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
exact Observations taken by a Quadrant of six foot and a quarter semidiameter in the years 1594. 1595. 1596. 1597. Finding therefore Taurus and the 20 degree in the upper part of this Table and 45 minutes in the first columne I have in the common meeting of the column descending from 20. and of the line proceeding from 45. minutes towards the right hand 18. degrees 0 minutes 18. seconds the Declination of the Sun the same day at noon here at London Example of the second The 15. of August the same year by the same Ephemerides the Sun is in 2 degr 2. minutes of Virgo Therefore I seek Virgo and 2. in the nether part of this Table and 50. minutes in the last columne towards the right hand ascending upwards Then following the line of 2 minutes leftwards and the column of 2. degrees upwards in the common meeting of the line and columne I find ten degres 47. minutes 19. sec. the declination of the Sun the same day at noon for the Meridian of London But the Declination of the Sun being first known by Observation or otherwise the place of the Sun shall most easily be found out by this Table after this manner Seek the Suns Declination in the Area of the Table then if the sign wherein the Sun is which you may for the most part easily know by estimation be in the head of the Table ascend upwards to the top of the same columne in which you found the Declination given for there you shal have the degree of the Sun follow also the line wherein you find the given Declination towards the left hand till you come to the first columne leftwards and there you shall have the minute also But if the name of the sign wherein the Sun is be in the nether part of the Table you must do all things contrariwise descending from the Declination found in the Area of this Table in the same columne till you come to the lowest part thereof where you shall find the degree of the Sun and proceeding from the Declination towards the right hand in the same line till you come to the last columne where you shall find the minutes to be adjoyned that you may have the true place of the Sun This way of finding out the place of the Sun by his Declination first known by Observation is then of especial use and truth when the Sun is neer the Equinoctial points for there his Declination altereth quickest increasing or decreasing about 24 min. in 24. houres But when the Sun is neer either of the Tropicks the missing of one minute yea or half a minute in observing the Declination may cause you err an whole degree and more in the place of the Sun He therefore that listeth trie how well the Ephemerides and Astronomical Tables hitherto published agree with the truth of the heavens had best make Observation when the Sun is in Pises Aries Virgo and Libra where mising one whole minute in Observing the declination will cause you misse not past two minutes and an half in the true place of the Sun When the Sun is neer either of the Equinoctial points there may sometimes be some smal difficultie in finding out what sign the Sun is in which may easily be avoided thus The Meridian Altitude of the Sun increasing as in Winter and Spring time if the height of the Sun be lesse then the complement of the Poles elevation the Sun is in Pisces otherwise in Aries But if the Meridian Altitudes of the Sun be every day lesse then other as in Summer and Autumne and the height of the Sun at noon greater then the height of the Equinoctial the Sun is in Virgo otherwise in Libra There may likewise be some doubt in what sign the Sun is being neer either of the Tropicks which may be resolved thus the Sun having South Declination increasing is in Sagittarie but if the Declination of the Sun be Southerly and decreasing he is in Capricorn Contrariwise the Declination of the Sun being Northerly and increasing he is in Gemini if decreasing he is Cancer Now whether the Declination of the Sun increase or decrease you may know by comparing the Declinations of two daies together For if the Declination answerable to the second day be greater the Declination increaseth otherwise it decreaseth If both daies have equal Declination the first day the Sun is in Gemini the second in Cancer if his Declination be Northerly if Southerly the first day he is in Sagittarie the second in Capricorn An example or two will make all plaine The eighth day of April 1597. the Declination of the Sun was found by Observation to be 10. degrees 55. minutes 27. seconds which I seek out in the Area of this Table and in the head of the same columne in which I find the Declination that commeth neerest unto this that is 10 degr 55. min. 33. sec. I see 28. degrees of Aries for in April the Sun cannot be in Libra and in the same line wherein I found this Declination in the furthest columne towards the left hand I find 21. minutes out of which abate 17. seconds that is the part proportional answerable to 6. sec. which is the excesse of 10 degr 55. minutes 33. sec. the Declination found in the Table above 10. degr 55. min 27. sec. the Declination found by Observation and there shall remain the true place of the Sun the same year and day 28. degr 20. min. 43. sec. of Aries Which Maginus following Copernicus and the Prutenical Tables as he professeth maketh to be the 27. degr 57. minutes of Aries almost that is 24. minutes lesse then truth that equation also being abated which is answerable to the difference of Longitude betwixt London and Venice The 11. of March the same year at London whereby many and diligent Observations by large and several Instruments the height of the Pole is found to be 51 degrees 32 minutes the apparent Meridian Altitude of the Sun was exactly Observed to be 38 degrees 49 minutes but being corrected by the Parallax and Refraction of the Sun answerable to that height his true height shal be 38 degr 51 min. 4 sec. Whereby it appeareth that his true Declination the same day at Noon was 0 degr 23 min 4 sec. And that Northerly because the height of the Sun was greater then the height of the Equinoctial It is plain therefore that at that time the Sun was entred into Aries But now to know how far he was entred seek out 0 degr 23 min. 4 sec. Or the number next to it which is 0 degr 23 min. 9 sec. In the Area of this Table wherewith you shall also find in the same line in the column next the left hand 58 minutes and in the top of the column right over this Declination you shall have 0 degr Therefore it is manifest that at that time the Sun was in 0 degr 58 min. of Aries almost for there wanteth
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
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
right side 41 38 2 56 2 The goat or wagoners left shoulder 44 30 4 49 1 The wagoners right shoulder 45 11 5 30 2 The first in the great bears fore-foot 40 30 8 24 3 The second in the same foot 41 28 8 32 3 In her former left knee 36 37 8 58 3 The great bears side 31 26 10 58 2 The great bears back 26 05 10 40 2 The end of the Dragons tail 18 26 11 08 3 The great bears thigh 34 03 11 32 2 The great bears rump 30 41 11 54 2 The next to the end of the Dragons tail 17 57 12 14 3 The first in the great bears tail next her rump 31 49 12 32 2 The middlemost in her tail 32 55 13 06 2 In the end of her tail 38 37 13 32 2 The next before the turning of the Dragons tail 23 40 13 53 3 The formost guard 14 11 14 54 2 In the turning of the Dragons tail 29 37 15 14 3 The hindmost guard 16 42 15 26 2 Next after the turning of the Dragons tail 30 20 15 54 3 The Dragons eye 37 18 17 22 3 The Dragons head 38 22 17 44 3 In the Swans right wing 45 44 19 34 3 In her tail 46 06 20 30 2 Cepheus his right shoulder 29 00 21 10 3 The back of Cassiopeia's chair 33 02 23 48 3 CHAP. XXXII To know at what time any of the foresaid fixed stars come to the Meridian for any day of the year NOw because the fixed stars are then onely meet to be observed for finding the latitude when they are in the meridian it is therefore good for him that meaneth to observe them to know at what time they come to the meridian To this end there are tables published and almost in every mariners hands pretending to shew at what hour and minute every star in the first of these two former tables commeth to the meridian for the beginning and midst of every moneth in the year agreeing likewise in every errour one with another but because these errours breed not at any time greater danger or damage to the Mariner that is ware of them then to make him watch for their coming to the meridian a quarter or half an hour longer then otherwise he needed this inconvenience onely provided for those tables may serve the turn well enough for them that list not trouble themselves to learn a better way But for them that are desirous of a more true and generall way I have also made the table following of the Suns right ascensions reduced into hours and minutes for every day of this present year 1599 according to the Ephemerides of the Sun before set down with help of which table it may easily be known for any day of any year in our age at what time not onely any of the foresaid fixed stars about the Equinoctial but those also about the Pole or any other whose right ascensions are known in hours and minutes come to the meridian and that after this manner Finde out in the table following the moneth and day wherein you observe the moneth in the upper margine of the table the day in the first column thereof next the left hand the common meeting of the column descending from the moneth and of the line proceeding from that day towards the right hand shall give you the Suns right ascension in hours and minutes for the same day This right ascension of the Sun subtract alwayes out of the right ascension of the star adding 24 hours to the stars right ascension if it be lesse then the right ascension of the Sun the remainder sheweth how many hours and minutes after noon the star cometh to the upper part of the meridian which if they be more then 12 hours subtract 12 from them and the remainder shall shew you how many hours and minutes after midnight the star cometh to the upper part of the meridian The upper part of the meridian I call that which passeth from the Pole by the Zenith to the Horizon southwards But it shall be needful also many times when you would observe the stars about the Pole which never set to know the time of their coming to the nether part of the meridian which may easily be done onely by adding 12 hours to the time of their coming to the upper part of the meridian if it be lesse then 12 hours or by subtracting as much if it be more Suppose for example the 25 of February 1599 I would know the time of the great dogs coming to the meridian First therefore in the next table following the column descending from February downwards and the line proceeding from the 25 day towards the right hand in the common meeting of them both I finde 23 hours 10 min. the Suns right ascension that day at noon Then in the first table of fixed stars I finde the great dogs right ascension to be 6 degr 27 min. to which because it is lesse then the Suns right ascension I adde 24 hours and the sum of both cometh to 30 hours 27 min. out of this I subtract the Suns right ascension 23 hours 10. min. and there remais 7 hours 17 min. the time of the great dogs coming to the upper part of the meridian in the afternoon Take one example also of a star that never setteth and admit the 20 of December the same year you would know what time the formost Guard cometh to the Meridian beneath the Pole First therefore you shall finde as before the Suns right ascension that day to be 18 hours 36 min. and the right ascension of that star in the second table of fixed stars 14 hours 54 min. to which being lesse then the Suns right ascension adde 24 hours and from the sum 38 hours 24 min. subtract the Suns right ascension 18 hours 36 min so there shall remain 20 hours 18 min. the time of the formost Guards coming to the upper part of the meridian from which subtract 12 so you have the time when it cometh to the nether part of the meridian 8 hours 18 min. after noon A Table of the Suns Right Ascension in hours and minutes for every day of the year  January February March April May June D. H. M. H. M. H. M. H. M. H. M. H. M. 1 19 30 21 39 23 25 1 18 3 11 5 15 2 19 34 21 43 23 28 1 22 3 15 5 19 3 19 39 21 47 23 32 1 26 3 19 5 25 4 19 43 21 50 23 36 1 29 3 23 5 27 5 19 47 21 54 23 40 1 33 3 27 5 31 6 19 52 21 58 23 44 1 36 3 30 5 36 7 19 56 22 02 23 47 1 40 3 34 5 40 8 20 00 22 06 23 51 1 43 3 38 5 45 9 20 04 22 09 23 55 1 47 3 42 5 49 10 20 08 22 14 23 58 1 51 3 46 5 53 11 20 13 22 18 0 02 1 55 3 50 5 57 12 20 17
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