example the Compasse here with us at London is set at halfe a point variation Eastward where it should be 10 degrees 38 minutes 45 seconds by my owne observations which was made in the yeere 1586. which maketh the west to be halfe a point to the north-ward of the west therefore in goâ—ng from Silly which is in latitude 50 degrées 15 minutes or there abouts west by the Compasse which is in truth west half north with Cape Race in New-found-land the places distant some 600 leagues from other causeth a falling more southerly into the latitude 46 degr 30 minutes or thereabouts which sheweth the way of the difference to rule in this distance And by a Compasse rectified to the truemeridian that is a Compasse that the north and south thereof delivereth or pointeth according to that true meridian of Silly on which meridian is delivered the arch of altitude or almicanter of the Sunnes height at nâ—ne by which or such Compasse Cape Race heareth from Silly due west and by north and there toucheth the paralell of north latitude 46 degrées 30 minutes likewise toucheth the meridian in longitude westward from Silly the 45 degrées 40 minutes according to the coarting of the meridians in this distance And to speake the truth in this distance there is but litle or novariation of the Compasse to be respected for the compasse at Silly set at the whole variation as it ought to be yet in sayling by that compasse you runne some 400 leagues before the north and south points thereof delivereth the true meridian and in sayling the other 200 leagues the compasse is varied westward a point and a halfe or there abouts which is no more then will answer the variation eastward as before so that in this distance the nutation of the Compasse eastward westward considered aright is as nothing to be respected but the one set against the other as by the examples following is proved The first Example Let a compasse be rectified to the nutation and sayle from Silly therewithall to Cape Race west when you come on the coast of Newfoundland you shall be delated from the paralell of Silly onely according to the difference and not otherwise The second Example Let the compasse be set at halfe a point nutation as most commonly it is and sayle by the Compasse from Silly west with Cape Race and you wall perforce keeping that course directly fall into more southerly latitude which is into 46 degrées 30 min. or thereabouts according to the difference and not otherwise The third Example Let the Compasse be rectified to the true meridian and sayle by that Compasse from Silly west with Cape Race and you shall likewise fall into the latitude 44 degr or thereabouts according to the difference And as for this way aboue said is delivered a delating from the paralell in going west so likewise in returning east froÌ„ thene againe you shall likewise delate from that paralell againe according to the difference which delivery overthroweth the whole Card. Againe looke how the difference of the east and west ruleth in the distance and differedce in longitude as aforesaid so in any other distance and difference in longitude it is likewise to be respected Also this difference of the east and west is the ground froÌ„ whence the difference is delivered for all the rest of the points of the Compasse So that you see this way upon the difference delivereth way outward to any place different unto the way homeward being not both alike as by the examples of the north-east and returning south-west likewise of the north-west and returning south-east as heereafter appeareth The 1 part of the 1 example from the Equator Being in the Equinoctiall in any one meridian I will there make my beginning of longitude from which equator and meridian of longitude I will deliver the line of inclination northeast continuing it to the latitude 75 degr 6 minutes 14 seconds according to the difference The 2 part of the 1 Example The line of the north-east continued to the latitude 75 degrees 6 minutes 14 seconds according to the difference endeth in the longitude 131 degrees from the first reckoned according to the meridians in this distance coarted The 3 part of the 1. Example Being in the latitude 75 degrees 6 minutes 14 seconds and in the longitude 131 degrees as aforesaid I am now to returne back againe by the line of inclination south west to the Equinoctiall Conclusion of the 1 Example Being returned to the Equinoctiall as aforesaid I doe â—nd the length of the line of inclination south-west homeward to be shorter then the line of north-north-east outward by 130 leagues and I am in longitude eastwerd from the first place on the Equinoctiall 70 leagues therefore the way out and home not all one Another Example North latitude 50 degrees I sayle north-west 50 leagues at the 50 leagues end I have altered my longitude from the first 2 degrées 38 minutes and my latitude 1 degrée 40 minutes I returne back againe south-east 50 leagues and being returned I find my selfe in lesse longitude or westward from the first 3 minutes and in latitude more then the first 6 minutes Another Example in the North latitude 60 degrees I sayle north-west 50 leagues at this sagment end my longitude from the first is 3 degrées 30 minutes and latitude from the first 1 degree 50 minutes I returne back againe south-east 50 leagues and being return'd I find my selfe in lesse longitude or westward from the first 5 minutes and in latitude more then the first 10 minutes And for the more confuting of the way out and home to be all one and the more justifying the delating from the paralell to be true I will deliver some more examples upon the east for a sagment of 20 leagues in the latitude 51 degrees 30 minutes and 75 degrees delivering the horizontall distance betweene the east according as is said to lead in a paralell and the way of the east according to the difference as followeth In Latitude 51 deg 30 minutes my first place From any one meridian of longitude I take a sagment of the paralell in this latitude of 20 leagues presupposed by some to be East from the first place and againe I doe depart from my first place of being 20 leagues eastward according to the difference now at this 20 leagues end I am delated from the paralell according to the way upon the difference which maketh my place now of being to heare from the first place two Azimuthes and 〈◊〉 more southerly As for Example To explaine it more briefly I imagine one lyne from the first place east according to the paralell 20 leagues imagine another line from the first place East by the Compasse according to the way upon the difference now the horizontall distance betweene these two lines at 20 leagues end from the first place shal be as before two Azimuths 〈◊〉 In the latitude 75 my first
place and meridian of longitude I take a sagment of the paralell in this latitude of 20 leagues presupposed likewise by many to be East from the first place and againe I doe depart from my first place of being 〈◊〉 leagues east according to the way upon the difference now at this twenty leagues end my horizontall distance betweene my place of being and place as aforesaid on the paralell from the first place in 3 azimuths 〈◊〉 Likewise this way of the difference delivereth upon any Aziemuth or point of Compasse sagments of great Circles different from other correspondent as they ought to bee for the difference in longitude as hereafter by thrée examples of the North north-west following appeareth which confuteth the 12 absurdity of the Card. Three Example of the North North west for the difference of the length of the Sagments in longitude from the Equinoctiall to 80 degrees in latitude as followeth The first Example from the Equator BEing in the Equinoctiall in one meridian the sagment of N. north-west to reach to the next Meridian which is one degree in longitude is in length 52 leagues â…“ The 2 Example from 40 deg of latitude Being in 40 degr of latitude and in one Meridian the sagment of north north-west to touch the next meridian is in length 17 leagues â…“ The 3 Example from 80 degrees of Latitude Being in 80 degrees of Latitude and in one meridian the sagment of north north-west to touch the next meridian is in length 〈◊〉 leagues â…” Also this way of the difference delivereth upon any Azimuth or point of the compasse sagments of great circles different from other for the laying or raising of a degree in latitude whatsoever as by 3 examples of the west north west following appeareth which confuteth the 13 absurdity of the card The 1 example from the Equator I Being in the equinoctiall am required to deliver a sagment of the west north west onely to raise a degree in latitude which according to the difference is 52 leagues and â…” The 2 example from 40 deg of Latitude I being in 40 degrees of latitude the sagment of west northwest to raise a deg in latitude upon the difference is 56 leagues The 3 example from 80 deg of Latitude I being in 80 degrees of latitude the Segment of a west north-west to raise a deg in latitude upon the differ once is 60 leagues And thas will I leave the way of the Compasse upon the difference for this time And because the variation or nutation concerneth the compasse and is a thing delivered in print meant belike to some purpose therefore I will touch this variation or nutation in some few words as hereafter followeth If a man for his delivery of the variation in print would observe by a needle touched by some who maketh the common or ordinary Compasses I take it precise fellowes would soone be delivering forth that the variation so set in print were wide from the truth Because with some men in the touching of a Needle or Compasse though the stone they touch withall be not the best neither shall an inch in bredth of the north part of that stone breake any square with them by whose compasses many time shipping at the Seas be indangered It were better for a man for the security of his charge or that purposed to set downe the variation in print to take a needle touched by a better stone and a more perfect man to handle the touching thereof truely when Robert Norman dyed who had a good stone Sea man had a great losse yet Maister Mullinux of Lambeth who having a better stone was as carefull as precise in hi◠〈◊〉 concerning the touching of Needles Compasses as over Maister Norman was Notwithstanding the variation by such a good Néedle set down in print and delivered as a generall thing * This 〈◊〉 to passe 〈◊〉 mistakin gâ— true place 〈◊〉 the Poles câ— Stone fâ— Master Gâ— brand anâ— ther 's with 〈◊〉 observing 〈◊〉 variation 〈◊〉 two severaâ— Needles to 〈◊〉 ed with twâ— verall Stoâ— found the 〈◊〉 riation to 〈◊〉 the same 〈◊〉 the like I 〈◊〉 seene beforâ— since H. Bâ— would bée but â—ested at and made a thing indéed that a man might spend much time to no purpose and lesse edifying to the Seamen as some have done my reason is this because this Stone though a notable one and I have not séene a better and good to make abservations withall to be kept to a mans selfe or out of print or for the amplyfying of some note in writing ☞ It cannot deliver the variation of another Stone for in truth the Variations delivered by many stoues are different you shall not have two Stones alike qualited or that will deliver one or a like Variation but the variation of every stone differeth from other there cannot generally be set downe a certaine variation for any one place which let suffice for this time Therefore that man that was conceited to set the Variation in print as a generall thing though it were my selfe all things to nothing I would there in my deliverie likewise hee condentning all mens knowledge saving my owne to justifie my doings But to the matter the variation or nutation of the compasse as it shall at any time or place be found is a thing to be noted yet my delivery is of it that it is not surpassing all other knowledge neither the overthrow of good knewledge neither will I accept of it as a thing notable above all the rest my reason is this because the way upon the difference being more excellent over ruleth it which indeed they impute to variation which is untrue and thus will I leave the nutation of the Compasse And whereas before in my delivery of the nutation I had forgotten to give a tast of the error which is likewise set in print and conceiveth the nice delivery of the said nutation I thought it now therefore good though late not to overpasse it but to give knowledge thereof it is said that the middle point betwéene any two Azimuthes observed upon equall elevations in forenoone and afternoone is the true Meridian For the confuting hereof I will deliver you an example in the north Latitude 51 degrées 32 minutes as followeth The Sun being in her swift declination in or néere the Equanor I purpose to make two observations the former observation to be 2 min before 8 of the clock in the forenoone the Almicanter delivered then by the center of the Sun being 18 deg in elevation the horizontall distance eastward from the true meridian delivered by the Azimuth of the Sunne to be 66 degr 38 min. The second observation in the afternoone the Sunne having the same Almicanter 18 degrées the declination increasting respected for 8 houres which is 8 min. North declination maketh the time to be 3 min. after 42 clock in the afternoone wherein there is a min. of time different from the South and
place that the Ship is remeved c. Aâ—confuting of the 2. absurdity of the Card. The 3. part The devisson that the Zenith horizon and Nadir hath or is diuided withall is onely by almicanter circles which otherwise are called circles of Altitude or height being above the horizon all which are paralels to the horizon but those from the Horizon to the Nadir notwithstanding paralell to the Horizon are circles of depression any one of which Almicanters may be delivered upon any degree or minute of the height above the Horizon likewise taken in some working spherically in profundity and depth under the Horizon The 4. part This demonstrature delivereth upon any Azimuth whatsoever the distance from the Zenith to the Horizon to be but 90 degrées The 5. part The East and west of this demonstrature from the zenith 90 degrees in longitude toucheth the Equinoctiall in the horizon at opposite points The 6. part Now the quality of the Globe is this the pole thereof being elevated or set to his purposed latitude in his horizon according to this demonstrature delivereth the obliquitie of the Sphere which in truth is a confuting of the East and west to lead in a paralell as for example The 1 Example The Globe set to the paralell of 50 degrees north latitude then a perpendienler lyne imagined to descend from this Zenith of 50 degrees North latitude delivereth his Nadir to be in 50 degr south latitude so that it delivereth the opposite part of the paralel to be from the Nadir or the arch of the meridian contayned betweene the opposite part of the paralell and the nadir to be a 100 degrees oblique or different and from the place of being in the zenith upon the meridian to the oposite part of the paralell directly is but 80 deg of a great circle so that this opposite part of the paralells is 10 deg aboue the Horizon which is oblique to the zenith and Nadir also 90 degr North from the east and west of the demonstrature in the equinoctial So that a Ship being in or having this zenith before spoken of the perpendicularity of the ship being in this Zenith and Nadir line and the opposite part of this Paralell so oblique unto her as before how is it possible for the East and west of the compasse to lead in a paralell The 2. Example Likewise when the ship the right line of her caping in the verticall circle of east and west extended both the wayes crosseth the equator at opposite points 90 degr different in longitude and the Ship being a segment of that great circle and no sagment of a smal circle as paralels are how is it possible then for the east and west to lead in a paralell it is not possible as the way of the difference justifieth c. The third Example Being in the paralell of 80 degrees North latitude * If the 〈◊〉 sayle upoâ— verticall 〈◊〉 of East oâ— that the 〈◊〉 passe doth 〈◊〉 whé the shâ— gins its coâ— but as the 〈◊〉 is guided bâ— magneticaâ— Wiers or 〈◊〉 dle so thaâ— Line or its 〈◊〉 makes eqâ— Angles wiâ— very magâ— call Meridâ— The way 〈◊〉 ship leadinâ— the East oâ— doth descriâ— magneticaâ— ralell a perpendiculer line delivereth the Nadir to be in 80 deg S. latitude so that the arch of the meridian contayned betweene the nadir and the opposite part of the paralell is 160 degrees But the arch of the meridian contained betweene the point of being and the opposite part of the paralell is but 20 degrees So that the opposite part of the paralell is 70 degrees above the horizon and likewise 90 deg North from the east and west according to the demonstrature in the equinoctiall ☞ Here you see the obliquity of the opposite part of the paralell to the zenith and his nadir shewing how unnaturall it is to deliver the way of a Ship leading in the east and west to describe a paralell And whereas before I have delivered the East and west of the demonstrature of the Compasse in the horizon and that the north and south is likewise very plain to be delivered therefore I will omit them and will give examples of the demonstrature in the latitude 51 degrées 30 min. and 80 degrées North latitude only of the north-east south-east south-west and north-west to the Horizon as bereafter followeth North-east in the Latitude 51 Degrees 30 Minutes FRom our point of being in our Meridian which is the beginning of our longtitude our Zenith being in the paralell of 51 degrees 30 min. north latitude I am to demonstrate 3 sagments of a great circle contayning 30 degrees a peece by the demonstrature north-north-east the end of which first sagment of 30 degrees shall touch the Meridian in longitude East-ward 54 degrees from the first and there likewise shall touch the paralell of north latitude 64. degrees And the end of the second sagment of 60 degrees in longitude shall touch the 105 degrees 30 min. or Meridian in longitude east-ward from the first and there likewise toucheth the 50. deg 30. min. paralell north Likewise the end of the third sagment at 90 degrees in longitude shall touch the 128 degree or Meridian in longitude East-ward from the first and there likewise toucheth the 26 degrée ward 13 min. paralell North also it there toucheth the horizon 45 deg either from the cardines East or North. North-west Likewise the demonstrature of the North-west cutteth the Meridians and paralels in longitude West-wards as the demonstrature of North-east cutteth them East-wards onely that it cutteth the Horizon 45 deg either from the cardines West or North. South-east in the same Latitude 51 deg 30 min. IN our place of being as aforesaid I am to demonstrate thrée sagments of a great Circle containing 20 deg a péece by the demonstrature South-east the end of which first sagment of 30 deg shall touch the 23 deg 30 min. or Meridian in longitude East-ward from the first and there likewise toucheth the 27 degrees 20 min. paralell North. And the end of the second sagment of 60 deg in Longitude wall touch the 3 deg 40 min. or meridian in longitude East-ward froÌ„ the first and there likewise toucheth in 〈◊〉 deg 25 min. N. latitude Likewise the end of the third sagment at 90 deg in Longitude shall touch the 51 degrée 40 min. or meridian in Longitude east-ward from the first and there likewise toucheth the 26 deg 15 m. paralell south Also there toucheth the Horizon 45 degrees either from the cardines East or south South-west Likewise the demonstrature of the South-west toucheth the meridians and paralell in longitude west-ward as the demonstrature of south-east toucheth them east-ward onely that it cutteth the horizon 45 deg either from the cardines south or west Examples in the Paralell of 80 deg North latitude beginning with the first example of North-east in the north latitude 8 deg FRom our point of being in
our meridian which is the beginning of our longitude our zenâ—th being in the paralel of 80. deg north latitude I am to demonstrate sagments of a great circle containing â—0 deg apéece by the demonstrature north-north-east the end of which first sagment of 30 degrées shall touch the meridian in longitude east-ward 119 degrees 30 minutes from the first and there likewise shall 〈◊〉 the paralell of North latitude 60 deâ—r And the end of the second sagment 160. deg in longitude wall touch the 130. deg â— min. or meridian in longitude east-ward froÌ„ the first there likewise toucheth the 36. deg 45. mi. paralel north Likewise tâ—t end of the 3. sagment at 90. deg in Longitude shall touch the 134 deg 30 min. or meridian in longitude east-ward from the first there likewise toucheth the 7 paralell north Also there toucheth the horizen 45 deg either from the cardines east or north North-west Likewise the demonstrature of north-west cutteth the meridians and paraellls in longitude west-ward as the demonâ—rature of north east cutteth them east-ward onely that it cutteth the horizon 45 deg either from the cardines west or north Example of the South-east in the same Latitude 8. deg IN our place of of being as aforesaid I am to demonstrate thrée sagments of a great circle containing 30 deg apéece by the demonstrature south-east the end of which first sagment of 30 deg shall touch the 35 deg 40 mi. or meridian in longitude east-ward from the first and there likewise toucheth the 52 degrée 10 min. paralell north And the end of the second sagment of 60 deg in longitude wall touch the 41 degrees 40 min. or meridian in longitude Eastward from the first and there likewise toucheth the 22 degrees â— min. paralell north Likewise the end of the third sagment at 90 deg in longitude wall touch the 45 deg 30 min. or meridian in longitude eastward from the first and there likewise toucheth the 7 paralell South Also there tuecheth the horizon 45 deg either from the cardines East or south South-west Likewise the demonstrature of south-west cutteth the meridians and paralells in longitude westward as the demonstrature of the south-east cutteth them eastward onely that it cutteth the horizon 45 deg either from the cardines south or west And as for the arches of depression from the horizon or senitor to the nadir of these points before spoken of the delivery of them is even as easie as the former and so is the arch of altitude or arch of depression upon any Azimuth whatsoever Onely this following to be respected as a preparative before I deliver any nice examples according to the difference it is necessary for me to explain in a more familiar sort at large some part of the difference onely according to the demonstrature for the more confuting of the Card and the opinion holden thereof for the way out and home to be all one It is delivered in the 15 absurdity of the Card that upon some points of the Compasse the Card delivereth a way outward to be 390 degrées of a great circle and to returne homeward to the first place againe the like distance upon the same line which shall be proved most false by the examples following which examples shall be from the latitude of 50 degr and from the first example as before in the latitude 51 degrées 30 min. yet these deliver not the truth neither as by examples upon the difference hereafter follow The 1 Example in North Latitude 50 deg IN which latitude our zenith or place of being in one meridian where we make our beginning of longitude and place of departure I am now to deliver from this our zenith or place of being the demonstrature of north-west for one sagment of 30 degrées in longitude which sagment end of 30 degr North-west there cutteth the 11 degr 30 minutes or meridian westward in longitude and the 63 degree paralell north Our Zenith now being altered and the latitude 63 degrées as aforesaid we will make proofe to returne back againe to our first place by the line south-east the like sagment of 30 degrées in longitude where this sagment end cutteth the 26 degree 20 minutes or meridian in longitude eastward and there likewise cutteth the 37 degree 40 minutes paralell north So that this line of north-west extended to 30 degrees as aforesaid and from thence returning south-east to 30 degrees likewise there is difference in longitude westward from the first meridian or place of departure 25 degrées 10 minutes or meridians and in latitude southward from the first 12 deg 20 minutes Here you sée the difference of the way out and home onely for 30 degrees according to the demonstrature and only for the lines of northwest and southeast the rest of the points hath their like difference in their kind The 2. example in north Latitude 51 deg 30 min. I Am now to deliver from this our zenith or place of being the demonstrature of the northeast to 90 degr which line of north-east there cutteth the 128 degree or meridian in longitude east-ward from the first and there likewise cutteth the 26 deg 15 minutes paralell north as in the demonstrature is delivered Our Zenith now being altered and in the latitude 26 degr 15 minutes as before said we will make a proofe to return back again to the first place by the demonstrature south-west to 90 degr where this line of south-west cutteth but the 65 degr 30 minutes meridian in longitude westward and there likewise cutteth the 39 degree 30 minutes paralell south So that this line of north-east extended to 90 degrees as aforesaid and from thence returning southwest to 90 degr likewise there is difference in longitude east-ward from the first 62 degrees 30 minutes and in latitude southward from the first 91 deg Here you see also the difference of the way out and home only for 90 degr according to the demonstrature and only for the lines of North-east and south-west and all the rest of the points is the like in their kind And so I leave the demonstrature Now will J deliver Example worthy the noting of the way of the Compasse according to the difference THe East or west of that Compasse rectified to the true meridian upon the difference maketh a spirall line in delatation to the equinoctiall froÌ„ what paralell soever by sagments of great circles correspondent for this purpose which sagments maketh right angles with the meridians and which sagments delivereth a right signe from the plaine of the verticall circle of east west for the way of a Ship in her navigation and the meridian according to this difference delivereth the other This part of the difference only confuteth the generall Card and the lines of inclination with the Geography of the Globe This difference the east and west thereof delating as aforesaid ruleth notwithstanding the variation of the Compasse generally spoken of as for
also being vnder the Equinoctiall the Northeast Southeast and Southwest Azimuths doe require 1 deg 24 min. 51 seconds 24 thirds to raise one degrée of Latitude But being in a paralell 60 deg 0 min. North the Northeast and Northwest require 1 deg 26 min. 13 seconds 3 thirds of distance to raise one degrée of Latitude And in the same paralell of 60 deg 0 min. the Southeast and Southwest require no more but 1 deg 23 min. 32 seconds 53 thirds for one degrée of the Poles depression Hereby it appeareth that the Segments of Northeast and Northwest are greater to raise one degrée then the Segments of Southeast and Southwest to depresse one degrée by 0 deg 2 min. 35 second 10 thirds Moreover the greater Segments which doe raise the Pole one degrée in that Latitude excéed these vnder the Equinoctiall by 0 deg 1 min. 21 seconds 39 thirds and the lesser Segments which depresse the Pole are lesse then those of the Equinoctiall by 0 deg 1 min 13 seconds 3 thirds which might serve for sufficient satisfaction that the way outward and homeward are not alike againe for your better vnderstanding you may note that being at the Equinoctiall a Segment of a great circle of 20 leagues which maketh with the Meridian an Angle of 45 deg 0 min. doth raise the Pole and differ the Longitude néere 0 deg 42 min. 25 seconds 3 thirds And in paralell 60 deg 0 min. North Latitude a Segment of 20 leagues Southeast or Southwest depresseth the Pole 0 deg 42 min. 58 seconds 8 thirds and differs the Longitude néere 1 deg 23 min. 4 seconds 6 thirds and in the same paralell of 60 deg 0 min. the like segment of 20 leagues distance Northeast or Northwest elevateth the Pole 0 deg 41 min. 57 seconds 40 thirds whereby it plainly appeare◠that if the way of a Ship be composed of Segments of great Circles the way outward and homeward being made by opposite Angles are not alike yet both Spirall Therefore a Ship making her way by any one Rhombe or point the Meridian onely excepted and returning by the opposite point thereof cannot by course fall with the place of her departure And further it must be considered that the greater Latitude is and the greater the Angle of the course is in respect of the Meridian the greater is the variety and the East and West are most variable moreover in North Latitude if the course be betwéene the South and the East or West then the way homeward returning by the opposite to the Meridian of the place of departure shall be shorter then the way outwards and falleth into a lesser Latitude according to the course distance and declination from the Equinoctiall but if the course be betweene the North and the East and the North and the West then in returning by the opposite to the Meridian of the place departure the way homewards shall be longer then the way outwards falling likewise into a lesser Latitude according to the course distance and the declination from the Equinoctiall Nautae If the Spirall or Helisphericall way of a Ship vpon the Superficies of the Sea being composed of Segments of great Circles had also those Segments limited or honded to containe 20 or 30 leagues a péece then should all your former allegations be true but those Segments in regard of their smalnesse cannot be sensibly distinguished neither can it be certainly said that a Ship in kéeping alwayes one course continueth vnder one great circle 1 league or 1 mile for when the course is alwaies continued according to any one point of the Compasse it maketh an oblique Angle with the Meridian and then so often as the Ship changeth her Zenith so often shée changeth likewise the great Circle shée maketh her way in that is to say so many Zeniths as shée passeth vnder so many great Circles shée maketh her way in and each of those Circles make severall Angles with the Equinoctiall and the greater the Latitudes are the greater are the Angles for in the Latitude of 59 deg 30 min. the verticall circle of Southwest and Northeast maketh an Angle of 68 deg 58 min. with the Equator and in Latitude 60 deg 0 min. the Azimuth of Southwest and Northeast maketh an Angle of 69 deg 18 min. with the Equinoctiall Also in paralell 60 deg 30 min. the Southwest and Northeast Azimuthes make an Angle of 69 deg 37 min. with the Equator and in the Latitude of 68 deg 58 min. it makes an Angle of 69 deg 18 min. and in the Latitude of 69 deg 37 min. the foresaid great circles make right Angles with the Meridian and are circles of West and East yet notwithstanding the variable Angles that these great circles make with the Equinoctiall and the contrary Angles that every great circle maketh with every new Meridian I say that in regard those Segments that a Ship maketh her way in are so small and insensible shée shall in kéeping one course outwards produce a spirall or Helisphericall line and returning by the opposite point thereof thée shall againe passe vnder all those Zenithes that shee did in her may outward and in like Segments and shall by the same lyne of inclination fall again with the place of her departure But when a Ship maketh an East or West way the lyne of her Caping maketh alwayes right Angles with the Meridian then shall those great Circles of whose Segments the Ships way is composed make like Angles with the Equator that is to say equall to the Latitude and the Ship shall according to that course runne a paralell to the Equinoctiall Geograph Mée thinkes that is strange that you will allow the East and West way of a Ship being made in Segments of great Circles to entersect the Equator at East and West by reason whereof they are Touch-lines to the paralell of Latitude and yet you will not allow or grant the East and West to make a spirall way as well as the rest For how is it possible that the lyne of Inclination or way of a Ship being composed of Segments of great Circles and those Touch-lines to the paralell of Latitude so that the Ships Caping is quite contrary to the paralell and maketh oblique Angles therewith and that especially in great Latitudes how then is it possible that the East and West should lead in a paralell or produce a lesser Circle or any part thereof Nautae Take a small Compasse slye and fasten it to a threed that may passe thorow the North and South points thereof and make a noose in the end of the threed and put it vpon the Axis of the Globe at the Pole then carrying the fly with the thréed about the body of the Globe and you shall sée the center of the fly describeth a paralell to the Equinoctiall and yet the East and West of the fly alwayes respecteth the Equinoctiall at 90 degrées 0 minut of distance
paralell 60 deg 0 min. Againe let 10800 Segments be produced in the same paralell of 60 deg 0 min. of 0 deg 1 min. one minute apeece due East or West and working according to the former manner the last Segment will end in 59 deg 57 min. ½ which dilateth from paralell 60 deg 0 min. but 2½ minutes wherefore the consideration hereof may serve for a sufficient satisfaction plainely to proove that the East and West directed by the magneticall Needle or Compasse doth lead in a Magneticall paralell for as great Segments have their great varieties and lesser Segments have their lesser alterations correspondent vnto them so by the same reason insensible Segments must have insensible differences and the like reason holdeth for any other point of the Compasse as well as for the East or West as I have formerly shewed you and at our next meeting I will set you downe or shew you the Theorems for operating of it But you will say here is in 10800 minutes a difference of 2½ minutes and Segments of minutes in a mans judgement are so small that a Ship cannot make her way in lesser Segments and yet these Segments are not voyd of a sensible difference I answer as before that neither in sayling East or West nor in the spirall or Melisphericall way by any other course or point of the Compasse a Ships continuance vnder a great Circle or Circles cannot be terminated and whereas 10800 minutes doe in the East or West from Latitude 60 deg 0 min. produce a difference of 2½ minutes I say inrespect of â—0 great a distance the difference is insousible But if you please to take so much paines for the former paralell of 60 deg 0 min. to make a tryall from second to second that is 〈◊〉 648000 Segments be produced East or West each Segment to containe one second and the end of the last Segment shall not be from the first place so much as one second and thus having prooved sufficiently that the East and West being directed by the magneticall Needle or Compasse doth lead in a magneticall paralell and also that in keeping one course the Ships way is spirall or Helisphericall and returning by the opposite point thereof the Ship shall againe fall with the place of her departure we will finish this discourse and speake of some principall rules which of all sea-men and Marriners ought to be knowne Geograph What is the first and most usefull Proposition in the Pariners practise to be taken notice of Nau. By the course and both Latitudes to find the difference of Longitude and the distance Geo. For what reason is that proposition is sayling the primary and most usefull Nau. Because the course is commonly given and the Latitudes may be knowne by observation but the distance and the difference of Longitude by sayling may be supposed but not certainly knowne without the helpe of the former and so likewise the distance in sayling East or West may be supposed but not certainly knowne Geo. I pray you Sir let vs then procéed 〈◊〉 the practise without any further circumstance that having both Latitudes and the course we may â—nde the difference of Longitude and the distance Nau. We will Sir Suppose a ship to be in Latitude 50 deg 0 min. North Latitude sayles South South-west ½ point West vntill she be in the Latitude of 47 deg 0 min. I demand the difference of Longitude and the distance the Ship hath runne The Theorem AS a meane proportionall betwéene the fines of the Complements of both Latitudes is to the Tangent of the course so is the difference of Latitude to the difference of Longitude which by the Logarithmes is thus Adde the Logarithme tangent of the course 28 deg 7 min. to 〈◊〉 Logarithme of the difference of Latitude 60 leagues and from that summe subtract halfe the sine Complement of 50 deg 0 min. which is halfe the sine of 40 deg 0 min. and halfe the sine Complement of 47 deg 0 min. which is halfe the sine of 43 deg 0 min. added together I meane Logarithme sines and the remainer shall be the Logarithme of the difference of Longitude Geo. What is the second most usefull proposition that a Marriner in his practice is to take notice of Nau. By both Latitudes and the departure from the Meridian to find the difference of Longitude the course and the distance Geo. Wherefore doe you account this to be the second most usefull proposition in the Marriners practice Nau. Because all Marriners that kéepe their account by difference of Latitude and difference of Longitude which onely is the true way after that they have caâ—â— vp their Traverse by difference of Latitude and departure from the Meridian doe find their difference of Longitude as well as their course and their distance from their first place where they began their Traverse this way Geo. I pray you Sir set me downe the Theorems for the operating of this Nau. I will Sir which are these following 1 As the summe of halfe the Logarithme sines of the Complements of both Latitudes is to the departure from the Meridian so is the Radius to the difference of Longitude 2 As the difference of Latitude is to the departure from the Meridian so is the Radius to the Tangent of the course 3 As the sine of the Complement of the course is to the Radius so is the difference of Latitude to the distance that the ship hath runne from the first place where she began her Traverse Geo. What is the third and as I remember you said the last usefull peoposition to be taken notice of in the Mariners practice Nau. By having given the Latitudes of two places and their difference of Longitude to find the magneticall course or Rhomb and the distance Geo. How can this be usefull for a Mariner in his practise Nau. Because many times it chanceth that a Marriner is to sayle from one port whose Latitude and Longitude he hath in Geographicall tables as in Mr. Hughes his use of the Globes or in the Tables of the Sea-mans Kalender and is to sayle so another port whose Latitude and Longitude he hath also in the said Tables and by this proposition be may examine the truth of his Sea-chart he sayles by Geo Set me downe the Theorems for this proposition and I will trouble you no further at this time Nau. Sir I am in some hast because the time is farther spent then I supposed since we met but I will performe your request and then I will take my leave of you for this time First as the difference of Latitude is to the difference of Longitude so is halfe the sines Complements of both Latitudes I meane of the Logarithme sines to the Tangent of the course Secondly as before as the sine Complement of the course is to Radius so is the difference of Latitude to the distance runne Geo. Master Nautae I thanke you very kindly for your company and your conference you have informed my judgment very much in the matter of Navigation Nau. Sir I am very joyfull of it fare you well FINIS