the Southeast it is then 20 minut before 9 a clock in the morning but if the Moone hath 5 degrees south latitude then it is 18 minutes past 8 if the Moone have 5 deg north latitude then it is 51 min. past 8 a clock Sunne in the Equator The Sunne at the southeast it is then 28 min. past 9 a clock in the morning but if the Moone have 5 degrées south latitude then it is 18 min. past 9 if the moone have 5 degr north latitude then it is 38 min. past 9 a clock Sunne in Cancer The Sunne at the southeast it is then 18 min past 10 a clock in the morning but if the Moone hath 5 degrées south latitude then it is 6 minut past 10. If the Moone have 5 degrées north latitude then it is 30 min. past 10 a clocke But at an East sunne it is then 22 min. past 7 a clocke in the morning but if the Moone have 5 degrees South latitude then it is 2 minutes past 7. If the moone have 5 degrées north latitude then it is 42 minutes past seven a clock likewise in this north latitude 51 degrées 32 minutes there is difference of time in the Moone being southeast 2 houres 2 minutes And in this same Latitude difference in the east from 6 a clock 1 houre 42 minutes the mistaking of so much time from the high water may overthrow their charge in going into a harbor where it is to be respected 2 And whereas they deliver in their Tide Tables a hoying of the tide in conjunction aspect or opposition to 48 m. after the order in that Tide Table it is not so but in a river or in-draft where the Tides in their prime runneth quick there Tides of flouds will runne 48 minutes after high water and thus I will leave the delating of the Tides Concerning the Time SUch is the conceit or knowledge of the Sea-men in these times they take a common Compasse little respecting the error thereof being touched with a Stone of no strength and made wise by a man of no knowledge which Compasse they devide into 24 houres to deliver unto them they observing the Sunne therewith the time they looke for which is as lame a delivery of the times as may be and is somewhat touched before in the delivery of the Tides and likewise as hereafter followeth Also they observe the time by an houre or halfe houre glasse made by as carefull a man as the Compasse before spoken off who indéed careth but little what error more or lesse is delivered in those glasses in 24 houres nay in halfe an houre with whom as the proverb is an inch breaketh no square Which Compasses and glasses had néede to be carefully respected nay rather to be reformed for the security as aforesaid of the Navy of England which is greatly indangered by them and although these appendances for Nauigation be méere false yet the Market-folkes being not experienced by them in consideration of the cheapenesse of them holding themselves thereby profitable servants to the owner And although the time generally from one Moone to the other cannot be perfectly delivered by any man as hereafter shall be shewed yet by precise Instruments carefully made the time may be delivered more truely which is the greatest helpe we have in Longitude and for a man most carefull in making of his Compases and running glasses I commend Maister Emerie Mollineux of Lambeth while he lived as for my conceit which I have learned concerning the time it is as hereafter followeth First for the confuting of the time delivered by the compasse as aforesaid which Compasse is delivered by 360 degrees which indeed are Azimuths and they justify as many Azimuths which is 15 for one houre as for another which is contrary therefore I will deliver three examples to that effect in the Latitude 51 degrees 32 minutes as followeth Sunne in Capricornus From the Sunne rising to one houre of time there is 12 Azimuths and a ¼ and from a 11 a clock to 12 at Noone there is 14 Azimuths Sunne in the Equator From the Sunne rise to one houre of time there is 12 Azimuthes and from a 11 a clock to 12 at noone there is 18 Azimuths and ¾ Sunne in Cancer From the Sunne rise to one houre of time there is a 11 Azimuths and ⅓ and from a 11 a clock to 12 at noone there is 28 Azimuths Also followeth two examples the one in the north latitude 51 degrees 32 minutes the other in the north latitude 66 degrees concerning the difference of time as followeth The 1 Example in Latitude 51 degr 32 min. Aries whole signe hath declination a 11 degrees 20 min. which reacheth in longitude Eastward according to the degrees on the Equator to the 28 meridian likewise this whole signe of Aries doth lengthen the dayes 1 houre and 58 min. Taurus his whole signe hath declination 8 degrees 50 min. which reacheth in longitude Eastward according to the degrees on the Equator to the 29 and a halfe Meridian also this whole signe of Taurus doth length the dayes one houre and 44 minutes Gemini his whole signe hath declination 3 degr 18 min. which reacheth in Longitude eastward according to the degrees on the equator to the 32 and a halfe Meridian also this whole signe of Gemini doth length the dayes 1 houre 40 minutes The 2 Example in North Latitude 66 degr Aries whole signe lengthen the dayes 3 hour and 46 min. Taurus whole signe lengthen the dayes 3 hour and 38 min. Gemini his whole signe lengthen the dayes 3 hour and 0 min. But seeing that generall time from one Noone to an other cannot be delivered certaine but there shall be error so that one 24 houres shall be longer or shorter then an other by 1 houre and 28 min. as hereafter shall be delivered what certaine time then can be delivered by any Instruments for that purpose which delivereth but a second error Now will I deliver some causes why the time from one noone to another cannot be of like time Mesline in his Astronomy delivereth that there is three Ecliptickes as followeth First the ecliptick of the 10 Spheare which is fixed Second the ecliptick of the 9 Spheare which is mooveable Thirdly the ecliptick of the 8 Spheare which is the true ecliptick of the starry firmament Likewise he delivereth that the Sunne in Aries of the 9 Sphere is gone to the Eastward of the Sunne in Aries of the 10 spheare 27 degrees and better but directly vnder it in the same plaine Also that the Sunne in Aries of the 8 sphears never is neerer to the Sunne in Aries of the 9 Spheare then by the semidiamiter of the small circle which is 9 degrees Now Mesline delivereth the difference of the judgements of the Astronomers and that Ptolomy maketh the 8 and 9 Sphears all one delivering the opinion of Prolomy and others as followeth The opinion of Prolomie concerning the motions of
the horizontall distance westward from the south to be 66 deg 53 min. So that I find this last observation to be farther from the true Meridian then the former by 15 min. but if the declination were decreasing then the last observation will be nearer the true meridian then the former by 15 minutes which maketh a difference of variation sometime too much or sometime too little by 15 minut good which is an error and therefore not the truth Concerning the Tides EVen as mens minds for the most part are setled in the absurdities of the Card and compasse accordingly so are they setled likewise in an absurd reckoning of their Tides as hereafter by the grace of God shall appeare divided into two parts first by the delivery of the Cpact next according to the time observed by the point of the Compasse as follweth The first part These men doth not only know the prime by the date of our Lord and the Epact by the prime and the day of conjunction by the epact which is tollerable according to the order of the Epact allowing 30 dayes to every Moone or on the 30 day end to be Conjunction which is notwithstanding partly at randome being without respect of the precise time of the conjunction But they justifie also the departure of Sunne and Moone in 24 houres to be continually 48 min. as though the motions of the Sunne and Moone continued all one or that 48 minut were their meane departure For they bring the 32 Points every poynt being a 11 degr and 〈◊〉 a sunder the whole being 260 degr to 30 whole dayes allowing to every 24 houres the departure to be as aforesaid 48 min. for 30 times 48 minutes is 24 houres and 4 minutes of time is â—nswerable to one degrée of the equator therefore the departure is 12 degrées in 24 houres allowing the just revolution of the Equator to be in 24 houres neither more nor lesse for 30 times 12 degrées is 360 degrées in which their reckoning in my conceit the course of the Sunne in those 30 daies which is about 29 degrées 30 min. is forgotten or not respected but either they must of necessity grant that the revolution of the Equator and the departure of the Sunne and Moone to be as hereafter shall be delivered or else they must allow the Moones error in her yéerely course to be 5 dayes 15 houres 2 minut too much which is an absurdity and maketh the sinodicall error more then it should be by 11 houres 15 minut 56 sec 49 thirds but if they doe acknowledge which I take it is in few or none of their heads that the whole revolution of the Equator is turned about in 24 houres as hereafter wall be delivered and so doe reckon the odde time to be for the meane course of the Sunne in the 30 daies yet they must acknowledge by that reckoning that the conjunction of the Sunne and Moone must happen almost at like times of every yéere or at least-wise make the difference sooner of the yeerely period of the conjunction to be but 5 dayes 6 houres 9 minutes which indeed should be 10 dayes 21 houres 11 minutes as hereafter shall be delivered The 2 part 1 Also these men I justify in reckoning their Tides in what place and time soever that where it floweth a southeast moone in conjunction or opposition and possible by a false Compasse then it floweth till 9 a clock or where it floweth an East Moone in conjunction or opposition then it floweth 6 a clock so it s their judgments generally of all the rest of the points of the Compasse 2. And to justifie my sayings to be true they have set forth printed tide tables thereof and in those tables also have set their judgements that in conjunction or opposition it floweth 48 min. after the time upon any point as aforesaid which is absurd Therefore these their judgements for the security of their charge had as much néed of refining as the East and west of the Compasse as is said before to lead in paralell Now to the matter for the refining of the first part as aforesaid let this first part following suffice To know the times of the Conjunction otherwise then by the Epact is delivered by Ephemerides or Alminacks but rather knowne by that man that hath the knowledge himselfe in the Theorickes of the Sunne and Moone which knowledge ought to be in a man that would be artificall to refine these absurdities In Meslâ—nes Astronomie the metions of the Sunne and Moone are distinguished into three parts Slow swift and meane that is to say in Apogaeum slow when they are farthest from the earth in Perigeun swift when they are néerest the earth and in their meane betwéene the Apogaeum and Perigenm notwithstanding by these thrée motions there is knowledge understood that the motions of the Sunne and Moone are alwayes different that is to say the Sunne from this place in Apogeum to his Perigeum likewise the Moone from her Apogeum and Perigeum of her epicicle from her Apogeum in her almost an oval forme of the center of her Epicicle to her Perigeum thereof being the like qualited To justifie the Motions to be the truer it is also delivered in this Astrouomy that the Sunne hath thrée Orbes or particular Spheres as followeth First an Excentricke which is called the difference of the body of the Sun second is called the difference of the Apogeum of the excentrick the which 2 doth containe the excentrick betwéen them and 3. maketh the whole sphéere of the Sun to be concentrick I could delate more of this theorick then I purpose but it would be to small effect concerning the tides only respect this that follows Three reasons to be delivered for this Hypothesis as aforesaid to be true 1 First reason which causeth the Sunne to be in an excentricke is the difference of the Sunnes motion which is prooved sometimes swift sometimes slow as aforesaid 2 Second reason is because the Diamiter of the Sunne is prooved sometime bigger as in Perigeum 33 min. 44 sec then at some other time by 2 minutes 6 seconds therefore néerer at sometimes then at other times 3 The third reason is the inequality of the Epicicles because it is proved that the Sun farthest from the earth causeth the Eclipses to be longer and neerer the earth to be sooner Mesline delivereth also in his Astronomy that the greatest excentricity of the Sunne is 48 semidiamiters of the earth And the least excentricity which is néere in this our age about the 9 degrée of Cancer is 37 semidiamiters of the earth So the difference is a 11 semidiamiters of the earth and the semediamiter of the earth is 3436 miles and 〈◊〉 So that the sunne is néerer unto us at some time then at some other times by 74 semediamiters of the earth Mesline delivereth likewise one yearely Period of the sunne to have 365 dayes 6 hour 9 min. 39 sec and
this yéere he calleth Sideriall or starry the diurnall mean motion of the Sunne accordingly to be 59 min. 8 sec 11 thirds 22 fourths 16 fifths The motions of the Sunne as followeth Her swift motion in 24 houres is 1 deg 1 min. 16 second Her meane motion in 24 houres is 0 59 8 Her slow motion in 24 houres is 0 57 0 Mesline delivereth likewise in his Astronomy that the Moone hath five Orbs or particular Spheres as followeth 1 First an Excentricity 2 Second the difference of the Epicicles center 3 Third the difference of the excentricity in Apogeum and Perigeum 4 Fourth is the Epicicle which carieth the body of Luna 5 Fifth which is Concentrick called aequans Luna Foure reasons following to prove this Hypothesis to be true 1 First reason which causeth the Moone to be in an excentrick is the difference of the Moones motion which is proved sometime swift sometime slow 2 Second reason is because the Diameter of the Moone is prooved sometime bigger as in Perigeum 35 miu 38 seconds then at some other time by 5 min. 38 sec therefore néerer at some times then at other times 3 Thirdly the inequality of the Eclipses because the moone farthest from the earth causeth the Eclipses to be longer and néerer the earth to be sooner 4 Fourthly the inequality of the Paralax because the Moone sarthest from the earth causeth the Horizontali paralax to be the lesse and néerer to be more And the greatest excentricity of the Moone is 10 semidiamiters of the earth and 〈◊〉 a little lesse And the semidiamiter of the Epicicle is 5 semidiamiters of the earth and 〈◊〉 So that the Moone is neerer unto us at sometime then at some other times by 30 semidiamiters of the earth and 〈◊〉 and likewise by the whole diamiter of the Circulus parvus which is 20 semidiamiters and 〈◊〉 For the Moone maketh a Circulus parvus contrary to her owne motion about the center of the world according to the semidiamiter of the excentrick which is 10 semidiamiters and 8 min. 30 seconds Likewise the Moone hath latitude of the Ecliptick on either side 5 degrées which for the tides is greatly to be respected Mesline delivereth one meane periodicall period of the Moone to have 27 dayes 7 houres 24 minutes Also delivereth the meane time to make vp the periodicall period to a meane sinodicall period to have dayes 2 dayes 5 houres 20 minutes So that the meane sinodicall month of the Moone to be in conjunction againe with the Sunne hath dayes 29 dayes 12 houres 44 minutes 3 sec 11 thirds The motions of the Moone as followeth The swift motion of the Moone sometimes in 24 houres is 15 degrées 0 min. The meane motion in 24 houres is 13 degrées 30 minutes And her slow motion in 24 houres is 12 degrées 0 minutes Now having delivered so much as needeth of the Theoricks of the Sunne and Moone concerning the Tides we are come to the point to know their departure which is as followeth The departure of the Sunne and Moone The Moone presently after the conjunction departeth Eastward from the Sunne in Apogeum in 24 houres 11 deg 3 min. which is answerable in min. to 44 min. 12 seconds The Moone presently after the conjunction departeth from the Sunne in Perigeum in 24 houres 13 degrees 58 minutes 44 seconds answerable in minutes to 55 min. 55 seconds The Moone presently after the conjunction departeth from the Sunne in meane motion in 24 houres 12 degrees 30 min. 52 seconds answerable in min. to 50 min. 3 seconds 〈◊〉 Sometimes the departure of the Sunne and Moone when the Sunne is in her slow motion and the Moone in her swift motion in 24 houres is 14 degrees 3 minut which maketh the departure in minutes answerable to be 56 min. 12 seconds And sometime the departure of the Sunne and Moone when the Sunne is in his swift motion and the Moone in her slow motion in 24 houres is but 10 degrees 58 min. 44 seconds which maketh the departure in min. answerable to be 43 min. 55 sec And the meane motion between both these motions next above in 24 houres is 50 min 2 seconds 30 thirds Which motion is justified twise as above therefore I conclude the meane departure of the Sunne and moone in 24 houres to be 50 min 3 seconds 30 thirds And the hourely departure accordingly to be 2 min. 5 secon 8 thirds 45 fourths Stadius affirmeth in his Ephemerides that in 24 houres the whole equator and 50 minutes 8 seconds is turned about which is most certaine Likewise in a meane be affirmeth that the conjunction of the Sunne and Moone in one period at any one time in the yeere shall differ from the same time the next yeere and be sooner 10 dayes 21 houres 11 min. as for example In the 12 meane sinodicall moneths the time that wanteth of 12 times 30 dayes is 5 dayes 15 houres 2 minutes which maketh 360 dayes the remainer of the dayes of the whole yeere is 5 dayes 6 houres 9 minutes which both together is 10 dayes 21 houres 11 min. Now for the refining of the first 2 parts let these last 2 parts following suffice concerning their error in reckoning their tides delivering the time by the points of the Compasse for the confuting hereof I will deliver six examples three examples in the north latitude 30 degr and the other 3 examples in the north latitude 51 degrees 32 minutes North latitude 30 degrees the Sunne in Capricorne 1 The Sunne at southeast it is then ¼ before 9 a clock in the morning but if the Moone hath 5 degrees South latitude then it is 24 minutes before 9 a clock if the Moone have 5 deg North latitude then it is 16 min. past 9 a clocke Sunne in the Equator The Sunne at Southeast it is then 14 min. past 10 aclock in the morning but if the Moone have 5 degrées south latitude then it is 7 min. before 10 if the Moone have 4 degrées north latitude then it is 30 minutes past 10 a clok Sunne in Cancer The Sunne at southeast it is then 32 min. past a 11 a clock in the morning but if the Moone have 5 degr south latitude then it is 15 minut past a 11 if the Moone hath 5 degr north latitude then it is 54 minutes past a 11 of the clock And at an east Sunne it is then 18 min. past 9 a clock in the morning but if the Moone have 5 degrées South latitude then it is 24 min. past 8 a clock if the Moone have 5 degr north latitide then it is 40 min past 10 a clock So that in this north latitude of 30 degrées there is difference of time in the Moones being sentheast 3 houres 18 min. and in the same latitude difference from 6 a clock in the east 4 houres 40 min. The other 3 Examples in the North Latitude 51 deg 32 min. the Sunne in Capricornus 1 The Sunne at
8 degrées 20 minutes Northward though it were at the East in the first place The 3 Example Being in 80 degrées 15 minutes North latitude and in one meridian of longitude which is my first place which hath his demonstrature of East and west accordingly being a tangent vnto this paralell and in crossing the equator at opposite points after the manner in the first example from whence I sayle west according to the difference to 90 degr in longitude which 90 degrées in longitude in these paralells is 15 degrées of a great circle little more which is my second place in which second place I find my selfe there to be delated from the paralell according to the difference And in which second place I purpose to deliver also the East and west according to the demonstrature which likewise crosseth the equator at opposite points according to the former but 90 degrées difference in longitude and these two demonstrated semicircles doe crosse each other in 75 degrées 45 minu in latitude 48 degrées in longitude from the first place and 42 degrées in longitude from the second place So that from my first place of departure the second place doth beare according to the demonstrature of the Compasse northwest and by west and 8 degrees northerly vpon which point the two places are distant 14 degrees of a great circle which also is an neerer way then by the west as aforesaid by one degree And from my second place of being the first place of departure doth beare according to the demonstrature of the Compasse north-East one degree 20 minutes northerly vpon which point the two places are distant 14 degrees of a great circle So that by this delivery being at the second place the wind is altered of me 4 points and one degree 20 minutes to the northward though it were at the East in the first place A thing worth the Noting In all the three examples as aforesaid this thing worthy the noting might be delivered yet I will deliver but one of them according to the second example in latitude 60 deg in which second example or delivery the intersection or crossing of these two semicircles of east west according to the demonstrature from the first place of departure and second place is in latitude 50 deg which intersection is from the first place west from the second place east Yet being in this intersection the first place beareth from it northeast by east and 5 degrees 38 minutes northerly and distant 27 degrées 32 minutes of this great circle And the second place beareth from it northwest by west 1 degrée 40 minutes northerly and distant 26 degrées 20 min. of this great circle according to the demonstrature of the compasse and thus much concerning the wind Concerning the way of a Ship or Shipping at Sea FIrst there is to be vnderstood and likewise to be respected by him that hath the charge whatsoever in navigation that there is two lawfull and good navigable courses to be vsed at the Seas and no more eyther of which courses is very artificiall the kéeping of them aright resteth in the good descretion of the said Master being likewise artificiall which of them he will use But if the said Master be not artificiall but a man of great conceit the manner or way of these courses be too deepe for his vnderstanding and therefore he not worthy to take charge at all My reason is this because all other courses whatsoever more then these two are absurd frivolous and false the names of which two courses followeth First the course vpon the great Circle being the neerest way from place to place The first course is to sayle vpon a great Circle which is after this manner being in any one latitude and longitude whatsoever which is your first place and doe purpose to sayle from thence vpon any Azimuths of demonstrature whatsoever which are great circles vntill you come to 90 degrees in longitude which is vnto the Horizon of your first place in which way you are to respect every day at noone your Latitude if you may and likewise your time as before or hereafter shall be delivered For the delivery of your longitude you are likewise to respect your Sagments being of what length soever vpon the Azimuths you sayle how you are vpon any distance to crosse the meridians and paralells for if you finde your selfe in such a latitude as you should be in and not in the right longitude which the Azimuths you should sayle vpon giveth then are you also wide and to seeke reformation also if you finde your selfe in such a longitude and not in the right latitude which your Azimuthes giveth then are you also wide to séeke reformation therefore being a harder way or course to sayle vpon the great circle notwithstanding this way the néerest way or course from place to place of all other wayes requiring alwayes reformation with great Judgement I will onely deliver 6 examples from one meridian of longitude and latitude 51 deg 32 min. vpon the demonstrature northwest and by north continuing it from the first place to the Horizon by Sagments of 15 deg of a great Circle a péece onely for a tast and your farther knowledge of this way and so will leave it and hereafter will deliver the remainer of the second course or way which is more easie according to the difference being the onely and naturall way indéed that the Compasse leadeth in The 1 Example Being in the Latitude and longitude as aforesaid 15 degrées of a great Circle from thence according to the demonstrature of N. west and by north crosseth the 18 deg 30 minutes or meridian in longitude westward from the first and the paralell of north latitude 62 degrées 50 minutes The 2 Example Other 15 degrées which maketh 30 deg from the first according to the demonstrature of northwest and by north toucheth the meridian of 50 degr in longitude westward from the first and the paralell of north latitude 69 deg 28 min. The 3 Example Other 15 degrées which maketh 45 degr from the first according to the demonstrature of Northwest and by north toucheth the Meridian of 92 deg 50 minutes in longitude westward from the first and the paralell of North latitude 66 degrées 45 minutes The 4 Example Other 15 degrees which maketh 60 degrees from the first according to the demonstrature of Northwest and by north toucheth the Meridian of 118 degrees in Longitude westward from the first and the paralell of north latitude 57 degrees The 5 Example Other 15 degrees which maketh 75 degrees from the first according to the demonstrature of N. west and by north toucheth the Meridian of 130 deg 32 min. in longitude westward from the first and the paralell of north latitude 44 degrees 35 minutes The 6 Example The other or last 15 degrees which maketh 90 degrees from the first and is the Horizon thereof according to the demonstrature