6 From the Meridian of Sierraleona 187 leagues VVestward 4 50 3 0 From the Meridian of Sierraleona 187 leagues VVestward 5 40 1 50 From the Meridian of Sierraleona 194 leagues VVestward 5 45 0 45    South From the Meridian of Sierraleona 195 leagues VVestward 5 26 0 10 From the Meridian of Sierraleona 198 leagues VVestward 5 30 0 35 From the Meridian of Sierraleona 206 leagues VVestward 6 33 2 0 From the Meridian of Sierraleona 210 leagues VVestward 6 55 2 35 From the Meridian of Sierraleona 220 leagues VVestward 6 45 3 35 From C.S. Augustine North and by VVest 7 0 7 16 From C.S. Augustine North by East Easterly 6 40 1 4 From C.S. Augustine North Northeast 8 0 4 0 From Cape S. Augustine East Northerly 30 leagues 8 10 8 20 From C.S. Augustine 100 leagues 11 6 8 30 From C.S. Augustine not 120 leagues 5 37 11 30 At the I le Fernando Laronho near Brasil 8 30 2 20 Close by the coast Brasil 3 45 7 0 8 0 10 0 A little VVest from the Meridian of Trinidad near Brasil 11 10 18 30 Among the Ilands of Trinidad and Ascension 12 8 20 35 On the backside of the I le of Ascension 12 10 20 30 At the I le of Ascension 10 0 20 0 In the Meridian of Trinidad Easterly 14 53 27 0 Between the Iles of Trinidad and Tristan de Acunha 18 0   19 0    Varia East Latit South  De. M De. M From the shoalds of Brasil East Southerly about 14 leagues 12 30 19 30 From the same shoalds South-east about 55 leagues 13 52 20 10 Also from the same shoalds Southeast by East 13 20 19 37 From the coast of Brasil 150 leagues 10 0 18 0 At Cape S. Vincent in Brasil 12 0   From the coast of Brasil 100 or 120 leagues 8 30 17 0 7 30 18 0 From Laronho Southwest 12 leagues 8 1 4 20 From Ascension Ile 20 or 30 leagues Eastward at the Cliffe Penedo de S. Pedro 5 30   Betwixt Ascension Ile and S. Helens 7 30   At S. Helena 2 48   3 46   5 37   7 30   From S. Helena a little VVestward 9 0   From S. Helens not 19 leagues 5 40 18 30 From S. Helena northwest by VVest 16 leagues 3 45   From S Helena northwest 156 leagues 7 40 10 20 From S Helena 230 leagues 5 38 8 20 From Ascension I le northeast half a point northerly about 12 leagues 6 0   About the Ilands of Martin Vaz 13 0 19 0 Alongst by those Iles 11 15   From those Ilands northerly 30 leagues 18 30   From the shoare of Africk VVestward some 130 leagues 4 8 27 0 Bearing from thence toward S. Helena 2 48 25 0 From the main of Africa 160 leagues 2 50 23 0 In the Longitude of 28 degrees 15 20 32 0 A little VVestward from the Meridian of the Iles of Martin Vaz 14 58 28 35 Eastward from thence 15 37 28 53 From the former Observation 60 leagues 16 8 29 0 From the last Observation Eastward 27 leagues 16 52 29 33 Beyond Tristan da cunha 70 or 80 leagues comming from Martin Vaz 16 53 33 0 From Tristan da cunha VVestward 17 52 34 35 14 0 At the Iland of Tristan da cunha 19 0   From thence northward 16 8 33 34 Past the Iland towards C. Bona Speranza 14 0   From Tristan da cunha VV. n. VV. 368 leagues 14 0 2◠25 At Cape Frio 13 0   Near Cape Frio 12 0 23 30 From Cape Frio Eastward towards Africa 17 0   18 0   From Cape Frio about 125 leagues Eastward 11 8   About 155 leagues from Cape Frio 14 8 25 0 At Port desire 5 0 47 40 At the East mouth or entrance into Magellans straits 5 30   In the straits of Magellan 5 0   From Cape Bonae spei 900 leagues VVest by north half a point northerly 15 52 26 50 From Cape Bonae spei almost VVest by N. 180 leagues 8 50 34 0 At the bay of Soldania 0 20 33 55 1 30 33 20 At Cape Buona Esperanza 0 15   1 30   About Cape Buona Esperanza 2 0 35 0 From Cape Buona Esperanza VVestwards 30 or 40 leagues 5 38   Betwixt C. Buona Esperanza and S. Helena 3 45   From C. Buona Esperanza South 3 45   From C. Bona Speranza VVestward 40 or 50 leagues 3 0   From C. Buona Esperanza due northwest 5 37 20 0  West   From C. Bonae spei S.w. by S. 36 leagues 4 10 35 25 From C. Bonae spei S.w. by S. 28 leagues 3 50 35 30 At Cape das Agulhas near C. Bonae Spei 0 0   From thence 80 leagues Eastward 0 0   At Cape Talhada 40 leagues East from Cape das Agulhas being in sight of land lying from us north by East 3 47 34 20 At C. Corientes beyond C. Bonae spei 7 30   11 0 25 0 From C. Corientes Southwards 8 30 30 30 About the Ilands Primeras towards Mozambique 15 0 18 0 In the I le Mozambique 12 0 14 45    North. At the Iles of Nicobar 7 36 7 30 10 0   From thence till you come to the Line going towards the East Indies 11 0   At the Ile de Almirant near the line 13 0   Near to C. Guarda fui or Porto Galeacea 8 15 13 15 At P. de estreito or the mouth of the Red sea 5 15 12 15 At Baxos de Cuaqem 1 15 19 15 At Port de Igidid 0 40 22 0 At Xuarit 0 15    East   At Sidon in the bottom of the straigts 2 35 33 30  West North. From the place that is 200 leagues Westward from Goa to Cape Comorin 15 0   At Goa 15 0 15 20 At the Iles Comoro 13 0   In the Bay of S. Augustine in Madagascar 15 0   At Cape Romano in Madagascar 17 40 26 0 Near Madagascar 8 30 26 0 20 0 From Cape Romano Southerly 14 4 27  30  From C. Romano VVest Southwest half a point Southerly 110 leagues 14 14 36 34  Variat East Latit North.  De. M De. M. From C. Romano Southwest 50 leagues 15 25 28 20 In the heighth of C. Romano 8 leagues off 16 45 25 50 At the I le of S. Mary entring the Bay of Antongil 17 0 17 0 In the bottome of the Bay of Antongil by many and exact Observations 20 0   At the Bay of Tanassarin 5 30   At the VVest side of the sands of Saya de Malha 15 0 11 30 At the Iland Ragapez 22 11 10 0 From the
according to that proportion wherewith the Meridian is greater then that Parallel Therefore the true difference of longitude betwixt Lisbon and Tercaera that is the arâ— of the Parallel or Aeqinoctial contained betwixt the Meridians of those places shall thus be found out It is a rule in Geometry that the Diameters and Peripheries and consequently the semidiameters and like arks of Circles have the same proportion Also it is manifest that the Sine of the complement of the distance of any Parallel from the Aequinoctial is the Semediameter of the same Parallel Now the distance of the Parallel of Lisbon and Tercaera from the Aequinoctial is about 39 degrees the complement whereof is 51 degrees whose sine is 777 which is the Semidiameter of the foresaid Parallel in such parts whereof the whole sine containeth 1000. which is the Semidiameter of the Meridan Therefore by the rule of proportion inversed if 262 Spanish leagues make 15 degrees in the Meridian whose Semidiamiter is 1000 parts then in the Parallel whose Semidiameter is 777 of the same parts they shall make 19 degrees and 237 777 parts of one degree that is 18 min. and little more which if it be true that the course from Lisbon to Madera is South-west and from Madera to Tercaera North-west and that the Latitude of Madera is 31 degrees 30 min. and the Latitude of Lisbon and Tercaera 39 deg shall be the difference of Longitude betwixt Lisbon and Tercaera Whereas Ortelius and Mercator following as it seemeth the Mariners Charts without correction in their universall Maps make them to differ in Longitude scarce 15 degrees of their Parallel as if it were equal to the Aequinoctial line 3. Moreover they are deceived not only in the situation of many places which the Marine Chart sheweth to be under the same Meridian but also in the lying or bearing of other places each from other For the Meridian is a certaine rule of the positions of places If therefore error shall be committed in the situation of the Meridian there must needs be error in the Inclinations of the other Rumbs points or lines of the Compasse And therefore not every Inclination or respective position of place to place which is set down in the Marine Chart is to be taken for true but that position or inclination only by which some have sailed from the one place to the other This may be seen in sayling to India For the Marine Chart placeth that promontorie of Africa called the promontorie of 3 points being in Latitude towards the North 4 degrees and one halfe and the Ilands of Tristan Acugna which have 36 degrees of Southern Latitude under the self same Meridian Also the Marine Chart sheweth the distance between these Ilands and the promontorie of Good Hope to be almost 400 leagues both which notwithstanding cannot stand together For if all the shore from the promontorie of 3 points unto the promontorie of Good Hope be rightly described and the promontorie of 3 points also lie under the same Meridian with those Ilands the foresaid distance must needs be much lesse but if it be not lesse it cannot be that they should have the same Meridian with the promontorie of 3 points but must needs be more to the Westward Hereof it commeth that the Mariners are very oft deceived when they go from one place to another following that direction which the Sea-Chart sheweth them Which place when they find not by that course they think that the cause of that error is either some swift current of the Sea that carrieth them another way or else the declination of the Poles of the Loadstone from the true Poles of the World although perchance they erred only because they knew not how those places did bear one from another 4. Neither are they only deceived in that because they think that the Sea-Chart can shew the situations of all places but also because that when they will translate the Sea coasts out of the Chart into the Globe they do it having respect only to the numbers of the degrees of Longitude and Latitude found therein and no otherwise then when they set the fixed stars into a Coelestial Globe So it commeth to pass that not only those errors are committed which do necessarily arise out of the common Sea-Chart but other errors also which might be avoyded if they first turned into degrees those distances of Longitude which they have truly known and then followed the Longitudes and Latitudes of places 5. In shewing the distance of places there is as great error committed as in any of the former For example If you imagine 2 ships to be under the Aequinoctial 100 leagues asunder and that each of them should sayl from thence due North or South under his Meridian until they come to the Parallel of 60 degrees Latitude they should be there but only 50 leagues distant because at that Parallel the Meridians are distant but half so much one from another as they were at the Aequinoctial as it may most manifestly appear by the Globe and yet the Chart will shew that those two ships have the self same distance of 100 leagues being under the parallel of 60 degrees which they had before when they were under the Aequinoctial line 6 There is yet another error remaining though all the former were avoyded which ariseth hereof because that by the direction of the Compasse they bend and turne the ship in such sort that they constrain it alwaies to make the same angles with the Meridian As when they sail from Vshent to Cape Raso both lying under the same Parallel they guide the ship in such sort that it maketh alwaies right angles with the Meridian and so holding on their course due West they keep themselves alwaies under the same Parallel whereas notwithstanding there is a more certain course whereby they may go from one place to another without that losse of way which they must needs make that keep themselves alwaies under the same Parallel There is moreover another commodity in this kind of sailing that we may find every day by a more certain accompt what way we have made and know in what place we are But this way is not to be defined by any of the lesser Circles but by a great Circle which is to be drawn by those two places and the ark of that great Circle contained betwixt the same places is lesse then the ark of the Parallel which lieth between them as may be concluded by an evident and necessary reason out of the principles of Geometry much like as a straight line is shorter then a crooked both being extended between the same pricks Therefore this commoditie is also hereunto adjoyned that in sailing by a great Circle the way is more short and compendious But he that entreth into this course of sayling must know that he must often change the point of the Compasse whereupon he guideth the ship because of the variable
and West from those degrees under which they are situate The fifth is the scale of leagues which you may see whether it be true by taking betwixt the points of your compasses just 4 degr out of the line of graduation which being applied to the scale of leagues must there agree exactly with 70 Spanish leagues or 80 English By the Sea-Chart are known five things The first is the lying or trending of the Coast. The second is the distance or number of leagues from one coast to another The third is the latitude or distance from the Equinoctial wherein all Lands both Continents and Islands as also every Port River Isle Shoald or Bank is situate The fourth is the rumb or rumbs by which we are to sail from one place to another The fifth is the point or place where we are with our ship when we are sailing The first is known with a pair of compasses putting one foot thereof upon the beginning of the coast whose trending we desire to know and the other foot upon the rumb which to our thinking is every where equally distant from the said coast For if one foot of the compasses running along the Coast the other foot keepeth by the said Rumb then we say the coast lieth even with that rumb And if our compasse runneth with out swerving one foot from the rumb and the other from the Coast till the point which runneth along the coast leaveth it then from that very place where it leaveth the same we may say that unto the other place where it began the coast runneth by such a rumb as if a man should say East and West Northeast and Southwest or any other rumb whatsoever The second thing which is the distance may be found by taking between the points of your compasses out of your scale of leagues if the distance be very great an hundred leagues and measuring with your compasse so opened from one place to another now if in so doing it falleth not just then remembring how many hundreds of leagues there are you must for the measuring of the rest pitch one foot of your compasse upon the point where the last hundred ended and the other foot upon the land whose distance you desire to know then bringing the compasse so opened to the scale of leagues you shall see manifestly how many leagues the said distance surmounteth above the hundreds But if the distance be lesse then an hundred leagues then setting the points of your compasses upon those two places whose distance you desire to know and removing the compasse so opened to the scale of leagues you shall easily know the distance of one of those places from the other The third which is the heighth or latitude wherein every Port River or Island standeth is to be found by pitching one foot of your compasses upon the Land Haven or Cape whose heighth you desire to know and the other foot upon the next East and West parallel and the compasse remaining in that sort move the point thereof along the said parallel or rumb to the line of graduation and there the other foot which lay upon the land will shew you the heighth thereof The fourth which is the rumb or rumbs by which you must sail from one place to another is known after this manner If you be to sail by one rumb only you may know it by pitching one foot of your compasses upon the place from which you are to depart and the other foot upon the very next rumb which to your thinking goeth most directly to the place whither you would go and running by that rumb with one foot of your compasse so opened the other foot will touch the place whither you are going But if it toucheth not the place whither you are going then pitch one foot of your compasses upon the same place and the other foot upon the second rumb which you suppose may lead you thither And placing one foot of another pair of compasses upon the place from whence we depart and the other upon the most direct rumb toward the place desired these two compasses running along the rumbs one toward another you must mark where those two points joyn together one whereof came from the place of your departure and the other from the place whither you are to go the point where they both concur is that to which we are to change our course As for example if I sail from the bar of S. Lucan to fall with Punta de Naga upon the Isle Teneriffe in time of winter it is evident that I must sail Southwest and by South till I bring my self East and West with Cape Cantin in 32 degrees and an half and from thence I must go Southwest and by west but not all the way because putting one point of the compasse upon Cape Cantin and the other point upon the South west and by west rumb next unto it my compasse thus running open alongst the said rumb the point which departed from Cape Cantin will run on the out-side of Punta de Naga But in such a case as this I place one point of one pair of compasses at Punta de Naga and the other point upon the Southwest rumb Likewise I place one point of another pair of compasses at Cape Cantin and the other upon the next Southwest and by west rumb Then let these two compasses so opened run by their said rumbs one against another and then you must look in what place heighth the very point is where those two points of the compasses which departed from Punta de Naga and Cape Cantin do meet and I say that when I am come to the said heighth and place having sailed from Cape Cantin Southwest and by west then I must change my course and run South-west CHAP. XX. Of the point of Imagination THe fifth thing to be known by the Sea-chart is the point of the ships place and this they term to cast a point or to set a prick upon the chart which is no other thing but to finde a point therein which is proportionally distant in the Chart from all the Lands and Islands there described so many leagues of the scale as there are leagues of distance upon the sea from the place where you are to the Lands and Islands round about you represented by these that are in the Chart. This point is to be found two wayes either by imagination or by traversing which may properly be called geometrical The point of imagination is usually found by the first of these two wayes when we sail directly by a parallel circle which is when we sail due East and West keeping alwayes in one heighth and distance from the Equinoctial or when we sail by any other rumb in close weather when neither the Sun at noon nor the North star in the night can be seen This point doth pre-suppose the knowledge of two things to wit the rumb by which we have sailed and that is known
the Rock near Lisbon 10 0 N 38 55 24 30 In the Westermost part of Ireland 11 0 N 52 8 24 12 In the West part of England 12 40 N 50 21 28 0 Decreasing About one mile Eastward from Plimmouth 13 24 N â—0 18 30 0 By Tin mouth in the Sea 12 40 N 55 0 33 0 At London in England 11 30 N 51 24 34 6 In the Foreland of England 11 0 N 51 8 35 40 In Amsterdam 9 30 N 52 20 39 30    Northwesting     The Northwesting or the West variation of the second part or space towards the North Increasing At Helmshade to the westward from the North Cape of Finmarke 0 0   60 0 At the North Cape of Finmarke 0 55 N 71 25 61 30 At Norquinda 2 0 N 71 10 63 30 At S. Michael or Archangel in Russia 12 30 N 64 54 83 30 In the South streight of Vaigatz 24 30 N 69 30 103 0 At Langeness in Nova Zembla 25 0 N 73 20 100 30 Decreasing In Williams Iland In Nova Zembla 33 0 N 75 35 110 0 At Yshouck In Nova Zembla 27 0 N 77 12 120 30 At Winter-house In Nova Zembla 26 0 N 76 0 120 30 The Northeasting of the first part or space towards the South Increasing 105 Spanish leagues Westwards from Cape S Augustine in Brasile 0 0 S  0 0 At Cape S. Augustine in Brasile 3 10 S 8 30 6 0 North and South with Cape das Almas in Guinea 12 15 S 0 0 29 0 Towards the Northwest Northerly from the Ilands of Tristan da Cuneha 19 0 S 31 30 30 0 Decreasing Towards the Northwest Westerly from the same Ilands 15 0 S 31 30 36 0 North and South with the Cape of Good Hope 2 30 S 35 30 57 0    Northwesting     The Northwesting of the second part or space towardâ— the South except Goe Cochin Cantan Incrâ—asing 17 German miles from Cape das Aguillas Eastwards 0 0 S  60 0 5 miles in the Sea froÌ„ Terra de Natal 4 30 S 33 0 66 0 At the shoalds of Indie 11 0 S 22 0 79 30 In Mâ—sambique 11 0 S 14 50 81 40 In the Bay of S. Augustine in Madaâ—gascar 13 0 S 23 30 83 0 Southwards from Cape S Romane 16 0 S 28 0 86 20 In Anthonie Gills Bay in Madagascar 15 0 S 16 20 91 0 Decreasing 34 German miles Southeast from Brandaon 22 0 S 19 20 110 0 In Goa a famous Mart town in Indie 15 10 N 25 30 120 0 In Cochin 15 0 N 9 45 120 0 25 German miles West a little Northerly from the Southwest corner of Sumatra 6 0 S 5 28 147 0 In Bantam a Mart town of Java 4 45 S 6 0 150 0 In the Iland Lubocqua 2 25 S 6 10 155 0 In the Southwest corner from the I le of Balij 1 30 S 8 40 157 0 In the mouth of the river Cantan in China 0 0 N 23 0 160 0 In Buâ—â—aâ— 46 Dutch miles Eastwardâ— from the East part of Java 0 0 S  160 0 A declaration of the form â—r Table or veiw of variations BEfore wee come to the Declaration of this Table this first of all we would not have unknown namely that if perchance hereafter by more diligent and more exact experience any other variation Longitude or Latitude of places can be found then that which is set down in this Table so as it should be needfull to change the difinitions and expositions of some things and words here set down yet we ought not therefore to be scared from this purpose but much rather ought we to strive with all our strength to attain thereto that by little and little we may come to a more certain knowledge of things building upon these as upon foundations we therefore following this opinion will prosecute that as true which at this time is most like to be true that if others also do the same when occasion is given we may alwayes come neerer to that which is most true in the nature of things Which things being omitted that we may come to the declaration of the former Table first of all we say that the first of the three columnes which thou seest in the Table sheweth the variation of the place the second the Latitude to which the third is adjoyned containing the Longitudes as we could by conjecture attain unto them that the places might so much the more easily be found in the Globe and the manner of the variations might more plainly be shewed in that which followeth hereafter The mark of the letter N in the second column signifieth North Latitude and S South Then because in them mention is made of the variation of the Northeasting or the Northwesting increasing or decreasing all which as proper words of art have need of there several definitons first of all we must know that the Magneticall needle in one and the same place doth alwayes shew the same part of heaven but not the same part in all places for in some places it pointeth due North in other places it declineth more or lesse to the East or West Therefore in manner of a definition we will say thus The first definition THE Declination of the Magnetical needle from the North towards the East is called the Northeasting towards the West Northwesting and with a generall name it is called the variation but the variation and the North pointing of the needle that is the pointing of the needle due North may by a generall name be called the needle pointing or pointing of the needle As concerning those words of increasing and decreasing as also of the first and second part or space before we come to the definitions of them they have need of some precedent declaration It may be seen in the Table of variations that in Corvo the Magneticall needle pointeth due North but after that the more a man shall goe towards the East so much the more also shall he see the needle varie towards the East till he come one mile to the eastward from Plimouth where the variation comming to the greatest is 13 degr 24 min. From hence the Northeasting beginneth to decrease till you come to Helmshude which place is Westwards from the North Cape of Finmark where again the needle pointeth due North. Now the Longitude from Corvo to Helmshude is 60 Degr Which things being well weighed it appeareth that the greatest variation 13 degr 24 minutes at Plimouth the Longitude whereof is 30 degr is in the midst between the places where the needle pointeth due North. For 30 degrees is the midst between the beginning and 60 degrees And what is here said of the North part experience teacheth that the same taketh place in the South part also for 105 Spanish miles from Cape S Augustine at the begining of Longitude again it pointeth due North as it doth 17 Germaine
for this time breefly suffice CHAP. XIII Error in the use of the Compasse by the Variation neglected and how to observe and avoid the same NExt the Sea-chart there is not any instrument of Navigation whereby greater error may ensue then by the Compasse if the Variation be neglected By which neglect alone we may often times misse an whole Point and more in directing the Course from place to place Notwithstanding M. Peter of Medina laboureth greatly to prove that there is no Variation of the Compasse and that many inconveniences and absurdities must needs follow out of that opinion as hee esteemeth it thinking it to have no better ground then the grosse and erroneous observations of unskilfull Mariners as by the third Chapter of his sixt booke of the Art of Navigation may appear more at large But daily experience by many and diligent observations with exact instruments heedâ—ully used by skilfull Observers not only at sea the unconstancie whereof which causeth the ship to be alwaies unsteadie might give some colour to M. Peters conceit of no Variation but also on firm land where most stedie and certain observation may easily be made I say daily experience hath so often so constantly so manifestly proved this varying propertie to be in the Compasse that it cannot by any means with reason be denyed Now then for the better finding of this Variation there must be conceived two Meridians a true Meridian and a Magnetical Meridian also a true Azimuth and a Magnetical Azimuth of the Sun The true Meridian is an Azimuth passing by the Poles of the world The Magnetical Meridian is an Azimuth that passeth by the points of the wires in the Compasse or of the Needle touched with the Loadstone The true Azimuth of the Sun is shewed by the arch of the Horizon contained betwixt the Azmiuth of the Sun and the true Meridian The Magnetical Azimuth of the Sun is shewed by the arch of the Horizon contained betwen the Magnetical Meridian and the Azimuth of the Sun The difference of these two arks of the Horizon is alwaies equal to the Variation of the Compasse To find out the Magnetical Azimuth of the Sun we must first know upon what point of the Compasse the Sun is which although it may be done by aim very neer the truth by him that is experienced especially when the Sun is low or at the Horizon rising or setting yet it may better be done with help of such a ruler and sights as land-measurers use with their Plain Tables wherewith you may thus find upon what point of the Compasse the Sun is Lay the edge of the ruler right over the center of the Compasse then holding the ruler so fixed and the Compasse levell so neer as you can aim turn it about untill the midst of the Sun-beams passing through one of the sights fall alongst upon the edge of the ruler or midst of the opposite sight Then holding your eye in such sort over the Compasse that the rulers edge may lie right upon the center of the Flie look also upon what point of the Compasse the edge of the ruler lieth to the Sun-wards for that is the point whereupon the Sun is at that time which for brevities sake may be called the Suns point This point you shall look in the instrument following and it shall shew you amongst the degrees the Magnetical Azimuth of the Sun As for example when the Sun is due East by the Compasse I would know in what Magnetical Azimuth he is Therefore I look the East point in this Instrument which directeth me to 84 degrees which is the Magnetical Azimuth desired And the difference betwixt this and the true Azimuth of the Sun is the Variation of the Compasse which we seek for This difference therefore shall thus be found out At the same time when you observe the Suns point let the height of the Sun be also observed It is best to take both these observations about the midst of the forenoon or afternoon for then the height of the Sun altereth quickly and the Refraction and Parallax cannot much deceive you therefore at that time the true Azimuth of the Sun shall easily be known thus First find-out the Declination of the Sun remembring alwaies to give allowance or take away according as the Declination increaseth or decreaseth for the place and time of your Observation Then set your Astrolabe to the Latitude of the place where you observe and follow the Parallel of the Suns Declination untill you come to the Almicantarath or height of the Sun known by observation for the Azimuth that passeth by their mutual intersection is the true Azimuth of the Sun that was sought for which if you follow down to the Horizon you shall have that Azimuth given Now of these two given Azimuths that is the true and Magnetical Azimuth of the Sun substract the lesser from the greater for the difference remaining is the Variation of the Compasse the denomination whereof that is whether it be Easterly or Westerly shall easily be discerned thus if the true Azimuth of the Sun counted from the South point in the forenoon be lesse then the Magnetical Azimuth the Variation is Easterly otherwise it is Westerly Contrariwise in the afternoon if the true Azimuth of the Sun be greater then the Magnetical Azimuth the Variation of the Compasse from the point of true North is Eastwards otherwise it is Westwards And for the better understanding of these rules I have in the Table following exemplified them by such Observations as I took both at Sea and Land in the year 1589. The instrument following is then to be used when Observation is made as before hath bin shewed by a Compasse wherein the North points of the wires are set half a point to the Eastwards from the North point of the Compasse of which sort are the Compasses that are commonly used by English Mariners whereas if the points of the wâ—res were set just under the points of North and South and the circumference of the Compasse divided into degrees both Eastwards and Westwards beginning at the North and South points and ending with 90 at East and West we might at the first have the Magnetical Azimuth of the Sun by Observation and so there should be no need of this Instrument In the Table here following the letters N W S E b in the first and second columns signifie North West South East by The fractions in the second column are parts of the point whereto they are annexed In the column intituled The time of Observation the letters BN and AN signifie before noon and After noon An Instrument for the readie finding of the Suns Magnetical Azimuth by the ordinary Compasse The place of Observation The Suns point of the Compasse The hight of the sun The Suns Magnetic Azimuth   Deg Min Deg Min About twenty leag from Spain W WNW â…“ N 0 0 69 30 30 or 40 leagues from Spain W ENE ½ E
any land This Horizon is of two sorts namely right and oblique The right Horizon is that which they have that live under the Equinoctial which passeth by their Zenith and therefore the Equinoctial line or circle falleth perpendicularly and right acrosse with their Horizon and both the South and the North Poles are in their Horizon The oblique Horizon is that which they have that live not directly under the Equinoctial for unto them the Equinoctial divideth the Horizon obliquely and not right acrosse and one Pole is alwayes above their Horizon and the other is beneath their Horizon and cannot be seen This Horizon is represented in the Sea-Chart by a certain imagined circle whose center is the point where our ship is From which center are imagined to proceed unto the said circle 32 lines which represent the 32 winds or rumbs which alwayes are drawn in our Sea-Compasse which likewise in a little peece of paper doth continually represent unto us both by day and night the whole Horizon with his 32 divisions CHAP. XVI Of the 32 Winds THis right or oblique Horizon is divided into 32 equal parts by 16 lines which they call Rumbs and they cut themselves in the point where we stand of which rumbs that which passeth by the points where the Equinoctial beginneth and endeth which are where the Sun riseth and setteth the 11 of March and the 13 of September is called East and West and that which cutteth it right acrosse is named North and South And the four extreams or ends of these two lines are distant upon the Horizon one fourth part of a circle and they make four quarters Every one of which quarters being divided in the midst do make four other points and that which falleth between the North and the East is called North-east and that between the North and the West North-west that between the South and the East South-east and that between the South and the West South-west And so the Horizon is divided by four lines or numbs into eight principal winds noted in the Sea-Chart with black lines And if you divide every one of those eight parts in the midst you shall have other eight lines and other four rumbs which in all are 16 winds And each one of these hath his name compounded of the names of those principal winds which are on either side thereof As for example that half winde which is between the North and the North-east is called North-north-east and that which bloweth between the East and the North-east is called East-north-east and that between the East and the South-east East-south-east and that between the South and the South-east South-south-east and that between the South-west and the VVest VVest-south-west and that between the VVest and North-west West-north-west and that between the North-west and the North North-north-west And these are noted in the Chart with green lines Finally if you divide every one of these sixteen winds in the midst they will yield you other 16 winds and will amount to 32 winds in all Which 16 last mentioned are drawn in the Sea-Chart with red lines and are by the Spaniards called quarters of the eighth first and principal winds and every one of these is called by the name of that principal wind which is next it together with an addition of the word By and the name of another principal wind which is next unto it As for example of the two quarter-winds which fall next the rumb of the North that which lieth towards the North-east is called North and by East and that which falleth towards the North-west is called North by West So likewise of those two winds which blow next the North-east that towards the North is called North-east and by North and that towards the East North-east and by East And after the same manner you may name all the rest The Figure of the Sea-Compasse and of the Horizon divided into 32 Winds by 16 Rumbs But here is to be noted that there is difference between the Rumb and the Wind because a Rumb is one direct line continued with two contrary winds as the Rumb of North South and the Rumb of East and West And so when we will name the lying of any Coast we will say that it lieth North and South or North and by East and South and by West But the wind is one line of those 32 into which the Horizon is divided and it is one part of those two which together are called the Rumb And so we say that Land lieth from us towards the South and towards the South and by West or towards the South-south-west c. CHAP. XVII Of the two Tropicks BEsides the six Circles above-mentioned which are drawn upon the superficies of the Sphere of the World there are other two which the Sun describeth with the motion of the Primum Mobile about the 12 day of June and of December of which two Circles that which the Sun describeth the 12 of June from the time of his rising till the time that he riseth the day following is called the Tropick of the Summer Sun-standing or the Tropick of Cancer for the Sun having departed from the Equinoctial and increasing his Declination towards the North when he cometh to describe that Circle for two or three dayes it semeth that he cometh no neerer to our Zenith nor departeth from the Equinoctial one day more then another but from thence forward he goeth back diminishing his Declination till he come to the Equinoctial and crossing the same he goeth on the other side increasing his Declination until the 12 of December upon which day from the time of his rising till he be come about to rise again the next morning he describeth another Circle called the Tropick of the Winter Sun-standing or the Tropick of Capricorn for the Sun being departed from the Equinoctial and increasing his Declination towards the South when he cometh to describe that Circle it seemeth for two or three dayes that he returneth not one whit towards the Equinoctial nor goeth further from our Zenith one day more then other but from thence forwards he commeth back again diminishing his Declination till he be returned to the Equinoctial and from thence towards our Zenith These two Circles in Sea-Charts are marked with two great red lines drawn from East to West which lie on either side of the Equinoctial being distant from thence about 23 deg and an half And wheresoever our ship be in any place between these two Circles or lines we may in some time of the year take the Sun in our Zenith at which time it maketh no shadow at all being then just 90 degr high above our Horizon But they which are without the said two Circles or lines shall never have the Sun in their Zenith because it cannot come to the height of 90 degr above their Horizon CHAP. XVIII Of the Parallels THe parallel Circles are those which are in all parts equally distant from the
by the Compasse and the leagues which we have run and this hath no certainty but is a little more or less then a good Mariner according to his imagination supposeth that he hath sailed whereof the said point tooke his name This point is found in the Chart by taking out of the scale of leagues so many leagues as a man can well estimate that the ship hath gone and pitching one foot of the compasse in the place from which you departed you shall set the other point in such sort that both may be equally distant from the Rumb or wind whereby you have sailed and where that second point of your Compasse shall fall there is your ship according to your imagination CHAP. XXI Of the Traverse or Geometrical point THe point found by imagination is not so certain as is convenient because it oft commeth to passe either because the Mariner hath not made true account of the way that his ship hath made or for some other causes therewith concurring that if he taketh the heighth by the Sun or by the North star after he hath cast his point he commeth not to find himself in that distance from the Equinoctial which his point of imagination doth shew him but in some other distance And to avoid this error there is another way of casting your point in the Chart which is called punto de esquadria the Traverse point which point presupposeth the assured knowledge of two things one is the Rumb by which you have sailed the other is your distance from the Equinoctial For all this art of Navigation is grounded upon the course and height which is in quantity all one with the distance from the Equinoctial The Rumb or course is alwaies known by the Compasse the height by the star and the distance from the Equinoctial by the Sun This being known set the foot of one Compasse at the port or place from whence you departed and the other foot in the next Rumb where upon you have sailed and placing one point of an other paire of Compasses upon the line of graduation in the degree of your distance from the Equinoctial and the other point upon the next East and West Rumb let these two pair of Compasses standing thus open run along the Rumbs one towards another till the point which came from the place of your departure and that other which came from the height of your graduation meet and where they meet there is the place of your ship And this point so found out is most certain when the height is carefully taken and the Rumb known CHAP. XXII Of the amending of the point of imagination HE that knoweth how to find out the point by traversing shall easily amend the point of imagination when having taken his height he findeth the said point not to be good and certain And here is to be noted that when you saile East and West and find the point by imagination this point cannot be amended but you must saile in doubt how many leagues you have gone untill you fall with the land because that sailing in that course neither the height of the pole nor your distance from the Equinoctial doth any whit alter But when you saile by any other rumb your point of imagination may be amended and the amendment thereof shall be so much the more certain as the rumb of your Navigation cometh neerer to the North or South and by so much the more uncertain as it cometh neerer to the East or West This amendment is made two manner of wayes namely either by traversing or by the amendment of North and South and East and West which second amendment though it be a kind of traversing yet it is called by another name to distinguish it from the first The amendment of the point of imagination by the traverse point When you will amend your point of imagination by traversing you must set one foot of one pair of your compasses in the point found by imagination and the other foot upon the next rumb by which you have sailed and setting the foot of another pair of compasses in the line of graduation upon the number of degrees which you finde your self distant from the Equinoctial and the other foot upon the next East and West line run with your compasses so opened by the foresaid rumbs till the point proceeding from the graduation and the other which proceedeth from the point of imagination do meet just together and then you may say that your point of imagination is mended by traversing The amendment of the point of imagination by North South East and West The amendment by North South East West is after this manner Set the foot of one compasse upon the point found by imagination and the other foot upon the next North and South rumb then place one foot of another compass in the line of graduation upon the degree wherein you find your self and the other upon the next East and West rumb and so let these two compasses run thus open by their rumbs till the point which 〈◊〉 from the point of imagination and the other which cometh from the graduation do meet for then is your point of imagination amended by the amendment of East West North South Of these two amendments the first serveth when you sail in a large gulf because you may run at liberty with the compass the second serveth neer unto any coast CHAP. XXIII The point by imagination and the heighth WHen you sail by the sixth or seventh rumb that is by the East and by North or East and by South or by the West and by North or West and by South or else by the East Northeast or VVest Southwest or by the East Southeast or West Northwest there is a certain difficulty which may breed great errour in finding the traverse point notwithstanding the latitude be taken by reason of the Rudder that guideth the ship which giveth certain yawes out of the course that the Pilot pretendeth or by reason of the winde which bloweth not right in the poop but maketh the ship fall to the leeward from the direct and true course which it ought to keep Wherefore because in such a case if you find your point by traversing suppose by East and by North the way which I think is made and hath been failed may be by the East Northeast which point so found must stand more forward then the true point by so much difference as there is between 42 and 88 Spanish leagues which is 46 leagues that is the difference of distance from the Meridian or North and South line in those two points In such a case as this it is not meet to find your point by traversing to avoid the errour which hereupon may insue which errour ariseth of such a cause as that a mans judgement be it never so good cannot easily determine thereupon and so consequently he cannot judge precisely But to avoid confusion and cause of errour he must
cast his point in manner following and he shall errer as little as is possible Let him examine according to the ordinary running of his ship how much way she might make every day that he hath sailed and the leagues that shall amount in all the dayes let him take between the points of one compass and let him place one point thereof upon the place from whence he departed and taking another compass let him set one point thereof upon the graduation according to the heighth which he hath taken and the other point upon the next East and West Rumb Now let this compass run by his East and West rumb till the point coming from the graduation meet with the second point of the other Compass which he holdeth not upon the Chart and in the place where they meet he may say that there is his point and his ship And because in this case all Pilots do not use this point of imagination and heighth there grow great diversities among them concerning their distance from land when as in long voyages they confer and communicate their opinions one with another insomuch that one according to his conjecture judgeth himself to be 50 leagues from land another 100 another 200 and another thinketh he is hard by the land The reason is because some of them cast their point by traversing others by imagination onely and others by imagination and heighth who are alwayes more certain then the rest CHAP. XXIV What it is to increase or diminish in heighth THe Mariners call it increasing in heighth when they go further and further from the Equinoctial and diminishing in height when they approach neerer to the Equinoctial So that in our Navigation we either sail from a greater to a less altitude of the pole and then we go towards the Equinoctial and then the height is said to be diminished or we sail from a less to a greater height of the pole and then we go from the Equinoctial and are said to increase our heighth And hence it is that casting our point by imagination and afterwards having taken the heigth amending it by traversing either the heighth wherein we find our selves being taken by the Sun or star is greater or else it is less then that which we made account of by imagination And hence do arise four rules The first is that when in sailing we do increase the heighth if the point amended by traversing be of greater heighth then the point of imagination the ship hath gone more then the point of imagination shewed us The second when we increase our heighth if the point amended by traversing be in lesse height then the point found by imagination then hath the ship gone less way then we imagined The third is when we diminish our height in sailing if the point amended by traversing be in a greater heighth then the point found by imagination then hath the ship made less way then we ghessed by our imagination The fourth is when we diminish our heighth if the point amended by traverse be in less heighth then the point found by imagination then hath the ship made more way then we imagined CHAP. XXV How you may cast a traverse point without Compasses IF a Mariner chance to lose his Compasses he may cast his point of traverse after this manner Let him take two slender threds and putting the end of one of them upon the place from whence he departed let him stretch it in equal distance from the Rumb by which he hath sailed and putting another thred in equall distance from the next East and West rumb let him make it to pass by the degrees of heighth in which he findeth himself and where the two threds cross one another there is the point of the ship and alwayes the first thred if it hath not changed the course sheweth the way which the ship hath gone and the second the parallel wherein the ship is CHAP. XXVI Of another kind of casting a point by traverse EXamine the difference of the degrees of distance from the Equinoctial which are between the place from whence the ship set forth and the place where the ship is Then taking the heighths of both places very precisely and subtracting the lesser out of the greater that which remaineth is the difference which difference you must multiply by the leagues which answer to one degree in the rumb by which you have sailed and those leagues which the degrees and minutes of difference shall make you shall take between the points of a pair of compasses out of your scale of leagues and holding the said compass so open set one foot thereof upon the point from whence the ship departed and the other foot stretching towards the place whithre the ship hath sailed you must hold up a little from the Chart and you must set one foot of the other Compasse at the degree of the distance wherein your ship is from the Equinoctial when the said point is sought for and the other point you must place upon the next East and West Parallel And let this second Compasse run by his next East and West Rumb untill the point of the first Compasse lifted up being set downe that point of the second Compasse which came from the said degree doth meete therewithal and where those two points shall meet there is the true point of the ship CHAP. XXVII Of the leagues which in Navigation answer to each degree of Latitude in every Rumb IF we suppose as we have before said in the chap. of the quantity of the earth that the greatest circle thereof conaineth in compasse 6300 common Spanish leagues then unto every degree of the Meridian which is the greatest circle doe answer 17 Spanish leagus and an half so that sailing North and South if your heighth of the Pole or your distance from the Equinoctial be varied one degree you may say that you have gone seventeen leagues and an half but if you varie one degree and hold your course upon the first point then have you sailed 17 leagues and ⅙ And you have declined from the Meridian or right line which passeth by the place from which you departed three leagus and an half And if you sail upon the second point from the North or South till your heighth of the Pole be changed one degree you have then gone 19 leagues and ⅜ and are distant from your right line 7 leagues and ¼ And varying a degree upon the third point of the Compasse from North or South you have gone 21 leagues and are departed from your right line 11 leagues and ⅔ Sailing upon the fourth point of the Compasse there doe answer unto every degree 24 leagues and three fourths and you are distant from the right line or Meridian 17 leagues and an half Upon the fifth point you must allow for one degree 31 leagues and an half and then are you distant from your right line 26 leagues and ⅕ Upon the sixth point doe
answer unto one degree of Latitude 45 leagues and ¾ and you are then parted from your right line 42 leagues and ¼ Upon the seventh point doe answer unto one degree of Latitude 89 leagues and ¾ and you are departed from your right line 88 leagues as it appeareth out of the Table following The Table of the Author which is more precise Leagues of the course or Rumb Distance from the right line 1 17 ◠6 3 ½ 2 19 ⅜ 7 ¼ 3 21 11 ⅔ 4 24 ¾ 17 ½ 5 31 ½ 26 ⅕ 6 45 ¾ 42 ¼ 7 89 ¾ 88 The old Table which is less certaine Leagus of the course or Rumb Distance from the right line or Meridian 18 3 ½ 18 ½ 7 ½ 21 ½ 11 ⅔ 25 17 ½ 31 ½ 26 ½ 46 ½ 42 ½ 88 85 CHAP. XXVIII How you may come to know the Longitude or the course from East to West THat which the Cosmographers call Longitude is called by the Mariners the distance from the right line and the course of East and West and the heighth of East and West and it is a part of an East and west Rumb contained between two Meridians one of which runneth by the point or place from whence we departed and the other by the point where the ship is This distance from the right line is known by the mean of two things namely of the course and of the difference of Latitude or of the course and distance The course and the difference of the heighth being given you may know the said distance by traverse or by numbers By Geometry or traverse it is known in manner following the heighth or the distance of your ship from the Equinoctial being known and the Rumb also upon which you have sailed you must cast upon your chart a point by traverse and placing upon that point one of the points of your Compasses and the other upon the next Rumb of East and West you must place one point of another paire of Compasses at the haven or point from whence the ship departed and the other point upon the North and South Rumb which is next These two Compasses thus opened running by their Rumbs one towards another you must mark where the two points meet namely that which came out of the part from whence you departed and that which you removed from the point where the ship presently is being found by traverse and where those two points doe meet there make another point or prick Then looke how many leagues there are from the said third point to the point of traverse where the ship is both which doe alwaies beare East and West one from another so many leagues is your distance from the right line And if in stead of the leagues set down in the scale wee measure with degrees taken out of the graduation we shall have the degrees of Longitude which are between the point of our departure and the point of the place where presently we are And it is to be noted that alwayes when we sail we either alter our latitude onely and that is when we sail North and South or we alter the longitude onely that is when we sail by the self-same latitude going alwayes East and West by the same parrallel or we alter both latitude and longitude when we sail by any of the other 28 winds When we alter the latitude only we swerve not one jot from the right line or Meridian when we alter both longitude and latitude then must we find the longitude or distance from the right line in manner above-said But when your longitude onely is altered because then you must find out the point where the ship is by imagination onely there is no certain manner to know the longitude or distance from the right line but onely little more or lesse setting down a point by imagination and measuring by leagues or by degrees what distance there is between that and the point from which the ship departed By numbers you may find out the longitude in manner following The difference of your distance from the Equinoctial being known which is so many degrees more or less as you have increased or diminished in the heighth of the Pole look in the Table annexed to the chapter next before this for the leagues of distance from the right line which answer unto one degree by the rumb or point of the compass upon which you have sailed and multiplying those leagues by the number of degrees which you have increased or diminished in the heighth of the pole in your Navigation you shall then see how many leagues you are distant from the right line which passeth by the place from whence you came which leagues if you divide by 17 and an half then will appear unto you the degrees of longitude between the place from whence you departed and the point where you are CHAP. XXIX How you may set down in your Chart a new Land never before discovered IT may sometimes fall out in new Discoveries or when your ship by means of a tempest is driven out of her right course that you shall come to the sight of some Isle Shoald or new Land whereof the Mariner is utterly ignorant And to make some relation of the same or to go unto it some other time if you desire to set it down in your Sea-chart in the true place you may do it after this manner So soon as you have sight thereof mark it well first with your compass observing diligently upon which point thereof it lieth And secondly you must there take the heighth of the Sun or of the Pole-star that you may know in what point your ship is and that point you must call the first point which being so done your ship may sail on her course all that day till the day following without losing her way and the next day mark the land again and see upon what point it lieth and then take your heighth and with it cast your point of traverse once again and that you may call your second point Then take a pair of compasses and placing one foot upon the first point and the other upon the rumb towards which the land did bear when you cast your first point set also one foot of another pair of compasses in the second point and the other foot upon the rumb upon which the land lay when you cast your second point and these two compasses thus opened you must move by their rumbs till those two feet of both compasses do meet together which were moved from the foresaid two points and where they do so meet together there may you say is the land which you discovered which land you may point out with the in-lets and out-lets or capes and other signes which you saw thereupon And by the graduation you may see the latitude thereof that thereby you may finde it if at any time after you go to seek for it CHAP. XXX Seeing two known points or Capes of land
two guards are in the same Azimuth or the one directly over the other betwixt the lowest and the East Heighth of the Pole Star Heighth of the Pole Heighth of thâ— Pole Star Heighth of â—he Pole Heighth of the Pole Star Heighth of the Pole Deg. degr mi. sec. Deg. degr mi. sec. Deg. degr mi. sec. 1 0 40 50 28 27 58 43 55 55 30 47 2 1 41 27 29 28 59 31 56 56 32 47 3 2 42 3 30 30 0 19 57 57 34 54 4 3 42 39 31 31 1 9 58 58 37 9 5 4 43 16 32 32 1 59 59 59 39 32 6 5 43 52 33 33 2 51 60 60 42 4 7 6 44 29 34 34 3 44 61 61 44 46 8 7 45 6 35 35 4 39 62 62 47 41 9 8 45 43 36 36 5 34 63 63 50 48 10 9 46 20 37 37 6 32 64 64 54 11 11 10 46 58 38 38 7 30 65 65 57 51 12 11 47 36 39 39 8 31 66 67 1 49 13 12 48 14 40 40 9 33 67 68 6 11 14 13 48 52 41 41 10 38 68 69 10 59 15 14 49 31 42 42 11 44 69 70 16 16 16 15 50 10 43 43 12 53 70 71 22 11 17 16 50 50 44 44 14 4 71 72 28 54 18 17 51 30 45 45 15 17 72 73 36 34 19 18 52 10 46 46 16 33 73 74 45 18 20 19 52 52 47 47 17 53 74 75 55 14 21 20 53 33 48 48 19 15     22 21 54 15 49 49 20 41     23 22 54 58 50 50 22 11     24 23 55 42 51 51 23 45     25 24 56 26 52 52 25 23     26 25 57 11 53 53 27 5     27 26 57 57 54 54 28 54     An Addition touching the Variation of the Compasse WHeras there have been some of opinion that there be two Magnetical Poles by knowledge whereof and of the Magnetical Variation Observed in any place they have imagined they could find the Longitude thereof to shew the great error and uncertainty of this their opinion I have here set down this Table of observations of the Variation of the Magnetical Needle which partly by my self but for the most part by others both English and strangers have bin taken in all parts of the World almost whither any Navigation hath bin made for these many years Which Observations I wish the Juditious Reader to compare together with so good advice and judgment as he can whereby I assure my self he will be enforced to acknowlege with me that there can be no such Magnetical Poles found as they imagine To prove these a few instances may be sufficâ—ent amongst many that may be gathered out of these Observations For if there be two such Magnetical Poles there can be but one common Magnetical Meridian passing by them and the poles of the World but by these Observations it is manifest that there be many Magnetical meridians passing by the Poles of the World as namely the Magnetical Meridian about Trinidado and Barbudas also the Meridian about the Westermost of the Azores also about P. das Agulhas lastly amongst the East Indian Ilands some what beyond Iava Maior the magnetical and true meridian must needs agree in one Now seeing that all these Magnetical Meridians passe by the Poles of the World there can be no reason given why the magnetical Poles should be said to be in one of them more then in another and if in any then in all whereof it must needs follow that as many Magnetical Meridians as you have that passe by the Poles of the World so many paire of Magnetical Poles must you have which is absurd and therefore no such Magnetical Poles Now if any shall think that the great difference that is found betwixt divers of these Observations taken at the same place by divers Observers doth make any thing against the intention of this Argument he is much deceived For although there be three or four degrees difference betwixt some Observations taken at the same place as namely at S. Helena some make the Variation to be almost three degrees some almost four others will have it to be about five degrees and an half and some others seven and an half And although there be some four or five score leagues difference in determining the place where the true and Magnetital Meridian should concur or where there should be no variation about Flores and Corvo and about P. das Agulhas some making to be about seventy or eighty leagues Westward from Flores and some about thirty leagues Eastward from thence where some others will have it hard by Flores or somewhat to the Eastwards thereof And at P. das Agulhas some say there is no variation at all but according to others we must goe 80 leagues further to the Eastward before we come to no variation All these differences notwithstanding how great soever they be can be of no validity to infringe the force of the foresaid argument for still these Observations will necessarily prove that either at Flores and at P. das Agulhas or at the most within three or four score leagues of those places there is a Magneticall Meridian passing by both the Poles of the World which two Meridians differing so much in Longitude each from other and having in all Latitudes great variations betwixt them it cannot be with any reason imagined how they may be reduced into one so to make two Magnetical Poles only But of all these so great differences either of the same or of divers mens Observations we may justly take occasion to admonish all Seamen especially such as are to take charge that they be very carefull both in providing themselves of the most convenient Instruments that can be gotten for this purpose and also in the circumspect and artificiall handling of them whensoever they goe about to make use of them in Observing to find the variation considering how great and excellent use there may be made hereof for finding out the place whereabouts you are betwixt East and West upon the huge and vast Ocean though you have seen no land for a long time  Variat West Latit North.  De. M De. M. In the Ice Haven at Nova Zembla 22 30 76 0 On the West side of Nova Zembla 26 0 76 0 From Nova Zembla Westward 20 leagues 31 0 73 0 At Crosse Iland near Nova Zembla 17 0   At the Hollanders Newland 16 0 81 0 In the Iland of Vaygats 7 0 71 0 Amongst the Iles of Vaygats 8 0 70 25 At S. James Ile 7 30 70 40 On Land near the bar of Pechora 3 30 69 10 At the North Cape 1 0 71 30 From Fowlay Iland half way almost to Friseland 11 15   From Friseland half way to Labrador now called Newfoundland 28 0 62 0  East
   Near England sayling from Yarmouth Northwards 12 40 55 14 In the way from London to Russia 13 0 55 20 West    3 30 69 0 7 0 70 40 8 0 70 30 East    4 0 65 40 5 10 64 30 3 0 66 30 At Antwerpe in Brabâ—â—t 9 0   Near London at Limehouse 11 0 51 30 11 15   About Portland 10 0   In S. Ives Churchyard in Cornwall 8 0 50 30 From Cape Lizard South by West 8 leagues 12 50 49 55 South Easterly from C. Clear comming from our Channel 7 36   At Youghall in Ireland 10 0   At Sylly 10 0    Variat East Latit North.  De. M. De. M. From Bell I le East-ward 350 leagues 1 0 52 10 From Syllie West Northwest 235 leagues 0 0 54 0  West    From Syllie West Northwest five hundred and thirtie leagues 10 0 60 0 From that place Northwest by North 16 0 63 30 From thence North and by West 22 0 66 0 From this last place North by West 28 0 73 0 From thence due West 40 leagues 33 0 73 0 At the Earle of Cumberlands Iles 30 0 64 0 At Hope Sanderson 28 0 72 12 At Cape Rase in Newfoundland 16 0 47 0 From Cape Rase South by West Southerly 2 52 34 35 5 35 35 30 From C. Rase South Southwest Southerly 6 30 39 40  East    At Cape Finister 8 30   From Cape Finister west by North 38 leagues 7 55 43 20 From the Rock Westward about 50 leagues 6 15 39 10 From the Rock West Northwest 7 leagues 7 0   About Lisbone 6 30   From Lisbone to Cape Verde almost 8 30   From C. Saker 3 or 4 leagues Eastward 5 38   From S. Maries one of the Azores 9 leagues East by South 2 20   At Fayal and from thence to Tercaera 3 45   From Tercaera to Lisbon 7 30   8 30   From Flores Eastward scarce 40 leagues and from C. Blanco 300 leagues 4 0   From Flores Eastward 70 or 80 leagues 0 0   Hard by Flores or betwixt it and Fayal 0 0   From Flores Westward 30 leagues 0 0    West    Crossing the Meridian of Flores and Corvo 1 0   From Flores 100 or 120 leagues Westward 2 0   1 0   Within sight of Flores Southeast from thence 5 37   From Flores West 230 leagues 3 30 39 19 Falling with the Pike 1 30   From the Canaries 300 leagues 1 0 19 0  East    At the Canaries 5 37   From the Grand Canarie Northward 4 37 32 0 Northeast from the I le Salvages 5 37 31 0 On the Southwest side of the Grand Canarie 5 20 28 0 From the Canaries 230 leagues 0 0 20 0 Sailing for the Canaries from the West Indies 0 0 33 0 0 0 31 0 Sailing further in 5 37 27 20 From Palma Sailing towards Cape Blanco 3 0 24 0 Near to C. Blanco not two leag from shore 2 40 21 0 Riding at anchor near C. Blanco 3 0 20 25 From C. Blanco West S. w. some 20 leagues 2 40   From C. Blanco Westward 63 leagues 5 37 19 20 From C. Blanco Westward 90 leagues 5 0 18 35 From C. Blanco Westward 100 leagues 6 0   From C. Blanco 436 leagues 7 30 17 42 From C. Blanco 470 leagues 7 30 11 57 From C. Blanco 476 leagues 7 36 16 35 From C. Blanco 535 leagues 7 30 10 59 From C. Blanco 595 leagues 5 0 10 15 From C. Blanco 640 leagues 4 36 10 0 From C. Blanco 700 leagues Westward 1 3 9 20 From C. Blanco going towards the West Indies in many distances 6 0   5 40 14 54 At Cape Verde 7 0   About the Ilands of C. Verde 4 0   From these Ilands 300 leagues Westward 5 38   At S Jago and S. Nicholas Iles of C. Verde 2 30   From C. Verde 100 or 120 leagues 3 45 14 0 From the Iles of Brava Fogo W.N. 12 leag 4 30   From Maio 46 leagues East by South 5 8 14 20 From Cape Verde in the way to the East Indies passing the Equinoctial 4 0   5 0   5 37   At the Iland of Trinidado 0 0 9 46 From Trinidado Iland Eastw 90 leagues 1 30   2 0    West    At Margarita 0 0   At S. Cruce near S. John de Porto Rico 0 0   At Cape Rosse of S. Johns Iland 1 52 17 44 In the Meridian of Porto Rico 2 52 21 30 At anker on the West side of S. John 1 52   At the West end of S. John de Porto Rico 2 30 17 44 From S. John de P. Rico North Northwest northerly half a point 8 0 23 0 Also in the same course 8 0 26 0 Again in the same course 8 0 26 20 From Dominica about some 140 leagues 0 0 14 0 In the Meridian of Barbados fiftie leagues from Martinico 0 0 14 20 At the Iland of Guardelupo 1 0 15 18 At Cursands an Iland of the West Indies 4 0 12 13 At the town of Rio de Hacha 7 36 11 20 At Cape la vela 7 0 11 50 Thwart Rio de Mayo 15 0 31 0 15 0 36 0 At Cape Codera 2 30 9 30 At Cape Corientes in Cuba 3 0   At Cape S. Anthonie in Cuba 13 0 22 0 At Cape Cameron 5 0 25 40 At Cape Florida 3 0 25 30 To the Northward of the Cape of Florida 13 0 28 0 Near the coast of America 11 0 35 30 From Barmudas Westward 140 leagues 10 0 30 35 From Barmudas Westward 100 leagues 10 3 34 0 Again from Barmudas 80 or 85 leagues 11 15 34 0 From Cape Raso S. Southwest Southerly 6 30 39 40  East    From Serraleona West by South and from the shoalds of Madrabombe or S. Anne West and by North 160 leagues 6 10 7 0  Varia West Latit South  De. M De. M In the harbour of Serraleona 1 50 8 30 From the shoar of Serraleona 17 leagues 2 2 3 54 From Serraleona 61 leagues VVest Southerly 2 56 7 58 From the Meridian of Sierraleona 76 leagues VVestward 3 29 7 25 From the Meridian of Sierraleona 97 leagues VVestward 3 45 6 0 From the Meridian of Sierraleona 153 leagues VVestward 4 20 4 50 From the Meridian of Sierraleona 137 leagues VVestward 4 12 4 40 From the Meridian of Sierraleona 127 leagues VVestward 3 56 4 30 From the Meridian of Sierraleona 142 leagues VVestward 4 20 4 18 From the Meridian of Sierraleona 160 leagues VVestward 4 58 4
Clavius his grosse demonstration hereof 90 A more exact demonst with the practise thereof 92 The angle of dipping for any heighth of the eye 96 3 Error by the Parallax of the Sun corrected 96 4 Error in Observing by the refraction of the Sun or Stars corrected 97 Chap. 16· Faults amended in the Table of the Suns declination commonly called the Regiment of the Sun 97 Chap. 17. Of the Table of Declination of every minute of the Ecliptick in degrees min. and sec. made according to the greatest obliquity of the Zodiack this present age which by exact Observation is found to be 23 degrees 31 min. and an half 98 A Table of the Declination of every minute of the Ecliptick in degrees min. and sec. 101 Chap. 18. The use of the former Table of Declination 116 Chap. 19. The description and use of a great Quadrant for observation of the Sun on Land 120 A Table of observations of the Suns Meridian Altitudes taken by the foresaid Quadrant in the years 1594 1595 1596 1597 at London  Chap. 20. The finding of the Suns Apogeum and eccentricity out of the former observation 142 To know the time of the Suns comming to any point of the Ecliptick 142 Chap. 21. The middle motion of the Sun corrected out of the former Observations 150 A Table of the Suns middle motions 152 Chap. 22. A new theorick of the Sun for the making of the Table of the Suns Prosthaphaereses 154 A Table of the Suns Prosthaphaereses 157 Chap. 23. The making of the Ephemerides of the Sun 159 Chap. 24. How to reduce the apparent time to the equal time answering thereto 162 A Table of the Aequation of natural days 162 Chap. 25. A Table of Aequations of the Suns Ephemerides to make them serve for many years 163 Ephemerides of the Sun 164 Chap. 26. The use of these Ephemerides 169 Chap. 27. The making of the Table of the Suns Declination 170 Prosthaphaereses of the Suns Declination 172 A Table of the Suns Declination 173 Chap. 28· The use of the former Table of Declination or Regiment of the Sun 181 Chap. 29 The Declinations of the principal fixed stars about the Equinoctial corrected by Observation 183 A Table of fixed Stars about the Equinoctial 198 Chap. 30. The use of the former Table 199 Chap. 31. The true distances of certain principal fixed Stars from the North Pole found by late Observation 199 Chap. 32. To know at what time any of the foresaid fixed Stars come to the Meridian for any day of the year 202 A Table of the Suns right Ascensions in hours and minutes for every day of the year 204 Chap. 33. By the former Tables of fixed Stars and the Suns right Ascensions to know the houre of the night at any time of the year 206 Chap. 34. Of finding the Elevation of the Pole by Observation of the Pole Star and Guard 207 Chap. 35. The description and parts of the Sea Quadrant 208 Chap. 36. The description of the Nocturnal or night Diall 210 Chap. 37. The use of the Sea Quadrant first in Observing the height of the Sun looking only to the Horizon at Sea 211 Chap. 38. How with this Quadrant to Observe the height of the Sun with â—our back turned towards the Sun 211 Chap. 39. How to Observe with this Quadrant the height of the Sun or Star looking both to the Sun or Star and to the Horizon 212 Chap 40. How to find the height of the Pole by Observation of the Pole-star and Guard without giving or taking any allowance or abatement at any time when the Pole-star the Guard and Horizon may be seen 213 To know the houre of the night by the Nocturnal 213 An answer to Simon Stevin shewing his erorrs in blaming me of error in my table of Rumbs 214 The Contents of the TREATISE Of the ART of NAVIGATION The division of the whole Art of Navigation pag. 1 Chap. 1. The definition of the Sphaere 2 2. That the whole World is a Sphaere 2 3. Of the division of the Sphaere 2 4. Of the motion of the Heavens 4 5. Of the figure of the Heavens 4 6. That the earth and water make one perfect Globe 5 7. That the earth is in the center of the world 5 8. The whole quantitie of the earth 5 9. Of the Equinoctial circle 6 10. Of the Poles of the world 6 11. Of the Ecliptick line 7 12. Of the Declination of the Sun 7 13. Of the Colures 8 14. Of the Meridian circle 8 15. Of the Horizon 9 16. Of the 32 Windes 10 17. Of the two Tropicks 12 18. Of the Parallels 13 19. Of the degrees 13 20. What is meant by Longitude and Latitude 14 THE SECOND PART OF THE ART OF Navigation wherein is handled the Practick part shewing the making and use of the principal Instruments belonging to this ART Chap. 1. The making of the Astrolabe pag. 15 Chap. 2. Of the heighth of the Sun pag. 17 3. Of the Shadowes 18 4. Of the Regiment and Rules of the Sun 19 5. Of the Declination of the Sun and of the Tables thereof 20 How the Declination of the Sun may be found out 21 6. The Equation of the Suns Declination 22 7. Foure examples for the plainer declaration of that which is said before 22 8. Another manner of accounting by the Sun as they use in Portugall 25 9. How the height of the Sun may be known in any place whatsoever without an Astrolabe first knowing your distance from the Equinoctial 25 10. The Rule or Regiment of the North-star for the knowledge of the height of the Pole 26 11. The making of the Crosse-staffe 27 12. Of the position of the North-star and the Guards 28 13. Of the height of the Star taken with the Crosse-staffe 30 14. The Regiment or Rules of the North Star 30 15. Other things to be noted in observing the height of the Pole 32 16. Of the Crosiers 34 17. Of the Sea-Compasse 34 18. How the variation of the Compasse may be found 37 The finding of the Meridian line 37 19. Of the Sea-Chart 38 20. Of the point of Imagination 41 21. Of the Traverse or Geometrical point 42 22. Of the amending of the point of Imagination 42 The amending of the point of Imagination by the Traverse point 43 The amendment of the point of Imagination by North South East West 43 23. The point by Imagination and the height 44 24. What it is to increase or diminish in height 45 25. How you may cast a traverse point without Compasses 46 26. Of another kind of casting a point by traverse 46 27. Of the leagues which in Navigation answer to each degree of latitude in every Rumb 47 Chap. 28. How you may come to know the Longitude or the course from East to West pag 48 29. How you may set down in your Chart a new land never before discovered 50 30. Seeing two known points or Capes of land as you sail along
miles from Cape das Aguillas as it appeareth by the Table of variations which place is in the Longitude of 60 degrees and in the middest betwixt both at 30 degr as in the North part again there is the greatest Northeasting of which place there was this mention made in the Table or view of variations towards the Northwest Norâ—herly from the Ilands of Tristan de Cuncha where the variation is 19 degrees Out of these we may conclude that the Magneticall needle doth point due North in every place situate in two Meridiaâ— half Circles drawn from the one pole to the other by Corvo and Helmshudâ— And that the greatest Northeasting is in all places situate in the Meridian Semicircle drawn by that place which we said was distant one mile from Plimouth towards the East So as that part of the Earth which is conteyned between two Meridian Semicircles distant each from other 60 degrees in Longitude is the space wherein the Magneticall needle alwayes declineth from the North towards the East And the half of that part that is that portion of the Earth which is included between two Meridian Semicircles the first of which is drawn by the beginning the other by the 30 degr of Longitude is every where the place of the Northeasting increasing but the other half is the place of the Northeasting decreasing to wit when one goeth from the west Eastward following the order of the degrees of Longitude By this that hath been spoken of the first Segment with the Northeasting and his parts in one of which parts the Northeasting is increasing in the other decreasing it may easily be understood what the manner of the second Segment is with the Northwesting and what is the manner of the parts thereof whereof one is the part of the Northwesting increasing the other is the part of the Northwesting decreasing for in the mouth of the River Cantan in China at the Longitude of 160 degrees distant from Corvo the needle pointeth due North the third time there therefore drawing the third Meridian Semicircle the portion of the earth between the foresaid second Meridian Semicircle and this third distant each from other 100 degrees in Longitude shall be the space wherein the Magneticall needle declineth from the North towards the West and in the middle of both in the Meridian Semicircle 50 degrees distant from the second and as much from the third or otherwise 110 degrees removed from the first Meridian drawn by Corvo shall be the greatest variation of the Magneticall needle as it appeareth out of the Table of variations in two places whereof one is in Williams Iland at Nova Zembla where the greatest Northwesting is found to be 33 degrees The other is distant 34 Dutch miles to the Southeast from Brandaon where the greatest variation is found to be 22 degrees and the Longitude of each of those places is 110 degrees So as in the half of the second space which portion of the earth is conteyned between the Meridian Semicircles of 60 degrees Longitude and of 110 degr the Northwesting is every where increasing in the other half decreasing Of these 160 degrees of Longitude which arch wanteth but 20 degrees of half the compasse of the earth Plancius hath attained to the knowledg of the variation in such sort as now we have shewed As concerning the other parts of the World distant either towards the West from Corvo or towards the East from Cantan the experiments which hitherto the hath gotten from the Spaniards the Englishmen and our countrymen the Netherlanders doe not well agree Neither is it any marvell seeing they had neither perfect knowledge nor needfull Instruments for that purpose yet he expecteth other experiments from the ships which have now been abroad 14 moneths and more In the mean time we will bring forth that to publique view which a man may without absurditie imagine If so be that the propertie of pointing due North take place not onely in the three foresaid Semicircles which we conjecture to be Meridian Semicircles drawn from the one Pole to the other but in the whole Circles also there should then be six such Semicircles upon the earth conteyning also between them six parts or spaces of the upper face of the earth The first with the Northeasting 60 degrees long The second with the Northwesting 100 degr long The third with the Northeasting 20 degr long The fourth with the Northwesting 60 degr long The fifth with the Northeasting 100 degr long The sixth with the Northwesting 20 degr long That those things which have been spoken may by certain Geometricall figures be more clearly conceived let ABCDEFGHIKLM be the Equinoctiall of the earth let N be the Poâ—e then let NA be the half of the first Meridian Semicircle drawn by Corvo NC half of the second Semicircle NE of the third NG of the fourth NI of the fifth NL of the sixth So as the arch AC may make 60 degrees CE. 100 degr and so AE 160 degr EG 20 degr and so AG 180 degr GI 60. degr· and so AI 240. IL 100 degrees and so AL 340 degr LA 20 degr and so the whole Circle 360 degrees Then let the six points BDFHKM be the middles between AC CE EG GI IL LA. Which being supposed ANC shall signifie the first space with the Northeasting ANB the Northeasting of the first space increasing BNC the Northeasting of the first space decreasing CNE the second space with the Northwesting CND the Northwesting of the second space increasing DNE the Northwesting of the second space decreasing ENG the third space with the Northeasting ENF the Northeasting of the third space increasing FNG the Northeasting of the third space decreasing GNI the fourth space with the Northwesting GNH the Northwesting of the 4 space increasing HNI the Northwesting of the 4 space decreasing INL the fift space with the Northeasting INK the Northeasting of the fift space increasing KNL the Northeasting of the fift space decreasing LNA the sixt space with the Northwesting LNM the Northwesting of the 6 space increasing MNA the Northwesting of the 6 space decreasing The second Definition The Northeasting or Northwesting increasing is that whereby the variation increaseth the Magneticall needle being caried from the West Eastwards and the Northeasting or the Northwesting decreasing is that whereby it decreaseth The third Definition The Semicircles of the Meridian in which the needle pointeth due North wee call the first and second Meridian Semicircles and so forwards according to the order of the degrees of Longitude how many soever such Semicircles there shal be beginning at the Semicircle drawn by Corvo The fourth Definition The portion of the Sphaericall superficies or round upper face of the earth conteyned by the first and second Meridian Semicircles is called the first part or space and the rest in order the second the third and so forth unto the end Having thus set down the manner of the variation it remaineth that we shew by examples that which