♒ Aqua. ♓ Pisces. 5 Vain 5 villains 3 jest, 3 into 1 A 8 Paradise. A Table, showing the Moon's Motion, in Signs, Degrees and Minute's, for every Day and Hour of her Age. The Days of the Moon's Age. ❍ Age, Si. Deg. Min. 1 0 13 11 2 0 26 21 3 1 9 32 4 1 22 42 5 2 5 53 6 2 19 3 7 3 2 14 8 3 15 25 9 3 28 35 10 4 11 46 11 4 24 56 12 5 8 7 13 5 21 18 14 6 4 28 15 6 17 39 16 7 0 49 17 7 14 0 18 7 27 11 19 8 10 21 20 8 23 32 21 9 0 42 22 9 19 53 23 10 3 3 24 10 16 14 25 10 29 25 26 11 12 35 27 11 29 46 28 0 8 56 29 0 22 7 30 The Hours of the Moon's Age. Ho. Deg. Min. 1 0 33 2 1 6 3 1 39 4 2 12 5 2 45 6 3 18 7 3 51 8 4 24 9 4 56 10 5 29 11 6 2 12 6 35 13 7 8 14 7 41 15 8 14 16 8 47 17 9 20 18 9 53 19 10 26 20 10 59 21 11 32 22 12 5 23 12 38 24 13 11 The use of this Table is as followeth, and first observing that the Sun and Moon are both in one Sign and Degree at the Change and Conjunction which you may have by your yearly Almanac or Ephemeris. As in the year 1683, I find the Conjunction or Change to be the 14 of july at 2 in the morning, (the minutes being omitted, as of no great concernment in this matter) then from 2 in the morning to 12 at midday, there are 10 hours, to the which answereth the hours of the Moon's age, 5 degrees, 29 minutes, which being added to 1 degree, 3 minutes of Leo▪ the sign and degree the Sun and Moon was into at the change, the sum is 6 degrees, 32 minutes and this is the place of the Moon the 14 of july at noon. But with more certainty by an Ephemeris into the 7 deg. of Leo the 14 day at noon. Secondly, I desire to know the Moon's place the 25 of july. so then between the 14 of july, and the 25 are 11 days inclusive, and in the table of the days of the Moon's age, are 4 signs 25 degrees. Lastly, seeing the Moon cometh to the Meridian the 11 day, at 8 hours, 48 minutes, to the which doth answer nearest in the table of hours, 4 degrees, 56 minutes, these four being added together S. D. M. First the ☽ being in the 1 deg. 3 min of ☊ being 4 1 3 Secondly from 2 morning to noon, being 10 hours, 0 5 29 Thirdly the 11 day at noon, 4 25 00 Lastly for 11 days in the first table, 8 ho▪ 48 min. is 0 4 56 The sum is 9 6 28 And this much for the first way. These 9 Signs 6 deg. 28 min. showeth the Moon to be in the year 1683, july 25th, into the 6 degree 28 minutes of Capricorn: minutes being omitted in both, so the difference is but small; and no wonder that there be a difference: the Ephemeris by calculation being more exact than that which we can expect from this Enchiridion: where you are to observe, having found the place of the Moon, which if it had exceeded 12 signs, ye were then to subtract 12, and the remainder counted from Aries inclusive, shall be the Moon's place. But having found the same to be in the 7 degree of Capricorn, and the Sun in the same; by the last table of the Suns rising and setting, ye shall find the Sun being in the 7 degree of Capricorn to set in the Latitude of 57 deg. 10 min. at 3 how 15 min. which being added to 8 hou. 48. min. the Moons coming to the Meridian, showeth the setting of the Moon, to be at 12 hou. 3 min. about midnight; and being substracted from 8 hou. 48 min. the remainder is 5 hou. 33 min. for the rising of the Moon in the afternoon. And accordingly you may know the rising and setting for any other day of her age, either increasing or decreasing. Upon these grounds an Instrument may be made for performing of the same without Tables. And this much for the second way. The Third Way. In the same year 1683, December 17 being the 10 day of the Moon, and coming to the Meridian at 8 a clock in the afternoon: I find the Moon to be in 23 degrees of Aries, having 5 degrees 16 minute's South-Latitude; which being substracted from 8 degrees, 58 minutes (the Sun's Declination being in 23 of Aries.) is 3 degrees 42 minutes, which may be called the Moon's Declination, or distance from the Equinoctial Northerly, though not propperly, because the Latitude of the Moon or Star, is said to be an Arch of a great Circle, contained between the body of the Moon or Star, and the Eccliptick passing by the Eccliptick Poles: and the Declination an Arch of a great Circle, contained between the body of Sun. Moon, or Star; and the Equinoctial passing by the Poles of the World. But the difference between the two Arches being small and of no great consequence to this matter, we look in the tables of Declination for 3 deg. 42 min. in Aries, in which sign and degree the Sun being, setteth about 6 hou. 10 min. which added to 8 how. the Moons coming to the Meridian the sum is 14 hou. 10 min. or 2 hou. 10 min. in the morning the Moon will set, and being substracted from 8 how. the remainder 1 hou. 50 min. for her rising afternoon. Now by the second way wherein there is no respect had to the Latitude of the Moon, we find the Sun being in 23 deg. of Aries to have his half semidiurnal Arch 6 hou. 56 min. which being added to 8 how. the Moons coming to the Meridian giveth 14 hou. 56 min. for her setting, and substracted from 8 how. giveth 1 hou. 4 min. this being an error ought to be seriously considered, as not being tollorable, the half semidiurnal Arch only being 6 hou. 10 min. and not 6 hou. 56 min. by considering the Latitude Having formerly made mention, that the Moon's Latitude being added or substracted from the Moons true Declination of Longitude, the difference is of no great consequence, as I shall illustrate in these following cases, supposing the Moon's Longitude to be in the 15 degree of Taurus. SECT. VIII. A description of the following Spherical Triangle. Let there be an oblique Spherical Triangle, as A, B, C, projected in the plain of the Solistitiall●olure, either Orthographice, according to Ptolemy's analemma, or Steriographice, according to Gemma ●risius his Astrolob: the Arch A, B, shall represent the distance between the two Poles, to wit, of ●he Diurnal and Annual Motion, being 23 deg. 30 min. B, C, an Arch of the Co. Latitude of the Moon, ●nd A, C, of the Co. Declination. Dat. A, B, the Angle at B, and B, C, to find A, C, or Compliment; being the Declination of the Moon. NORTH. ☽ Lat. ☽ Decl. Decl. 15 ♉ added Diff Deg. deg. min. deg. min. min▪ 5 21 8 21 24 16 4 20 11 20 24 13 3 19 14 19 24 10 2 18 16 18 24 8 1 17 19 17 24 5 SOUTH. ☽ Lat. ☽ Decl. Substracted Diff Deg. deg. min. deg. min. min▪ 5 11 35 16 24 11 4 12 32 16 24 8 3 13 30 16 24 6 2 14 27 16 24 3 1 15 24 16 24 0 These two Tables I have composed; for showing of the difference between the Moon's Declination, (being had by the resolution of the former Triangle,) and the place of the Moon in the Eccliptick; having either N. or S. Latitude. As for Example, I have taken the Moon's Longitude to be in the 15 deg. of Taurus, whose Declination is 16 deg. 24 min In the first table, there are 5 columns, First, the Moon's Latitude to 5 deg. of N. Latitude. Secondly, the Moon's Declination. Thirdly, the Declination of the 15 deg. of Taurus being 16 deg. 24 min. added to 5 deg. of N. Latitude, giveth 21 deg. 24 min. the difference from the Moon's Declination 21 deg. 8 min. being only 16 min. and ●hat for the fifth column, and so accordingly in all ●he rest. The second table, where the Moon hath South Latitude, the Moon being in the same degree of ●he Eccliptick, according to her Longitude, ye have ●n the first column as formerly, the Moon's Latitude S. Secondly, the Moon's Declination: and thirdly, the Declination of 15 deg of Taurus, from which if ye subtract ●he Moon's Latitude, the remainder shall be 11 deg. 24 min differing from the Moon's Declination 11 min. What I have said here concerning N. or S. Latitude, in the Northern Signs, may be applied to N. or S. Latitude in Southern Signs. But if it be required, when the Declination with the Latitude added, is more than 23 deg. 30 min. as I suppose the Moon to be in the 25 deg. of Gemini; having Declination 23 deg. 26 min. North, and the Latitude 5 deg. 16 min. North, the sum is 28 deg: 26 min: now to know the 20 day of the Moon, at what time the Moon riseth and setteth. Having found the Declination of the Moon by what formerly hath been said, to be 28 deg. 40 min, with the Poles Elevation 57 deg. 10 min. we may find the difference assentionall to be 57 deg. 55 min, in time 3 hou. 52 min; which added to 6 how. the sum is 9 hou. 52 min. added to 4 how. in the morning, the Moons coming to the Meridian, giveth 13 hou. 52 min. or, 52 min. past 1 how. afternoon; and substracted from 4, leaveth 6 how 8 min. at which time the Moon will rise the former day in the afternoon. As for the horizontal refraction and Parallax, being of no great concernment in this matter to handle any further, I desist. Lastly, I would advise Seamen, that are versed in the principles o● Navigation, as in the Sphere and Globs, to furnish themselves with Ephemerideses, either Argol, or john Gadbury their Ephemerideses, which will continue these 28 years; wherein they may have the true place of the Luminaries, with the Moon's Latitude, for the Meridian or 12 a cloak each day. SECT. IX. A declaration, for the better understanding of these Everlasting Tables, for the Ebbs and Floods following▪ IF you be desirous at any time to know when i● is a full-Sea, or high water at any Port or Haven either in Scotland, England, France or Ireland, or any other part of the World: If first by your own knowledge, or the knowledge of any expert Mariner, you know, when you see the Moon in such a part of the Firmament, that then it is ful-Sea at such a Port or Haven, than these Tables shall be needless for you: But if you cannot so do, and would learn, then resort to this Table: And first consider with yourself, how many days old the Moon is, the day that you desire to know the Tide: And in the middle of this Table you shall find in the uppermost part thereof; this tittle, The Age of the Moon: and right against the day of the Age of the Moon, you shall find on both sides, the places and points of the Firmament, as South, South by West; South South-West, etc. And next under that Line, are these letters, Ho. and Min. which signifieth Hours and Minute's: Then having in memory the Age of the Moon, as aforesaid, go directly to the tittle of that place of the Firmament, to the which when the Moon cometh, maketh a high Water, and there you shall find the exact Hour and Minute when it is ful-Sea in that place, As for Example. Where it flows South by West, as at Aberdeen, I desire to know at what time it will be full-Sea at that place, the 10 day of the Moon: I apply myself to the Table, and I find the flowing at Aberdeen, South by West, then looking in the Column of the Age of the Moon, I find the day of the Moon 10, and right against the same upon the left hand I find 8 hours 45 minutes: at which time in the Evening it will be full-Sea at that place: but if it be the 25 day of the Moon, you shall find the same flowing to be at 8 hours 45 minutes in the morning. Another Example, Where it flows South-West by South, as at Lieth, I desire to know at what time it will be full-Sea at that place, the said 10 day of the Moon: I apply myself to the Table, and I find the flowing at Lieth, South-West by South: then looking in the Column of the Age of the Moon, I find the day of the Moon 10, and right against the same upon the right hand I find 10 hours 15 minutes: at which time in the Evening it will be full-Sea at that place: but if it be the 25 day of the Moon, you shall find the same flowing 10 be at 10 hours 15 minutes in the morning and accordingly throughout these following Everlasting Tyde-Tables. at Buchamness, and all the Southside of the Murray-Firth, Cromarty, Millorchy, Inverness, Findorne, Spey, Bamff, Peterhead, Isle of Wight, at Deal, at Dover-Peer, on the Coast of Flanders, etc. at Newbrugh Aberdeen, Sto●hyve, Redbane, at Flushing, within the Maes, at Maldox, at the West-end of the Nower, at Blacktail, at Rochester, at Winchelsey, and within Terveer, etc. The Age of the Moon. at Montrose, the out-end of ●ay, St. Andrews, Cryle, E●ster, and all along the Coast of ●isse to Brunt Island, before Gaurie and at Gravesend, under Holy-Island, and at Horn, etc. at Lieth in the Firth, at Dundee, Brunt Island, Holy-Island, St. Lucas, without Bluet at Denby, without Fountnay, at Lisbon, before the Weiling, etc. South. S. by W. ☽ ☽ S. S. W. S. W. by S. North. N. by E. N. N. E. N. E. by N. Ho. Min. Ho. Min. In. De. Ho. Min. Ho. Min. 12 48 1 33 1 16 2 18 3 3 1 36 2 21 2 17 3 6 3 51 2 24 3 9 3 18 3 54 4 39 3 12 3 57 4 19 4 42 5 27 4 0 4 45 5 20 5 30 6 15 4 48 5 33 6 21 6 18 7 3 5 36 6 21 7 22 7 6 7 51 6 24 7 9 8 23 7 54 8 39 7 12 7 57 9 24 8 42 9 27 8 0 8 45 10 25 9 30 10 15 8 48 9 33 11 26 10 18 11 3 9 36 10 21 12 27 11 6 11 51 10 24 11 9 13 28 11 54 12 39 11 12 11 57 14 29 12 42 1 27 12 0 12 45 15 30 1 30 2 15 at Ennerkything, Quensferrie, st. Margarets-Hoop. Borrowstonness, Lyme-Kills, & all above In●hgarvie, except Stirling-Bridge, at LONDON and before Newcastle, at Amsterdan, & Armentiers, etc. from Buchan-ness, and all alongst the Coast without, above the May, or Highland in the South-Firth, and from Flambrough-head, to Birdling tun Bay without, Ostend, at Breast, before the Bass etc. The Age of the Moon. A little off the Shore before Humber between Brid lington, and Lowerness, at Landsend of Golph, from Ostend to Saint Catherine's, at Aberwark, in the Bree sound: Baltimore, Mousehole, Dungarvan, etc. at Arbroth, Falmouth, between Silly and Lizard, in Milford, Moonless, St. Maloes, at Caldy, and in the Bay of Canaruan, at the mouth of Severn, Foy, Humber Newcastle, Garnsey, and Wales, etc. S. W. S. W by W. ☽ ☽ W. S. W. W. by S. N. E. N. E. by E. E N. E. E. by N. Ho. Min. Ho. Min. In. De. Ho. Min. Ho. Min. 3 48 4 33 1 16 5 18 6 3 4 36 5 21 2 17 6 6 6 51 5 24 6 9 3 ●8 6 54 7 39 6 12 6 57 4 19 7 42 8 27 7 0 7 45 5 20 8 30 9 15 7 48 8 33 6 21 9 18 10 3 8 36 9 21 7 22 10 6 10 51 9 24 10 9 8 23 10 54 11 39 10 12 10 57 9 24 11 42 12 27 11 0 11 45 10 25 12 30 1 15 11 48 12 33 11 26 1 18 2 3 12 36 1 21 12 27 2 6 2 51 1 24 2 9 13 28 2 54 3 39 2 12 2 57 14 29 3 42 4 27 3 0 3 45 15 30 4 30 5 15 At Lin half-tyde, Weighmouth, Wells, and Waterford, Hull, Londey, at Holms, Bristol, Concallo, at Abermorick, and Antwerp, before Hambrough, and the Tessel, etc. between Foy and Falmouth and at Bristol-Key, and Weighmouth-Key, at Lime, Foul-ness, at Sedmouth, and at the Start. before St. Nicholas, & Podessinsk in Russia, etc. The Age of the Moon. Bridgewater, at the Fly, before the Coast of Frizland, Ex water, at the Lizard by the Land, at Cape Clear in the Road of the tessel, and off the Start in the Channel. etc. at Yarmouth, the Hague, between Beachy and the Isle of Wight and also in St. Magnes Sound, and at Machnells' Castle, at Dublin, at Lambey, Peterport, without the Fly, etc. East. E. by S. ☽ ☽ E. S. E. S. E. by E. West. W. by N. W. N. W. N. W by W. Ho. Min. Ho. Min. In. De. Ho Min. Ho. Min. 6 48 7 33 1 16 8 18 9 3 7 36 8 21 2 17 9 6 9 51 8 24 9 9 3 18 9 54 10 39 9 12 9 57 4 19 10 42 11 27 10 0 10 45 5 20 11 30 12 15 10 48 11 33 6 21 12 28 1 3 1● 36 12 21 7 22 1 6 1 51 12 24 1 9 8 23 1 54 2 39 1 12 1 57 9 24 2 42 3 27 2 0 2 45 10 25 3 30 4 15 2 48 3 33 11 26 4 18 5 3 3 36 4 21 12 27 5 6 5 5● 4 24 5 9 13 28 5 54 6 39 5 12 5 57 14 29 6 42 7 27 6 0 6 45 15 30 7 30 8 15 at Penthland-●irth, at Kirkwa, at Elwick, at the Mull-head at Cateness, at Orkney, at Dumbar, at the Bass Island, at Kildrens, at the Isle of Man, at Harlem, and at Homehead, etc. at Alborough at the Caskets, and at Chamberness, at Dungeness, and Dun●ose, thwart of Garnsey in the Channel, at Leystaff, and thwart of it without the Banks, at Orfordness, at Shoram▪ at Tergow, at Deep. etc. The Age of the Moon. in the Week of Cateness, Bulleyn-deep at Cows, in Calais Road, at Dover, and in the Downs at Harwich, without the Banks of Harwich, at St. Helen's, all the Coast of Normandy and Picardy, in Yarmouth-Road, etc. before the Haven of Caven, in the Chamber, between Cripple-sand and the Creyl, and at Culsbot, in fair Isle-Rhoads, and at the Northfore land, in the Chamber, and Gor-end, at Harwich within, at Rye, etc. S. E. S. E by S. ☽ ☽ S. S E. S. by E. N. W. N W. by N. N. N. W. N. by W. Ho. Min. Ho. Min. In. De. Ho. Min. Ho. Min. 9 48 10 33 1 16 11 ●8 12 3 10 36 11 22 2 17 12 6 12 51 11 24 12 9 3 18 12 54 1 39 12 12 12 57 4 19 1 42 2 27 1 0 1 45 5 20 2 30 3 ●5 1 48 2 33 6 21 3 18 4 3 2 36 3 21 7 22 4 6 4 51 3 24 4 9 8 23 4 54 5 39 4 12 4 57 9 24 5 42 6 27 5 0 5 45 10 25 6 30 7 15 5 48 6 33 11 26 7 18 8 3 6 36 7 21 12 27 8 6 8 ●● 7 24 8 9 13 28 8 54 9 ●9 8 12 8 57 14 29 9 42 10 17 9 0 9 45 15 30 10 30 11 15 A full and complete Everlasting Tyde-Table, for all the Seacoasts and Harbours of Great Britain, France and Ireland, Holland, Spain, Flanders, Norway. Biscay, etc. Showing exactly what Moon maketh a full-Sea, in all the aforesaid places, or into any other place of the World; according to these foregoing Everlasting Tyde-Tables, of the Ebb and Flow, Hours and Minute's of the Moons daily Age: because that all could not be contained into the said foregoing Tables. The like never heretofore by any, so fully published. South and North Moon, maketh a full-Sea, at Buchan-ness, and all along the Southside of the Murray-F●rth, (viz) Cromarty, Millorchy, Inverness, Findorne, Spey: also Ba●●ff, Peterhead, Isle of Wight, at Deal, at Beachy, and before the Race of Blanket, in the Condado, at Dover-Peer, and before Dunkirk, at Emden, before the Elve, before the Eyder, and before Enchusen, on the Coast of Flanders, in the Road of Gibraltar, at Gravelling and before Gherbrough, before the Hever, before Horn, and at Hampton-Key, at Jutland-Islands, Kentish Knock, at Liegh, and at Newport half Tide, at Portsmouth half Tide, at Qu●brough, in the Sleeve, between Vshant and Silly, at the Shoe, at the Spits, at South-Hampton, and all along the Swim, before Vr●ck S. by W. or, N. by E. Moon, at New-burgh, ABERDEEN, Stonhyve, Redbane, at Blacktail, and thwart of Beachy in the Offing, in the Camber of Rye, at Flushing within the Maes, and at Maldon, at the West end of the Nower, at Rochester, within Terveer, at Winchelsey. S. S. W. or, N. N. E. Moon, at Montrose, the out end of Tay, St. Andrews, Cryle, E●ster, and all along the Coast of Fife to Brunt-Island, at Army, at Black-ness in Bluet, at Bell-Isle, at Baraik●, without Calais, at Corpus-Christi point, before Camfer, and at Camfor, at Edam, before the Fen in the Channel, before Gourie, and at Gravesend, under Holy-Island, and at Horn, before the Maes, at Ramkins, before Terveer, before the River of Thames, and at Tinmouth, at the Weiling, and from the West end of the Weight, before Yarmouth, on the Coast of Zealand, at Fern-head. S. W. by S. or, N. E. by N. Moon, at LIETH in the Firth, Dundee, Brunt-Island, Holy-Island, Lucas, without Bluet, at Denby, without Fountnay, at Lisbon, before the Weiling. S. W. or, N. E. Moon, at Ennerkything, Queens-ferrie, St. Margarets-hoop, Borrowstonness, Lyme-Kills, and all above Inchgarvie, except Stirling-Bridge, at LONDON, and before Newcastle, at Amsterdam, and Armentiers, the River of Bourdeaux, the South Coast of Britaign, the Coast of Biscay, at Bockness, between Calais and Dover, before Conquer, and at the North-Cape, at Dort, without the Banks of Flanders. at Groy, at Gascoign, and the Coast of Gallicia, before Hartlepool, on the West Coast of Ireland, Killiars, and before the River of Nantz, at Orkness, at the Penns, Porthus, and Picton; at Rotterdam, in Robin-Hoods Bay, and from the Race to the Pole-head, upon the Coast of Spain, and in Shotland, before the Tees, and before the Bay of Tinmouth, at Use, and in the Zierick-Sea. S. W. by W. or, N. E. by E. Moon, from Buchan-ness, and all alongst the Coast without, above the May, or Highland in the South-Firth, and from Flambrough-head, to Birdlington-Bay without, Ostond, at Breast before the Bass, the River of Bourdeaux within the Haven, and at Berwick, at Huntclif-foot, at the Maes, and before St. Mathews Point, on the Coast of Portugal, at Roven, and before Rochel, at Silly, and in the Sound, at Staples, between Vshant and the Main. W. S. W. or, E. N. E. Moon, A little off the Shore before Humber, between Bridlington and Lowerness, at Landsend of Golph, from Ostend to St. Catharines', at Aberwark, in the Bree-sound, Bloy, Baltimore, at Cork, at Calais, and in the Creek, at Dungarvan, at Flambrough, and Bridlington, at Kingsale, in Mousehole, at Mathews, and within Mounts Bay, at the Clefts of the Texel, in the Vourd, at the Bay within Vshant, in the Sea of Wales, and Severn, at Yough-Hall, before Scarbrough, at Seven-Isles, without the Haven in the Broad Sound, at Lawrens, in Cork-Haven. W. by S. or, E. by N. Moon, at Ar●roth, at Caldy, and in the Bay of Canaruan, at the Fourn, in Foy, at Falmouth, at Garnsey▪ at Humber, in all the Havens on the South Coast of Ireland, thwart of Londey, and before Line, in Malford, at Moonless, at St. Maloes', at Newcastle, in Plymouth, and before St. Paul's, in Ramsey, at the mouth of Severn, between Silly and the Lizard, at the Spurn, in Wales, at Merles, and all along the Coast of Bristol. E. or W. Moon, at Abermorick, and Antwerp, before Bremen, and at Blackney, in the Channel before Bourdeaux, and at Bristol, at Concallo, at Dartmouth, before Hambrough, at Hull, at the Holms, and before Humber's mouth, at Lin half side, at Londey, at St Paul's in the Haven, without Silly, in the Channel, and at Salcomb, in Torbay, and before the tessel, without Vshant, at Wells, at Weighmouth, and at Waterford, and St. Davids-head. E. by S▪ or, W. by N. Moon, at Bristol-Key, between Foy and Falmouth▪ in the Channel, and at Foulness, at Lime, before St. Nicolas, before Podessinsk, in Russia, at Sedmouth, and at the Start, at Weighmouth-Key. E. S, E. or, W. N. W. Moon, at Bridgwater, at Cape Clear, before the Coast of Friezland, and the Fly, at Kilduyn, at the Lizard by the Land, between Musehole and Falmouth, and in Milford Haven, thwart of Plymouth, Off the Start in the Channel, in the Road of the Texel, at the Ness by Wieringben, and at Winterton, at Exwater, at Landsend. S. E. by E. or, N. W. by W. Moon, between Beachy and the Isle of Wight without the Caskets in the Channel, at Dublin, without the Fly, at Lambey, in St. Magnes Sound, at Machnells' Castle, at the Needles, at Isle of Wight, thwart of the Isle of Wight in the Channel, all within the Isle of Wight, between the Isle of Wight and Beachy by the Shore, at Yarmouth, at Peterport, at Harflew, at the Hague. S. E. or, N. W. Moon, at Penthland-Firth, at Kirkwa, at Elwick, at the Mull-head, at Catness, at Orkney, the Bass-Island, at Dumbar, at Kildrens, at the Isle of Man, between Garnsey and the Caskets, before Cromer, before the Casket, and Garnsey, at Seven-Clifts, before the Eastern and Western Emes, and at Egmont, at Frieze, and Fair-Isles, between Garnsey and Caskets, at Harlem, and at Homehead, at Kildive, at the Race of Portland, within the said, before Schelbagh, and at Seven Cliffs, at the East end of the Weight, and on Wieringen-Flats, at Pool, at Farro-head in the Channel, between Farro head, and the Mull of Kintire S. E. by S. or, N W. by N. Moon, at Alborough, at the Caskets, and at Chamberness, at Dungeness, and Dunnose, thwart of Garnsey in the Channel, at Leystaff, and thwart of it without the Banks, at Orfordness, at Shoram, at Tergow, at Deep. S. S. E. or, N. N. W. Moon, Bulleyn deep, at Cows, in the Foss of Caen, in Calais Road, and in Chamberness-Road, at Dover, and in the Downs, in the Freith, and at the South-Foreland, at St. Helen's, at Harwich, and without the Banks of Harwich, in Leystaff Road, and at Long-sand-head, all the Coast of Normandy, and Picardy, at Orfordness without the Banks, and between Orford and Orwell-Waves, at Seyn-head, in Yarmouth Road, and in Yarmouth-Haven, at Brassie-Sound, at St. johns-deluce, at Ca●estoun, and at Scra●sler. S. by E. or, N. by W. Moon, before the Haven of Caven, in the Chamber, between Cripple Sand and the Creyl, and at Culshot, in Fair-Isle Roads, and at the North-Foreland, in the Chamber, and Gore●end, at Harwich within, before Margate, between the Naze and Warhead of Lower, at Orfordness within the Sands, at Rye, and into Thames-Roads, at Calshot. A Table, showing the exact Rising and Setting of the Sun, for every five days of each Month, with the Degrees of the twelve Signs proper to the Suns-Place; for the Lat. of 57 degrees. JANVARY. Sun's Place Days of the Monoth. The Sun riseth, The Sun setteth. 22 ♑ 1 8 Hours 32 Min 3 Hours 28 Min. 26 5 8 Hours 24 Min. 3 Hours 36 Min▪ 1 ♒ 10 8 Hours 18 Min 3 Hours 42 Min. 6 15 8 Hours 6 Min. 3 Hours 54 Min▪ 11 20 7 Hours 55 Min. 4 Hours 5 Min. 16 25 7 Hours 46 Min. 4 Hours 14 Min. FEBRVARY. Sun's Place Days of the Month The Sun riseth. The Sun setteth. 22 ♑ 1 7 Hours 29 Min. 4 Hours 31 Min. 27 5 7 Hours 20 Min. 4 Hours 40 Min. 2 ●● 10 7 Hours 8 Min. 4 Hours 52 Min. 7 15 6 Hours 54 Min. 5 Hours 6 Min. 12 20 6 Hours 44 Min. 5 Hours 16 Min. 17 25 6 Hours 31 Min. 5 Hours 29 Min. MARCH. Sun's Place Days of the Month The Sun riseth. The Sun setteth. 21 ●● 1 6 Hours 22 Min. 5 Hours 38 Min. 25 5 6 Hours 12 Min. 5 Hours 48 Min. 1 ●● 10 6 Hours 0 Min. 6 Hours 0 Min. 5 15 5 Hours 48 Min. 6 Hours 12 Min. 10 20 5 Hours 36 Min. 6 Hours 24 Min. 15 25 5 Hours 23 Min. 6 Hours 37 Min. APRIL, Sun's Place Days of the Month. The Sun riseth The Sun setteth. 22 ♈ 1 5 Hours 7 Min. 6 Hours 53 Min. 26 5 5 Hours 0 Min. 7 Hours 0 Min. 1 ♉ 10 4 Hours 47 Min. 7 Hours 13 Min. 5 15 4 Hours 35 Min▪ 7 Hours 25 Min. 10 20 4 Hours 26 Min. 7 Hours 34 Min. 15 25 4 Hours 12 Min. 7 Hours 48 Min. MAY. Sun's Place Days of the Month. The Sun riseth. The Sun setteth. 21 ♉ 1 4 Hours 0 Min. 8 Hours 0 Min. 25 5 3 Hours 52 Min. 8 Hours 8 Min. 30 10 3 Hours 42 Min. 8 Hours 18 Min. 4 ♊ 15 3 Hours 36 Min 8 Hours 24 Min. 6 20 3 Hours 27 Min. 8 Hours 33 Min. 14 25 3 Hours 20 Min. 8 Hours 40 Min. JUNE, Sun's Place Days of the Month The Sun riseth. The Sun setteth. 21 ♊ 1 3 Hours 15 Min. 8 Hours 45 Min. 24 5 3 Hours 13 Min. 8 Hours 47 Min. 27 10 3 Hours 12 Min 8 Hours 48 Min. 4 ♋ 15 3 Hours 12 Min. 8 Hours 48 Min. 9 20 3 Hours 15 Min. 8 Hours 45 Min. 13 25 3 Hours 16 Min. 8 Hours 42 Min. JULY. Sun's Place Days of the Month The Sun riseth. The Sun setteth. 19 ♋ 1 3 Hours 25 Min. 8 Hours 35 Min. 23 5 3 Hours 34 Min. 8 Hours 26 Min. 28 10 3 Hours 38 Min 8 Hours 22 Min. 2 ♌ 15 3 Hours 47 Min. 8 Hours 13 Min. 7 20 3 Hours 56 Min, 8 Hours 4 Min. 12 25 4 Hours 6 Min. 7 Hours 54 Min. AUGUST. Sun's Place Days of the Month. The Sun riseth, The Sun setteth. 19 ♌ 1 4 Hours 21 Min. 7 Hours 39 Min. 23 5 4 Hours 33 Min. 7 Hours 29 Min 27 10 4 Hours 40 Min 7 Hours 20 Min 2 ♍ 15 4 Hours 52 Min. 7 Hours 8 Min 7 20 5 Hours 3 Min 6 Hours 57 Min. 12 25 5 Hours 16 Min. 6 Hours 44 Min. SEPTEMBER. Sun's Place Days of the Month. The Sun riseth, The Sun setteth. ●9 ♍ 1 5 Hours 33 Min. 6 Hours 27 Min. 23 5 5 Hours 43 Min. 6 Hours 17 Min. 27 10 5 Hours 55 Min. 6 Hours 5 Min. 2 ♎ 15 6 Hours 4 Min 5 Hours 56 Min. 7 20 6 Hours 17 Min. 5 Hours 43 Min. 12 25 6 Hours 29 Min. 5 Hours 31 Min. OCTOBER Sun's Place Days of the Month. The Sun riseth, The Sun setteth. 18 ♎ 1 6 Hours 44 Min. 5 Hours 16 Min. 22 5 6 Hours 53 Min. 5 Hours 7 Min. 27 10 7 Hours 6 Min. 4 Hours 54 Min. 2 ♏ 15 7 Hours 15 Min. 4 Hours 45 Min. 7 20 7 Hours 29 Min. 4 Hours 31 Min. 12 25 7 Hours 41 Min. 4 Hours 19 Min. NOVEMBER. Sun's Place Days of the Month. The Sun riseth, The Sun setteth. 19 ♏ 1 7 Ho. 56 Min. 4 Ho. 4 Min. 23 5 8 Ho. 4 Min. 3 Ho. 56 Min. 28 10 8 Ho. 10 Min. 3 Ho. 50 Min. 3 ♐ 15 8 Ho. 23 Min. 3 Ho. 37 Min. 9 20 8 Ho. 33 Min 3 Ho. 27 Min. 14 25 8 Ho. 39 Min 3 Ho. 21 Min. DECEMBER, Sun's Place Days of the Month. The Sun riseth. The Sun setteth. 20 ♐ 1 8 Ho. 4 Min. 3 Ho. 8 Min. 24 5 8 Ho. 47 Min 3 Ho. 13 Min. 29 10 8 Ho. 48 Min. 3 Ho. 12 Min. 1 ♑ 15 8 Ho. 48 Min 3 Ho. 12 Min. 9 20 8 Ho. 45 Min. 3 Ho. 15 Min. 14 25 8 Ho. 41 Min. 3 Ho. 19 Min. Thus Courteous Reader, so much here is done, Which may please all, save Paterson alone: Therefore to Our Dialogue, let's proceed, In which I hope to clear myself indeed. A Mathematical Dialogue, BETWIXT james Paterson Mathematician at Edinburgh, And john Forbes Printer to Aberdeen, & 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. (Paterson.) I charge the Printer with several Errors in his Almanac, set forth and printed by him for the Year 1683. And first, concerning the Eclipse which did fall out upon the 17 day of januar in the afternoon, wherein he is deficient in giving the Digits Eclipsed; as also, in reference to the time of the Eclipse duration. (Printer.) Courteous Reader, I confess, being about my serious Employments in the Printing Press, I could not have leisure to Calculate that Eclipse, but made use of several Ephemerideses; as Vincent Wing, and Samuel Morland, etc. And Argolus doth assert the Digits Eclipsed to be 10 and more, john Gadbury 9: Paterson 8 dig. 13 min. as for the time, john Gadbury sayeth, the middle will be at 3 how. afternoon, the end at 4 hou. 3 min, or after the going down of the Sun: for in the Latitude of 57 degrees 10 minutes, being for Aberdeen, the Sun seateth being in the 8 degree of Aquarius, at 3 hou. 57 min. but Paterson sayeth 10 min. before 4 how. at Aberdeen, which is near half an hour; (a Prodigy which was never seen, the Sun to set at 3 hou. 30 min. at Aberdeen!) but by reason of the refraction, the Sun may appear or show himself above the Horizon, when he is not, If so the parallax be lesser than the refraction; and so I may truly and warrantably say, the Sun doth set at Aberdeen, the 17 day of Januar, at 4 hou. 18 min. afternoon. But granting I be redundant in some Minute's, but not so grossly, and as to say, not so deficient as he is, in saying the Sun being in the 8 degree of Aquarius, seateth at 3 hou. 30 min. but in truth, at 3 hou. 57 min. But what doth this concern me? My Antagonist cannot say, there is any wrong done to the Vulgar, or Horascopographier. But, as for that Eclipse which by an Telescope of 6 foot long, I did observe at the setting of the Sun, and did not find above two digits of the Sun's body obscured, with no apparent darkness, or shadow of change by that Eclipse: it was (as we all say,) to Westward Inhabitants. But lastly, I shall lay down some certain things to be observed in going about this Eclipse, and some things I shall demand of this Mathematician, in which I hope he will satisfy me, except he be, Mathematicus nomine tenus, (as I suppose) for I shall be as Laconic as I can, intending not to trouble the Reader with frivolous Expressions. First, supposing the middle time of the Eclipse to be at 3 a clock in the afternoon, according to john Gadbury. First, Granting the true places of the Luminaries, with the Mo●ns-Latitude, either by Calculation or Ephimerides. Secondly, I find the right ascension of the Sun in 8 degrees of Aquarius to be 310 degrees, added to 45 degrees or 3 hours, giveth 23 hou. 42 min. which showeth the 25 degree of Pisces to be on the Meridian or Medium Coeli; and the Ascendent 28 deg. 28 min. of Cancer: and consequently, the Nonagisimo degree falleth in 28 deg. 28 min. of Aries, being East ward of the Meridian 33 deg. 28 min. Thirdly, The Declination of the 25 deg. of Pisces, added to 57 deg. 10 min. giveth 59 deg. 9 min, the Arch of the Meridian between the 25 degree of Pisces and the Zenith. Fourthly, The Angle of the Ecliptic with the Meridian, being 66 deg. 33 min. giveth the Arch between the Nonagesim and the Zenith, by saying as R: Sine 59 deg. 9 min●●: Sine 66 deg. 33 min: Sine of 51 deg. 48 min. Fifthly, Having the true Latitude of the Moon, with the Parallax of Altitude, and having found the Parallacticall Angle, that is to say, the Angle made by the Ecliptic, and Vertical drawn through the Centre of the Moon to be 52 deg. 11 min. Sixthly, The Altitude of the Sun being at 3 hours in the afternoon, in the Latitude of 57 deg. 10 min. is 5 deg, 41 min. These being premised, I desire to know of James Paterson, the Parallax of Altitude, Longitud, right Ascention and Declination: whereby we may know the time of the visible Conjunction, the beginning of the Eclipse, the middle, and end end; with the Digits Eclipsed: whither above or under the Centre of the Sun. There are here required the resolution of several Triangles, wherein, ex tribus datis quartus requiritur, either by Calculation, or Projection. (Paterson.) Also he errs again in his Tyde-Table at Lieth, as if the Moon were not able to rule the Tide here as at Aberdeen. (Printer.) As for the flow at Lieth, which he carps at, they are not set down by myself, at upon my own account, but in so far, as they have been approved of, by ancient Seamen, Masters and Coasters; asserting that at Lieth, a S. W. by S. Moon maketh at nearest a full-Sea. This being a general Observation, therefore doth admit of some particulars; as the Wind blowing at such and such an Art, causeth the flow to vary, sometimes an half point, and sometimes more, in setting the flow high, and other times low: yea, the Seasons of the year, sometimes doth alter and change the streams, as about Lambas, the streams than are higher, then at certain other times, and consequently the general Role doth not hold altogether certain at all times; but doth sometime vary. It is holden as a general Rule by most of Seamen, that 3 quarters of an hour doth answer to a point of the Compass, the reason foe this is, (as they say,) because a quarter of the Horizon, answereth to a quarter of the Equinoctial, and consequently, 8 Points to 6 hours: so that they would have the Equinoctial equally divided, as they do the Points of the Compass. I confess, into a Parallel Sphere, it will hold true, but not into an Oblique Sphere: As admit, in the Latitude of 56 degrees, S. W. by S. being 3 Points, or 33 deg. 45 min. or 2 hou. 15 min. I find in the Equinoctial 29 deg. to which in time answereth to 1 hou. 56 min. of difference, being 19 min. in tyme. And this found out by a Spherical right Angled Triangle, by saying, as R: S: Lat:: Tang. Arch of the Horizon: Tang. of the Equinoctial Arch. The neglect of this is an Error, although not admitted by many Seamen; but constantly asserting that 45 min. in time doth answer to a point of the Compass. James Paterson, in his Corrected Tyde-Table, doth make Lieth to differ from other Tables, sometimes a whole hour, sometimes less; and in some agreeing, (to the great detriment and hazard of Ships seeking Lieth Harbour.) not determinating the true place of the Moon, which maketh a full Sea at Lieth; for if he shall have his recourse to the Theory of the Moon, except only the middle Motion, he shall involve himself into such a Labyrinth, out of which he shall never be able to extricate himself. Therefore by all that I have said, I see no ground for his Corrected Tyde-Table: And no marvel, he not being bred a Seaman, nei●her educate in Letters or Learning, as I am informed, and ●et calls himself, Mathematicus; O horrid Impudence! ●ut being a while in Ireland, and having gotten some smat●erings in the Mathematics, cometh to Edinburgh, and ●ayeth himself forth for Mathematicus: if it be otherwise then is related, certainly he will show himself in giving a solution to these five following Problems, not ●y Assertion, but by Mathematical Demonstration, I call them ●irocinia Nautica. PROBLEM I. There are two Islands in the parallel of 40 degrees, distant from each other 70 Leagues, a Ship sailing from the Westermost Island, between the N, and E. doth meet with a Ship that had sailed from the Eastermost, between the N. and W. and they are both in the Latitude of 41 degrees 30 minutes, and these two Ships have sailed 100 Leagues, I demand by what Courses these two Ships have sailed? and how many Leagues in every particular Course? PROBLEM II. There are 3 Islands, A, B, C, the Island A, and B, in the parallel of 40 degrees, and are distant from each other 30 Leagues, the third Island C, distant from A, 45 Leagues, and bearing of A, North-West: a Ship steering her Course East-South-East from C, so long, till she cometh to the parallel of 40 degrees. I demand how far she hath sailed from the Island C, before she bring the two Islands A, and B, sub maximo Angulo, or greatest Angle? PROBLEM III. A Ship in the Latitude of 40 degrees, is bound Westward, and being at A, she setteth an Island B, bearing of her South, and keeping her Course West, being at C, she setteth the same Island bearing of her South by East, 5 degrees Easterly. Again, being at D, South-South East 4 degrees Easterly. Lastly, being at E, she setteth the same to bear of her Southeast by East 6 deg, 15 min. Easterly: and hath sailed between D, and E, 2, 9 Leaug, more than between C, and D. I demand how far B was distant from A, when bearing Southerly. PROBLEM IU. A Ship in the Latitude of 40 degrees, saileth so long between the North and East, till she altereth her Longitude 10 degrees, and hath departed from her first Meridian, 96 Leagus, 2 Miles: I demand how far she hath sailed? and by what Course? PROBLEM V. Mr. Norwood, in his application of Spherical trigonometry, to the third kind of sailing, by the Arch of a great Circle, which is demonstrated by him, and others, to be the best way of sailing. (Consideratis Considerandis) Therefore, supposing two Places or Islands, lying in the parallel of 60 degrees, distant from each other 20 degrees in Longitude; and there are two Ships, the one sailing in the parallel, the other upon the Arch of a great Circle: I demand whither or no, he that saileth upon the Arch of a great Circle, doth make a major, or, minor ratio, to the great Circle, than he that sailoth upon the Arch of the Parallel, doth to the Parallel in which he saileth? In all these five Problems, I have given Letters Alphabetical, by which any Mathematician may form Triangles at pleasure, secundum data & requisita: And this much as to this purpose in the Art Nautical; and so I proceed to another head. (Paterson.) I have in the said Almanac for the Year 1683, described an Instrument, called the Line of chord, with a Scale of inch, and half inch, divided in 8 equal parts, the former, serving for measuring of all right lined Angles, the latter, for measuring the length, breadth, and thickness on Paper; and may serve for Foots, els, Falls, Roods, Miles, or Leagues: all which the Printer hath not in his Prognostication. (Printer.) I confess I have not the Line of Chords, or equal par●s mentioned in my Almanac, wha●thee, cannot a right lined Angle, be measured by a line of Sines, or Tangents, as well as by a line of Chords? especially by a line of Sines, seeing Sins are halfs of Choras▪ so that what i● performed by the whole, may be performed by the half: & contra. As for your line of Chords, with your use ye make of them; if there be no more, * Cabin-boy can say al● much as you can say, without any detriment to the Mathematicall-Science. What do ye say, as not being acquaint (as I suppose) with the Orthographical Projection, wherein the Object, either Sphere or Glob is supposed to be projected in plano, at an infinite or indeterminate distance from the eye; from whence cometh or ariseth Ptolimie his Analemma, wherein the Solisticiall Colour being seen directly, is circularly projected. The other five, to wit, the Horizon, Equinoctial, and Ecliptic; with the hour of Sex, and Prime Azimuth o● East and West, being seen perpendicularly, are projected in strait Lines: the Eye being in the intersection of all those Circles in principio Arietis. The other Circles that are seen Obliquly, are projected Eliptically, the parallels to these five mentioned are projected in strait lyns, according to the nature of their Primatius. These being premised the Primatives are divided accordingly, by Sines, and so are contracted; the nearer they approach the Solisticial Colour. From hence I say, that all the Problems performed by Ptolemie his Analemma, may be performed by a Line of Chords: yea, all the Problems performed by the Sins in the Scamans' Calendar, may be performed by the Line of Chords. Lastly, I say, that a Line of Chords of four inches Radius, will perform a Problem, either Astronomical or Geographical, better than a Globe of two foot Radius. And in so far, I have exalted your Line of Chords, in that wherein ye was deficient. As for measuring right Lined Angles by a Line of Tangents, I hold it a more ready way, then by a Line of Chords; for in the one a Compass is required, for drawing an Arch from the Angular Point, but in the other, no Compass or Arch is required; save only the Radius, and therefore, a Tangent Lyne is more useful than a Line of Chords. This Tangent Line is wonderful useful in the Steriographicall Projection, which supposeth the Object, be it Sphere or Glob, contiguous with the Organ or Eye. But it may be said, that visibile positum supra visorum non facit visionem. I answer, it is true in opacuous, thick, and dark Bodies, but not in Diaphanus and Transparent Objects. This Projection is of greater use and concernment than the Orthographical, because in the Orthographical, the divisions of the Radius from the Centre, doth shorten and become lesser and lesser towards the periphery, according to the nature of Sines: but in the Steriographicall, they increase from the Centre towards the periphery, according to the nature of Tangents; so that the increment of the one, doth supply the decrement of the other: in this projection Circles directly or obliquely seen, are projected in Circles, but perpendicularly in strait Lines. I could enlarge and delate myself in this purpose, but fearing my enlargement should seem tedious to the Reader, I shall at present produce some Instruments, framed by this Projection, and where the Organ is placed. And first, john Stoph●erus his Astrolob, where the Organ is placed at the Intersection of Aries and Libra; so that the aforenamed five great Circles, are projected in strait Lines, and the rest Circularly. john Blackgrave, his Mathematical Jewel, yea, the Universal Maps divided into two Hemispheres, where Meridian's and Parallels, are circularly projected; the Equator in a strait Line, but the Ecliptic in a Curve Line: I admire to see the same, as having no ground for that projection; I pray you Mathematicus, let me know if there be any ground for the same? nam cupio docere vel doceri. I desire to know of you, if a Spherical Triangle, such as formerly I have described, i● in the Solistitial Colour the same, or any other Oblique Angled Spherical Triangle be decircinated, peradventure without any term given? if the quantity or measure of the sides and Angles may be had? I doubt not, but as Mathematicus ye can perform the same; if otherwise, send to Aberdeen, and you shall have the solution from me. And this much for the Steriographical Projectiion, the Organ placed at the intersection of Aries and Libra. The second position, is at the Poles of the Equinox, and from thence ariseth Stofler his Astrolob; from whence Mr. Gunter's Quadrant is taken: this Astrolob hath the Equinoctial directly seen, with all the Parallels, the Meridian's Perpendicularly, and are projected in straight-Lines; the rest of the Circles Obliquly, and projected in Circles. The last is, when the Organ or Eye, is placed in the Zenith according to Clayius his Astrolob, or according to Mr. Gunter's Fundamental Diagram for plain dyaling; in which he doth project 10 great Circles, each of them having two Surfaces▪ except only the Horizon; so there doth arise 19 Faces, upon which plain Dial's may be described, the Horizon, with all the Almicanters, are projected circularly from the primative, the Az●muthes in straight Lines, the rest Circularly; all which is performed Practically by Mr Gunter his last Edition: look Gunter Lib: 2. Cap: 3. Sect. 1. 2. 3. But if ye desire a complete Demonstration of Mr. Gunter his Practice, consult Aguilonius in the 6 book of his Optics. I doubt not but what is said, will put you to a studere, but stud●isse had been more proper for a Mathematician. There is another projection called Scenographical, keeping a middle between the former two, in debita distantia: but because it consists in shortening and lengthening of Objects, as they are diversely seen, being more proppe● for Painters and Limners then for Seamen, to speak further I desist. Only observe, that all Spherical trigonometry by calculation doth depend upon the projections: consult Theodosius de Sphericis. As for your inch, and half inch, the one divided into 16 equal parts, the other into eight; it had been better, and more like an Artist, to have divided each of them▪ Diagonally in 100 parts, both for Navigation and Surveying: for Navigation by dividing the Meridian Line according to Mercator his projection, according to degrees of increasing Latitude: and in Surveying, as afterward in the next shall be made manifest. (Paterson.) I have several Measures, for length, bread●● and thickness, beginning from Barley Corn in reference to an inch, from thence to 12 inches making a foot, and 5 foot to a pace, and 1000 paces to a mile, and so forward; as you may see into my Almanac, all which ye have not at all expressea into your Almanac. (Printer.) I do confess, I have not expressed any Measures into my Almanac, neither is it required I should do so, being different because of their Objects: for the Almanak is in reference to Celestial things, and the other to Terrestrial. But let us proceed to the purpose, wherein he ●ayeth 5 foot makes a pace, and therefore I desire to know of him, if paces in all Nations and Countries be equal, or unequal; equal (I say) they cannot be, because the feet 〈◊〉 divers Nations are unequal; for the longer the foot be, ●r shorter; the fewer or more ●oots goeth to a pace: and herefore the paces are ●nequal, and if paces, than miles; ●nd if miles, than no certain●ie can be had for the meager of a degree upon the Arch of a great Circle; which is ●bsurd, and not consistent with reason. But now, let us ●ome to find the method and way, how the Ancient and Modern Geographers, did find out certain measures upon ●arth, in reference to the Heavens. I will begin first, ●ith the Egyptian Geographers, as Eratosthenes, who lived ●6 Years before CHRIST; and Ptolemy who lived ●o Year after CHRIST: They having chosen two places ●ing under or near the same Meridian, differing only observation, at 2 or 3 degrees in Latitude, which afterwards by a customary and standard Measure of that Kingdom of Egypt, they did find five foot to go to a pace, and 1000 paces to a mile. But the Learned Mr. Norwood did of late into his Book, called the Seaman's Practice, following the Ancient Geographers, in their practice, in measuring▪ between York and London, find a degree upon the Meridian, to contain 367200 foot English; and a mile 6120, so that an Egyptian pace containeth 6, 15 English, and an Egyptian foot 14, 75 English inches at nearest. But passing the fraction we take in numero ro●undo, 6 foot to the English pace, and consequently, 6000 foot to a mile in English measure. Now let us compare Scots with English, and first, ye say that 37 English inches according to your standard at Edinburgh giveth an Ell; Then a Fall, o● Pole being 6 Ell, giveth 2●2 Inches, 222 by 4, the length of a Chain, the product is 888: which being multiplied by 80, giveth 71040: and divyded by 12, the quotient is 5920 Foots short of 6000, by 80 Foot. Again, 42 Scots Inches in an Ell, as of the old standard, that is, 3 Foot and a half; the Pole or Fall being 21 Foot, the Chain 84 Foot, multiplied by 80, giveth 6720 Foot, for the length of a Scots Mile; which being reduced to an English Mile, say as 10: 9:: 6720: 6048 English, so that here the difference is only 48 Foot, whereby the Scots Mile exceeds the English: and no wonder, because 6000 doth admit a Fraction, which will be near equivalent to 48 Foot: and therefore, Mr Norwood's Practice doth altogether agree with a Scots Mile. But it may be said, or inquired of me, the reason why I say, as 10: 9:: 6720: 6048. I answer, because if an English Inch be divided in 10 parts, 9 of these doth answer to a Scots Inch: Therefore, being to reduce English to Scots measure, say as 9: 10; but Scots to English, say as 10: 9 These being premised, I would advise Surveyors here, as in England● to divide their 4 Pole Chain into a 100 parts, which we call Links; and there will answer 10 Inch to a Link, this Chain so divided, is very profitable for Surveying of Grounds, or Plating; and giving the Area, as ye say, 4 Pole in Latitude, and 10 in Longitude, giveth 160 square Poles for the Area: so also 1 Chain or 100 Links in breadth, multiplied by 10 Chains or 1000 Links in length, giveth for the Area 10 square Chains, or 100000 square Links; 75000 Links, 3 Rood, 50000 Links, 2 Rood; 25000 Links, 1 Rood: or 40 Pole, 625 Links square for a Pole. This I have premised for the benefit of Surveyors, they making use of the Diagonall-Scale, of Inch, and half Inch, or of any other Measure, Diagonally divided. (Paterson.) Also in my Advertisement, being the last in my Almanac, such as desire Mathematicall-Arts or Instruments thereto belonging, especially a Spirall-Lyne, which I have so framed, that you may work more Arithmetic in one hour, than any other in two days with the pen. (Printer.) Ye s●y ye have framed a Spiral-Line, so as the same had never been framed before; I had a true relation, from one that was a teacher of Mathematics at London 40 years ago, who told me, that one Mr. Brown a Carpenter, who lived at London, in the Minaries, near Tower-hill, was the first that did frame 3 Spiral-Lines upon a Circular Instrument, for Artificial-Numbers, Sins and Ta●gents; having two Brass Indices or Legs, fixed upon the Centre, and opening in manner of a Sector, so that, when 3 Terms were given to find a fourth, the one Leg was placed to the first Term, and the other to the second; then turning the Legs upon the Centre, (not being altered or changed) the first to the third Term, the second shall give the fourth required: whither the work be in trigonometry, Plain, or Spherical; or in Arithmetic simply. This Instrument can be had at London, being more serviceable than his, which is only for Arithmetic He sayeth, ●hat by this Instrument, they may work more Arithmetic in one hour, than any other in two days with the Pen▪ But I say, (in Arithmetical-Problems,) with the Pen shall work more in one hour, than he and his Spiral Line shall do n 10 days. — MART. Carpere vel noli nostra, vel ede tua. A POSTSCRIPT By way of Epistle to the Candid-Reader. Courteous Reader, IT was an excellent Saying of CICERO, All the Praise of inward Virtue, consisteth in the Good of outward Actions. Therefore, not only is it my Genius, but earnest desire to serve my Country, into every thing most useful and necessary for the Good thereof: especially, into that Noble and Famous Art of Navigation, without which, all Trade and Commerce in every Kingdom, should quite languish and decay. I have therefore, in this small Treatise, explained the three several Motions of the Moon, (viz.) her slow Motion, her middle Motion, and her swift Motion; together with Tables for her true rising and setting: also, showing her Motion, in Signs, Degrees and Minute's, for every day of her Age: with Everlasting Tyde-Tables for the Ebbs and Flow of the Sea, according to the Points of the Compass, and the Moons daily Age; (with the Hours and Minute's) not only for the Coast of Scotland, which was never yet so fully mentioned by any; but also, for all other places in the World. And having revised and compared the best Authors, who mention these Flow, and finding the most part of them differing from each other in the same; have therefore by advyce of judicious Seamen, made use of the best, and surest of them: Nevertheless, I humbly entreat any of our Experienced, Industrious, and most Laborious Seamen, who have Navigated these places, that they will be pleased to help any small oversights, (if there be any,) and send me information thereof by a Line, and accordingly I shall be most careful to amend the same in the next Impression: being most willing to extend myself for the Advancement of that Noble Art, intending (if this Impression go well off for my Encouragement, and be well taken,) to publish another Excellent piece of Navigation very shortly. Lastly, You have here a Mathematical Dialogue, betwixt james Paterson pretended Mathematician at Edinburgh, and Me, john Forbes Printer to the City, and King's University of Aberdeen: in which Dialogue, I have converted Vulgar Fractions into decimals, and therefore any intelligent Person may reap some knowledge, and I hope, be well pleased with the same. For, without any just Ground, or Provocation given, james Paterson did most ignorantly Rhyme against me, into his Almanac, for the year 1683, and likewise into his Almanac for the year 1684: making a great noise, concerning the mistake of two days for Hallow-Even, although Hallow-Day was exactly right, both for the day of the Week, and day of the Month: for all the World knoweth, Hollow Even to fall upon the night before Hallow-Day. But his Errors are more gross, making the Flood of Noah in his Chronologie, in all his Almanacs three hundred years short: A very beastly Error, besides other gross Errors, which I forbear at this occasion, any more to mention. For, as the good old Saying is, Envy shooteth at others, and woundeth herself. Truly I am heartily sorry, that both Mathematician and Printers are so evil Principled in the Grounds of Christianity, as holy Ambrose sayeth, Envy is nothing else, but a Grief of the Mind, at other men's Prosperity. And for my own part, I do declare it to the whole World, I hate such unrighteous and base Practices. For Agnes Campbel Spouse to Patrick Telfer, hath caused Counterfeit and Re-print my Almanacs into her Printing-house these several years bygone, sometimes Entituling them by Aberdeens' Almanac, and other times, according to Forbesses' Almanac, besides she hath for the ensuing year 1684, caused Print an Almanac as it were set fourth at Aberdeen, and Printed in Aberdeen, which is a most notorious untruth: impudently affixing thereto, some Lynes in the End, of Doggerel Rhyme, whereby she would have me to Patronise her base Execrations; as though 〈◊〉, (contrary to Christianity and the good Conduct of Nature,) should wish any man for any cause to hang himself. For, I seriously declare, though I be but one of the meanest of his MAJESTY'S Subjects: yet, I not only heartily pray for his long Life, and good Health; which I hold more to be my Duty, then to drink: but also, I have so much presumption, as to strive to follow my GRACIOUS SOVEREIGN in this matter, who by his numerous Acts of Clemency, hath (indeed) sufficiently declared to all the World, that he exactly followeth his Great LORD and MASTER in this, that he wisheth not the Death or Ruin of his Subjects; but rather that they would Repent and Live. For as Horace said well, Subjects follow the Example of their Princes, as certain Flowers turn according to the Sun. Almighty GOD, preserve Our Gracious KING, And's Subjects Hearts to due Obedience bring. And as for Robert Sanders, Printer in Glasgow, he hath not only inserted a notorious untruth into all his Almanacs these divers years bygone, (saying set forth at Aberdeen, as if the Famous College of Glasgow had not so much Mathematics, as to set forth an yearly Almanac, which in him, was no great Act of Prudence,) but also, contrare to the Good and Just Laws of this Ancient Kingdom, he hath caused Counterfeit the City of Aberdeen's Arms, and affixed them upon his most Erroneous, and Uncorrected Almanac, for the year 1684: whereof I am ashamed to speak, that such an Almanac should be published in this Kingdom; as may be seen into the Termly Quarters and Asspects, etc. tending much to the Discredit of that Famous City of Glasgow: not deserving to be called their Printer, Consideratis, Considerandis. All which unrighteous Practices, proceedeth more from Envy then sound Christianity; according to the good old Saying, The Envious man thinketh his Neighbour's losses to be his Gains. And as the Apostle sayeth, Titus 1. 15. Unto the Pure all things are pure, but unto them that are defiled and unbelieving is nothing pure; but even their very Mind and Conscience is defiled. And as for their Lying which is such a gross Sin, that the Holy Spirit of GOD, in the Scriptures doth very often expressly prohibet, as Rev. 21. 27. Rev. 22 15 and very many other places in Scripture. Yea, King David himself sayeth Psalm 63. 11. The mouth of them that speak Lie shall be stopped, etc. I might very largely insist upon this, only I shall desire the Guilty to be mor● studious, and serious with the Holy Scriptures 〈◊〉 GOD, which is the Rule of our Life. For, 〈◊〉 very Heathen Egyptians, they made a Law, that ever Liar should be put to Death. And Xenophon sayeth, that a Lie is not capable of Pardon. Courteous Reader, having Patiently born with all these injuries and Wrongs done unto me, for a long time, I could not (having this Opportunity) but clear myself, in giving you a view thereof, for which I humbly crave your Charitable Censure. For, as Augustin sayeth, Patience being often provoked with Injuries, breaketh forth at last into Fury. I shall not (at present) Enlarge any farther, but (as I did begin with my Antagonist james Paterson, who was the Principal Occasioner of this Discourse) shut up all with that good Saying of Augustin, Amongst the Foolish he is the greatest Fool, that knoweth little, and yet would seem ●o know much. And therefore I Conclude thus: ●ames Paterson, your Wisdom is not great, As may be seen into your Works of late: For though you say that I do Art disgrace, Not knowing where I do my Errors place; ●et sure I am, they should have a Clean-Pow, Who always call their Neighbour Nittie-Now. ●or all the Errors you put to my Door. ●re less than yours, even by an hundred score. ●our Hollow Even, and your Corrected Table, ●re but two frolicks, coming from a Babble. 〈◊〉 for your Eclipses and Moon's-Aspects, ●ou are ashamed thereof in all respects. ●here's nothing then, whereof I shall think shame, ●ver to publish in my Country's Name. But notice Sir, Here is a pretty Jest; That Vulgar still esteems our Works the best; As you confess, into your Almanac For Eighty-foure, which is a pretty Knack. It being holden for a real truth, When men confess the same with their own Mouth. Yea, fie upon it. You should Art disgrace! And wrong GOD'S Word with such a brazen face; Making GOD'S Works three hundred Years to sleep, Since Noah's-Ark did float upon the Deep. Which beastly Error, I shall make appear, From Almanacs you have made Year by Year. Now if this be the best part of your Pratticks; Which do proceed from Irish-Mathematicks: SCOTLAND will then have no more of the same, But keep themselves by BON-ACCORD'S Good Name: Who still shall have the Praise what ere befall, Because your Errors are so gross, in all. Your Spirall-Line, and eke your Line of Chords, Both of them little Wit, or Skill affords. Such learned Subjects, and such stately Knacks, Are most unfit for Yearly Almanacs. Whose Matter still should be for Vulgar use, Neglecting which, you do yourself abuse Now if you will Rhyme more in the next Year, My Answers then shall be apparent clear. Your Almanacs by Mine. I pray to mend, I'll say no more. I think it time to end. F1I6N8I3S quod FORBES. GOD SAVE THE KING.