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
2 30 39 Â 21 6 9 5 43 Â 8 6 18 57 40 14 45 6 Â 25 53 2 4 7 2 7 18 Â 22 7 9 27 51 21 58 7 19 12 25 14 23 7 Â 27 57 1 45 8 1 43 56 Â 27 8 9 49 49 Â 52 8 19 26 48 14 1 8 Â 29 32 1 8 9 1 20 29 Â 27 9 10 11 41 Â 42 9 19 40 49 13 40 9 Â 30 40 0 39 10 0 57 2 Â 29 10 10 33 23 Â 33 10 19 54 29 13 18 10 Â 31 19 0 11 11 0 33 33 Â 31 11 10 54 56 21 23 11 20 7 47 12 55 11 Â 31 30 0 18 12 0 10 2 Â 32 12 11 16 19 Â 13 12 20 20 42 12 34 12 Â 31 12 0 48 13 0 13 30 Â 33 13 11 37 32 Â 2 13 20 33 16 12 9 13 Â 30 24 1 14 14 0 37 3 Â 32 14 11 58 34 20 51 14 20 45 25 11 48 14 Â 29 10 1 44 15 1 0 35 23 34 15 12 19 25 Â 39 15 20 57 12 11 23 15 Â 27 26 2 13 16 1 24 9 Â 32 16 12 40 4 Â 28 16 21 8 35 10 59 16 Â 25 13 2 40 17 1 47 41 Â 31 17 13 0 32 Â 16 17 21 19 34 10 34 17 Â 22 33 3 9 18 2 11 12 Â 31 18 13 20 48 20 3 18 21 30 8 10 9 18 Â 19 24 3 37 19 2 34 43 Â 29 19 13 40 51 19 49 19 21 40 17 9 46 19 Â 15 47 4 5 20 2 58 12 Â 28 20 14 0 40 19 36 20 21 50 3 9 19 20 Â 11 42 4 34 21 3 21 40 Â 26 21 14 20 16 19 23 21 21 59 22 8 53 21 Â 7 8 5 0 22 3 45 6 Â 22 22 14 39 39 19 8 22 22 8 15 8 28 22 Â 2 8 5 29 23 4 8 28 Â 19 23 14 58 47 18 53 23 22 16 43 8 2 23 22 56 39 5 56 24 4 31 47 Â 17 24 15 17 40 18 38 24 Â 24 45 7 36 24 Â 50 43 6 23 25 4 55 4 Â 12 25 15 36 18 18 22 25 Â 32 21 7 9 25 Â 44 20 6 51 26 5 18 16 Â 9 26 15 54 40 18 7 26 Â 39 30 6 42 26 Â 37 29 7 10 27 5 41 25 23 5 27 16 12 47 17 50 27 Â 46 12 6 15 27 Â 30 19 7 52 28 6 4 30 Â 0 28 16 30 37 17 33 28 Â 52 27 5 48 28 Â 22 27 8 11 29 6 27 30 22 54 29 16 48 10 17 16 29 Â 58 15 5 20 29 Â 14 16 8 36 30 6 50 24 22 49 30 17 5 26 16 58 30 23 3 35 4 53 30 Â 5 40 9 3 Â Â Â Â Â Â 31 17 22 24 16 41 Â Â Â Â Â Â 31 21 56 37 9 26 CHAP. XXVIII The use of the former Table or regiment of the Sun THis Table of the Suns declinations as it differeth nothing in form from others that have been published heretofore so likewise the manner of using it is altogether the same that hath been accustomed in former Tables of this kind saving that I must give warning of one error that hath been committed herein which is as I have observed that some of our Sea-men do take the Suns declination out of their regiments without any aequation by addition or subtraction of the part proportional agreeable to the difference of Longitude of the place where they are as if they were alwayes at the same place or under the same meridian for which their Regiments were made for which cause alone though they avoid all other errors it may so fall out that they may be deceived somtimes 10 or 12. minutes or more in a long voyage in taking the Suns declination For there is not any Table of the Suns declination but that it must needs be made for some one meridian as this former Table was made for the meridian of London and therefore cannot be truely used in any other without some Equation answerable to the distance of the meridians or difference of Longitude To avoid this error therefore first learn how much you differ in Longitude from the place for which your Table was made and though you misse half a dozen or half a score degrees herein it cannot in this point breed any sensible error Secondly take out the difference of the Suns declination agreable to the space of 24. hours about the time of your observation Thirdly as 360. is to this difference of declination so is the difference of Longitude to the part proportional or Equation of the declination which Equation is to be added to the declination of the day of observation if the declination of the Sun be either increasing and the place of observation westward or else decreasing and the place of observation eastwards from the place for which your Table of declination was made otherwise this Equation is to be subtracted from the declination of your day of observation that you may have the true declination of the Sun for the time and place of your observation But if the time of your observation be the noon-tide immediately before or after the Suns entrance into either of the aequinoctial points you must follow another rule and that is this divide the difference of Longitude by 15 mark how many unites the quotient conteineth and so many minutes adde to the Declination found in the former Table if you be either Eastward from the Meridian of London and observe the noontide before the Equinoctium or if you be Westward from that Meridian and observe the noontide after the Equinoctium for the sum shall be the Declination desired Otherwise if you be either Westward from the Meridian of London and observe the noontide next before the Equinoctium or Eastward from that Meridian and Observe the day immediatly after the Equinoctium compare the Declination found in the Table with the foresaid quotient and subtract the lesser out of the greater for that remaineth is the Declination desired Which Declination hath the same denomination of North or South that the Table sheweth if the quotient be lesse then the Declination found in the Table but if the quotient be greater the denomination must be altered from North to South or from South to North contrary to that the Table sheweth If the quotient be equal to the Declination found in the former Table the Sun is in the very Equinoctial point and hath no Declination at all A few examples will make these rules more plain suppose therefore the 30 of March 1610. you were sailing in the bay of Mexico differing in Longitude to the Westwards from the Meridian of London about 90 degrees by estimation the Declination of the Sun for that day found in the former Table is 7 degrees 39 minutes
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
years which are also leap years themselves Under every one of these ranks of years there are two columns the first whereof containeth the degrees and min. of the Suns Declination answerable to every day of the moneth superscribed in each of those years without sensible error In the second column are set down the minutes of the differences of the Suns Declinations for every one of those dayes for the readier finding of the part proportional of this difference answering to any difference of Longitude from London whereof you may read more pag. 181 c. In the first column of each of these Tables next the left hand are placed the numbers of the days of the moneth that is set down in the head thereof The use of this Table for knowing the Declination of the Sun at any time is thus look the moneth and year wherein you would know the same in the head of the Table and the day of the moneth in the first column next the left hand then proceeding from that day directly in the same line towards the right hand till you come right under the same year you shall there find the Declination you sought for Take for example the 24 day of February in the year 1610. Finding therefore that moneth and year in the head of the Table and the 24 day in the first column in the same line proceeding towards the right hand till you come right under that year you have there the Suns Declination for that time 5 degrees 34 minutes towards the South January  1 2 3 4 Day 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 deg mi. di deg mi. di deg mi. di deg mi. di 1 21 47  21 50  21 52  21 54  2 21 37 10 21 40 10 21 42 10 21 45 9 3 21 27 10 21 30 10 21 32 10 21 35 10 4 21 17 10 21 19 11 21 22 10 21 24 11 5 21 6 11 21 8 11 21 11 11 21 13 11 6 20 54 12 20 57 11 21 0 11 21 2 11 7 20 42 12 20 45 12 20 48 12 20 51 11 8 20 30 12 20 33 12 20 36 12 20 39 12 9 20 17 13 20 20 13 20 23 13 20 26 13 10 20 4 13 20 7 13 20 10 13 20 13 13 11 19 50 14 19 54 13 19 57 13 20 0 13 12 19 36 14 19 40 14 19 43 14 19 47 13 13 19 22 14 19 26 14 19 29 14 19 33 14 14 19 8 14 19 11 15 19 15 14 19 18 15 15 18 53 15 18 56 15 19 0 15 19 4 14 16 18 38 15 18 41 15 18 45 15 18 49 15 17 18 22 16 18 26 15 18 30 15 18 33 16 18 18 6 16 18 10 16 18 14 16 18 18 15 19 17 50 16 17 54 16 17 58 16 18 2 16 20 17 33 17 17 37 17 17 41 17 17 45 17 21 17 16 17 17 21 16 17 25 16 17 29 16 22 16 59 17 17 4 17 17 8 17 17 12 17 23 16 42 17 16 46 18 16 50 18 16 55 17 24 16 24 18 16 29 17 16 33 17 16 37 18 25 16 6 18 16 11 18 16 15 18 16 19 18 26 15 48 18 15 52 19 15 57 18 16 1 18 27 15 29 19 15 34 18 15 38 19 15 43 18 28 15 10 19 15 15 19 15 20 18 15 24 19 29 14 51 19 14 56 19 15 1 19 15 5 19 30 14 32 19 14 37 19 14 41 20 14 46 19 31 14 13 19 14 17 20 14 22 19 14 27 19 February  1 2 3 4 Day 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 deg mi. di deg mi. di deg mi. di deg mi. di 1 13 53  13 58  14 2  14 7  2 13 33 20 13 38 20 13 42 20 13 47 20 3 13 12 21 13 17 21 13 22 20 13 27 20 4 12 52 20 12 57 20 13 2 20 13 6 21 5 12 31 21 12 36 21 12 41 21 12 46 20 6 12 10 21 12 16 20 12 21 20 12 26 20 7 11 49 21 11 55 21 12 0 21 12 5 21 8 11 28 21 11 33 22 11 38 22 11 44 21 9 11 7 21 11 12 21 11 17 21 11 22 22 10 10 45 22 10 50 22 10 56 21 11 1 21 11 10 23 22 10 28 22 10 34 22 10 39 22 12 10 1 22 10 7 21 10 12 22 10 17 22 13 9 39 22 9 45 22 9 50 22 9 55 22 14 9 17 22 9 23 22 9 28 22 9 33 22 15 8 55 22 9 0 23 9 6 22 9 11 22 16 8 32 23 8 38 22 8 43 23 8 49 22 17 8 10 22 8 15 23 8 21 22 8 26 23 18 7 47 23 7 53 22 7 58 23 8 4 22 19 7 24 23 7 30 23 7 35 23 7 41 23 20 7 1 23 7 7 23 7 12 23 7 18 23 21 6 38 23 6 44 23 6 49 23 6 55 23 22 6 15 23 6 21 23 6 26 23 6 32 23 23 5 52 23 5 58 23 6 3 23 6 9 23 24 5 29 23 5 34 24 5 40 23 5 46 23 25 5 5 24 5 11 23 5 17 23 5 22 24 26 4 42 23 4 48 23 4 53 24 4 59 23 27 4 18 24 4 24 24 4 30 23 4 36 23 28 3 55 23 4 1 23 4 6 24 4 12 24 29          3 49 23 March  1 2 3 4 Day 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 degr mi di Deg. M di De. mi. di Deg. M di 1 3 31  3 37  3 43  3 23  2 3 8 23 3 13 24 3 19 24 3 1 24 3 2 44 24 2 50 23 2 56 23 2 37 24 4 2 20 24 2 26 24 2 32 24 2 14 23 5 1 57 23 2 3 23 2 8 24 1 50 24 6 1 33 24 1 39 24 1 45 23 1 27 23 7 1 9 24 1 15 24 1 21 24 1 3 24 8 0 46 23 0 51 24 0 57 24 0 39 24 9 0 22 24 0 28 23 0 33 24 0 15 24    24 0 4 24 0 10 23   23 10 0 2 23   24   24 0 8 24 11 0 25 24 0 20 23 0 14 24 0 32 24 12 0 49 24 0 43 24 0 38 23 0 56 23 13 1 13 23 1 7 24 1 1 24 1 19 24 14 1 36 24 1 31 23 1 25 24 1 43 23 15 2 0 24 1 54 24 1 49 23 2 6 24 16 2 24 23 2 18 23 2 12 24 2 30 23 17 2 47 23 2 41 24 2 36 23 2 53 24 18 3 10 24 3 5 23 2 59 23 3 17 23 19 3 34 23 3 28 23 3 22 24 3 40 23 20 3 57 23 3 51 24 3 46 23
seconds A fourth cause of error is the refraction of the Beams of the Sun or Stars which we observe by reason of the Vaporous thickness of the ayre that is betwixt us and them especially when they are neer the Horizon For the finding whereof not having hitherto had sufficient means by mine own observation for my full satisfaction herein I have therefore thought good to adjoyne these Tables of the Suns and fixed Stars refractions out of Tycho Brahe which differ little from such observations as I have made for triall hereof the use wherof is this In the first column seek the Altitude or height of the Sun or fixed Star and in the second you shall have the refraction answering thereto which being subtracted out of the observed height you shall have the height of the Sun or Star remaining without refraction CHAP. XVI Faults amended in the Table of the Suns Declination commonly called the Regiment of the Sun NOtwithstanding the Sun and Stars are at Sea the most certain markes and guides the Navigator hath whereby he may direct himself to rectify his course and know where he is after many turnings and traversings this way and that way especially in long Voiages wherein he may be forced many times by contrary Winds and Calms to sing with the Poet for many Weekes and Moneths together Coelum undique undique Pontus and Nihil est nisi Pontus aether Yet the Tables of Declinations of the Sun and fixed Stars hitherto published which I have compared together and examined by observation are oft times very faulty the declination of the Sun in them set down being many times lesse then truth by 10 11 or 12 minutes especially in the moneths of February and March and some of the principal fixed Stars that are of most use in Navigation differing in declination from that is set down in the Tables more then one whole degree as I have found by many observations For the easier mending of these faults in the Tables of the Suns declination I thought it meet first to set down the Table following which sheweth the declination of every minute of the Ecliptik in degrees minutes and seconds whereby the place of the Sun is presently known his declination being first given by observation and consequently his Eccentricity and Apogeum were easily found and the Theorick of the Sun corrected out of which the Ephemerides hereafter following were calculated shewing the true place of the Sun for every day of five years agreeable without notable error to the truth of the Heavens and out of these with help of this Table of declination a new Regiment or Table of the Suns declination for every day of five years was most easily made free from such errors wherewith the Tables hitherto published and commonly used have been too much pestered as by comparison of this and those Tables with the observations hereafter following may evidently appeare CHAP. XVII Of the Table of declination of every minute of the Ecliptick in degrees minutes and seconds Made according to the greatest obliquitie of the Zodiak this present age which by exact observation is found to bo 23 degrees 31 minutes and an halfe· BEcause the table of declination here following doth differ something from the Table heretofore published by others whereof some make the greatest declination of the Sun to be 23 degr and 28 minutes only as Copernicus and his followers according to which the Tables of declination and regiments of the Sun that have been used for the most part by our English Mariners are made whereas others of late as that noble Astronomer Thyco Brahe in his second book De recentioribus aetherei mundi phoenomenis findeth the same to be by his observations 23 degr 27 mi. pag. 38. 23 degr 31 mi. pag. 386. 23 degr 31 mi. 30 sec. pag. 217. according to which there is a Table of Declination already published by Maginus and that excellent Geometrician Regiomontanus whom Petrus Nonius compared by Ramus to Archimedes and Clavius chose rather to follow maketh it to be but 23 degr 30 min. I thought it therefore needfull to shew what reasons moved me to make choise of the greatest of all the Declinations before recited being thereunto induced not only by the authoritie of that famous Astronomer of our time Tycho Brahe but resting also upon many and diligent observations of mine owne taken by a quadrant of more then six foot semidiameter so exactly made and divided into minutes and half minutes as I could and as heedfully used and truly rectified by Plumbline every time I observed as my sight could discern All which observations do prove with one consent that the greatest declination of the Sun in this our age is 23 degrees 31 minutes and an halfe as thus it may appear In the year 1594 the 11 and 12 dayes of Iune the apparent Meridian altitude of the Sun was observed to be 61 degr 58 min. whereto the observations of the 8 9 10 13 14 and 15 days of the same moneth do well agree wherein the apparent Meridian altitudes of the Sun were 61 degr 55 ½ mi. 61 degr 56 ½ mi. 61 degr 57 mi. 61 degr 57 ½ mi. 61 degr 57 mi. 61 degr 56 mi. almost as also the observations of the 9 11 12 and 13 dayes of Iune in the year 1597 in which dayes the apparent Meridian altitudes of the Sun were 61 degr 57 mi. 61 degr 58 ½ mi. almost 61 degr 58 mi. 61 degr 57 ½ mi. By all which observations it may be certainly concluded that the greatest apparent height of the Sun here at London is 61 degr and 58 minutes Moreover by many and heedfull observations of the Pole-star taken about the year 1593 and 1594 I found the greatest height thereof at that time here in London to be 54 degrees 24 minutes and an half and the least height 48 degr 39 ½ minutes the difference of which heights is 5 degrees 45 minutes the half whereof is 2 degrees 52 ½ min. that is the distance of the Pole-star from the Pole at that time added to the lowest height of the Pole-star sheweth the height of the Pole at London to be 51 degrees 32 minutes the complement whereof 38 degrees 28 minutes is the height of the Equinoctial which substracted out of the greatest apparent height of the Sun 61 degrees 58 minutes there remaineth the greatest apparent declination of the Sun 23 degrees 30 minutes whereto if wee ad 1 minute 22 seconds that is the parallax of the Sun answerable to that height we shall have the greatest true height of the Sun 61 degrees 59 minutes 22 seconds and consequently the greatest true declination of the Sun for our time 23 degrees 31 minutes 22 seconds differing but half a quarter of one minute from the greatest declination finally determined and resoluedly set down by Tycho Brahe for this our age 23 degrees 31 minutes and one half Aries Libra  Degr. 0 di Degr. 1 di Degr. 2
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
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 Sun and the shadow are both one way Then I look for the height which is 85 degrees and three quarters so that it lacketh of 90 degrees four degrees and one quarter which is fifteen minutes These four degrees and fifteen minutes being added to the Declination which is twenty degrees and 41 minutes amount in all to 24 degrees and 56 minutes And so much am I distant from the Equinoctial towards the North which is the part of the Sun and of the shadowes An example of the fifth Rule Upon the 17 of October 1609 which is the first year after the leap year the Sun now going his course towards the South suppose I took his Altitude in 50 degrees and one third And when I took it the lower vain of mine Astrolabe Declined toward the North of my Compasse wherefore I say that the Sun and the shadowes are different And so adding 05 degrees and 20 minutes which is one third part of a degree with 12 degrees and 55 minutes which upon that day is the Suns Declination they amount in all to 63 degrees and 15 minutes which are lesse then 90 degrees by 26 degrees and 45 minutes and so far I am distant from the Equinoctial to the part of the shadowes that is to the North for the Sun and shadowes being different the heigth and Declination came not to 90 degr A second example of the fifth Rule The same day and year suppose that some man found the Sun in 77 degrees and five minutes of heighth the Sun it self declining to the South and the shadowes falling to the North which being added to 12 degrees and 55 minutes of Declination amounteth in all to 90 degrees just whereby I know that the ship wherein this Altitude is taken is under the Equinoctial because the Sun and shadowes being different the heigth and Declination make just 90 degrees The third example of the fifth Rule Upon the 20 of May 1608 suppose a certain man found the Suns heighth to be 88 degrees and two third parts the Sun and shadowes being different which being added to 21 degr 54 minutes the Suns Declination that day amounteth to 110 degrees 34 minutes which exceed 90 by 20 degrees and 34 minutes I say therefore that this man is 20 degrees 34 minutes distant from the Equinoctial towards the part of the Sun which is to the North because the Sun and the shadowes being diffeâ—rent the heigth of the Sun and the Declination being added together exceed 90 degrees CHAP. VIII Another manner of accounting by the Sun as they use in Portugall SOme Astrolabes there bee whose account beginneth not from the Horizon but from the Zenith and endeth with 90 degr in the Horizon and the heigth taken by them is nothing else but the distance of the Sun from our Zenith And to make an account of the Sun according to the Altitude taken with such Astrolabes there are these Rules following to be Observed 1. When the Sun and the shadows are both one way add the heighth unto the Declination and the product will shew how far you are distant from the line towards the part of the Sun and shadows 2. If the Sun and the shadow be differing subduct the Declination from the height or the height from the Declination the lesser from the greater and the remainder will shew how far you are from the line towards the part of that which is greater and if the height be greater then are you on the part of the shadowes 3. When the Sun is in the line and hath no Declination so much altitude as you shall find so far are you distant from the Equinoctial towards the part of the shadowes 4. When you shall take the Sun in your Zenith having then no altitude his Declination will shew you how far you are distant from the line towards the part of the Sun These Rules because they are so easie and plain need no examples CHAP. IX How the height of the Sun may be known in any place whatsoever without an Astrolabe first knowing your distance from the Equinoctial SOme Pilots for their curiosities sake desire to know the height of the Sun for any day without an Astrolabe For the performance whereof it is expedient that they know three things that is to say the Declination of the Sun the distance of the place from the Equinoctial and the part whereunto the shadows do incline at mid-day These three things being known you shall come to the knowledge of the Suns heighth by four Rules 1 When you and the Sun be both on one side of the Equinoctial if your distance from the line be equal to the Suns declination you shall finde the Sun in your Zenith in 90 degr and shall have no shadow 2 When the Sun hath no declination look how much your distance from the Equinoctial wanteth of 90 deg for so much is heighth of the Sun 3 When the Sun and the shadows are both towards one part subtract out of your distance from the Equinoctial the Declination of the Sun that day and that which the remainder shall want of 90 deg shall be the heighth of the Sun 4 VVhen the Sun and the shadows are different if the Equinoctial be between you and the Sun adde the Declination of the Sun to your distance from the Equinoctial and that which these two numbers added together shall want of 90 deg shall be the heighth of the Sun But if you be between the Sun and the line you must subduct your distance from the line out of the Suns Declination and then that which the remainder shall want of 90 deg shall be the heighth of the Sun CHAP. X. The Rule or Regiment of the North-star for the knowledge of the heighth of the Pole THe Zenith is the Pole of the Horizon because it is every where distant from it just 90 deg And hence it is that the Pole of the World is so much elevated above our Horizon as our Zenith is distant from the Equinoctial which is very manifest for having 90 deg of the Meridian from our Zenith by the Pole of the World to the Horizon and other 90 deg of the Meridian from the Pole of the World by our Zenith to the Equinoctial because they are two quadrants of one and the same Circle they must needs be of equal quantity from both which that part being taken away which is common to both that is the whole distance from the Pole of the world to our Zenith that which remaineth on both parts shall be equal And so that space from our Zenith to the Equinoctial which is called the distance from the line is equal â—o the distance that is between the Pole of the World and the Horizon which is called the heighth of the Pole VVhereby it is manifest that the heighth of the Pole is so much as our distance from the line is And although they are two different things yet the one is taken for the other
the very degree of the Compasse upon which the Sun riseth or setteth Then the Horizon being set fast as we have shewed in the former chapter mark in the Instrument by which part or degree of those upon the Horizon the Parallel of the Suns Declination that day doth cross the same counting in the numbers of the Horizon from the center towards the North Pole if it be from the 11 of March to the 13 of September or towards the South Pole the other half of the year And mark also whether this crossing be so many deg distant from the division of the Equinoctial of your Instrument as the Sun in his rising was distant from the East of the Compasse or at his going down was distant from the West thereof for then you may say that the Compasse hath no variation at all But if it be not so mark the Rules following 1 When the Sun riseth by the same Rumb of the Compasse which the Instrument doth shew the Compasse hath no variation at all 2 When the Sun riseth more to the North of the Compasse or goeth down more to the South then is shewed by the Instrument all the difference between the Instrument and the Compasse is the North-easting or variation thereof to the East-ward 3 If the Sun riseth more to the South of the Compasse or seteth more to the North then the Instrument sheweth all the difference between the Instrument and the Compasse is the North-westing or Westerly variation thereof CHAP. XXXVIII At what hour the Sun riseth and setteth every day in all parts of the world THE heighth of the Pole in that part where you desire to know this being known place the Horizon in such sort as was shewed in the 36 chapter And finding by the Table of the Suns Declinations the Declination which the Sun hath that day count the same from the Equinoctial of the Instrument towards that part whither the Sun declineth among the Parallels and then mark the Parallel whereat your account endeth in what hour and in what part of the hour it cutteth the Horizon noting that every hour hath two numbers one afternoon which is the hour of the Suns setting and another before noon which is that wherein the Sun riseth CHAP. XXXIX Of the length of the Day and of the Night THe hour of the Suns going down being known double it and the double number of hours will shew you the length of the day Also the hour of the Suns rising being known and doubled will manifest unto you the length of the Night in that part of the year when you desire to know the same CHAP. XL. Of a Night-diall by the North. THAT being known which is before declared of the situation of the North Star and of the guards we may easily know in the night what a clock it is wheresoever we can see the North Stars presupposing that upon the 15 of April at the very point of mid-night the former guard goeth a-head in respect of the North Star And because by this account of the hour of the night we must take for a beginning the very instant when the former guard maketh mid-night the Rule following is to be Observed The Rule The number of the whole moneths which have passed since the 15 of April forward being double you have the number of the hour wherein the former guard maketh midnight being head-most and if the moneths fall not out just add for every fifteen days above the whole moneths one day and for every day four minutes and you shall know when it is midnight As for example If I would know upon the 15 of November where the former Guard maketh midnight I account the whole moneths from the 15 of April and I find them to be seven which being doubled make fourteen I say therefore that upon the 15 of November it shall be midnight when the former Guard hath passed before the North or head fourteen hours And so allowing three to the North-west three to the West and six to the foot it may be said that the former Guard going two hours before the foot towards the South-west that it is midnight which shall come to passe when the former Guard goeth an hour before from the South-west This being thus presupposed when I would know in the night what a clock it is I must note two things the one is in what part the former Guard maketh mid-night the same night The second is in what part the said Guard is at the same instant when I would know the time of the night which being understood I will make mine account from that which the Guard wanteth of being come to the place where that day it maketh midnight or from so much as it hath passed the same place making mine account that one third part of four points of the compasse is an hour and that which it wanteth of being come or which it hath passed forward are the hours before midnight if it be not come to the place or after mid-night if it have gone beyond As for example I see the former Guard in the Northwest upon the 15 of Iuly because that upon the 15 of Iuly by the account before mentioned the former Guard maketh midnight in the West and from the North or head to the West are six hours and from the Northwest where I saw the Guard to the West where it maketh midnight are three hours I say therefore that it is three hours before midnight that is to say nine of the clock at night FINIS BEcause the Tables of the Suns Declination that have bin most in use amongst English Sea-men doe both in fashion and manner of using something differ from those before set down pag. 173 174 c. Least any therefore of the meanner sort might be mistaken or should not rightly conceive the manner of using these Tables I thought good to adjoyn these also here following bearing in a manner the same form and shape and therefore also to be used altogether almost in the same sort that those Tables have been which for these many years have been most used by English Mariners This Table of the Suns Declination containeth twelve particular Tables shewing the Declinations of the Sun for every day of the twelve moneths of the year for four years together from leap year to leap year In the head of every one of these Tables is first set down the moneth for which that Table is made Under this are placed the years of our Lord for which those Tables may serve which years are divided into four ranks signified by the four Arithmeticall characters 1 2 3 4 that are set over them The first rank containeth the first years immediately following after the leap year the next rank containeth the second years after the leap year in the third rank are set down the years that follow three years after the leap year and in the fourth and last rank are the fourth years after the precedent leap
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
of the raritie or densitie of the Vapours in the air interposed betwixt our sight and the Sun he shall I say quit himself well that neither by one nor some nor all these shall misse a minute and more somtimes in Observing the meridian Altitude of the Sun whereby if error be committed both at the beginning and ending of the aforesaid arks especially of those arks that are contained between the midst of Taurus and Leo of Leo and Scorpio of Scorpio and Aquarius of Aquarius and Taurus the place of the Sun found by such Observation may be more or lesse then truth by three or four minutes and both errors together may amount to six or eight min. error in the motion of the Sun whereof may follow two or three hours error in the time of the Suns abiding in one of those arks Out of the former Table I found by the Observations of the two last years especially that the time of the Suns Revolution through the Zodiack in our time is 365. dayes 5. hours and about 48. min. Also the Suns continuance in the Northerly Semicircle of the Ecliptick from the beginning of Aries to the begining of Libra to be 186. dayes 18. hours and about one half and consequently in the Southerly Semicircle from Libra to Aries 178. dayes 11. houres 18. minutes whereby the arks of the Suns Eccentrick answerable to those Semicircles appeared to be 184 degrees 5 min. 25. sec. from Aries to Libra and 175 degrees 54. min. 35. sec. from Libra to Aries Therefore because the place of the Sun being at or neer the Equinoctial points is most certainly known his Meridian Altitude and Declination altering there most swiftly and consequently the ark of the Eccentrick contained betwixt those points are most certainly found it appeareth to be most certain that the Eccentricitie of the Sun at this time must needs be at the least 3.569 such parts whereof the Semidiameter of the Eccentrick containeth 100,000 though the Suns Apogeum were but in the beginning of Cancer whereas if it be in 9. degr 22. min. of Cancer as Copernicus would have it the Eccentricitie cannot be lesse then 3616. of the same parts notwithstanding he maketh it to be little more then 3220. such parts in this Age. But finding by the Observations I took in the year 1596. that the Sun is also in going from the beginning of Aries to the midst of Taurus 46. daies and about three hours and foure minutes and consequently the arch of the Suns Eccentrick answerable to that time and arch of the Ecliptick 45. degr 27 min. 56. sec. I found hereby the Suns Eccentricitie and place of his Apogeum as followeth Past this upon the Margin of Letter Z. fol. 148 so as it may ly open all the while the following matter of the 20 and 21 chap are reading Which may yet also be more easily found by the Tetragonical Table or Table of Roots and Squares for taking AO and OB to be 2290 and 2757 their Squares will be 5,244,100 And 7,601,049 Which added together make 12,845,149 The Square Root or side whereof is 3584. The Suns Eccentricitie in such parts whereof the Semidiameter of the Eccentrick Be containeth 100,000 Agreeing exactly with the Suns Eccentricitie found by Tycho Brahe Progymnasmat Pag. 26. The same may also be further confirmed thus We have found the arch of the Suns Eccentrick from the beginning of Aries to the beginning of Libra to be 184 5 26 the excesse wherof above a Semicircle is 4 5 26 the half of this is the arch IK 2 2 43 the Sine whereof IX equal to AD is 356,892 whereof the semidiameter of the Eccentrick is 10,000,000 which should be the Suns Eccentricitie if his Apogeum were in the beginning of Cancer But having found that the Suns Apogeum is about 5 degrees 17 minutes of Cancer therfore as the whole Sine 10,000,000 is to the Secant of 5 degr 17 min. 10,042,667 so is AD in the Right Angled Triangle ADB 356,892 to AB the Eccentricitie of the Sun 358,414 which hath not any sensible difference from that we found before But the place of the Suns Apogeum found by the foresaid Observations differeth from Tycho twenty minutes if we add â—o his place of the Apogeum of the Sun 7 minutes for the Moâ—â—on of the Suns Apogeum in the ten years space betwixt his Observation and mine All which difference notwithstanding may arise by erring little more then half a quarter of a minute in Observing the the Suns height about the midst of Tarus Which error although it be so smal that it may worthily be neglected for whether of them soever you follow either his Apogeum or mine for the making of the Ephemerides and Tables ensuing there cannot hereof arise any such disagreement as can by sight be diserned yet in that smal difference that is though insensible I shall not unwillingly yeeld unto him considering with how great Preparation cost skill diligence and circumspection every way he went about this business as all they that have any judgment and use of Observation will easily grant I say therefore not building only upon his authoritie though in this kind it be greater then any others yet known to the world that following the ordinary received Hypothesis of an Eccentrick for saâ—ving the Suns apparent inequalitie of motion the Suns Eccentricitie and place of his Apogeum set down by Tycho as before we have shewed are in this our Age very agreeable to truth and without all such error as can by sense be discerned And as for the difference that seemeth to be betwixt us being so smal and insensible so far ought it to be from breeding doubtfulness in any that it may rather make not a little for the confirmation of the truth both of his and my Observations so as none shall need to make scruple of the certaintie and infallibilitie of those Tables of the Suns Declination which for the Navigators use shall out of these grounds be gathered and diduced CHAP. XXI The middle motion of the Sun Corrected out of the former Observations THE Eccentricitie therefore and Apogeum of the Sun being thus known together with his true place which by so exact Observation as we could in the year 1597. the 11. of March at noon we found to be 0 degr 57. min. 48. sec. of Aries his middle motion from the beginning of Aries was also easily found after this manner Let a be the place of the Sun in his Eccentrick b the Suns true place in the Zodiack B a a line drawn from the center of the Eccentrick to the center of the Sun A d a line drawn from the center of the Ecliptick Parallel to B a shewing the middle place of the Sun in the Zodiack AB a line drawn from the center of the Ecliptick by the center of the Sun to the Zodiack shewing the true place of the Sun Therefore the Angle BAD being 5. degr 37. min. and consequently the Angle BAI 95. degr
37 min. because DAI is a right Angle the Angle aAI found by Observation to be 0 degrees 57. min. 48. seconds being subtracted from the Angle BAI there shall remain the angle BA a in the Triangle BA a 94. degr 39. min. 12 sec. and two sides also of the same Triangle being given aB 100.000 parts and BA 3584 of the same parts therefore by the doctrine of Triangles the Angle B aA equal to aA d because B a and AD are Parallels shall likewise be found to be 2. degrees 2. min. 52. sec. the Prostapheraeresis or equation of the Sun at that time which subtracted from E b the true motion of the Sun that is 57. min. 58. sec adding thereto an whole circle there shall remain the middle motion of the sun from the beginning of Aries EFGH d 358. degr 54. min 56. sec. According to Tycho his Tables Progymnasmat part 1. page 59. if we account the difference of Longitude between London and Vraniburg to be about 11. deg 15. min. as by our best Sea-Charts it seemeth it should be it is then 358. degr 55. min. 45. sec. differing from the former only 49. sec Which difference may arise almost of one third part of a minute error in Observing the Meridian Altitude of the Sun Notwithstanding the account of the Prutenick Tables maketh it to be 358 degrees 35. min. 15. sec. differing from both the former about 20 minutes Thus having found that neither in the place the Suns Apogeum nor in his Eccentricitie or middle motion there is any sensible difference betwixt the accounts arising out of Tycho Brahe his Observations and mine own I have therefore here set down the Tables of the Suns middle motions altogether agreeable to those of his Progymnasmat part 1. pag. 57.58.59 allowing only to his Epochaes so much more as is answerable to the difference of Longitude between the place of his Observation and mine that is to the Epochaes of the Suns middle motion of Longitude 1. min. 52. sec. answerable to 45. min. of an hour almost or 11 degr and ¼ that is so much as the Citie of London seemeth to be more Westerly then Vraniburg EPOCHAES OF THE MIDDLE MOTIONS OF THE SVN  Apogeum Longitude  Apogeum Longitude Years Si. P. Mi. Se· Si. P. Mi. Se. Years Si. P. Mi. Se. Si. P. Mi. Se. 1500 3 4 24 45 9 20 10 52 1625 3 5 58 30 9 20 53 50 1520 3 4 39 45 9 20 20 6 1626 3 5 59 15 9 20 39 30 1540 3 4 54 45 9 20 29 20 1627 3 6 0 0 9 20 25 11 1560 3 5 9 45 9 20 38 35 1628 3 6 0 45 9 21 10 0 1580 3 5 24 45 9 20 47 49 1629 3 6 1 30 9 20 55 40 1600 3 5 39 45 9 20 57 4 1630 3 6 2 15 9 20 41 21 1601 3 5 40 30 9 20 42 44 1631 3 6 3 0 9 20 27 2 1602 3 5 41 15 9 20 28 25 1632 3 6 3 45 9 21 11 51 1603 3 5 42 0 9 20 14 6 Middle motions in single years until 20. 1604 3 5 42 45 9 20 58 54 1605 3 5 43 30 9 20 44 35 1 0 0 0 45 11 29 45 41 1606 3 5 44 15 9 20 30 16 2 0 0 1 30 11 29 31 21 1607 3 5 45 0 9 20 15 56 3 0 0 2 15 11 29 17 2 1608 3 5 45 45 9 21 0 45 4 0 0 3 0 0 0 1 51 1609 3 5 46 30 9 20 46 26 5 0 0 3 45 11 29 47 32 1610 3 5 47 15 9 20 32 7 6 0 0 4 30 11 29 33 12 1611 3 5 48 0 9 20 17 47 7 0 0 5 15 11 29 18 53 1612 3 5 48 45 9 21 2 36 8 0 0 6 0 0 0 3 42 1613 3 5 49 30 9 20 48 17 9 0 0 6 45 11 29 49 22 1611 3 5 50 15 9 20 33 58 10 0 0 7 30 11 29 35 3 1615 3 5 51 0 9 20 19 38 11 0 0 8 15 11 29 20 44 1616 3 5 51 45 9 21 4 7 12 0 0 9 0 0 0 5 33 1617 3 5 52 30 9 20 50 8 13 0 0 9 45 11 29 51 13 1618 3 5 53 15 9 20 35 48 14 0 0 10 30 11 29 36 54 1619 3 5 54 0 9 20 21 29 15 0 0 11 15 11 29 22 35 1620 3 5 54 45 9 21 6 18 16 0 0 12 0 0 0 7 24 1621 3 5 55 37 9 20 52 1 17 0 0 12 45 11 29 53 4 1622 3 5 56 15 9 20 37 39 18 0 0 13 30 11 29 38 45 1623 3 5 57 0 9 20 23 20 19 0 0 14 15 11 29 24 26 1624 3 5 57 45 9 21 8 9 20 0 0 15 0 0 0 9 14 THE SVNS EQVAL MOTION OF LONGITVDE In moneths of the common year In dayes In houres In minutes  S. D. M. Se. Da De. M. Se H Mi. S. M M. S. M M. S. Ianu. 1 0 33 18 1 0 59 8 1 2 28 0 0 0 30 1 14 Febr. 1 28 9 11 2 1 58 17 2 4 56 1 0 2 31 1 16 Mar. 2 28 42 30 3 2 50 25 3 7 24 2 0 5 32 1 19 April 3 28 16 39 4 3 56 33 4 9 51 3 0 7 33 1 21 May. 4 28 49 58 5 4 55 42 5 12 19 4 0 10 34 1 24 Iune 5 28 24 7 6 5 54 50 6 14 47 5 0 12 35 1 26 Iuly 6 23 57 26 7 6 53 58 7 17 15 6 0 15 36 1 29 Aug. 7 29 30 44 8 7 53 7 8 19 34 7 0 17 37 1 31 Sept. 8 29 4 54 9 8 52 15 9 22 11 8 0 20 38 1 34 Octob. 9 29 38 12 10 9 51 23 10 24 38 9 0 22 39 1 36 Nov. 10 29 12 22 11 10 50 32 11 27 6 10 0 25 40 1 39 Dec. 11 29 45 40 12 11 49 40 12 29 34 11 0 27 41 1 41 In moneths of the leap year 13 12 48 48 13 32 2 12 0 30 42 1 43 14 13 47 57 14 34 30 13 0 32 43 1 46 15 14 47 5 15 36 58 14 0 34 44 1 48      16 15 46 13 16 39 26 15 0 37 45 1 51  S. D. M. Se· 17 16 45 21 17 41 53 16 0 39 46 1 53 18 10 44 30 18 44 21 17 0 42 40 1 56 Ianu. 1 0 33 18 19 18 43 38 19 46 49 18 0 44 48 1 58 Febr. 1 29 8 20 20 19 42 47 20 49 17 19 0 47 49 2 1 Mar. 2 29 41 38 21 20 41 55 21 51 45 20 0 49 50 2 3 April 3 29 15 48 22 21 41 3 22 54 13 21 0 52 51 2 6 May. 4 29 49 6 23 22 40 12 23 56 40 22 0 54 52 2 8 Iune 5 29 23 16 24 23 39 20 24 59 8 23 0 57 53 2 11 Iuly 6 29 56
6 0 48 45 1 54 28 3 2 3 3 0 4 1 44 17 1 8 0 56 49 1 56 27 4 2 2 58 0 5 1 43 7 1 10 0 94 52 1 57 26 5 2 2 50 0 8 1 41 54 1 13 0 52 55 1 57 25 6 2 2 40 0 10 1 40 40 1 14 0 50 56 1 59 24 7 2 2 28 0 12 1 39 24 1 16 0 48 56 2 0 23 8 2 2 13 0 15 1 38 7 1 17 0 46 55 2 1 22 9 2 1 56 0 17 1 36 47 1 20 0 44 53 2 2 21 10 2 1 37 0 19 1 35 25 1 22 0 42 51 2 2 20 11 2 1 16 0 21 1 34 2 1 23 0 40 47 2 4 19 12 2 0 52 0 24 1 32 37 1 25 0 38 43 2 4 18 13 2 0 27 0 25 1 31 10 1 27 0 36 38 2 5 17 14 1 59 59 0 28 1 29 42 1 28 0 34 33 2 5 16 15 1 59 28 0 31 1 28 11 1 31 0 32 26 2 7 15 16 1 58 56 0 32 1 26 39 1 32 0 30 19 2 7 14 17 1 58 21 0 35 1 25 6 1 33 0 28 12 2 7 13 18 1 57 44 0 37 1 23 30 1 36 0 26 4 2 8 12 19 1 57 5 0 39 1 21 54 1 36 0 23 55 2 9 11 20 1 56 24 0 41 1 20 15 1 39 0 21 46 2 9 10 21 1 55 41 0 43 1 18 43 1 40 0 19 37 2 9 9 22 1 54 55 0 46 1 16 54 1 41 0 17 27 2 10 8 23 1 54 8 0 47 1 15 11 1 43 0 15 17 2 10 7 24 1 53 18 0 50 1 13 27 1 44 0 13 6 2 11 6 25 1 52 26 0 52 1 11 41 1 46 0 10 56 2 10 5 26 1 51 32 0 54 1 9 54 1 47 0 8 45 2 11 4 27 1 50 36 0 56 1 8 6 1 48 0 6 34 2 11 3 28 1 49 38 0 58 1 6 16 1 50 0 4 23 2 11 2 29 1 48 38 1 0 1 4 25 1 51 0 2 11 2 12 1 30 1 47 35 1 3 1 2 33 1 52 0 0 0 2 11 0  8 Add. Dif ad 7 Add. Dif ad 6. Add. Dif ad  CHAP. XXIII The making of the Ephemerides of the Sun here following WIth help of the two former Tables of the Suns middle motions and of his prosthaphaereses the Suns true place may be readily found and so the Ephemerides following easily made after this manner Reduce the apparent time given to the equal time answering thereto with help of Tycho Brahe his table of Equation of natural dayes and for that time so reduced adde together the Suns middle motions of longitude in years moneths dayes hours and minutes out of the summe subtract the place of the Suns Apogaeum the remainder shall be the Suns motion of Anomaly or his distance from his Apogaeum Now if this Anomaly be lesse then a semicircle look the signe thereof in the head of the table of the Suns prostaphaereses and the degree in the first column towards the left hand descending and proceed in the same line towards the right hand till you come under the foresaid sign of the Suns Anomaly for there shall you have the Suns prostaphaeresis for that tâ—me remembring this withal that if there be any minutes adhering to those degrees of Anomaly that prostaphaeresis must be corrected by the part of the adjacent difference proportional to those minutes adding or subtracting the same hereto according as you are directed in the head of the column wherein that difference is set down But if the Suns Anomaly be more then a semicircle you must finde the signes thereof in the foot of the table and the degrees in the last column next the right hand ascending and in the common meeting of the line wherein you finde this degree and of the column of the said sign of the Suns Anomaly you shall finde the Suns Prostaphaeresis as before which if there be any minutes adherent to the Suns Anomaly must be corrected by the part proportional of the disterence adjoyning as before adding or subtracting the same according as you finde your direction in the foot of the column containing that difference As for example Suppose you would know the Suns true place the 6 of May at noon that is the 5 of May complete according to Astronomical account in the year 1608 which time reduced to equality by the foresaid Table shall be the 4 of May complete 23 hours 48 minutes for the Sun being at that time about the 26 degree of Taurus that Table sheweth you that 12 minutes are to be subtracted from the apparent time to make it equal For this time therefore let the middle motions of the Sun be gathered together in this manner The Suns middle motion of Longitude for  Si. D. M. Se. the year of Christ 1607 complete 9 20 15 56 Four moneths of the leap year 3 29 15 48 Four dayes  3 56 33 23 hours   56 40 48 minutes   1 58  Si. D. M S. The summe of all these is the Suns middle motion of Longitude for the time aforesaid 1 24 26 55 The place of the Suns Apogaeum for the year of Christ 1607 complete is 3 5 45 0 The motion thereof in the moneths dayes hours c. remaining is    15 which put together make the place of the Suns Apogaeum for the time aforesaid 3 5 45 15 This being subducted out of the Suns middle motion 1 24 26 55 There shall remain the Suns motion of Anomaly 10 18 41 40 The Prosthaphaeresis answerable to 10 signes 18 degr you shall find in the Table of Prosthaphaeresis  1 21 19 with the difference answering thereto   1 36 the part proportional whereof answering to 41 min. 40 seconds you shall finde to be   1 7 which subtracted out of the Prosthaphaeresis answering to 10 sig 18 de  1 21 19 there remaineth the Prosthaphaeresis corrected  1 20 12 which being added to the Suns middle motion of Longitude for the time aforesaid 1 24 26 25 you shall have the Suns true place for that time 1 25 47 7 agreeing justly with the Ephemerides following where you shall finde the Sun at that time to be in 25 degr 47 min 7 sec. of Taurus Admit also I would know the true place of the Sun the 27. of October 1609. at noon as we commonly account that is for the 26. of October complete by the foresaid account Astronomical which reduced to the equal time will make 25. dayes 23. hours 36. min. The Suns middle motion therefore together with the rest of the account for finding the Suns true place for that time may be shortly gathered after this manner The Suns middle motion of Longitude for  Si. D. M Se the year of Christ 1608 complete 9 21 0 45 September
of the common year complete 8 29 4 54 Five and twenty dayes  24 38 28 Twenty three hours   56 40 Thirty six minutes   1 29 The summe of these is the Suns middle motion of Longitude for that time 7 15 42 14 From whence subtract the place of the Suns Apogaeum 3 5 46 18 there remaineth the Suns Anomalie 4 9 55 56 whereby is found the Suns Prosthaphaeresis  1 35 31 and by subtraction hereof his true Longitude 7 14 6 45 agreeing likewise justly with the Emphemerides following after which manner also they may be wholy made Notwithstanding it is sufficient to make some convenient part of them in this manner and for sparing time and labour to supply the rest by convenient parts proportional whereof there may somtimes arise some small difference of a few seconds which may worthily be neglected seeing they can breed no sensible error in this business CHAP. XXIV How to reduce the apparent time to the equal time answering thereto NOtwithstanding the greatest difference between the apparent and equal time to be small that by neglect thereof there can scarce at any time arise thereof so much as one minute error in the place of the Sun and consequently not so much as half a minute error in his declination yet because the rules and grounds of Arts ought so much as may be to be free from all error I have therefore thought it better here to set down the foresaid Table of Equation of natural dayes rather then to leave the Reader to seek any further for so small a matter if any perhaps shall be desirous to exercise himself in calculating the Suns true place according to the manner here before set down either for the examining of the Suns Ephemerides here following or any other or for making some other like to these when the date of them shall be expired wherein if perhaps you finde some little difference of a few seconds from your calculation you need not therewith to be any thing troubled seeing it cannot produce any sensible error neither in the Suns declination nor yet in his place A Table of Equation of natural dayes  ♈ ♉ ♊ ♋ ♌ ♠♎ ♠♠♑ ♒ ♓  S S S S S S S S S S A A D. M Mi Mi. M M Mi. Mi. Mi. Mi. Mi. M M 2 0 9 12 6 2 6 16 ½ 24 21 7 5 7 4 1 9 ½ 11 6 2 7 17 24 20 6 6 7 6 1 10 11 5 ½ 2 7 18 24 19 ½ 5 6 7 8 2 10 11 5 2 8 18 24 ½ 19 4 6 ½ 6 ½ 10 3 11 11 5 2 9 19 24 18 3 ½ 7 6 12 3 11 10 4 2 9 20 24 17 2 ½ 7 6 14 4 11 10 4 3 10 20 24 16 2 7 ½ 5 16 5 11 10 3 ½ 3 11 21 24 15 1 8 5 18 5 11 ½ 9 3 3 11 ½ 21 24 14 0 8 4 20 6 12 9 3 3 12 22 23 ½ 13 ½ A 1 8 4 22 6 12 8 ½ 3 4 13 22 23 12 1 ◠2 8 3 24 7 12 8 2 ½ 4 13 ½ 23 23 11 ½ 3 8 2 ½ 26 7 ½ 12 8 2 5 14 23 22 10 ½ 3 8 2 28 8 12 7 2 5 15 23 22 9 ½ 4 8 1 30 8 ½ 12 7 2 6 16 24 21 8 ½ 5 7 ½ 0 ½ This Table must be thus used With the sign and degree of the Suns true place take out in the common meeting the minutes of time which according to the letters A S in the head of the Table must be added to or subtracted from the apparent time to make it equal remembring to do contrariwise if the equal time must be changed into the apparent CHAP. XXV A Table of Equations of the Suns Ephemerides  Ianuary Febr. March April May. Iune Day Mi. Se Mi. Se Mi. Se Mi. Se Mi. Se Mi. Se 3 1 53 1 51 1 49 1 47 1 46 1 45 6 1 52 1 50 1 49 1 47 1 46 1 45 9 1 52 1 50 1 49 1 47 1 45 1 45 12 1 52 1 51 1 48 1 46 1 46 1 44 15 1 52 1 50 1 49 1 47 1 45 1 45 18 1 52 1 50 1 48 1 46 1 45 1 45 21 1 51 1 50 1 48 1 46 1 45 1 45 24 1 52 1 50 1 48 1 46 1 45 1 44 27 1 51 1 50 1 48 1 46 1 45 1 45 30 1 52   1 47 1 46 1 45 1 45  Iuly August Sept. Octob Novem Decem. Day Mi. Se Mi. Se. Mi. Se. Mi. Se. Mi. Se. Mi. Se. 3 1 45 1 45 1 48 1 49 1 51 1 52 6 1 45 1 46 1 48 1 50 1 52 1 52 9 1 45 1 46 1 48 1 50 1 52 1 52 12 1 45 1 46 1 48 1 50 1 52 1 53 15 1 45 1 47 1 49 1 50 1 52 1 52 18 1 45 1 47 1 48 1 51 1 52 1 52 21 1 45 1 47 1 49 1 50 1 52 1 52 24 1 46 1 47 1 49 1 51 1 52 1 53 27 1 46 1 47 1 49 1 51 1 52 1 52 30 1 45 1 47 1 49 1 52 1 53 1 52 By means of this Table and these Ephemerides the true place of the Sun may most easily be found for many years either past or to come as shall hereafter be shewed in the next Chapter Ephemerides the Sun 1608. Leap year  January  Februar  March.  April  May.  June D gr mi. sec D gr mi. se. D gr mi. se. D gr mi se D gr mi. sec D gr mi. sec 1 20 47 21 1 22 17 51 1 21 23 9 1 21 56 7 1 20 59 3 1 20 37 23 2 21 48 38 2 23 18 28 2 22 22 49 2 22 54 41 2 21 56 43 2 21 34 31 3 22 49 52 3 24 19 3 3 23 22 27 3 23 53 13 3 22 54 21 3 22 31 38 4 23 51 6 4 25 19 37 4 24 22 2 4 24 51 42 4 23 51 58 4 23 28 46 5 24 52 18 5 26 20 8 5 25 21 36 5 25 50 10 5 24 49 33 5 24 25 52 6 25 53 30 6 27 20 39 6 26 21 7 6 26 48 35 6 25 47 7 6 25 22 58 7 26 54 40 7 28 21 7 7 27 20 37 7 27 46 58 7 26 44 40 7 26 20 4 8 27 55 49 8 29 21 34 8 28 20 4 8 28 45 19 8 27 42 11 8 27 17 10 9 28 56 57 9 ♓ 21 59 9 29 19 28 9 29 43 37 9 28 39 41 9 28 14 15 10 29 58 5 10 1 22 22 10 ♈ 18 51 10 ♉ 41 55 10 29 37 9 10 29 11 20 11 ♒ 59 11 11 2 22 43 11 1 18 12 11 1 40 10 11 ♊ 34 36 11 ♋ 8 24 12 2 0 16 12 3 23 2 12 2 17 31 12 2 38 24 12 1 32 2 12 1 5 29 13 3
50 28 15 22 30 28 15 23 46 28 16 51 58 28 17 30 35 29 15 56 12 29 15 53 16 29 16 22 3 29 16 24 19 29 17 53 10 29 18 31 51 30 16 53 46 30 16 51 44 30 17 21 37 30 17 24 53 30 18 54 23 30 19 33 7 31 17 51 21 31 17 50 14 Â Â Â Â 31 18 25 29 Â Â Â Â 31 20 34 22 CHAP. XXVI The use of these Ephemerides OF the use of these Ephemerides because they be altogether of the same forme that others generally are and have bin heretofore and to be used also in all points after the same manner for finding out by them the true place of the Sun at any time desired for so many years as they serve I think it needless for me in this place to make any further mention it being my purpose in this book rather to make supplie of that is wanting in others then to meddle with that which is by them sufficiently handled and already published This notwithstanding I thought good to advertise the Reader that these Ephemerides though thâ—y be made for five years only yet may profitably serve for many years to come after this manner Subtract 1612 out of the year of Christ given divide that remaineth by four if any thing remain after division made it sheweth which of the three common years in these Ephemerides answereth to the year given if nothing remain the fourth year is answerable to the year given Then seek out the moneth and day of the time given both in these Ephemerides for that year and in the Table of their Equations and out of them take both the place of the Sun and the Equation answerable to that moneth and day for the product of this Equation by the quotient added to the said place of the Sun if the number of the year given be more then 1612 or subtracted if it be less shall give you the true place of the Sun for the time given As for example the 1 of July 1620 suppose you would know the place of the Sun Subtracting therfore 1612 out of 1620 the remainder is 8 which being divided by 4 the quotient is 2 and nothing remaining which sheweth that the fourth year viz. 1612 answereth to the year given Also the said moneth and day sought out in these Ephemerides and in the Table of their Equations give you the place of the Sun 19 degr 11 min. 45 sec. of Cancer and the Equation 1 min. 45 seconds which multiplied by the quotient 2 make 3 min. 30 sec. And this added to the said place of the Sun the 1 of July 1612 sheweth you the true place of the Sun for the time given to be 19 degr 15 min. and 15 sec. of Cancer CHAP XXVII The making of the Table of the Suns Declination THE place of the Sun being thus easily known by these Ephemerides for every day of five years the Declinations of the Sun for every day of the same years were easily found out of the former Table of the Declination of every minute of the Ecliptick in such sort as was shewed in the use of that Table before set down chap. 18. pag. 116. and 117 And so was made with no less facility the Table following of the Suns Declination for every day of five years together commonly called by Sea-men A Regiment of the Sun For although it hath been thought sufficient in books of Navigation hitherto published to make the Regiment of the Sun or the Table of the Suns Declination for every day of 4 years beginning with the first year after the leap year and ending with the next Leap year because the Declinations of the Sun for the 4 years following have bin supposed to be the same in a manner that they were the 4 years before and so to continue alike without any notable difference for many years yet to bring this matter to some more certainty I have to this Table of Declination prefixed the fift year also viz. the leap year going before the first of the said common years that by comparing the Declinations of both leap years together it might the better appear what difference of Declination there is in every 4 years by addition or subtraction of which difference to the Declinations set down in this Table this Table may be made to serve for a great many years yet to come as truly as if it were made of purpose for them And for the more easie and readier use of all Sea-men I have to this end gathered into this little Table the differences of the Suns Declinations for every day of the first and last years set down in this Table of the Suns Declinations here following which differences may be called the Prosthaphaereses or Equations of the Suns Declination because that by adding them to or subtracting them from the Declinations contained in this Table the true Declination of the Sun for any day though many years hence may easily be found and that after this manner Out of the number of the year of Christ given subtract 1612 divide the remainder by four and set aside the quotient if any thing remain that remainder sheweth in which of the 3 common years you are to seek the Suns Declination if nothing remain you must look the Suns Declination in the fourth and last year which is leap yeare Then seek the moneth and day of the time given both in that year so found in the Table of the Suns Declination and also in this little Table of Prosthaphaereses of the Suns Declination here immediatly following taking out of that the Suns Declination and out of this little Table the Equation of that Declination for four years which Equation you shall multiply by the said quotient and add the product to the Declination found in the Table in the Spring and Autumn that is if the Sun be in Aries Taurus Gemini Libra Scorpio or Sagittarie or subtract it in Summer and winter viz. the Sun being in Cancer Leo Virgo Capricorn Aquarie or Pisces for so shall you have the Suns true Declination for the time given Take for example the 15 of March in the year of Christ 1630 out of this subtract 1612 the remainder is 18 which being divided by 4 the quotient is also 4 and 2 remain which sheweth that you must seek the Suns Declination in the second year after the leap year for the moneth and day aforesaid Therefore I find the Suns Declination in that year viz. 1610 to be 1 degr 54 min. 16 sec. and in this little Table of Prosthaphaereses his difference of Declination for 4 years 44 sec. which multiplied by the foresaid quotient 4 make 2 min. 56 sec. to be added to the said Declination 1 degr 54 min 16 sec. that so you may have the true Declination of the Sun for that time viz. 1 degr 57 min. 12 sec. Take also the 30 of August in the year of our Lord 1659 out
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
22 21 0 06 1 58 3 54 6 01 13 20 22 22 25 0 09 2 02 3 58 6 05 14 20 26 22 29 0 12 2 06 4 03 6 09 15 20 30 22 32 0 16 2 10 4 07 6 13 16 20 34 22 36 0 20 2 14 4 11 6 18 17 20 38 22 40 0 23 2 18 4 15 6 22 18 20 42 22 44 0 27 2 22 4 19 6 26 19 20 46 22 48 0 31 2 26 4 23 6 30 20 20 50 22 52 0 35 2 30 4 27 6 34 21 20 54 22 56 0 38 2 33 4 31 6 38 22 20 58 22 59 0 42 2 37 4 35 6 42 23 21 03 23 03 0 46 2 41 4 39 6 46 24 21 07 23 07 0 49 2 44 4 43 6 51 25 21 11 23 10 0 53 2 48 4 47 6 55 26 21 15 23 14 0 57 2 52 4 51 6 59 27 21 19 23 18 1 00 2 56 4 56 7 03 28 21 23 23 22 1 03 3 00 5 00 7 07 29 21 27 Â Â 1 07 3 04 5 03 7 11 30 21 31 Â Â 1 11 3 07 5 07 7 15 31 21 35 Â Â 1 15 Â Â 5 11 Â Â Â July August Septemb. October Novemb. Decemb D. H. M. H. M. H. M. H. M. H. M. H. M. 1 7 19 9 22 11 16 13 05 15 05 17 12 2 7 23 9 26 11 20 13 08 15 09 17 17 3 7 27 9 30 11 23 13 12 15 13 17 21 4 7 31 9 33 11 27 13 16 15 17 17 25 5 7 35 9 36 11 30 13 19 15 21 17 30 6 7 40 9 40 11 33 13 23 15 25 17 34 7 7 44 9 44 11 37 13 27 15 29 17 39 8 7 48 9 48 11 41 13 31 15 33 17 43 9 7 52 9 52 11 44 13 34 15 37 17 47 10 7 56 9 56 11 48 13 38 15 42 17 52 11 8 00 9 59 11 52 13 42 15 46 17 56 12 8 04 10 03 11 55 13 45 15 50 18 00 13 8 08 10 07 11 59 13 49 15 54 18 05 14 8 12 10 11 12 03 13 53 15 58 18 10 15 8 16 10 15 12 07 13 57 16 03 18 14 16 8 20 10 18 12 11 14 01 16 07 18 18 17 8 24 10 22 12 14 14 05 16 11 18 23 18 8 28 10 26 12 18 14 09 16 16 18 27 19 8 31 10 29 12 22 14 13 16 20 18 32 20 8 35 10 33 12 25 14 17 16 24 18 36 21 8 39 10 36 12 29 14 20 16 28 18 41 22 8 43 10 40 12 32 14 24 16 33 18 45 23 8 47 10 44 12 36 14 28 16 37 18 50 24 8 52 10 47 12 40 14 32 16 41 18 55 25 8 55 10 51 12 43 14 36 16 46 18 59 26 8 59 10 54 12 47 14 40 16 50 19 03 27 9 03 10 58 12 51 14 44 16 55 19 07 28 9 07 11 02 12 54 14 48 16 59 19 12 29 9 11 11 06 12 58 14 53 17 03 19 16 30 9 15 11 09 13 02 14 57 17 08 19 21 31 9 19 11 13 Â Â 15 01 Â Â 19 25 CHAP. XXXIII By the former Tables of the fixed Stars and the Suns right ascensions to know the hour of the night at any time of the year BY these tables of fixed stars and right ascensions of the Sun you may easily know also the hour of the night at any time of the year after this manner look which of those starres is at the meridian which may easily be known by a Needle-Dial or Compasse or if you will observe the North stars that never set which indeed are fittest for this purpose especially when they come to the meridian under the Pole you shall first find the place of the Pole in the heavens so neer as you can by estimation for a little errour herein breaks no square which may be done thus From the Pole-star directly towards the first star next the rump in the great Bears tail imagine almost so much space as the Guards are distant asunder for neer thereabouts is the place of the Pole Now betwixt your eye and this place of the Pole hold a plumb-line hanging as perpendicularly and stedfastly as you may and mark withall if that plumb-line come betwixt your sight and any of the stars noted in the table of fixed stars about the Pole for that star is at the meridian Then learn as before was shewed at what time that star cometh to the meridian and so you shall have the hour of the night Suppose for example the 10 of February you finde after this manner the Swans tail at the meridian under the Pole desiring hereby to know the hour of the night at that time The right ascension of the Sun for that day you shall finde as before to be 22 hours 14 minutes whereto you may adde a minute or two more because that star will come to the meridian very late in the evening so making the Suns right ascension 22 hours 16 minutes The right ascension of that star in the second table of fixed stars you shall finde to be 20 hours 30 minutes From which because now you desire to know the time of that stars coming to the nether part of the meridian you may subtract 12 hours and there shall remain 8 hours 30 minutes To this remainer because it is lesse then then the Suns right ascension adde 24 hours and from the summe 32 hours 30 minutes subtract the right ascension of the Sun 22 hours 16 minutes so there shall remain 10 hours 14 minutes the time of the night desired CHAP. XXXIV Of finding the elevation of the Pole by observation of the Pole-star and Guard BEsides the wayes already spoken of to finde the elevation of the Pole by the meridian altitudes and declinations of the Sunne and fixed stars in general there hath been also used another way more special by the height of the pole-star when the fore-guard is situate from it either towards the East West North or South or else upon the middle points betwixt these principal as upon the Northeast Northwest Southeast and Southwest points Of which way as it hath been hitherto published and used I must for the present onely give the Mariner warning that he trust not to it being very erroneous and grounded upon two false positions The one is that the distance of the pole-star from the pole is 3 degrees 30 minutes which by often and exact observation is found to be at this time not above 2 degrees 48 minutes The other is that the equations or allowances to be added to or subtracted from the height of the pole-star to finde thereby the height of the pole are made the same for all latitudes But having already shewed sufficiently how to know the latitude almost at any time of the night by the fixed stars in the former tables I hope to be the easilier
excused for finding a fault herein and not amending it at this time and that so much the rather because that according to promise made in the first Edition of this Book I will now shew the meanes how by observation of the pole-star and guards to finde presently the height of the pole not onely when the fore-guard is in some one of those eight principal positions before-mentioned as the manner hath been hitherto but in any other position also and at any time of the night when the pole-star and guards may be seen and that without any allowance or abatement giving or taking by addition or subtraction of any Equation in regard of the pole-stars being higher or lower then the Pole All which besides divers other pleasant and profitable conclusions may easily be performed by means of an Instrument by me divised which may not unfitly be called the Sea-Quadrant the description and use whereof here followeth The figure of the Sea-quadrant CHAP. XXXV The description and parts of the Sea-Quadrant THis Quadrant consisteth of many parts whereof some may be called principal and some lesse principal The principal parts of this Quadrant are the Semidiameter thereof and the Arch. The Semidiameter I call the streight square Ruler The arch I call that part of the Quadrant that is made crooked like a bow The lesse principal parts are the double box or â—ocket and the sights or Vanes The double box or socket hath two square holes made crosse-wise thorow it in such sort that the arch and semidiameter of the Quadrant may be fitly put thorow them the flat side of the one passing close by the flat side of the other By means of this double crosse socket the arch and semidiameter of the Quadrant are so to be joyned together that the two angles made by the hollow side of the arch with the semidiameter may be equal each to other The sights or vanes are either fixed or moveable There be two fixed sights the one greater the other lesser The greater fixed sight is fastened upon the double socket and hath a narrow slit cut through the midst thereof The lesser fixed sight is fastened to the end of the arch of the Quadrant and hath a small sight-hole bored thorow it even with the end of the Arch. The moveable sights are three in number whereof two are to be moved up and down upon the arch of the Quadrant as need shall require for observation The third is to be put on or taken off that end of the semidiameter of the Quadrant where the center is which center is shewed by the little round hole bored overthwart thorow the midst of the thicknesse of the square Ruler neer the end thereof which Ruler we called the Semidiameter of the Quadrant This sight whensoever it is to be used must so be put on upon the end of that Ruler that the flat side thereof which must be set towards the arch of the Quadrant may divide the foresaid round hole even by the midst thereof the sharp edge of that sight arising perpendicularly from the very midst or center of that hole which is also the center of the Quadrant when the other end of the square Ruler or Semidiameter thereof being put into his socket is thrust so far forwards that the end thereof cometh to be even with the fore-end of the socket Two sides of the arch of the Quadrant that is to say one of the straight or plain sides and the hollow side thereof are divided into 90 degrees and every degree into 6 parts each part conteining 10 min. and upon the straight side of the Quadrant there be figures set to every fifth degree and that in two ranks or limbs the one beginning from that end of the arch where the small fixed sight is placed the other beginning and proceeding from the other end of the arch where the Nocturnal is to be fastened or put on that so the number of the degrees and minutes might the easilier be reckoned from either end of the arch as need shall require CHAP. XXXVI Of the Nocturnal or Night-dial THe Nocturnal containeth three circles that is the hour circle the day circle and the pole-star circle The biggest of these circles which is to be fastened to the end of the arch of the Quadrant I call the Hour-circle and it is divided into 24 hours and half hours with figures set to every hour for the easier reckoning of them Next within this is the Day-circle or circle of dayes because it conteineth the dayes of all the moneths of the year which dayes are signified by the smal divisions round about at the circumference of this circle Every fifth day hath his stroke drawn a little longer then the rest that so any day you desire may the easilier be found The smal divisions contein but one day apiece The lines shewing the beginnings and endings of the moneths are drawn overthwart the whole breadth of this circle The beginning of January is known by the two lines drawn neer together overthwart this circle whereof one sheweth the end of the moneth of December and the other sheweth the beginning of the moneth of January which is marked with two pricks February is easily known in this circle because it hath but onely 28 dayes March is by the little pole-star circle and so all the rest of the moneths may easily be known by their order Upon the center of this arch which representeth the Pole of the World there be two Indices fastened the longer of them may be called the Guard-Index whereto a short pin is fastened underneath which serveth to set this Index right upon the place of the middle Guard in the day-circle by putting it into the smal hole that there is made in that circle The shorter Index reaching from the center of the day-circle unto the limb or circumference thereof that is divided into dayes may be called the Day-Index This smal circle placed between the center of the day-circle and the moneth of March may not unfitly be called the Pole-star circle because the distance of the center thereof from the center of the day-circle is answerable to the distance of the pole-star from the Pole which at this time I have often found by exact observation not to be more then 2 degrees and 48 minutes CHAP. XXXVII The use of the Sea-Quadrant and that first in observing the height of the Sun looking onely by the sight at the center to the Horizon at Sea TUrn the center of the Quadrant towards the Sun so as the shadow of the Vane or sight placed at the center may fall upon the hollow side of the arch of the Quadrant then looking thorow the little sight fastened in the end of the arch of the Quadrant lay the upper edge of the sight placed at the center even with the Horizon and at the same instant let one that standeth by mark deligently upon what degree and minute of the Quadrant the edge of the shadow
of the Ruler in the midst standing upright the very midst of both Vanes being placed upon the line HI Through the centers of which two Vanes shall be made two little holes both which must stand directly over the line HI and in equal distance from the upper face of the Ruler This Ruler by a hole bored thorow the midst thereof shall be fastened upon the said Astrolabe through another hole of the bignesse of that in the Ruler at the very center A with a nail which may be made fast with a little pin as is to be seen in the figure CHAP. II. Of the heighth of the Sun TO take the heighth of the Sun you must hold the Astrolabe by the ring or knot D in your left hand and turning your right side to the Sun lift up the Ruler with your right hand till the beam of the Sun entring by the hole of the uppermost Vane doth also pierce thorow the hole of the nethermost Vane And then note the degree and part of the degree which the line HI doth touch for that is the heighth of the Sun above the Horizon which if it be the greatest heighth that the Sun hath that day it will teach us how far we are distant from the Equinoctial This greatest heighth is to be taken at mid-day lifting up the uppermost Vane till we be assured that the Sun ceaseth to rise any higher but beginneth to fall again Then note that greatest heighth and keep it for the making of your account of the Latitude by the Sun CHAP. III. Of the Shadows THe shadowes being compared with the Sun may be of three sorts for at high noon the shadow falleth either towards that part of the World â—o which the Sun declineth or towards the contrary part or else we make no shadow at all The first and second sort are when the heighth of the Sun is lesse then 90 degrees and the third is when it is just 90 degrees high The first is when the Sun keepeth his course on the North side of the Equinoctial which is from the 1â— of March to the 13 of September and likewise when the shadows fall towards the North of the Compasse or when the Sun runneth on the South side of the Equinoctial which is from the 14 of September to the 10 of March and the shadows likewise fall towards the South of the Compasse and this is when the Sun and the shadows go both one way The second is when the Sun coming towards the North the shadows are cast towards the South of the Compasse or when the Sun is on the South side of the Equinoctial the shadows fall towards the North and this is when the Sun and the shadows are differing The rule of the shadowes is that we look well to the lower Vane of the Astrolabe when we are taking the height of the Sun at noon For if the line HI fall directly upon the line of the Astrolabe DE then we have no shadow because the Sun is in our Zenith 90 degrees high But if the line HI fall not upon the line DE you must mark towards what part of the World the lower part of the Ruler doth decline from the point E which if it decline towards the North of the Compasse then the shadowes fall Northwards But if it decline towards the South of the Compasse then the shadows fall Southwards CHAP. IIII. Of the Regiment and Rules of the Sun WHen you know the part or parts of the Sun and shadows and desire by the Sun to know how far you are distant from the Equinoctial you have five rules The first whereof sheweth in what part of the Heavens the Sun is that is whether he be North or South from the Equinoctial at the time of your observation The second teacheth what account we are to take of the Sun when he casteth no shadow because he is in our Zenith and is found in the Astrolabe to be just 90 deg high The third is of the account to be made by the Sun when taking the heighth thereof in lesse then 90 degr it maketh a shadow at high noon and hath no Declination because it is under the Equinoctâ—al The fourth is of the account that is to be made when the Sun and the shadows are both one way from the line The fifth is when the Sun and the shadows are different onâ— being towards the North and the other towards the South The first Rule of the Sun From the 11 of Mâ—rch to the 13 of September the Sun runneth on the North side of the Equinoctial And from the 14 of September to the 10 of March he goeth on the South side thereof The second Rule of the Sun When we observe the Sun in 00 degrees of heighth we must see what degrees and minutes of Decâ—ination the Sun hath the same day And then we may say that we are so much distant from the Equinoctial towards that part of the world to which the Sun declineth The third Rule of the Sun When the Sun is less then 90 degrees high if there be no Declination the same day then so much as it wanteth in heigth of 90 degrees so much are we distant from the Equinoctial towards that part of the world towards which the shadow falleth The fourth Rule of the Sun· When the Sun and the shadowes are both towards the same part of the world we must note how much the Sun wanteth of 90 degrees in heighth And that which it wanteth being added to the Declination of the Sun the same day is our just distance from the Equinoctial towards that part of the world to which the Sun and shadowes decline The fifth Rule of the Sun When the Declination of the Sun and the shadowes be different we must add the height of the Sun unto the Declination which it hath the same day And if the Sun amount to 90 degr just then are we under the Equinoctial line but if it exceed 90 degrees we are so much distant from the Equinoctial towards that part of the world wherein the Sun is as that excesse or overpluss commeth to And if the heigth and Declination added together come to lesse then 90 look how many degrees and minutes you want of 90 so many are you distant from the Equinoctial towards that part to which the shadowes fall And here is to be noted that we must likewise make account of the minutes because they may be both in Declination and in heigth and so alwaies in that Declination where we shall find 60 minutes we must make of them one degree And if in taking the heighth we find half a degree besides all the whole degrees it is as much as 30 minutes and one third part of a degree is 20 minutes one fourth 15 minutes one fifth part 12 minutes and one sixth part 10 minutes CHAP. V. Of the Declination of the Sun and of his Tables THat wee may know what use to make of the five foresaid
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
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
Clavius his grosse demonstration hereof 90 A more exact demonst with the practise thereof 92 The angle of dipping for any heighth of the eye 96 3 Error by the Parallax of the Sun corrected 96 4 Error in Observing by the refraction of the Sun or Stars corrected 97 Chap. 16· Faults amended in the Table of the Suns declination commonly called the Regiment of the Sun 97 Chap. 17. Of the Table of Declination of every minute of the Ecliptick in degrees min. and sec. made according to the greatest obliquity of the Zodiack this present age which by exact Observation is found to be 23 degrees 31 min. and an half 98 A Table of the Declination of every minute of the Ecliptick in degrees min. and sec. 101 Chap. 18. The use of the former Table of Declination 116 Chap. 19. The description and use of a great Quadrant for observation of the Sun on Land 120 A Table of observations of the Suns Meridian Altitudes taken by the foresaid Quadrant in the years 1594 1595 1596 1597 at London  Chap. 20. The finding of the Suns Apogeum and eccentricity out of the former observation 142 To know the time of the Suns comming to any point of the Ecliptick 142 Chap. 21. The middle motion of the Sun corrected out of the former Observations 150 A Table of the Suns middle motions 152 Chap. 22. A new theorick of the Sun for the making of the Table of the Suns Prosthaphaereses 154 A Table of the Suns Prosthaphaereses 157 Chap. 23. The making of the Ephemerides of the Sun 159 Chap. 24. How to reduce the apparent time to the equal time answering thereto 162 A Table of the Aequation of natural days 162 Chap. 25. A Table of Aequations of the Suns Ephemerides to make them serve for many years 163 Ephemerides of the Sun 164 Chap. 26. The use of these Ephemerides 169 Chap. 27. The making of the Table of the Suns Declination 170 Prosthaphaereses of the Suns Declination 172 A Table of the Suns Declination 173 Chap. 28· The use of the former Table of Declination or Regiment of the Sun 181 Chap. 29 The Declinations of the principal fixed stars about the Equinoctial corrected by Observation 183 A Table of fixed Stars about the Equinoctial 198 Chap. 30. The use of the former Table 199 Chap. 31. The true distances of certain principal fixed Stars from the North Pole found by late Observation 199 Chap. 32. To know at what time any of the foresaid fixed Stars come to the Meridian for any day of the year 202 A Table of the Suns right Ascensions in hours and minutes for every day of the year 204 Chap. 33. By the former Tables of fixed Stars and the Suns right Ascensions to know the houre of the night at any time of the year 206 Chap. 34. Of finding the Elevation of the Pole by Observation of the Pole Star and Guard 207 Chap. 35. The description and parts of the Sea Quadrant 208 Chap. 36. The description of the Nocturnal or night Diall 210 Chap. 37. The use of the Sea Quadrant first in Observing the height of the Sun looking only to the Horizon at Sea 211 Chap. 38. How with this Quadrant to Observe the height of the Sun with â—our back turned towards the Sun 211 Chap. 39. How to Observe with this Quadrant the height of the Sun or Star looking both to the Sun or Star and to the Horizon 212 Chap 40. How to find the height of the Pole by Observation of the Pole-star and Guard without giving or taking any allowance or abatement at any time when the Pole-star the Guard and Horizon may be seen 213 To know the houre of the night by the Nocturnal 213 An answer to Simon Stevin shewing his erorrs in blaming me of error in my table of Rumbs 214 The Contents of the TREATISE Of the ART of NAVIGATION The division of the whole Art of Navigation pag. 1 Chap. 1. The definition of the Sphaere 2 2. That the whole World is a Sphaere 2 3. Of the division of the Sphaere 2 4. Of the motion of the Heavens 4 5. Of the figure of the Heavens 4 6. That the earth and water make one perfect Globe 5 7. That the earth is in the center of the world 5 8. The whole quantitie of the earth 5 9. Of the Equinoctial circle 6 10. Of the Poles of the world 6 11. Of the Ecliptick line 7 12. Of the Declination of the Sun 7 13. Of the Colures 8 14. Of the Meridian circle 8 15. Of the Horizon 9 16. Of the 32 Windes 10 17. Of the two Tropicks 12 18. Of the Parallels 13 19. Of the degrees 13 20. What is meant by Longitude and Latitude 14 THE SECOND PART OF THE ART OF Navigation wherein is handled the Practick part shewing the making and use of the principal Instruments belonging to this ART Chap. 1. The making of the Astrolabe pag. 15 Chap. 2. Of the heighth of the Sun pag. 17 3. Of the Shadowes 18 4. Of the Regiment and Rules of the Sun 19 5. Of the Declination of the Sun and of the Tables thereof 20 How the Declination of the Sun may be found out 21 6. The Equation of the Suns Declination 22 7. Foure examples for the plainer declaration of that which is said before 22 8. Another manner of accounting by the Sun as they use in Portugall 25 9. How the height of the Sun may be known in any place whatsoever without an Astrolabe first knowing your distance from the Equinoctial 25 10. The Rule or Regiment of the North-star for the knowledge of the height of the Pole 26 11. The making of the Crosse-staffe 27 12. Of the position of the North-star and the Guards 28 13. Of the height of the Star taken with the Crosse-staffe 30 14. The Regiment or Rules of the North Star 30 15. Other things to be noted in observing the height of the Pole 32 16. Of the Crosiers 34 17. Of the Sea-Compasse 34 18. How the variation of the Compasse may be found 37 The finding of the Meridian line 37 19. Of the Sea-Chart 38 20. Of the point of Imagination 41 21. Of the Traverse or Geometrical point 42 22. Of the amending of the point of Imagination 42 The amending of the point of Imagination by the Traverse point 43 The amendment of the point of Imagination by North South East West 43 23. The point by Imagination and the height 44 24. What it is to increase or diminish in height 45 25. How you may cast a traverse point without Compasses 46 26. Of another kind of casting a point by traverse 46 27. Of the leagues which in Navigation answer to each degree of latitude in every Rumb 47 Chap. 28. How you may come to know the Longitude or the course from East to West pag 48 29. How you may set down in your Chart a new land never before discovered 50 30. Seeing two known points or Capes of land as you sail along