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-south-west homeward to be shorter then the line of 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
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
And so would a Ship if shée had a haser or some thing else fast about the Pole to attract her thereunto Geograph But by the Globe thus doe fasten the quadrant of Altitude to the Equinoctiall in the brasse Meridian and bring the beginning of the degrées of the quadrant to paralell 60 deg 0 min. and then from that point where the beginning of the degrées of the quadrant do touch in paralell 60 deg 0 min. along by the edge of the quadrant to the Equinoctiall is the lyne of East and West now with the point of an néedle or some such thing prick of by the edge of the quadrant 1 deg 0 min. and make a marke there then moove â—â—lobe vntill the beginning of the degrees of the quadrant doe fit with that marke and then as before prick of againe 1 deg 0 min by the edge of the quadrant and so proceed by 1 deg 0 min. vntill you have gone round about the Globe and that the point of the Néedle fall in the first Meridian where you began and you shall find the lyne of the Inclination to be dilated from Latitude 60 deg 0 min. about 2 deg 20 min. and for further proofe hereof suppose your selfe to be vnder the Equinoctiall and the Compasse to have no variation and the Ship to cape East or West also the Maine-mast to stand vpright in the steppe the head thereof pointing to the Zenith and the heele to the Nadir or rather to the center of the earth and the mid-ship beame making right Angles with the mast to be paralell to the Axis of the world I say that this Ship proceeding East or West in this manner maketh her way in a great Circle to wit in the Equinoctiall and returning by the opposite point thereof shall againe fall with the place of her departure Now I say by the same reason that if the said Ship being in any Latitude between the Equator and either of the Poles in Caping East or West her mid-ship beame shall then be a paralell to the plane of the Horizon and also to the Axis of that great Circle or Circles which in her proceeding lyne of Inclination she maketh her way in the head of the maine-Mast pointing to the Zenith and the heele to the Nadir and the lyne of her Caping maketh contrary Angles with every new paralell Now if a Ship in sayling vnder one Circle must have her mid-ship beame alwayes paralell to the Axis of that great Circle shee maketh her way in then in keeping directly vnder one paralell her mid-ship beame must be alwayes paralell to the Axis of the world for that is the Axis of every paralell and so likewise the maine-must being rectified perpendicularly in manner as aforesaid must be also a paralell to the Equinoctials diameter and make an Angle with the Horizon equall to the Latitude the head thereof not respecting the Zenith nor the heele the Nadir nor the Center of the earth but the Center of the paralell of her Latitude and in this manner a Ship may runne in a paralell to the Equinoctiall But now this may stand with humane reason I leave to your further construction Nautae Here in you are notably deceived as it shall presently at large be made plaine and evident for whereas you say that the way of a Ship cannot describe a paralell to the Equinoctiall except her mid-ship beame be paralell to the Axis of the world I say that so long as the mid-ship-beame remaineth due North and South that is to say paralell to the Meridians Diameter in the plane of the Horizon although the head of the maine-Mast it being perpendicularly erected point to the Zenith and the héele to the Nadir so long I say her way shall describe a paralell to the Equinoctiall but as I said before you séeme by all your former allegations to proove that the way of a Ship being composed of Segments of great Circles should have those Segments limited or terminated to containe 15 20 or 30 leagues a péece which if it were so then should it be altogether according to your saying But now far as much as there is some difficulty in the premises and few Mariners know how to censure thereof I will therefore briefly proove by Arithmeticall calculation the East and West in any Latitude to lead in a paralell as well as the Equinoctiall Example The paralell of 60 deg 0 min. is equall to the length of halfe the Equinoctiall or 180 deg 0 min. of a great Circle we will therefore in the same make our beginning and from the first place being scituate therein produce 18 Segments which containe 10 deg 0 min. a péece which by Arithemeticall calculation may be thus found out The Theorem viz. AS the Radius is to the sine of the Latitude 60 deg 0 min. so is the sine of the Complement of the distance the sine of 80 deg 0 min. to the sine of the Latitude of that place where the first Segment of 10 deg 0 min. endeth and so againe in like manner for the second Segment viz. As the Radius is to the sine of the Latitude where the first Segment endeth so is the sine of the Complement of 10 deg 0 min. to the sine of the Latitude where the second Segment endeth and this is to be continued 18 times so shall you find the last worke to bring forth the sine of 41 deg 06 min. but if you worke by Logarithme sines multiply the Legarithme sine of 80 deg 0 min. the Complement of 10 deg 0 min. by 18 because there are 18 Segments and the product adde to the Logarithme sine of 60 deg 0 min. the Latitude given the summe will be the Logarithme sine of 41 deg 06 min. the Latitude of the 18 Segment which dilateth from Latitude 60 deg 0 min. the sum of 19 deg 0 min. wanting but 0 deg 06 min. From whence we may sée that if great Segments haue such great alterations then lesser Segments must have their correspondent varieties proportionall vnto them but marke what followes and I make no doubt but that anon you will be of another opinion then formerly you have bin concerning this matter as from the aforesaid paralel 60 deg 0 min. let there be produced 36 Segments according as was afore shewed each Segment containing 5 deg 0 min. or 100 leagues a peece and you shall find the end of the last Segment to fall in Latitude 49 deg 41 min. which is dilated from paralell 60 deg 0 min. but 10 deg 59 min. where note that this dilatation is lesse then the former by 7 deg 55 min. In like manner in the same paralell 60 deg 0 min. let there be produced 180 Segments of 1 deg 0 min. or 20 leagues apèece and you shall find the end of the last Segment to fall in Latitude 57 deg 25 min. which is dilated but 2 deg 35 min. from
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