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
the fixestarres comparing the observations made 400 yeeres before him with his owne he finding therby that the fixed Starres had mooved in consequence 4 deg therefore Prolomie all owed to the whole revolution of the fixed starres to accomplish one period according to the rate of 36000 yeeres that was for every 100 yeeres one deg Mesline delivereth also that the opinion of the Alfonfines concerning our revolution or accomplishing of one period of the 9 Spheere is in 49000 yéeres but according to Copernicus his observations one periodicall revolution is in 25816 yeeres delivering that an houre of the longest day is 63 minut 40 seconds such as an houre of the shortest day is onely 60 min. Copernicus maketh likewise the yeere 365 dayes 5 houres 49 min. 15 seconds 46 thirds which he calleth the yeere Tropicall equally supputated or counted to the middle Equinoctiall The Aifonsines in their account wanteth in their yeerely period 13 thirds Mesline maketh the yeere 365 dayes 6 houres 9 minutes 39 seconds and this yeere he calleth syderiall or starry numbred under the Spheere of the fixed Starres which is more then the yeere delivered by Copernicus by 20 min. 23 seconds 14 thirds Delivering the causes of this difference to be this making these beginning of the yéeres to be in one point of the 10 and 9 sphéeres and the 9 Sphéere before the yeere end being remooved Easterly from the 10 spheere the yeere end comming to that point of the 12 Spheare againe is to proceed from it to that point of the 9 sphere also before the yeere endeth Mesline delivereth the Sunne being in the Apogeum part that from middle motion to middle motion the sun passeth 176 deg 20 min. of the ecliptick And the sun being in the Perigeum part from middle motion to middle motion passeth 183 degr 40 minutes of the ecliptick which maketh a difference of 7 degr 20 minutes But from the points of true motions the halfes are equall each 180 deg of the Ecliptick and the arch of time betweene the middle and middle motion of the Sunne in Apogeum part is 182 dayes and 6 houres Also the Arch of time betweene the true motion and true motion of the Sun in the Perigeum part is 179 dayes which maketh the arch of time betweene the middle the midle motion of the sunne in Apogeum more then in Perigeum by three dayes and 6 houres Also maketh the arch of time betweene the midle and true motion of the sunne in both the meane motions to be 4 dayes and the arch of time different from the true motion to the true motion of the sunne in Apogeum from the same points in his Perigeum to be 7 dayes and 6 houres And as for the rest of the Theoricks of the Sunne and Moone I have delivered sufficient in my delivery before concerning the tides But to conclude Stadius in his Ephemerides folio 57 of the Equation of the naturall dayes delivereth as followeth concerning the time We have computed all the places of all the Planets and also of the Sunne and Poone in this our Ephemerides for the naturall dayes to wit for the space in the which the whole equator is turned about and moreover 59 minutes and 8 seconds but because the apparent and true day now and then doth exceed this time and now and then is lesse to wit Partly when the Sunne goeth swifter or flower by reason of his Prosthopherisis Partly for that equall times of the Equator in the diurnall coartation or revolution doe not answer to equall sagments or parts of the Zodiack it commeth to passe that this inequality of time also needeth a prosthopherists the which notwithstanding cannot be alwayes equall nor certaine For the conversion of the Circle of the Equator though vnto the middle and equall Equinoctium which is the yéere divided into foure equall parts is evermore equally constant yet neverthelesse unto the apparant Equinoctium which are the true equinoctiis which the excentrick yeelds is found not equall Neither doth the Sunnes Apogeum occupy a stable seat because the Apogeum flecteth in the ecliptick every 13 yeeres 1 degree 27 minutes moreover the Sunne in his excentricity doth some hurt by his shifting for the excentricity is more and lesse by a eleven semidiamiters of the Earth as aforesaid and goeth about with the ecliptick Wherefore also no limit can be appointed perpetually to this insquallity but in this our Age all these causes conferred one with another and added together doe show that the greatest day and lesse day doe differ one from an other one houre and 28 minutes that is to say 22 times or Meridians and 20 minutes of the Equator But seeing that this inequality of dayes cannot missever the rest of the motions therefore it is necessary that we should admit them to be equall vnto the which equall dayes the Tables of the motions sâ—ould be both made and set together the which course we have taken in this our Ephemerides and for that cause we have borrowed the Canon of equation of dayes out of Erasmus Rheinholdus which agréeth neerest with our age vntill the yéere 1600. Therefore according as you find the number in that cannon to adde or substract that is the time that the day is eyther longer or shorter then the equall day or the day of the Ephemerides that is the first equated day or day equated vpon the difference of 88 minutes whereas the second equation is of dayes once equated and now doth equate them vpon the difference of 44 minutes whose halfe is 22 minutes the greatest number within the cannon Séeing there is a first error concerning the time delvered even in the motions of the Heavens as aforesaid therefore these running Glasses delivering but a second error the reason is this because they cannot be made without their imperfections had need to be most carefully made and by the precisest workman that the time delivered by them may be but according to the second error for the delivery of the Longitude by which running glasses next hereafter nominated the longitude is better delivered then by any other Instruments A glasse whose sand is mettall and the mettal said by some will not rust notwithstanding in my opinion it will rust somewhat and be sometimes moyster then at other times likewise the hole that the sand runneth thorough will grow wider with the force of the sand the rather being violated by the surges of the sea which impersections considered the glasse must needs deliver the time sometime shorter and sometime longer according to the weather therefore a second error yet this glasse is more tollerable then the rest for this delivery and is to be vsed before all other of which glasses there may be divers sorts for the delivery of more and lesse at pleasure And because the running glasses with sand is more grosser and that clockes and watches hath their more imperfections then the former glasse I will omit them and leave the delivery