as you sail along how you may know the distance of your ship from them IT is the custome of passengers when they first descrie that land which they would arrive at to ask the Pilot how far they are from land Unto which question he may well answer if he know two capes or points or notable places thereupon which places the further they be asunder one from another the more certainly may he answer to that question Let him pitch therefore one foot of one pair of compasses upon one of the two foresaid capes and the other foot upon the rumb which in his compasse pointeth towards that cape And in like manner shall he do with another pair of compasses placing one foot thereof upon the other known cape and the other foot upon the rumb which stretcheth towards the said second cape and moving the two Compasses so opened by their two Rumbs off from the land the very same point where the two feet which came from the two capes do meet you may affirm to be the very point where your ship is And then taking measure by the scale of leagues you may see what distance there is from the said point to either of the foresaid capes or to any other place which you think good for it is a very easie matter if you know the point where your ship is CHAP. XXXI Of the account of the Moone THe account of the Moone and of the tides is most necessarie to be known of Mariners to enter and depart from any Havens Rivers or Barres and to pass by some banks and shoalds A tide is a regular motion of the Sea whereby at some times it seemeth more increased then at other And these tides are of two sorts for some are such as we call spring-tides and neap-tides and the course of this motion hapneth from one half moneth to another half moneth Others be those which we call more properly by the names of tides to wit a full sea and a low sea a swelling and a falling sea and these are from the one half lunar day to the other half Which tides as well the first as the second have their course and moving from the motion of the Moone which is of two sorts one proper from West to East by means whereof in thirty days almost it is in conjunction with the Sun which we call the new Moone and in opposition which wee call the full of the Moone and those wee name the quarters when it shineth half unto us The other motion is from East to West by the force of the Primum mobile or the first moveable heaven whereby in one lunar day the Moone passeth over all the two and thirty points of the compasse or to speak more plainly it riseth and setteth and returneth again to arise which two motions of the Moone being known we may easily discerne the manner of both kinds of the foresaid tides And because that to the knowledge hereof it is requisite that we know the middle motion of the Moone I will first set down how it may be known and then how thereby wee may discerne the seasons of the tides For which purpose we are to note that the golden number as it is commonly called is a certain number of years wherein the Moone hath all the diversities of aspects with the Sun that can happen between them which is done in every nineteen years almost As for example if in the year 1588 there be a conjunction of the Sun and Moone upon the 26 of April or an opposition upon the 11 of April I say that there shall not happen a conjunction of the Sun and Moone upon the 26 of April nor an opposition upon the 11 of April till 19 years be expired which will be in the year of our Lord 1607. And so are wee to conceive likewise of the quarters and other aspects The second thing to be noted is that from this golden number springeth another which is called the concurrent being the days of the Moone at the beginning of the year which year according to that account beginneth from the last of February about twelve a clock at night which is the beginning of March. And the days of the Moone which then remain besides all the whole lunare moneths of the year past are called by Calculators The concurrents because they serve to know the account of the Moone throughout the whole year that is to come and they concur with other numbers to know the age of the Moone Now by these two numbers to be able to discern the days of the Moone or the distance thereof from the Sun you are to note the Rules following The first Rule of the Golden number From the present year of our Lord you must deduct 1500. and out of the remainder taking one in every twenty we shall finde the golden number if they be just twenties But if they be not just twenties above the number of twenties wee must add that which remaineth above the twenties all which being added together if it exceed not nineteene shall be the golden number But if it exceed nineteen cast away nineteen and the remainder is the golden number The second Rule of the concurrent Divide the golden number by three and if there remaine one the concurrent is equall with the golden number and if there remaine two the concurrent is greater then the golden number by ten but if nothing remaine the concurrent exceedeth the golden number by twenty And if this concurrent exceed the number of thirty then the remainder or surplussage shall be the concurent The third Rule of the Conjunction The number of the concurent being known you must add it unto the number of moneths which have passed from the beginning of March last past till the end of that moneth wherein you would know the same and if the whole product amounteth not to thirty mark how much it wanteth of thirty and if it exceedeth thirty see what it lacketh of sixty and that which it wanteth either of thirty or sixty is the number of the days of such a moneth wherein the Conjunction hapneth The fourth Rule of the full and quarters of the Moone If the day of the Conjunction be before the 15 day of the moneth add 15 unto the day of the Conjunction and you shall find the day of the full Moone and if the Conjunction happen after the 15 day take away 15 from the number of the day of the Conjunction and you shall have the full Moone of that moneth The first quarter is seven daies after the Conjunction and the last quarter seven days after the full Moone The fifth Rule of the Spring-tides and Neap-tides Upon the day of the Conjunction and of the full Moone are the Spring-tides and upon the two quarter days are the Neap-tides and so much the more doe the waters increase as the Conjunction or full Moon are nerer and so much the more they decrease also the neerer they come unto
the quarters An example whereby the foresaid Rules are made more plain Suppose a fleet of Ships lie within the heaven of San Lucar de barrameda expecting a fit time to passe over the barre towards the Indies It is evident that if the Ships be great they have need of much water to pass the bank or the barre which quantity of water is only in the Spring-tides And because they are twice in one moneth namely in the Conjunction and in the full of the Moon I desire to know when the Spring-tides and Neap-tides of the moneth of Iune in the year 1588 were to be expected in which moneth I presuppose the fleet was to depart First therefore I cast away 1500 and cut of the 88 remaining I take from each 20. One which make four in all which being added to the 8 that surmount 80. they make the golden number to be 12 according to the first Rule I divide these twelve by three and the quotient is foure and nothing remaineth and because there is no remainder I will take two more of the concurrent thâ—n of the golden number and there shall be two of the concurrent casting away thirty by the second Rule Adding these two to the four moneths which are from the beginning of March past till this present moneth of Iune I find that they make six And because six want twenty four to make up thirty I say that in the year 1588 we had a Conjunction of the Moon upon the 24 of Iune by the third Rule and adding seven unto the day of this Conjunction you have the first day of Iuly which is the day of the first quarter And taking away 15 from 24 being the number of the Conjunction day there remain nine and upon that day of the moneth you have the full Moon And adding other seven unto the nine days of the full Moon you have the last quarter upon the sixteenth of Iune by the fourth Rule I say therefore that the Spring-tides or greatest waters of the moneth of Iune were in that year upon the ninth and four and twentieth days of Iune and the Neap-tides or less waters were upon the sixteenth-day of Iune and the first of Iuly by the fifth Rule CHAP. XXXII Of the daily Tides NOW that we know the Rules of the Spring-tides and neap-tides let us say somewhat of the Tides that happen every day which depend upon another swift motion of the Moon whereby turning round about the world from East to West it passeth every day by the 32 points of the Compasse and this dayly motion of the Sea falleth not every day at the same hour because the Moon doth not alwaies keep one and the same distance from the Sun For the Moon moveth almost thirteene degrees of her proper motion in one natural day whereas the Sun moveth scarce one and so one being taken from thirteene there remain 12. And because the Sun doth give and marke out unto us hours and the Moon Tides it commeth to pass that an hour being that space of time wherein fifteene degrees of the Equinoctial pass by every point of the Compasse the part by which the Moon is distant from the Sun shall be twelve degrees which twelve are â…˜ of fifteene degrees contained in each hour Insomuch that the Moon by her middle motion is every day distant from the Sun about twelve degrees which being reduced into time do make â…˜ parts of an hour whereby the Moon is every day slower then the Sun in comming to each point of the Heavens by the motion from East to West in regard of that which she hath borrowed for her own proper motion from West to East Whereof it commeth to passe that so many days as the Moon is old so many times â…˜ parts of an hour it is slower then the Sun in passing by each Rumb untill the day of their conjunction when as they passe both by the same Rumb in one and the same hour And so accordingly because we are to set down the certain hour of every day wherein the Tide happeneth we must diligently Observe the Rules following The first Rule In divers parts of the Sea coast the Moon maketh a full Sea every day being in divers Rumbs according to the disposition of the Land But upon all the coast of Spain in the Ocean it is full Sea when the Moon is in the North-east and South-west The second Rule Upon the day of the conjunction and full Moon you have a full Sea at three a clock in the morning and at three in the after noon for at those hours the Moon goeth with the Sun at the North-East and at the South-west But upon other daies of the Moon the full Sea falleth out at the same hour when the Moon commeth to those two points which is known by counting the age of the Moon The third Rule That you may know at all times how many daies old the Moon is you must add three numbers together to wit the concurrent and the moneths from the beginning of March to the moneth present and the daies of the moneth wherein you would know this and if the whole product exceedeth not thirtie it containeth just the daies of the Moon but if it doth exceed thirtie the surplussage sheweth the daies of the Moons age The fourth Rule Multiplie the daies of the Moons age by four and divide the product by five and the remainder after division containeth the hours whereby the Moon commeth more slowly then the Sun to the North-east or South-west or to that Rumb wherein it maketh a full Sea which hours shall be added to the three hours of the morning and then you have the hours of the first Tide or of the full and swelling Sea and six hours and almost a quarter after commeth the first ebbe or low water and 12 hours and â…• after the first full Sea commeth the second Tide and other six hours and â…• after the second Tide commeth the second ebbe The fifth Rule When the daies of the Moons age are less then fifteene we may make by them our account for the Tides but if they exceed fifteene we must make our account by the surplussage An example of the said Rules Upon the 29 of July 1588 I desired to know the hours of the full Sea and of the ebbe to make choice of that which might seem most expedient for my Voyage By the formâ—r example I find that the golden number of this year is 12 and the concurrent 2 according to the correction of the year by Pope Gregorie the 13. Then I add this number of 2 to the number of 5 moneths which have passed from the beginning of March and the 29 days of the moneth of July all which 3 numbers make 36 then I cast away 30 and there remain six daies for the age of the Moon and because they exceed not fifteene I multiply them by â…˜ of an hour according to the fourth Rule and they may make 24
25 day I may notwithstanding find the time of the Suns entrance into the midst of Taurus by the Observations of the 24 and 26 dayes after this manner Subtract 14 degr 9 min. 40 sec. Of Taurus out of 16 degr 3 min. 42 sec. of Taurus the remainder will be one degr 54 min. 2 sec. that is the motion of the Sun for two dayes between the 24 and 26 dayes at Noon Therefore as 1 degr 54 min. is to 48 hours so are 50 min. 20 sec. That is the Difference of the place of the Sun the 24 day from the midst of Taurus found out as before to 21 hours and 12. min. almost So as hereby it seemeth the Sun should enter into the midst of Taurus the 25 day about two hours and 48 minutes before Noon that is at nine of the clock and 12 minutes But if it so fall out that you do not or cannot Observe both before and after the time of the Suns comming to the point desired as suppose I could not have Observed the 24 day but only the 25 and 26 dayes in both which dayes the Sun is gone past the point desired notwithstanding you may Obtain your desire thus Subtract 15 degr 5 min. 20 sec Taurus the place of the Sun the 25 day out of 16 degr 3 min. 42 sec. Taurus the place of the Sun the 26 day there will remain 58 min. 22 sec. the Diurn motion of the Sun between the Noon-tides of the 25 and 26 dayes Now because that on the 25 day at Noon the Sun was gone 5 min. 20 sec. past the point desired therefore as 58. min. 20 sec. Are to 24 hours so are 5 min. 20 sec. to 2 hours 12 min. almost By this account then the Sun should enter into the midst of Taurus the 25 day 2 hours and about 12 min. before Noon that is at nine of the clock and 48 minutes Neither ought that smal difference that appeareth between these accounts to be greatly regarded which amounts not to so much as half an hour in which time the motion of the Sun is little above a minute and the Declination of the Sun in that part of the Zodiack cannot alter so much as â…“ of a minute which is so smal as can by sense very hardly be Observed or discerned Neither yet ought that little difference of a minute or two that appeareth between the Diurn motions of the Sun found by Observation greatly move any man in that by the first and second Observations the Diurn motion should be almost 56 min. by the first and third 57 min. by the second and third 58 min. and more the greatest of which differences may almost arise by erring but one half minute only in taking the height of the Sun which error is in a manner altogether insensible and will be easily pardoned by them that have or shall accustom themselves to make the like Observations when besides their own experience they shall find that they which have most excelled in this Art as Tycho Brahe de recentiorâ—b Aetherei mundi phaenom lib 2 cap. 10. part 1. Copern Revol Libr. 4. cap. 21. and Ptoleme himself in all his Catalogue of the fixed Stars Almagest lib. 7. cap. 5. When they shall find I say that even these Princes in Astronomy so greatly exercised in Observations have accounted an whole minute or two hardly sensible Ptoleme also in his Almagest Contenting himself for the most part to have set down the places of the fixed Stars to sixth parts of degrees and very seldom comming to twelfth parts thinking it sufficient as it may seem by the perpetual course of that Catalogue to come within five or ten minutes of the truth But to return again to that from whence we have a little digressed After this manner now shewed we found the time of the Suns entrance into the beginning of ♈ and ♎ and into the midst of ♉ ♌ â™ and â™’ as into places serving most fitly for finding out of the Suns Eccentricitie and Apogeum following also herein the example of Copernicus lib. 3. cap. 16. Revol Who well perceiving how hard yea rather impossible a thing it is to find by Observation the time of the Suns entrance into the Solsâ—itial points where the Meridian Altitudes and Declinations of the Sun continue almost the same without any sensible difference for two or three dayes together chose rather the parts of the Zodiack already mentioned where the place of the Sun may more truly be known by reason of the quicker altering of his Declination the difference thereof in the space of 24 hours amounting to more then 17 min. The times therefore of the Suns comming to the foresaid points in the years 1594 1595 1596 1597. We found to be such as are set down in the Table following  1594 1595 1596 1597    Da. Ho. Mi. Da. Ho. Mi. Da. Ho. Mi. Da. Ho. Mi. Sig. De. Ian.    24 17 35 25 0 7 24 5 54 â™’ 15 Mar.    10 13 26 9 18 43 10 0 37 ♈ 0 April    25 16 50 24 21 47 25 3 54 ♉ 15 Iuly 28 15 35 28 20 4 28 1 43 28 9 56 ♌ 15 Sept. 13 2 45 13 7 39 12 13 48 12 19 15 ♎ 0 Octob. 28 5 46 28 9 36 27 15 23 272 1 50 â™ 15 Hereby the times of the Suns continuance in the arks of the Zodiack betwixt those points as also the arks of the Eccentrick answerable to those times were more easily found then that it should now be needfull for me to be further tedious in setting down the manner of finding the same wherein notwithstanding there may some difference of an hour or two sometimes appear by comparing together those times in several years yet this error being such as may arise by missing little more then one minute in one Observation or little more then half a minute in two Observations of the Meridian Altitudes of the Sun one Observation being made when the Sun is about the beginning of the ark the other when he is about the ending thereof I make no doubt but that it will at the least be favourably censured by them that have acquainted themselves with some practise of Observing wherein he shall in my opinion quit himself meetly well who neither through imperfection of sense either in making or dividing or in rectifying or in using his Instrument and every part thereof nor through the difficultie of noting precisely the edges of the shadow of the upper sight falling upon the nether the limits or bounds of which shadow are but a confused mixture as it were of light and darkness or else a mean equally compounded of them both which can no better be discerned then by guessing nor yet by Rrefraction of the Sun beams through the thickness of the air especially when the Sun is in the Southerly Semicircle of the Zodiack which Refraction admitteth some alteration according to the diversitie
35 seconds the difference of the declination in 24 hours at that time 22 minutes 13 seconds Now as 360 is to 22 minutes 13 seconds so is 90 degrees to 5 minutes 33 seconds the part proportional or equation desired which because the Declination increaseth and the bay of Mexico is also Westward from the Meridian of London must be added to the Declination before found in the Table and so shall you have the true Declination of the Sun that day at noon for that place 7 degr 45 min. 8 sec. But admit you had sailed Eastwards and were in the East Indian Ocean sea differing likewise in Longitude from London about 90 deg therefore the difference of Declination and the part proportional thereof or equation of the Declination shall be the same they were before But because you are gone so much Eastwards the Sun commeth 6 hours sooner to your Meridian there then it doth to ours here at London and therefore because the Declination also is increasing and will be greater when the Sun commeth to our Meridian then it was the Sun being under the Meridian of the East indies that equation of Declination must there be subtracted out of the Declination found in the Table which before was to be added when we supposed you to be in the bay of Mexico because the Sun commeth later by six hours to the Meridian of that place then to ours and therefore the Declination of the Sun increasing in the mean time will be greater there then here Now imagine you sail in the year 1612 through the Streights of Magellan and having passed over the South Sea come the 12 of September to the Philippinas differing in Longitude from London VVestwards about 210 degrees In this example because the Sun is neer the Equinoctial point altering his Declination about 24 min. in 24 hours that is for every houre one minute therefore divide 210. the difference of Longitude by 15 the number of degrees conteined in one hour the Quotient will be 14 minutes the difference of Declination answerable to that difference of Longitude The Declination found in the Table for that day is 10 minutes 2 seconds Northerly which Declination because it decreaseth the Sun not being yet come to the Equinoctial must be subtracted out of 14. and there shall remain 3 min. 58 sec. the Declination of the Sun that day at noon for that place But this Declination is Southerly because the Quotient 14 min. is greater then 10 min. 2 sec. the Declination found in the Table It would be at this time too tedious for me further to exemplifie every particularity specified in the former Rules which may cause some small diversitie in the use of the Suns Declination having already given examples of the hardest cases that may befall herein which if they be well considered and especially compared with the Globe or Sphere wherein the whole manner of the Suns motion and Declinations may most easily not onely be seen but also felt as it were with the fingers ends the reason and Demonstration of all those Rules and of all the diversities of working therein specified may most plainly appear to him that is but of a mean capacity CHAP. XXIX The Declinations of the principal fixed stars about the Equinoctial corrected by Observation BUt because the Declination of the Sun is then only of good use for knowing the Latitude at Sea when his Meridian Altitude may be Observed so as although all the rest of the day and night be fair and cleer if a Cloud cover the Sun but one quarter of an hour only about noon your Tables of the Suns Declination will stand you in no stead there have been therefore other means divised for attaining to the knowledge of the height of the Pole not only in particular by Observation of the Pole-star and Guards but also in generall by the Meridian Altitude and Declination of any notable fixed star whatsoever So as not in the day time alone and that onely at noon but almost at any time of the night if any small portion of the heavens towards the North or South appear but a small time cleer through the raking Clouds the Latitude of the place where you are may hereby bee more easily known then by Observation of the Suns Meridian Altitude For to omit the changing of the Suns Declination from North to South and from South to North twice in every year which notwithstanding breedeth some diversity of working by neglect whereof some have grosâ—y erred the Sun by reason of his swiftness of motion increaseth or diminisheth his Declination dayly yea hourly and that very sensibly many times whereof there must needs arise many severall considerations to be had of the right use and application of the Suns Declination found in the Table as well in respect of the part of Declination whether it be North or South as also in regard of the difference of Longitude between the place for which the Tables of the Suns Declination were made and the place of Observation whether it be Easterly or VVesterly from thence besides many other particularities lately related and needlesse here to be repeated But the fixed stars mooving so exceeding slowly that in more then 70 years they go not so much as one degree in there proper motion from the west Eastwards keep not only the same part of the North or South but almost the same point and minute of Declination for many years together I mean those stars especialy that are placed in the signs of Gemini Cancer Sagittarie or Capricorne neer the Solstitiall Colure which in an hundred years or two can alter their Declination scarce one minute whereas those stars that bee in Pisces Aries Virgo or Libra especialy if they be neer the Equinoctial colure may differ in there Declinations about one minute in 3 years which difference though it be something yet for a dozen or twenty years will hardly be so much as can at Sea be Observed by any Instrument hitherto had in use there For these two causes therefore that is for the more easie and generall use of the Declinations of the fixed stars then of the Sun I wish they were more generally known and observed by our sea-men then they are as whereby they might not onely most easily know the elevation of the Pole at any time of the night but also in any place of the world much more commodiously then otherwise they can because that in what latitude and how far soever they should come either Northwards or Southwards they might alwayes have their choice of divers fixed stars neer the meridian both towards the North and South of a convenient height to be observed But herewith it were also to be wished that the tables of the fixed stars declinations which are most common amongst English Mariners had been more free from errour then they are I mean especially the Tables published in Bourns regiment and Normans new Attractive which tables agreeing almost in
with the Regiment of the Sun and of the star the rules of the Moon and of the Tides the declaration of the Sea-chart and other things appertaining hereunto CHAP. I. The Definition of the Sphere A Sphere is a solid or massie body without hollownesse and perfectly round in the midst whereof there is a prick called the center by which there passeth a right line named the Axtree and the points where this line endeth upon the superficies of the whole body are called Poles because upon them the Sphere is moved CHAP. II. That the whole World is a Sphere AND so it is evident that the whole frame of the World wherein we live is a Sphere being as it is solid so that in the whole World there is no empty place also it is perfectly round upon the upper Superficies of the highest heaven and it hath in the very midst a certain point to wit the center of the earth by which we do imagine a right line or Axtree to passe from one pole to another upon which the World is moved about from East to West CHAP. III. Of the division of the Sphere THE whole Sphere of the World is divided into two parts or Regions the Elementary and Celestial The Elementary part or Region hath four parts the first whereof is the earth which together with the element of water which is the second maketh one perfect Globe and round about both these are two other elements namely the Air and above that the fire which filleth the space between the Air and the Sphere of the Moon of which Elements by vertue of the heat of the Heavens are made and compounded all corruptible things in the world The celestial Region consisteth of other ten parts the first whereof is the Sphere of the Moon the second the Sphere of Mercury the third of Venus the fourth is the Sphere of the Sun the fifth of Mars the sixth of Jupiter the seventh of Saturn the eighth is the Sphere of the fixed stars which is called the Firmament the ninth is the Crystalline heaven and lastly the tenth and highest is the Sphere called the Primum mobile that is the first or highest moveable heaven That which remaineth called the Empyreal heaven because it hath no motion cometh not to be considered on in the Art of Navigation A Figure wherein may be seen the Composition of the whole Sphere of the World CHAP. IV. Of the motion of the Heavens THe number of the Heavens is known by the motions observed in them which are ten distinct one from another For the Moon moveth her proper and peculiar motion in 27 dayes and 8 hours which is one Revolution Mercury Venus and the Sun finish their motion in one year which conteineth 365 dayes and almost a quarter of a day Mars runneth his course in two years Jupiter in twelve years Saturn in thirty years the eight Sphere according to the opinion of some in seven thousand years the ninth in five and twenty thousand and eight hundred years and the tenth in four and twenty hours almost Which ten motions are reduced unto three principal the first is that of the first moveable upon the two ends of the Axletree which are called the Poles of the World from East to West turning about again unto the East in 24 hours and this Sphere by the force of his motion carrieth about with it all the other lower Spheres in the space of 24 hours Howbeit they move also the contrary way with a second motion which is from West to East upon two other poles distant from the first about three and twenty and an half such parts whereof the whole compasse of heaven conteineth three hundred and sixty And this second motion is accomplished in each of the lower Heavens in divers spaces of time as is before said The third motion is proper to the eighth Heaven wherein the fixed stars are placed which motion is the cause that the distance of the poles of the first motion from them of the second motion doth vary being sometimes greater and sometimes lesse CHAP. V. Of the Figure of the Heavens THat the Heavens are round it is proved because roundnesse is the most perfect Figure of all others being whole and intire having no need of any joynts being also of the greatest capacity of all figures that have the same compasse and in that respect most fit to contain all other things Also the principal bodies of the World as the Sun the Moon and the stars are of this Figure and we see the same likewise in those things which are bounded by themselves as it is manifest in drops of water and all other liquid things CHAP. VI. That the Earth and Water make one perfect Globe THere is nothing that sheweth more cleerly that the earth and water make one round Globe then the shadow which they make in the Eclipses of the Moon which shadow we alwayes see to be a part of a circle For if the body which is the cause of the same shadow were three-square or four-square the shadow it self also would appear in the same fashion Wherefore the shadow of these two bodies together being round it is manifest that they are round also CHAP. VII That the Earth is in the center of the World ONe sign we have to be assured that the Earth is in the midst and center of the World namely that wheresoever we are upon the face of the earth we alwayes see one half of the Heavens the other half being hidden out of our sight Moreover the stars in what part of the Heavens soever they be either in the East West or South we see that they are alwayes of the very same bignesse Whereby we may easily perceive that they are alwayes equally distant from our sight and whereas they move round about it it followeth that we are upon the center of that body on whose superficies the said stars describe their circles CHAP. VIII The whole quantity of the Earth ANd albeit the Globe of the Earth and Water compared with the Spheres of the Stars is as it were a center or prick yet being considered by it self it conteineth in the greatest circle thereof 6300 common Spanish leagues Which a man may easily perceive by taking two such points or head-lands of the earth as are under the same Meridian and which differ in distance one from another so much as one of those parts is whereof the compasse of the whole world conteineth 360 and it is found both by Navigation at Sea and also by travel on land that the two foresaid points are distant each from other 17 leagues and an half of which leagues each one conteineth 4000 paces every pace 5 foot every foot 16 fingers and every finger 4 grains of barley CHAP. IX Of the Equinoctial Circle BEing to treat of the Circles of the Sphere of the World the first which offereth it self to be spoken of is the Equinoctial Circle by means whereof we do know in
Rules of the Declination of the Sun we are to note that the year which is the time of the Suns motion from any point of the Ecliptick till he return again to the same point consisteth not alwaies of an equal number of days For besides 365 days it containeth almost one quarter of a day but the year which we commonly account containeth 365 days in common years and in leap years 366. It was therefore needfull to make foure Tables of twelve moneths apeece whereof the three first contain 365 days and the fourth 366 and in such sort to distribute the Declination of the Sun among them that you may make account of the Declination which is wanting to the Sun at the end of 365 days for lack of those six hours almost which the Sun wanteth to come unto the point from which it departed at the begining of the year and also of the Declination which resulteth in the fourth year because it consisteth of 366 days at what time it cometh to recover that which in the three former years it had lost Therfore to know at all times which of the foure Tables we ought to make use of I will set down a Rule whereby you may know whether the present year be leap year or whether it be the first second or third year after the leap year And the Rule is this that taking from the years of our Lord which run in our common account the number of 1600 if the remainder thereof be an even number and half of the remainder and even number then that year is leap year and if the remainder be even and the half thereof odd then that year is the second year after the leap year But if the remainder of the years numbred be odd we must try the year next going before to see whether the remainder thereof and half the remainder be even numbers for then the present year is the first after the leap year And if the remainder of the year going before be even and the half thereof odd then the present year is the third year after the leap year How the Declination of the Sun may be found out Now to know the Suns Declination every day we must look in that Table which answereth to the present year and seeking the moneth in the upper part of the page and the day of the moneth wherein we would know the Declination in the column which defendeth towards the left hand right over against the said day and under the title of our moneth we shall find two numbers one of degrees and the other of minutes which are the Declination of the Sun that day towards that part of the world which the first Rule of the Sun doth teach CHAP. VI. The Equation of the Suns Declination THey which sail in the moneth of Iune and December need not much to make any Equation in the Table of the Suns Declination because that in those moneths the Declination of one day differeth very little from the Declination of another But at all other times of the year we ought to make some kind of Equation to know precisely our height or our distance from the Equinoctial This Equation is to be made after this manner You must subtract the Declination of the Sun for the present day from the Declination of the day following or contrariwise subtract alwaies the lesse out oâ— the greater and the difference or remainder shall be multiplied by the leagues which our ship hath sailed from the Meridian of London and the product of the multiplication must be divided by 7200 leagues which are contained in the compasse of the whole earth then if you have sailed Westward the Quotient must be added to the Declination of the Sun that day if it be from the 11 of March to the 12 of Iune or from the 13 of September to the 12 of December or it must if the shippe also hath sailed Westward be subtracted if you find it in any other time of the year except in the daies of the Equinoctium for then this difference is known by taking the Declination of the present day with that of the day following but if you be to the Eastward from the Meridian of London you must doe contrariwise subtracting the said Squation where before you added it In stead of the Table of the Suns Declination here inserted by Roderigo Samorano use the Table before set down from the 174 page to the 180 page CHAP. VII Foure examples for the plainer declaration of that which is said before An example of the second Rule IN the year 1608 the 15 of April suppose I was sailing and took the height of the Sun with my Astrolabe at noone and found the height thereof to be iust 90 degrees First therefore I took from 1608. the number of 1600. and their remain 8 whicâ— remainder being an even number and foure the half thereof being even also I say the year 1608 is the Leape year And so I goe unto the fourth year in the Table of the Suns Declination which is leap year and under the moneth of April over against the 15 day I find 13 degrees and 25 minutes 41 seconds I say therefore that I am distant from the Equinoctial towards the North 13 degrees and 26 minutes almost because it is betwen the 11 of March and the 13 of September in which space falleth the 15 day of April The second example of the third Rule In the year 1602 upon the 13 day of September admit I tooke the height of the Sun and found it in my Astrolabe to be 70 degrees and an half and that in the Table of Declination belonging to the same year upon the foresaid day of September I found that the Sun had no declination but that it was under the very Equinoctial line Now because the degrees of the height which the Sun wanteth of 90 are 19 and an half I say that I am so much distant from the Equinoctial toward that part of the world unto which the shadow falleth Example of the fourth Rule Upon the 13 of May 1609 suppose I took the height of the Sun at noon in my Astrolabe and found it to be 85 degrees and three quarters Now because 1609 is an odde number I goe back to the former year of 1608. and I find according to the Rule of leap years that the year 1608 is leap year and hence I judge that the year 1609 is the year next following the leap year Then I go to the Tables of Declination belonging to the first year after the leap year and under the moneth of May against the 13 day the Suns Declination is found to be 20 degrees 41 minutes 15 seconds and because that from the 11 of March to the 13 of September the Sun keepeth his course to the Northwards of the Equinoctial having marked the shadow at midday I see that the lower vain of mine Astrolabe looketh to the North of the Compasse and so I say that
the Ruler as before you shall cut the line BD in another point which shall represent eight of the clock in the morning and four in the afternoon And accounting higher fifteen degrees more one both sides and placing your Ruler upon the end of your account it will divide the line BD at another point which shall be nine a clock in the morning and three in the afternoon and so you shall proceed from fifteen to fifteen degrees till you come to eleven of the clock in the morning and one in the afternoon And if you will have the half hours also you must account from seven degrees and an half to seven and an half and doing as you did with the fifteenth degrees you shall have the half hours also Then placing your compasses upon the center E and upon every division of the line EB you shall draw the same divisions likewise upon the line ED which being done draw certain obscure lines from the point A to the divisions of the line EB and drawing the right line GF see where GF is cut at the highest of the obscure lines which must be at the point N from whence the line NO is to be drawn equally distant from the line BE. And this line NO shall be divided proportionally by the obscure lines even as the line BE. Then let the divisions of the line NO be transferred into the lines MG MI LF LH and then the Tropicks also shall be divided Then by every three points answerable in the Equinoctial and the two Tropicks you shall draw certain parts of Circles seeking the center of those three points in the Equinoctial line extended forth on either side and these parts of Circles represent the hours then make an account of the degr of Declination from the point B and from D on both sides by every 2 degr and draw lines Parallel to the Equinoctiall from one to another and those shall be the Parallels of the Suns Declination Moreover you shall make an Horizon as large as the Diameter of the inner Circle which shall be divided after this manner Count from the points AC towards B five degrees and putting your Ruler upon the end of the account of both parts see where it cutteth the line EB and there make a mark and then counting on both sides other five degrees and putting the Ruler once again at the end of your account make another mark where it cutteth the line EB And so the line EB must be divided from five to five degrees which divisions shall be removed into the said Horizon fastning it to the Center and laying it to the line BD and dividing it both ways as the line EB is divided and set numbers thereinto from 5 to 5 which may begin in the midst and end with 90 at the ends of the Horizon and let every one of these parts be divided into five other parts or degrees Then accounting from the Center E in the Horizon eleven degrees and ¼ you shall set there a mark which shall be the seventh point from North and South that is it shall represent the points which are next to the East and West in the Compasse And accounting another eleven degrees and a quarter and making there a mark it shall represent the sixth point from North and South And so you must doe with the other points and then your Instrument is finished CHAP. XXXV Of the parts of this Instrument IN this Instrument the first thing is a Circle divided into 360 degrees which is the Meridian and the line of twelve a clock The second are the right lines of which that in the midst is the Equinoctial and the two others are the Tropicks of Cancer and Capricorn And the other lines between those are the Parallels of the Suns Declination which have their numbers agreeable to them And those that are between the Equinoctial and the Tropick of Cancer doe serve from the 11 of March to the 13 of September and the others for the residue of the year The crooked lines which cross those Parallels are the hour lines And the point of the Meridian which in 90 degrees distant from the Equinoctial towards the left hand is the North Pole and the point opposite to that is the South Pole In the Horizon there are first the degrees and then the points of the Compass distinguished by the small pricked lines CHAP. XXXVI How you may know what a clock it is by this Instrument AT any time of the day when you would know what a clock it is take the heighth of the Sun with your Astrolabe and seeking the Table of the Suns Declination what Declination it hath the same day and the height of the Pole which a good Mariner knoweth at all times because he must direct his course thereby This being known place the Horizon Instrument on the one side under the North and on the other side above the South so many degrees as his distance from the Equinoctial is the same day and fasten it there with a little wax that it may not move Then count in the Meridian on either side from the Horizon which now standeth firm the height of the Sun above the Horizon take with your Astrolabe and by the end of the account draw a line or thred overthwart which shall be equally distant from the Horizon Then reckon the Suns Declination in the parallels beginning from the Equinoctial of the Instrument that way which the Sun Declineth and mark the line or Parallel at which the account of the Declination endeth where and at what hour it is crossed by the thred for that hour is the hour of the day But note this that if the crossing of the thred and Parallel doe fall upon the division of the Parallel and of the hour it is a just hour but if it fall beside the common meeting of the Parallel and of the hour-line upon that side where it falleth see how much more there is then an hour whether ¼ or 1 ◠or ½ c. Now although every hour line hath two numbers one of the morning and another of the afternoon yet it is an easie matter to distinguish which of them will serve your turn if you know whether your Observation be before high noon or after which is to be known by your Astrolabe for if the Sun ascend it is before noon but if it descend it is afternoon CHAP. XXXVII Of the Variation of the Compasse by this Instrument IF you would know by this Instrument the Variation of the Compasse you must doe thus When the Sun riseth or goeth down at the Horizon Observe him with your Compasse noting very diligently upon what Rumb and part of the Rumb he riseth or falleth And if the compasse be divided into 360 parts beginning to reckon them from the East and from the West on either side and ending in the North and South with 90 degrees it shall be the fitter for this purpose because then you shall see
how you may know the distance of the Ship from them 51 31. Of the account of the Moon 51 The first Rule of the golden number 53 The second Rule of the concurrent 53 The third Rule of the Conjunction 53 The fourth Rule of the full and quarters of the Moon 53 The first Rule of the Spring-tides and Neap-tides 54 An example whereby the foresaid Rules are made more plain 54 32. Of the daily tides 55 The first Rule 56 The second Rule 56 The third Rule 56 The fourth Rule 56 The fifth Rule 57 An example of the said Rules 57 33. Of a certaine Instrument whereby you may in generall judge of the tides 58 The use of this Instrument 59 34. Of the making of an uniuersal Diall which may serve generally all the World over 60 35. Of the parts of this Instrument 62 36. How you may know what a clock it is by this Instrument 36 37. Of the variation of the Compasse by this Instrument 64 38. At what hour the Sun riseth and setteth every day in all parts of the World 65 39. Of the length of the day and of the night 65 40. Of a night Diall by the North stars 65 The use of the Table of the Suns declnation 67 A Table of the Suns declination 69 By the height of the Pole-star to know the height of the Pole 81 1 When the greater or former Guard is in the East of the same height with the Pole-star 83 2 When the two Guards are of equall height betwixt the East and the highest 84 3 When the greatest or formost Guard is right above the Pole-star 85 4 When the two Guards are directly one over another betwixt the highest and the West 86 5 When the greater or formost Guard is in the West of the same height with the Pole-star 87 6 When the two Guards are of equall height betwixt the West and the lowest 88 7 When the greater or former Guard is directly under the Pole-star 89 8 When the two Guards are directly the one over the other betwixt the lowest and the East 90 FINIS Made and sold by Joseph Moxon at his shop on Cornhil at the signe of Atlas GLobes Coelestial and Terrestrial of all sizes and Books for the use of them Sphaers great and small according to the Ptolemean Systeme Sphaers great and small according to the Tychonean Systeme Sphaers great and small according to the Copernican Systeme With Books for the use of them Blagraves Mathematical Jewel Oughtreds Circles of Proportion The Spiral Line Gunters Quadrant and Nocturnal Stirrups Universal Quadrat These with divers other Mathematical Instruments are printed on Papers and exactly pasted on Boards c. with Indexes and other appurtenances proper to each Instrument very commodious for any mans use Also Books for the use of every of the foresaid Instruments Sea-plats printed on paper or parchment and pasted on Boards Vignola or the compleat Architect useful for all Carpenters Masons Painters Carvers or any Gentlemen or others that delight in rare Building A new Invention to raise water higher then the Spring with certain Engines to produce either motion or sound by the water very useful profitable and delightful for such as are addicted to rare curiosities by Isaac de Caus. A Help to calculation By J. Newton A Mathematical Manuel shewing the use of Napiers bones by J. Dansie A Tutor to Astrology with an Ephemeris for the year 1657 intended to be annually continued by W. E. Also all manner of Mathematical Books or Instruments and Maps whatsoever are sold by the foresaid Joseph Moxon The Haven-finding Art Or The way to find any Haven or place appoynted at Sea THere is no man I suppose that knoweth not with how great diligence now of a long time especially since men leaving no part of the world unattempted have sayled into America and to the utmost Indies the searchers out of excellent things have sought some certain way whereby they which take charge of Ships might know assuredly the situation and Longitude of what place soever they would goe unto and so come to any Haven or place appointed at Sea But I know not how it hath come to passe that there could not hitherto any certain knowledge of that matter be attayned unto For some when they indevoured to find this thing by the magnetical needle gave the Load-stone it self a Pole which of the Load-stone called also the Magnet they named the Magnetical Pole or Pole of the Load-stone But that this is otherwise the thing it self hath taught us because the variation of the needle is found not to follow the Rule of that Pole Yet in the mean time this continual searching gave occasion of another mean whereby a Ship might certainly direct her course unto any Haven or place at Sea whereto you would desire to go although the true Longitude both of the place wherein the Ship is as also of the place where the Haven is were both unknown Which that it may in some sort be rudely shewed and that the circumstances hereof may more clearely be set forth before your eyes whereby there may ensue a more certain and general use of the same first of all it must be known that we are taught by dayly experience that the Magnetical Needle touched with the Load-stone or Magnet which therefore we call the Magnetical needle doth not always point out the same part of the world but without any respect of that Magnetical Pole wherof we made mention before sometimes indeed it sheweth the true place of the North but for the most part it declineth either towards the East or West which variation yea even in a smal distance of places hath most manifestly appeared to them which have directed their course from the Easterne parts towards the West For examples sake at Amsterdam the variation is 9 degrees and 30 min. towards the East In the Foreland of England 11 degr At London 11 degr 30 min· Near Tinmouth in the Sea 12 degr 40 min. and so forth How any Haven or place at Sea may be found the Latitude and variation of the same place only being known THe variation of the Magnetical Needle and the Latitude of the place being known the same place may be found although the Longitude be unknown and that dayly experience plentifully teacheth For that we may make this matter plain by examples especially if the Mariner know that the Latitude of the Citie of Amsterdam is 52 degr and 20 min. and that the variation of the Compasse in the same place is 9 deg and 30 min. he must needs not be ignorant that when he hath brought himself to that Latitude and variation he is not far from Amsterdam what Longitude soever that Citie have But some man may object that there are many places which have the same Latitude and variation that the Citie of Amsterdam hath whereto we may readily answer that indeed there be such places but yet very far distant from thence and
41 12 49 53 26 11 36 26 5 0 6 36            3 36 9 9 ♎ 3 26 8 ♎ 57 0 6 26 6 42 5 16 59 57 16 51 0 8 57            8 57 54 22 58 13 22 48 0 10 13 11 8 15 28 56 34 28 46 0 10 34 11 50 55 0 ♠57 28 0 ♠45 0 12 28 15 12 37 11 5 41 10 46 0 19 41 16 17 10 14 4 23 13 46 0 18 23 16 43 19 16 7 30 15 47 0 20 30            8 5 58 21 6 26 20 48 0 18 26 16 9 0 25 16 16 24 50 0 26 16 22 7 55 10 ♠42 36 10 ♠1 0 41 36 CHAP. XX. The finding of the Suns Apogeum and Eccentricitie out of the former Observations NOw by the whole course of these Observations it manifestly appeareth that the Declinations set down in the Regiments of the Sun that are and have bin hitherto ordinarily used by our Seamen do for the most part notably err from the truth of the Heavens Which errors as they may most truly be corrected by Observation only in those dayes wherein certain Observation was made so for finding out the Declinations of the middle dayes between the Observations I thought it the best way first to make the Ephemerides of the Sun hereafter following agreeable to the former Observations and then to find out the Declinations answerable to the places of the Sun for every day of four years together because that after that number of years the same places of the Sun and the same Declinations return again without sensible error which also by a certain Equation may be corrected and for the easier finding out of this Equation I have continued these Tables for one year more making them for five years and so including two Leap years by the difference of which years we may easily find the said Equation by means whereof these Tables may be made serviceable for many years First therefore for making these Ephemerides it is needful to know the time of the Suns entrance into certain principal points of the Zodiack as also the time of the Suns continuance in the arches of the Zodiack contained between those points whereby the proportion of the Suns motion may Geometrically be found out his Eccentricitie and place of his Apogeum being hereby known To know the time of the Suns commnig to any point of the Ecliptick it is best to Observe exactly the Meridian Altitude of the Sun not only the same day wherein he is like to enter into the point desired but every day also for two or three dayes together both before and after that day that both by the testimony of so many Observations compared together you may have the more assured truth as also that if the day you most desire fall not out to be so clear as you would wish you may notwithstanding by the Observations of the dayes going before and following after or either of them obtain your desire Having thus Observed the Meridian Altitudes of the Sun and thereby also found his Declinations for every one of those dayes wherein you Observed you shall easily know also the true place of the Sun in every each one of the same dayes with help of the former Table of the Declination of every minute of the Ecliptick in such sort as before was declared when I shewed the use of that Table Now if it fall out so happily that both the day be clear when the Sun entreth into the desired point of the Ecliptick and that the place of the Sun answerable to the Declination of that day be all one with the point desired you have already that you sought for without any more ado viz. That the Sun entreth that day at Noon into the point desired Otherwise subtract the Observed place of the Sun next before the point desired out of the Observed place of the Sun next following that point and the remainder shall shew you the true motion of the Sun answerable to the time between those Observations Subtract also the former place of the Sun from his place in the point desired and note the difference for as the former remainder that is the apparent motion of the Sun between the Observations is to the time between those Observations so is this difference to the time between the first Observation and the Suns entrance into the point desired Example of the first I desired to know the time of the Suns entrance into 17 degrees 0 min. of ♌ in the year 1595. I Observed therefore at London the apparent height of the Sun at Noon the 31 of Iuly the same year and found it to be 54 degrees 14 minutes out of which his true height corrected by his Parallax was found to be 54 degr 15 min. 46 sec. Whereby his Declination was gathered to be 15. degrees 47 minutes 46 sec. And consequently his place in 17 degrees 0 minutes of ♌ that day at Noon Example of the second admit the year following 1596 You would know the time of the Suns entrance into the midst of Taurus Having therfore to this end Observed the apparent Meridian Altitudes of the Sun the 24 25 and 26. Dayes of April in that year within the space of which dayes I am sure the Sun must needs be in that point to be 54 degrees 35 minutes 54 degrees 51 min. ½ 55 degrees 8 min. ½ and consequently the true heights 54 degr 36 min. 44 sec. 54 degr 53 min. 13 sec. 55 degrees 10 min. 13 sec And out of these the true Declinations 16 degr 8 min. 44 sec. 16 degr 25 min. 13 sec. 16. degr 52 min. 13. sec. Hereby I found the true places of the Sun the same dayes to be 14 degr 9 min. 40 sec. Of Taurus 15 degr 5 min. 20 sec. of Taurus 16 degr 3 min. 42 sec. Of Taurus Subtracting therefore 14 degr 9 min 40 sec. Of Taurus that is the place of the Sun the 24 day out of 15 degr 5 min. 20 sec. of Taurus the place of the Sun the 25 day the remainder shall be 55 min. 40 sec. Which is the true motion of the Sun between the 24 and 25. Dayes at Noon that is the Diurn motion of the Sun at that time Subtracting also 14 degr 9 min. 40 sec. Of Taurus out of 15 degr 0 min. of Taurus the difference is 50 min. 20 sec. Now as 55 min. 40 sec is to 50 min. 20 sec. so are 24 houres to 21 houres 42 min. and 2 sec It appeareth therefore by subtracting 21 hours 42 min. 2 sec. Out of 24 hours that the Sun should enter into the midst of Taurus the 25 day about two hours and almost 18 min. before Noon that is at nine a clock and 42 minutes Now supposing I had not or could not have Observed the